GTA
All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: lloyd-ss on July 14, 2015, 10:47:59 PM
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I can hardly believe the rate of change in PCP performance and functionality these days! Both from our members, and from companies, large and small. Simply amazing!! The Golden Age of PCP advancements. Velocity and power! The greed for speed! We’ve all got it to some extent, especially those of us who never really grew up.
Now the real purpose of the post: A fun question. What is The Theoretical Maximum Muzzle Velocity that you can get from a PCP? The answer is all basic physics and you only need 3 equations, all of which have been around for close to 400 years. We will be using Imperial units ( feet, pounds, and slugs) and seconds.
The Three Basic Equations –
1) F = m x a (Force equals mass times acceleration)
Rearrange to get a = F/m
2) d = 1/2 a x t2 (distance[barrel length] equals one half of the acceleration, times the seconds spent in the barrel squared)
Rearrange to get t = square root of [(2 x d)/a]
3) v = a x t ( muzzle velocity equals acceleration times time.)
You have to use all 3 equations together to get the velocity so we’ll dive right into it.
Using the rearranged versions of equations (1) and (2) to substitute for “a” and “t” in the velocity equation (3), we get
v = (F/m) x {sqrt ([2 x d x m]/F)}
The final velocity equation looks ugly, but it’s really not that bad. We know the Force, the mass, and the distance, but we want to find the velocity, so we need to calculate the acceleration of the projectile and the time it is in the barrel. Here is how, but first some definitions:
Definitions:
F, the force in pounds that is accelerating the projectile through the barrel.
m, mass of the bullet in “slugs”, basically the weight in pounds divided by the value of gravity, g.
a, the acceleration of the projectile through the barrel due to the applied force, F.
g, gravitational constant for earth, 32.174 ft/sec2 . Just as a side note, the value of g varies around the earth, 32.38 at the poles, 32.05 at the equator, less at high altitudes, greater in the bottom of deep oceanic trenches.
t, the time in seconds that the projectile is accelerating through the barrel.
d, distance, the length of the barrel in feet.
v, the final velocity, the muzzle velocity, of the projectile.
Example of Calculating Maximum THEORETICAL Velocity-
Let’s assume .50 cal, 500 gn, 30” (2.5 ft) barrel, and 3500 psi.
We want to solve for “v” in the equation we rearranged above:
v = (F/m) x {sqrt ([2 x d x m]/F)}
Here is one way to solve it:
First, find the force, “F”, that is accelerating the bullet. F is the product of the bullet’s cross sectional area (.196 sq in for a .50 cal bullet) times the pressure, so the force on the bullet = .196 sqin x 3500lbs/sqin = 686 pounds of force trying to push, i.e., accelerate, the bullet through the barrel.
F = 686 pounds
Next, calculate the mass, “m” of the bullet. Mass is the weight of the bullet in pounds, divided by the gravitational constant “g”. (We need the mass of the bullet, not the weight.)
Mass= (500 gns/7000 gns per pound)/32.174 = .00222 slugs ( the slug is the imperial unit of mass, a bit confusing).
mass = .00222 slugs
Now, plug those calculated values for F and m into the velocity equation:
v = (F/m) x {sqrt ([2 x d x m]/F)}
v= (686/.00222) x {sqrt ([ 2 x 2.5 x .00222]/686}
v = (309,009) x {sqrt (.0000161} [note that 309,009 is the acceleration in ft/sec2, or 9,604 g’s]
v = 309,009 x .00401
v = 1,239 feet/sec MAXIMUM THEORETICAL MUZZLE VELOCITY for this example.
And to take it one step farther, the MAXIMUM THEORETICAL MUZZLE ENERGY for this example is:
FPE = (bullet grains x velocity x velocity ) / 450,240 = 1,705 ftlbs
We know that both of those theoretical maximums are impossible to achieve because of “real” losses and physical "laws" within a PCP air rifle. And there are LOTS of predictable energy losses in a PCP. What are the system losses? 50%? 75%? Yup. So even a very efficient airgun probably isn't very efficient, but that is another discussion.
Fun stuff ;)
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Cool stuff. Now I need some advil.
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Very nice Lloyd. You really made that simple and easily understood. Yes, the predictable losses are plenty. Just considering break away friction is impressive. Increase it by 1 lb and the effect is bigger than one would think. The smaller the caliber the more influence it has. The porting and dead volume is another easily considered influence. Those are probably 2 of the biggest influences on efficiency. Well, other than proper tuning.
Bill G
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Lloyd, thanks so much for posting this.... It shows that it is possible to predict the absolute maximum a PCP can deliver, based on Physics, with only four known quantities, the pressure (psi), the caliber (in.), the barrel length (ft.), and the bullet weight (lbs.).... Everybody knows how to convert inches to feet (divide by 12), but you can also convert the bullet weight in grains to the mass in slugs by using a constant (7000 x 32.174) = 225218.... ie the bullet mass in slugs = bullet weight in grains / 225218.... Incidently, there is another number in Lloyd's explanation that is interesting.... In the solution, one step before the answer, we find the equation....
v = 309,009 x 0.00401
Lloyd explained that the 309,009 is the acceleration in ft/sec2, which is 9,604 g's.... The other number is the time the bullet spends in the barrel, 0.00401 sec, or just over 4 milliseconds.... When you think about the bullet being subjected to over 9,600 g for 4 milliseconds, it gives you a good appreciation for what is happening inside a PCP....
With all the steps being laid out and explained, those of you familiar with spreadsheets will realize it is a simple matter to build one to give all the intermediate numbers.... ie Force (lbs.), mass (slugs), acceleration (ft/sec2 or g) and time (sec) as well as the final results of velocity (fps) and energy (FPE).... Then by changing the input, you can see what happens to all the numbers.... handy if you are truly a geek.... ;D
I would point out that these calculations make some broad assumptions.... The pressure is assumed to be a constant, equal to the reservoir pressure, and the only way that can happen is for the reservoir to be of infinite (or nearly infinite) size, and for the valve to be open until after the bullet leaves the barrel.... In all real PCPs, you are dealing with a finite reservoir volume, and even if that volume can flow freely to the bullet, that means that the pressure, and hence the force and acceleration, reduce as the bullet moves down the barrel.... The smaller the reservoir (eg. the plenum in a regulated PCP), the faster the pressure drops, and the less velocity and energy can be produced.... It ignores the friction of the bullet as it moves down the barrel, and also the force required to break it loose in the chamber, both of which also absorb energy.... It also ignores the mass of the gas itself which is accelerating down the barrel behind the bullet, which in a high performance PCP actually takes a lot of energy.... On top of those things, all of which can be either measured, calculated, or estimated, there is the efficiency of the system itself, which robs an additional but unknown quantity.... So, when you use Lloyd's equation to calculate the maximum possible velocity and energy, remember that number will never be met in practice.... How close you come, comparing the FPE you get with the theoretical maximum, will give you a real world measure of the overall efficiency of your PCP....
Bob
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Thanks guys. And thanks Bob for the additional thoughts on the subject. There is a lot of predictability in PCP performance, but there are still enough mystifying incidents to keep it interesting.
I just noticed another interesting phenomenon about max velocity, and some of this might already been covered in previous threads. ( Darn, such geek stuff. ::) )
If the pressure, and barrel length, and sectional density of the bullet are held constant, all calibers of airgun will have the same theoretical max velocity. Notice that if all slugs are cylindrical wad cutters, that they also all have the same length.
Think about it and it makes sense. If the slug length is held constant, both the bullet weight and the cross sectional area change by the square of the change in diameter. So if you double the bullet diameter, the force goes up by 4 and the weight also goes up by four. Pushing with 4 times the force on a bullet that is 4 times heavier, therefore, the max velocity remains the same.
cal gns S.D. slug length psi barrel theo max vel
.22 97 .286 .886 3500 30 1239
.25 125 .286 .886 3500 30 1239
.30 180 .286 .886 3500 30 1239
.357 255 .286 .886 3500 30 1239
.50 500 .286 .886 3500 30 1239
This also shows why if the bullet length-to-diameter ratio is held constant (say 2 to 1 for example) that the small calibers will have an extreme advantage on making bigger velocity numbers. I believe it also shows that it is theoretically easier to get higher velocities from bullets with lower sectional densities.
cal gns S.D. length psi barrel theo max vel
.22 48 .142 .44 3500 30 1743
.25 71 .162 .50 3500 30 1646
.30 122 .194 .60 3500 30 1507
.357 206 .231 .714 3500 30 1380
.50 565 .323 1.00 3500 30 1168
Interesting numbers games.
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Interesting. Just one observation: Long time ago I was interested which value the scale is really giving me, weight or mass. I found out that scales are, if done correctly, calibrated with certain known mass. So scale is measuring the weight but actually showing the mass. That conversion is already done by "weighting".
Because of that the scales are measuring equally everywhere on earth regardless of local gravity.
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Lloyd, I covered a lot of those comparisons and ratios in my thread "What Makes Sense for PCPs".... http://www.gatewaytoairguns.org/GTA/index.php?topic=57828.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=57828.0)
I likely covered some of it in other threads as well, but that is the main repository I think.... You are correct that for cylindrical slugs, for constant SD the length is constant, and vice-versa.... In fact, that pretty much applies to a large degree for other bullet shapes as well.... Also, for a given length/diameter ratio and shape, the SD is proportional to the caliber.... You can also show that if you choose a velocity, barrel length, and pressure, there is a maximum SD that you can push at that.... I find that of particular importance, as it sets the design parameters that make sense if you know barrel length and pressure, and have a velocity in mind, you can make a good decision on the SD.... For a given SD, the smaller the caliber the longer the length/diameter ratio, which favours low drag shapes in the smaller calibers (although if you go too far, the "wetted surface" or skin drag limits that).... There are many, many decisions that can be made easier and better, once you have an understanding of how these factors interact.... Ultimately, it all boils down to Sir Isacc....
Bob
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Scales measure weight.... the pull of gravity on a mass.... In a zero-gravity environment they cannot register a difference in mass.... Only if you recalibrate a scale using a known mass will it show the same weight everywhere on Earth.... If you weigh a mass of 1 Slug at the top of Mt. Everest on a spring scale, and then transport it unchanged to sea level at the North Pole, it will show a slightly heavier weight because the local value of G is higher.... If you are using a beam balance, however, with the same, known mass on both sides, it will still balance.... If you recalibrate a scale with a known mass, then you can eliminate the effect of local gravity.... For our purposes, using 32.174 as the constant for G is close enough, it's within ~1/2% for nearly all habitable locations....
Bob
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Lloyd did you have to give us the answer in the first post ? LOL. It's like my house, I quiz my kids on their math and before they can respond my Wife will blurt out the answer! Oh and sometimes she is wrong.
Tom
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Lloyd did you have to give us the answer in the first post ? LOL. It's like my house, I quiz my kids on their math and before they can respond my Wife will blurt out the answer! Oh and sometimes she is wrong.
Tom
Tom,
Based on that last sentence, I assume that your wife never reads anything on the GTA?
Lloyd
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Variability of the value of G.
I worked for many years at a company that manufactured high end inertial navigation systems for naval combatant ships and submarines. Spinning mass, ring laser, fiber optic, mems. It wasn't too hard to get them to just "work", the skill (by people a whole lot smarter than me!) came in the multitude of incremental improvements in accuracy that were necessary to achieve the necessary performance. In a way, like what we do tinkering with our airguns.
One thing that I found very interesting was that during the start-up phase of a system you gave it coordinates of its current location so that it had a known starting point. But actually it only needed longitude, because it could determine with some accuracy the latitude based on the value of g that it detected. The system software also had global mappings of the value of g that were used in error compensation within the system. The value of g gets a bit wonky over oceanic trenches.
Lloyd
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Bob, scale readouts are calibrated to equal mass, everywhere. You can check where ever you want. I have two powder scales for weighting bullets and with both of them were delivered known mass calibration weights. At least the calibration should be done in conditions where weighting happens. That works in the moon as well and I wrote: scale is measuring the weight but showing the mass...
Well, I'm not sure about russian markets, they just may have another methods of calibration ;D
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I repeat, only if you calibrate the scale with a known mass before using it.... In addition, you must use the correct units in the equation anyway, so please don't get people thinking they can forget the constant to convert weight to mass.... I overestimated the difference in the values of g on the earths surface anyway.... It only varies a total of 0.7% from the highest point of land near the equator to the surface of the Arctic ocean.... For most habitable locations, the total variation is g is about 1/2%, putting the error by using 32.174 at 1/4% or less, and much less for locations in the middle latitudes of North America (where we commonly use the Imperial system).... The decrease in g with increase in altitude is only about 0.1% at 10,000 ft...
If you use a digital scale, and calibrate it with the known mass supplied, it won't matter where you are (including on the moon), the weight of your bullet in grains can be converted to the mass in Slugs by dividing by 225,218.... right, Lloyd?.... A weight to within 0.1 gr. on a 100 gr. bullet is only 0.1% error.... I think a much more likely source of error is the pressure gauge, even reasonably good ones are 1% at mid scale, and the cheap ones are 5% (or sometimes worse).... Caliber should be easy to know within a thou (0.3% on a .30 cal), and barrel length within 1/8" (0.5% on a 25" barrel).... With a good pressure gauge and scale, the total errors in the measurements could add up to 2% error.... with a poor gauge, a lot more.... Barrel length should be measured from the base of the bullet in the chamber to the crown.... ie the total length of travel during acceleration....
Bob
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There ain't no such thing as standard weight, therefor standard masses are used for scale calibration.
Difference between weight and mass is close to 1.8% out of mass on earth.
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Difference between weight and mass is close to 1.8% out of mass on earth.
I have no idea what that means.... ???
Bob
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Interesting conversation.
Mass and weight are certainly different but are often used interchangeably and incorrectly..... by almost everyone. :o
In the metric system mass is in kilograms and weight is in Newtons, but the "weight" of everything is almost always stated in kilograms (or grams, etc) not in Newtons.
In the imperial system we do just the opposite. Go figure. :P The Russians lift 150 kilos (mass) and the Americans lift 330 pounds (weight). Huh?
So long as we use the correct units for mass and weight in our calcs, and use a commonly accepted value of g, everything should work out ok.
Lloyd
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There is nothing wrong if the correct unit is used in calculation but when compared to real world it is good to understand that scale indication is already mass value. Because scale is set, calibrated in another word, to give directly the mass value. It is calibrated using suitable standard mass.
By the difference between those two I mean that 1 kg mass is weighting appr. 9.81 -9.82 Newtons and that difference, 19 - 18 grams is about 1.8 % of 1 kg. So if scale reading, which is mass, is converted to mass by gravity, there is an error of about 2%. I agree there are a lot of error possibilities, so why add one to to formula knowing its wrong?
If you convert something, you should calculate the weight from scale reading, it is a mass value although the scale is actually measuring force.
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Lloyd did you have to give us the answer in the first post ? LOL. It's like my house, I quiz my kids on their math and before they can respond my Wife will blurt out the answer! Oh and sometimes she is wrong.
Tom
Tom,
Based on that last sentence, I assume that your wife never reads anything on the GTA?
Lloyd
She has no knowledge of the GTA and I prefer to keep it that way ;)
Tom
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Here’s an example of working backwards from a theoretical max velocity to what we might actually get from a real PCP.
.25 cal , 25 gn, 24” barrel , 3000 psi, infinite tank volume, zero dead volume between the valve and pellet. No deductions taken for any losses within the PCP system. Valve is wide open.
1) Max Theoretical velocity and FPE, with the valve staying open until the pellet leaves the barrel:
2292 fps, 292 FPE (more like a powder burner, LOL)
Now let’s start deducting for the losses within the system:
2) Reduce the tank volume to 230 ccs.
2241 fps, 279 FPE
3) Add the mass of the column of air that must be accelerated in the barrel behind the pellet:
1562 fps, 136 FPE (major reduction ! )
4) Add dead volume between the valve and pellet. Use 0.5 cc.
1531 fps, 130 FPE
5) Add a pellet break-away force of 5 pounds and a barrel friction force of 1 pound:
1525 fps, 129 FPE
6) Restrict the airflow (in the calcs) to keep it below Mach 1 in the T-port:
1346 fps, 101 FPE
7) Shut the valve when the pellet is halfway down the barrel:
1319 fps, 97 FPE
8 Subtract about 15% more losses for flow impediments:
1168 fps, 76 FPE
9) Shut the valve when the pellet is one quarter of the way down the barrel:
1106 fps, 68 FPE
It’s like watching your paycheck get whittled away!
Lloyd
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TPL, sorry, but you are completely incorrect in mixing Kg. (mass) and Newtons (weight), the factor 9.81-9.82 is NOT an error of 1.8% as you state.... You must MULTIPLY the mass in Kg. by 9.81-9.82 (the acceleration due to gravity in the Metric system) to get the weight in Newtons, nothing is in error by 1.8%.... If you typically work in the Metric system, then I can understand your confusion, because Kg. are indeed a unit of mass, not weight, although people usually say something weighs "X kilograms".... Lloyd explained the difference in the Metric and Imperial systems in Post #15 above.... in the Imperial system, pounds are a unit of weight, the unit of mass is the slug.... If you are working in Imperial, you must convert the weight of the bullet in grains to the mass in slugs.... In the Metric system you would use the mass in Kilograms directly, but you must calculate the force on the bullet in Newtons, which is a whole other can of worms....
Bob
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I'm not mixing anything, believe me. It seems to very hard to explain. I mean that if you measure the mass value of a bullet but assume it to be weight and make conversion which is already made in scale you will end up with appr. 2% error.
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Now the real purpose of the post: A fun question. What is The Theoretical Maximum Muzzle Velocity that you can get from a PCP? The answer is all basic physics and you only need 3 equations, all of which have been around for close to 400 years. We will be using Imperial units ( feet, pounds, and slugs) and seconds.
Interesting post, Lloyd. Since the physics is the same regardless of whether the pressure comes from compressed air (air gun), or from explosives (powder burner)... have you run your numbers to see what you get for theoretical maximum velocities for a powder burner? Something in the 60,000 psi range, let's say.
Testing your formula using powder-burner numbers might be an interesting sanity-check on the formula, or show where the mathematical model hits some of those real-world limits that you and Bob have talked about (or needs additional physics factored in).
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Actually, no, if you convert using 9.812, you will end up with a 981.2% error.... We are getting this thread totally off track, I suggest if you wish to continue this, you start your own thread on Mass and Weight in the Metric system....
Bob
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wwonka.... The initial formula only applies when the pressure is constant for the entire trip down the barrel, which with a PB it most certainly is NOT.... It might peak at 50-60K, but by the time the bullet reaches the muzzle is only a fraction of that.... The burn rate of the powder is part of that equation.... In addition, you are introducing heat into the system, which changes things again.... If you use a constant pressure of 35,000 psi in Lloyd's original example, you get 3934 fps (17,179 FPE), but that formula is much too simple to use for decreasing pressures like in a PB....
Bob
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There is nothing wrong if the correct unit is used in calculation but when compared to real world it is good to understand that scale indication is already mass value. Because scale is set, calibrated in another word, to give directly the mass value. It is calibrated using suitable standard mass.
By the difference between those two I mean that 1 kg mass is weighting appr. 9.81 -9.82 Newtons and that difference, 19 - 18 grams is about 1.8 % of 1 kg. So if scale reading, which is mass, is converted to mass by gravity, there is an error of about 2%. I agree there are a lot of error possibilities, so why add one to to formula knowing its wrong?
If you convert something, you should calculate the weight from scale reading, it is a mass value although the scale is actually measuring force.
Timo, I think I understand what you are saying, at least in the first paragraph. I will paraphrase: If your scale is reading in metric (grams, kilograms) and you calibrate it with a known mass prior to weighing, then it will indeed read the mass because it was calibrated to the local force of g.
In the second paragraph, I understand what you are saying, but I think you moved a decimal point. The difference between the 9.81 and 9.82 Newtons (which might be the difference in g within a reasonable travel radius), would only be 0.1%, I think, not 1.8%.
Yes, it is a difficult concept to explain, especially across measurement systems.
Lloyd
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Ok, one more post to this thread, then I will shut up.
I didn't move decimal point. Earth gravity in SI-system is 9.81 m/s2. It will affect the mass of 1 kg according to F=ma, so 1 kg * 9.81 m/s2 = 9.81 kgm/s2, which is Newton. If we are talking about weight we should use force units, not mass units. Still it is everyday practice.
But I really think that scales in US are displaying mass too, because those are adjusted by using some standard mass. Calibration by weight would be also possible but in that case we must know the exact local gravity. And there cannot be a standard weight for understandable reason.
By that about 2% error I mean the one that we will have if we make conversion from weight to mass starting already from mass(from the scale display). Not local variation due to location, that is negligible.
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The Three Basic Equations –
1) F = m x a (Force equals mass times acceleration)
Rearrange to get a = F/m
2) d = 1/2 a x t2 (distance[barrel length] equals one half of the acceleration, times the seconds spent in the barrel squared)
Rearrange to get t = square root of [(2 x d)/a]
3) v = a x t ( muzzle velocity equals acceleration times time.)
You have to use all 3 equations together to get the velocity so we’ll dive right into it.
Using the rearranged versions of equations (1) and (2) to substitute for “a” and “t” in the velocity equation (3), we get
v = (F/m) x {sqrt ([2 x d x m]/F)}
Just for the *(&^ of it, I used a slightly different method. Good news is I got the same number as Lloyd! (thumbs up to you, Lloyd).
1) I started off with the equation: v2^2 = v1^2 + 2ad
"v1" = initial velocity. "d" is distance (the length of the barrel). "v2" is the muzzle velocity. "a" = acceleration.
Since v1 = 0 for a bullet, we get v2 = sqrt(2 * a * d)
2) I now use the formulas F = m*a and F = p * A
where "a" is the acceleration. "F" = force. "m" = mass of bullet. "p" = Pressure. "A" = sectional Area of bullet.
3) I combine 1 and 2, simplify with some maths and get the final formula:
==> v = c/2 * sqrt( (2 * p * PI * l)/m )
where "v"=muzzle velocity; "c"=calibre; "p"=pressure of reservoir; PI = 3.14159; "l"=barrel length; "m"=mass of bullet.
To test this, I converted Lloyd's (.50 cal, 3500 psi, 30" barrel, 500 gn) numbers to Standard Metric Units (meters, Pascals, kilograms)... plug into the equation above... and I get.... 379.19 meters/second = 1244 fps! Which is reasonably close to Lloyd's result, +/- some rounding.
So here is a formula you can use as well:
=> v = c/2 * sqrt( (2 * p * PI * l)/m )
where "v"=muzzle velocity; "c"=calibre; "p"=pressure of reservoir; PI = 3.14159; "l"=barrel length; "m"=mass of bullet.
- Just make sure you convert everything into (meters, Pascals, kilograms) and you will get an answer in meters/second. (which is easy to convert to fps). Also, by "calibre" I mean the actual bullet diameter as in ".357", not ".38".
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wwonka,
It's nice when we each take our own crooked paths and end up at the same place. Thanks for going to the trouble of doing that.
The powder burner comparison really is a different animal, and quite complicated. Same with springers. For the volume of uncompressed air that a springer uses, they make a LOT more power than a similar volume of un-compressed air (standard cubic inches of air) in a PCP. Thermodynamics and lots of heat. The math for PCPs is complicated enough without adding all that heat, LOL.
Lloyd
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wwonka,
It's nice when we each take our own crooked paths and end up at the same place. Thanks for going to the trouble of doing that.
The powder burner comparison really is a different animal, and quite complicated. Same with springers. For the volume of uncompressed air that a springer uses, they make a LOT more power than a similar volume of un-compressed air (standard cubic inches of air) in a PCP. Thermodynamics and lots of heat. The math for PCPs is complicated enough without adding all that heat, LOL.
Lloyd
Yeah, I hear you and Bob about the added complications for high explosives.
Thanks to you, Lloyd: you provided the spark (pardon the pun). On a day when we're taking snapshots of Pluto (amazing) it's nice to see the power of many of the same Physics equations.
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Here’s an example of working backwards from a theoretical max velocity to what we might actually get from a real PCP.
.25 cal , 25 gn, 24” barrel , 3000 psi, infinite tank volume, zero dead volume between the valve and pellet. No deductions taken for any losses within the PCP system. Valve is wide open.
1) Max Theoretical velocity and FPE, with the valve staying open until the pellet leaves the barrel:
2292 fps, 292 FPE (more like a powder burner, LOL)
Now let’s start deducting for the losses within the system:
2) Reduce the tank volume to 230 ccs.
2241 fps, 279 FPE
3) Add the mass of the column of air that must be accelerated in the barrel behind the pellet:
1562 fps, 136 FPE (major reduction ! )
Back to my Reply # 16, bullet point # 3), about losses within the system, I am always surprised at how much the column of compressed air accelerating behind the bullet weighs, and basically makes the bullet seem heavier as it accelerates down the barrel.
For a .357 cal barrel, (.100 sq inch) filled with 3000 psi air, each lineal inch of barrel is holding about 7.7 grains of compressed air. So if the valve is closing when the bullet is 10" down the barrel, that 120 grain bullet accelerates much more slowly like it weighed 197 grains.
Of course, once it leaves the barrel, it is that same old 120 gn bullet and the horizontal component of its acceleration has dropped to zero (actually slightly negative due to drag).
Lloyd
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The value of g gets a bit wonky over oceanic trenches.
Lloyd
Don't worry, the Trieste is not leaving the museum it is currently ensconced in...:)
cheers,
Douglas
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Douglas, Is the name similarity a coincidence?
Lloyd
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I've been playing with this tonight, and added a calculation for the maximum theoretical FPE, just taking Lloyd's result for the velocity and converting it.... I found out two interesting facts....
1. The maximum theoretical FPE is independent of the bullet weight.... the velocity changes but the energy does not....
2. You can calculate the maximum theoretical FPE using an extremely simple formula....
Max.Energy (ft.lb) = Distance (ft) x Force (lb) .... gee, the units even work out....
The Distance is the barrel length in feet.... The Force (lb) is the Pressure (lb/in2) x Bore Area (in2)....
Calculate the bore area, using caliber2 x PI/4 .... multiply by the Pressure in psi to get the Force in lbs.... and then multiply by the barrel length in feet....
Voila!.... you have the maximum theoretical FPE from just those three factors.... Using Lloyd's first example, .50 cal, 500 gr, 3500 psi, 30" barrel.... Lloyd got 1239 fps, and 1705 FPE with some small rounding errors.... When I work through it without those, I get 1244.1 fps and 1718.06 FPE.... (I used your spreadsheet, Lloyd!)....
Area of .50 cal = 0.19635 in2 x 3500 psi = 687.223 lbs. force.... multiply by the barrel length of 2.5 ft. and you also get 1718.06 FPE.... Talk about simple !!!
Bob
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Bob,
Well darn, right you are! And thinking about it, it makes perfect sense because that is basically a definition of foot pounds of energy: "force applied over a distance"!
So, Max FPE = [(bore2 x pi)/4] x psi x barrel length in ft
Now that you have Max FPE, and using the actual bullet weight, finding the max fps is super easy!
Max fps = squareroot of [ ( MaxFPE x 450240 ) / grains ]
For once, life got simpler! ;D
Lloyd
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Just one thing, Lloyd.... If g = 32.174, the proper divisor for the FPE equation is 450436.... If you are using 450240, the equivalent value of g is 32.16.... which is, incidently, what I learned in school.... The difference between the two, however, is only 0.044%.... so in practical terms, there is nothing wrong with using the (universally accepted but out of date) 450240.... I think perhaps that 32.16 was the value at sea level at 45* latitude.... or maybe at Greenwich England, 51.5*N.... which used to be where everything was measured, before the Metric system took over.... ;D
Using 1244.1 fps and 500 gr., if we use 450436, we get 1718.096 FPE.... while using 450240, we get 1718.844 FPE.... I don't think that 0.748 FPE will make any difference.... *LOL*.... The constant, for those who don't know, consists of (value of g x grains per pound x 2) = (32.174 x 7000 x 2) = 450436....
Bob
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Bob, Bob, Bob, such a stickler ! LOL ::) I am going to hack your calculator so that it limits all of your answers to three significant digits. Then everything will be fine with the world and we will all sleep better at night. :D
I do get the point, though. The conversion factor of 450240 is not used universally. A powder burner friend of mine uses something different, but I forget what he said. I told him that his factor was just as good as mine and we hugged and are still friends. ;)
If your chrony has an error of say, 0.1% of full scale, (which is very good) you are back to 3 significant digits, so from that perspective it is a moot point. For hard core geek calculations, the difference between g used in the calcs and g used for the fpe conversion can cause error build-up if you go back and forth on the conversions. I don't think we can totally fix this one.
Lloyd
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Lloyd, I'm with you 100% on the significant digits issue.... I admit to being guilty as charged in this thread, whereas normally I'm the one screaming when someone posts that his gun shoots 783.25 fps with a 25.39 gr. pellet, which works out to 34.58043 FPE.... When you consider that all our measurements are lucky to be accurate to within 0.1% (and many 0.5%, some 1% or less), and that 0.1% is 1 part per 1000, or 3 significant digits.... we should only be stating velocities without decimals to the nearest fps, weight to 0.1 gr., and FPE to 1 decimal at best.... and when the numbers get larger (over 100), increments of 1 gr. and 1 FPE are about all we need to use.... In fact, using extra decimal points implies an accuracy that doesn't exist, a scientific no-no....
On the other hand, I detest using exponents to be a slave to significant digits, and refuse to express a velocity of 1064 fps as 1.06 x 103 fps just to stay with three sig.figs.... ;D ;D
PS, I already hacked my calculator to limit the sig.figs to what I like anyway.... :P
Bob
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Douglas, Is the name similarity a coincidence?
Lloyd
Nope. Same with the Solar Impulse project.
cheers,
Douglas
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So the name is NOT a coincidence?.... are we in the presence of greatness?....
Bob
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At normal temperatures.
At some point, the mass of the propellant overrides the mass the the projectile. Efficiency plummets and you run up against the velocity limit of the gas.
Just thought I'd throw that in.
Helium would allow a higher velocity.
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Douglas, Is the name similarity a coincidence?
Lloyd
Nope. Same with the Solar Impulse project.
cheers,
Douglas
Wow !
Lloyd
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Douglas, Is the name similarity a coincidence?
Lloyd
Nope. Same with the Solar Impulse project.
cheers,
Douglas
Wow !
Lloyd
No problem with the math but this has me totally lost ???
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At normal temperatures.
At some point, the mass of the propellant overrides the mass the the projectile. Efficiency plummets and you run up against the velocity limit of the gas.
Just thought I'd throw that in.
Helium would allow a higher velocity.
So many factors to complicate a seemingly simple process!
I am very tempted to take an aggressively tuned Discovery, tethered to a regulated air supply, and shoot it across a chrony, sawing an inch off the barrel between each shot (or group of shots.) The delta v data would provide soooooooo much information. I hope this has already been done and that the data is available somewhere.
Anybody aware of it??
Thanks,
Lloyd
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Douglas, Is the name similarity a coincidence?
Lloyd
Nope. Same with the Solar Impulse project.
cheers,
Douglas
Wow !
Lloyd
No problem with the math but this has me totally lost ???
So long as Douglas doesn't say ,"and same with the Enterprise," we are ok...... I think. ;)
Lloyd
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So many factors to complicate a seemingly simple process!
I am very tempted to take an aggressively tuned Discovery, tethered to a regulated air supply, and shoot it across a chrony, sawing an inch off the barrel between each shot (or group of shots.) The delta v data would provide soooooooo much information. I hope this has already been done and that the data is available somewhere.
Anybody aware of it??
Thanks,
Lloyd
- Like you said though, lots of factors. To get useful data from that Discovery, you would need to saw off each inch and then chrony at 1000 psi, 2000 psi, 3000 psi, 4000 psi - before you saw off the next inch. You would then want to do this for a .177, .22, .30, .357, .45 and .50 barrel... since the length/pressure/speed variation would probably also depend on the inner bore of the tube.
It would be a long experiment, but these are the data points that would be needed. Otherwise, any measurements could be a very limited special case.
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Yeah, Scott, I tend to agree that the 1650 fps RMS velocity for air molecules has something to do with limiting how fast we can shoot with air.... but you have to remember that is the "root mean square" velocity, and the actual velocity of any given molecule of Oxygen or Nitrogen could be many times that.... Helium atoms in the upper atmosphere can actually exceed escape velocity (which is why the supply of Helium on Earth is dwindling), even though the RMS velocity of Helium is only about 4436 fps at 70*F.... I once was quite vocal about it being theoretically impossible to exceed 1650 fps with a PCP on air, and that prompted a guy with a .177 Condor to crank it wide open shooting the 1.7 gr. plastic sabot from a pellet at 1705 fps.... OOPS !!!.... The efficiency of the shot was less than 3%, but I guess enough of the air molecules had high enough velocities to still provide the push need to trash the theory.... "A little bit of knowledge..........."
There is no question that as you approach muzzle velocities of Mach 1 and beyond using air, the efficiency plummets.... For one thing, you can get "sonic choking" once the speed of sound in the compressed gas in the ports and barrel reaches Mach 1 at that point, which limits the mass airflow, it can never be greater than at that point.... Here is a chart showing the speed of sound at high pressures....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/SpeedofSound_zpsbe789913.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/SpeedofSound_zpsbe789913.jpg.html)
At 3000 psi, we are looking at 1360 fps in air.... Even with bore-sized porting, the mass airflow will peak at that point, and although that doesn't create a hard speed limit, it sure puts a crimp on the efficiency after (and in fact before) that point.... I was unable to find the data to add Helium to that chart, but since the speed of sound with it is 3305 fps at 70*F and 1 atmosphere, sonic choking just isn't an issue.... Plus, the mass of the gas itself is only 1/7th that of air.... However, none of these factors change the basic Physics of Lloyd's original post giving the maximum possible FPE for a given pressure, caliber, and barrel length.... even though the likelihood of approaching it with Helium would be low, and with air even lower....
Bob
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wwonka,
I am extremely glad you are volunteering to conduct this experiment. ;D Yes, it will be a lot of work, but we will all thank you profusely for it. Also, please use different weight pellets and bullets, and probably transfer ports, too. It will be a preponderance of data to crunch through. :P
I disagree that not running a multi-caliber matrix of testing would produce limited special case results. My modeling already produces results that are close to real-world, and some limited testing would provide data for a correction algorithm. Look at the following two graphs. I think the accuracy of the rate of decline in acceleration (change in delta v) along the length of the barrel is the missing ingredient. I am close, but empirical data would be invaluable. Once applied and corrected for a single situation, empirical data from another caliber/barrel length/ pressure, etc, could be compared against the corrected model to check its calculation accuracy. The corrections should be scaleable across various calibers. I think a single caliber with variables of: pressure, barrel length, and transfer port dia would provide adequate data, without the experiment becoming unmanageable. Also, testing at the fringes of the normal ranges of operation might show where the internal flow does become compromised.
Just my thoughts on the situation.
Lloyd
(http://i226.photobucket.com/albums/dd79/loyd500/V8-1.jpg) (http://s226.photobucket.com/user/loyd500/media/V8-1.jpg.html)
(http://i226.photobucket.com/albums/dd79/loyd500/V7-1.jpg) (http://s226.photobucket.com/user/loyd500/media/V7-1.jpg.html)
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Don't know if this will help ......
http://www.network54.com/Forum/79537/thread/1418165148/2/Gaylord+%26amp%3B+DQ+max+velocity+test (http://www.network54.com/Forum/79537/thread/1418165148/2/Gaylord+%26amp%3B+DQ+max+velocity+test).
The subject of high speed compressible flow is often misunderstood. And regarding the idea that Vmax = 1650.......
an approach based solely on the principle of superposition, coupled with a bit of thought, easily puts it to rest.
Ron
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Don't know if this will help ......
http://www.network54.com/Forum/79537/thread/1418165148/2/Gaylord+%26amp%3B+DQ+max+velocity+test (http://www.network54.com/Forum/79537/thread/1418165148/2/Gaylord+%26amp%3B+DQ+max+velocity+test).
The subject of high speed compressible flow is often misunderstood. And regarding the idea that Vmax = 1650.......
an approach based solely on the principle of superposition, coupled with a bit of thought, easily puts it to rest.
Ron
Ron
Thank you, that helps immensely, although I felt like I was on a bit of a scavenger hunt ;) looking through the various references. I did pull out my old Cardew book but have been unable to find adequate detail information about the valve in the "Projector." Your mention of a floating piston valve in your velocity test "aid" is intriguing. I am familiar with a few types from other applications, but not with HPA. Did yours allow actual straight shot flow behind the projectile, or was it more of a full 360 degree annular flow arrangement?
Anyway, your serious efforts, and comments and references and testing, and that of others, does tend to put most of the currently stated velocity limits into serious question. As already stated, maybe not a hard velocity limit, but the additional gains become extremely hard fought.
Lloyd
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Extremely interesting, Ron.... I never really gave much thought to the Chrony position when they recorded the ~1500ish velocities, and I should have twigged, because for a few years now I have been harping on how quickly pellets slow down over the first few yards of flight when launched supersonic.... One measurement on a Hobby gave me a BC of 0.007 over 5 yards, starting at 1131 fps.... If a lead projectile can loose nearly 100 fps in that distance, a plastic cylinder could easily loose a couple of hundred in 3 yards.... resulting in muzzle velocities of over 1650 fps, even though they didn't know it at the time....
When you consider that the Cd for a cylinder at 1600 fps is about 1.5 (compared with the Cd for the G1 or GA profile of about 0.67), and that the Sectional Density for a 7 gr. cylinder of .25 cal is only 0.016.... the initial loss in velocity will be dramatic.... The new ChairGun has the GC (cylindrical) drag profile built in, and if we assume that the plastic "pellet" they used has a Form Factor of 1.0 (it is, after all, a cylinder), that would mean that the GC Ballistics Coefficient was equal to the SD, or 0.016 (GC).... Plugging in a muzzle velocity of 1700, gives a velocity at 3 yards of just 1500 fps, a pretty reasonable estimate of what is going on.... Incidently, it would have dropped subsonic at about 10 yards....
While this is interesting, of course, it still has little to do with the purpose of Lloyd's OP, which was to show the Physics behind the maximum possible FPE from a PCP of given caliber, barrel length, and pressure....
Bob
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What a great post, love it :o
Very intersting for sure,
So now if we throw in some Slick 50 what happens ;D
Ok, have a nice day, going to go see the Minions, I am sure I can relate more to that lol
William
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Lloyd, I don't have any good pics or drawings of the floating piston,
the sketch will have to do. Shown is the barrel with a pellet inserted,
valve in full open position, drawn somewhat to scale. Annular or
straight in (?)..........more of a combination. Cardew's valve was
essentially the same minus the piston.
Ron
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How would one factor in the velocity /inertia/momentum component of the propelling gas? Such as would be present with "typical" valve and transfer port configurations?
Then too, there is the uncertainty of temperature. Expansion , friction and stirring. etc.
Theoretical maximums become a target that seldom prove unreachable. ;-)
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Theoretical maximums become a target that seldom prove unreachable
I would think it would always prove unreachable.... ;D
Bob
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How would one factor in the velocity /inertia/momentum component of the propelling gas? Such as would be present with "typical" valve and transfer port configurations?
Then too, there is the uncertainty of temperature. Expansion , friction and stirring. etc.
Believe it or not, there are equations that can be used for all that. It just depends on how deep into the Physics you want to get. But we don't calculate the theoretical maximum to figure out how a gun will perform (that's what engineering and trial-error is for)... we calculate the theoretical maximum to know what the absolute best is that we could get. That helps in making some decisions about calibre, pressure to use, barrel length, etc - and also helps to weed out bad chrony numbers that turn up every now and again (nobody's fault, just user/mechanical error).
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Ron,
Thank you for making the sketch. I believe I understand the concept of the pintle style valve portion of the unit. In this application is the floating piston used only to allow changing the shot volume, or do the piston and valve move as a single unit, where dumping the pressure on the back of the piston opens the valve almost instantaneously?
Thanks,
Lloyd
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How would one factor in the velocity /inertia/momentum component of the propelling gas? Such as would be present with "typical" valve and transfer port configurations?
Then too, there is the uncertainty of temperature. Expansion , friction and stirring. etc.
Believe it or not, there are equations that can be used for all that. It just depends on how deep into the Physics you want to get. But we don't calculate the theoretical maximum to figure out how a gun will perform (that's what engineering and trial-error is for)... we calculate the theoretical maximum to know what the absolute best is that we could get. That helps in making some decisions about calibre, pressure to use, barrel length, etc - and also helps to weed out bad chrony numbers that turn up every now and again (nobody's fault, just user/mechanical error).
Believe it or not, That is just so much talk! Emperical evidence always trumps theory!
If one could actually know what happens in the brief moments and strict confines, then "the equations" might provide perspective.
Alas.. these studies remain mostly approximation and guesstimation. Meaninful data remains scarce.
please, can you link to the actual calcs? ...... I think not... for the depth of physics nearly always draws up short of reality. After all, it is mostly comprised of Theory.
Theory suggests that nothing can move faster than light speed, yet I can think of events across the universe and back again in a moments time...,.. So much for theory. Is light a particle ? or a wave? or only a theory?
Read up on "the theory of light gas guns". It will set a precident.....
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There is nothing to brake or even redefine any laws of physics there. Exactly the same rules apply. I made some digging and found numbers. They are using high temperature high pressure hydrogen as working fluid in those light gas guns. Speed is very high but so are all other numbers as well.
50000 PSI of hot hydrogen, bore diameter 4", barrel length 100 ft and mass of projectile 5 kg. If we throw these numbers to equations introduced here, we will have speed up to 17 Mach.
Only the scale is very different. Anyway, that is like comparing our microscopes to their space telescopes. By the way, when high temperature and pressure hydrogen gets out of barrel it ignites and makes 100 ft muzzle blast. I must admit it would be very impressive but unattainable for airgunners.
These equations are giving really theoretical maximum absolute limit which is always beyond reach in reality. It is calculation assuming we could have infinite pressure supply and there are no losses of any kind. Still it is good to know the max. absolute limit as then we know the point we are on and can evaluate achieved numbers in completely different light.
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Cal, please don't drag yet another topic wayyyyyyyyyy off track.... If you want to start a thread on "Light Gas Guns", the Back Room would be a suitable Gate, IMO....
Bob
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If there is a projectile moving away from a volume of gas at its mean molecule velocity...what happens to the pressure? Take this over a dx long bit of travel and a dt long time period so we won't have to worry about replenishing the volume behind it...:) Better still answer this at any particular velocity and find out what this available pressure v. projectile speed plot looks like.
cheers,
Douglas
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HI Douglas.... Good questions, please supply the answers.... The "simple" answer that the pressure is zero is the wrong one, because some of the molecules are moving much faster, or we wouldn't be able to achieve more than ~1650 fps using air, and that has definitely been done.... To answer the second part, we need to know if the speed of the molecules is relative to the moving mass of the gas, or the barrel.... All I can tell you is that the idea that you can't exceed 1650 fps in a barrel using air is wrong....
Once again, all of these things are reasons that we cannot achieve the calculated maximum FPE for (bore area) x (pressure) x (length)....
Bob
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A few more details for Lloyd.
Chamber D has a fixed charge pressure of ~ 900 psi. Initially, before
the gun is pumped, the valve will be closed by moving it all the way
to the left and the piston will be against wall A. Pressurized air from
the pump is introduced thru a transfer passage in corner B. The
additional ~ 12 cu. in. of air will move the piston to the right approximately
.2 in. and the pressure in both C and D will rise to ~ 1000 psi. The valve
is self opening because of the larger diameter at E. The discharge
part should be self explanatory.
Ron
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If there is a projectile moving away from a volume of gas at its mean molecule velocity...what happens to the pressure? Take this over a dx long bit of travel and a dt long time period so we won't have to worry about replenishing the volume behind it...:) Better still answer this at any particular velocity and find out what this available pressure v. projectile speed plot looks like.
cheers,
Douglas
I hear you. But whatever that answer is, the absolute ceiling for any given starting pressure is going to be the simple formula that has already been calculated in this thread. That is the beauty of that formula. It's not trying to predict what the actual performance will be, it's giving you a quick back-of-the-envelope limit on the performance. And that limit is useful for a lot of things.
If someone with TOO much time on their hands wanted to, they could go full-blown calculus on this thing, but that would just give lower ceilings based on the attenuation of pressure as the bullet travels, and the effects of friction, etc. But then, you're doing something else - and it's not as useful as the simple formula.
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Yes Wonka, I am quite familiar with the 'neglecting air resistance' answer...:) The better means of figuring out what the real ceiling is would require knowing what the pressure v. delivered velocity is. At least we would know how close the first approximation is....or, how big is the effect at less than 2/3 mean molecular velocity?
If I am going to discount something, I want to know how big it really is...LOL
cheers,
Douglas
Bob, I have no idea what the answer is...I have a suspicion but no proof.
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Well, As the moderator discourages the introduction of elements that may cast reality on a theoretical model, I will "interject" instead of "derail". That is, no reply comments expected. ;-)
When I look at theoretical calculations and models, I look to the extreme conditions and see how things hold up.
In this thread, one extreme might be a zero mass projectile or one of "point Oh so small" mass anyway . Think of it as the propelling gas mass velocity limit.
Another extreme might be a <1 psi propelling force (think blow gun). Viscosity must come to play, but that is definetly OT, so no sense to bring that up (even if the mere mention of hydrogen implies as much)
Combinations of any and all does tend to get confusing. If it could only be as simple as the math implies.
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Here’s an example of working backwards from a theoretical max velocity to what we might actually get from a real PCP.
...
3) Add the mass of the column of air that must be accelerated in the barrel behind the pellet:
1562 fps, 136 FPE (major reduction ! )
Would using helium improve these results?
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Here’s an example of working backwards from a theoretical max velocity to what we might actually get from a real PCP.
...
3) Add the mass of the column of air that must be accelerated in the barrel behind the pellet:
1562 fps, 136 FPE (major reduction ! )
Would using helium improve these results?
Yes, there is less energy spent on accelerating the column because helium is a lighter gas than either Nitrogen (which is mostly what we call "air"), or Oxygen (which is a small part of what we call "air"). 7 times lighter than Nitrogen, 8 times lighter than Oxygen.
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To be clear, the gas makes no difference to the MAXIMUM FPE, that is dependent only on pressure, caliber (bore area), and barrel length.... However, the reduction in power that occurs from including the mass of the gas in the calculations is greater with Air than with Helium.... ie Helium can come closer to the theoretical maximum than air can.... The loss of power with Air is 7.2 times as much as the loss with Helium....
Bob
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Here is a graph I published a while back showing the force on a bullet for various pressures and calibers....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/ForcevsCaliber2_zps1e8cdd4c.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/ForcevsCaliber2_zps1e8cdd4c.jpg.html)
If you multiply by the barrel length in feet, that will give you the maximum FPE possible for that combination, as per the simple Physics discussed in this thread.... I have found that for air, if you use 50% of that figure you will have a lofty goal to try and achieve.... I've never quite made it.... As an example, if you look at 3000 psi with a .357 cal and a 24" barrel (2 feet), the maximum is about 600 FPE.... A good goal would be 300 FPE.... Anybody ever done that with a 24" barrel on air?....
Bob
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I have been absent (online) from the thread for a few days but have been diligently working on this topic. A lot of theory and questions being passed around, mostly with more questions than answers. But that is the nature of this subject.
And as has been stated here by several of us, there is nothing like hard data to bounce against the theory. rgb1 Ron posted a sketch of a test set-up and that got me back to thinking of making an apparatus strictly for max velocity testing. So for the past few days (my wife keeps asking, What have you got going in the shop?) I have been building a "Max Velocity" gun. Or more like a barrel with a tank. I think I have taken a different approach to the actual firing than anyone else has. Very different from Ron's, and probably not practical for a field gun, but who knows?
I might start a new thread with the actual gun and testing, not sure yet. I built it strictly for .25 cal barrels, because I have a bunch of those on hand. The first set-up uses a short barrel with an effective length of only 8". I figured I would see if my idea worked before continuing with other barrel lengths, pressures, grain weights, ports, etc.
I took the first shots last night. Technical details will follow. I first tried some 9 grain plastic projectiles and they didn't function very well in the gun. :-[ So I resorted to making a brass projectile, which is re-useable, but it is hefty 54 grains (.25 cal). It worked decently for a first try, but I only got one good shot before I had an equipment malfunction. :( (The wooden filler plugs I was using inside the tube to reduce the shot volume kind of exploded :'( ). More work will be needed in the next few days as this gun evolves. But anyway, the good shot is as follows:
.25 cal
8" barrel
54 gn brass "bullet"
20 cc air
2800 psi
Actual velocity 707 fps
Actual energy 60 fpe
Theoretical Maximum Velocity 874 fps (for this gn wt, psi, barrel cal and length)
Percent of Theoretical Maximum Velocity achieved 81% ;D
I am pleased with the result for a first try, but there is much more work to be done with lighter projectiles and longer barrels.
Here are a couple of pics.
Lloyd
View of the straight shot through the 8" barrel.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxGun-1a_zpscxjsrwag.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxGun-1a_zpscxjsrwag.jpg.html)
The test set-up
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxGun-2a_zpsczxihjpo.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxGun-2a_zpsczxihjpo.jpg.html)
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Pretty interesting, Lloyd.... I'm actually pretty shocked you got to over 80% on air.... Got any Helium?.... ;)
EDIT: Did I do the math right?.... .25 cal.... area = (.25^2) x PI/4 = 0.0491 sq.in.... times 2800 psi = 137 lb.f.... time 8/12 ft. = 91.6 FPE.... 60 FPE is 66% of that.... If the barrel is .257 cal, the max. would be 96.8 FPE, and you would be at 62%.... Oh, wait a minute, you are talking velocity, not energy, we got the same thing.... ::)
Bob
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Bob, The set-up needs some tweaks, but the method is solid. I hope to exceed 80%.
Helium? I have been thinking about that.
Lloyd
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See Edit above....
Ran the numbers through your spreadsheet, using 20cc, no TP volume, 1 lb. drag, 2 lb. breakaway, air mass included, isothermal, got 89% efficiency.... Changed to Helium, got 753 fps at the same efficiency.... Overall efficiency of your one "good" shot is 60 FPE / 235 CI = 0.26 FPE/CI....
Bob
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See Edit above....
Ran the numbers through your spreadsheet, using 20cc, no TP volume, 1 lb. drag, 2 lb. breakaway, air mass included, isothermal, got 89% efficiency.... Changed to Helium, got 753 fps at the same efficiency.... Overall efficiency of your one "good" shot is 60 FPE / 235 CI = 0.26 FPE/CI....
Bob
Bob,
For this exercise, a test set-up that can only make dump shots, efficiency in FPE/stdcuin based only on reservoir volume is irrelevant and misleading. "IF" the valve could have been closed when the bullet left the muzzle, efficiency would have been about 1.02 FPE/cuin, which gives the relevant information about the actual flow characteristics and efficiency of valve and barrel.
I chose to compare the actual shot results against the theoretical maximum velocity rather than FPE for a particular reason.
I think the linear change in velocity represents a more realistic perspective on the changes made in the airgun performance, when the performance is judged against the THEORETICAL maximum. For instance, your velocity might be at 60% of the max theoretical, but the FPE would only be at 36%. The FPE comparison shows an unnecessarily bleak and discouraging comparison to what really is rather good performance. This not trying to sugar coat the results, it is just choosing a more realistic perspective, IMHO.
EDIT: Bob, I re-read some of your previous posts about theoretical maximums and see how you have been referring to percent of max theoretical FPE, not FPS. Either approach will work, obviously, it is just which one do you decide to use and the purpose of the testing or the goal of the project. So lets try it both ways in this thread. For the one "good" shot that I managed to take, it achieved 81% of max theoretical velocity and 65% of max theoretical energy. More work to be done! ;) Lloyd
Lloyd
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Lloyd that looks like something Mythbusters. Way cool. Maybe hook up a vacuum like they did to shoot a ping pong ball at over Mach.
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Lloyd, the FPE approach is independent of bullet weight, that is why I prefer it.... and it is much simpler to calculate.... However, stating both is probably a good idea.... Either way, I think heavy bullets will be favoured, don't you?.... particularly if it makes a difference between pushing Mach or not....
Bob
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Bob, Yes, the heavy bullets should favor approaching the max theo FPE, but as the title of this thread indicates, chasing that illusive "Maximum Velocity" of a projectile propelled by compressed air (or nitrogen or helium) is one of the driving factors of this experiment. That will require a very light projectile, and my 54 grain brass one certainly isn't a lightweight, ;D
I am making some aluminum projectiles right now.
Lloyd
Sixshootertexan, mentioning me in the same breath as Mythbusters is quite flattering. I will see if I can live up to that "myth"! ;)
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My gut feel is that you will be able to more easily reach a higher percentage of the "maximum theoretical velocity" with a heavy bullet than a light one.... particularly once you start pushing supersonic.... but that is what experiments are for is to find out, right?.... 8)
Bob
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I made a 17gn, 25 cal aluminum projectile to try in the test set-up. Managed to get one shot tonight and here are the results.
Specs:
25 cal, 8 inch barrel, 30ccs, 17gn, 2900 psi.
Results:
1110 fps, (70 %of theo max) 46.5fpe (49% of theo max.)
The results were a little disappointing compared to the heavier pellet, but still, for an 8" barrel, not too bad.
Here are a few pics of the test.
The aluminum bullet and the barrel
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxGun-3a_zpscmmpn3ab.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxGun-3a_zpscmmpn3ab.jpg.html)
The bullet loaded into the barrel.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxGun-4_zps1wohcrdf.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxGun-4_zps1wohcrdf.jpg.html)
1110FPS from an 8" barrel.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxGun-5a_zpscsdesanv.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxGun-5a_zpscsdesanv.jpg.html)
Retrieving the bullet, unscathed, from the box of plastic grocery bags.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxGun-7a_zpsojkiimy3.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxGun-7a_zpsojkiimy3.jpg.html)
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Lloyd, do you just rotate a half moon rod and off goes the projectile?
Tom
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Tom, Yes, that is basically how it works. The cross shaft and the barrel and the bullet all have matching half moon notches and the centerlines are offset by the radius of the notch. That way, when the cross shaft is in the fired position, the barrel can be screwed in and out f the breech for loading. For firing, the cross shaft is rotated as quickly as possible Clockwise to achieve (usually) instantaneous release of the bullet. The watch spring shown in the pic of the trigger wasn't quite strong enough to twist the shaft once the bullet was pressurized, so that needs to be improved.
The key to this set-up is that the the bullet is fully pressurized (without leaking !), and then its holding mechanism releases it like a cork from a champagne bottle. That way the bullet feels full force from the very beginning without having to wait for the air pressure to build up behind it.
Lloyd
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/CrossShaftDetails-8a_zpsntarzwba.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/CrossShaftDetails-8a_zpsntarzwba.jpg.html)
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/Trigger-9a_zpsqdi7p00t.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/Trigger-9a_zpsqdi7p00t.jpg.html)
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Lloyd.... Now that I see how the mechanism works, I put the following into your spreadsheet....
.25 cal, 54 gr., 2800psi, 0.003 sec. dwell (dump shot), 20cc reservoir, 0 TP volume, 8" barrel, 0 drag and breakaway, air mass included....
To get it to balance out at 707 fps, the efficiency factor needed is 0.88.... If I then change only the weight to 17 gr., guess what your spreadsheet predicts for a velocity?....
1119 fps.... :o 8) ;D
I think your model works pretty well, even with a very unusual design.... ;)
Bob
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More testing. Originally, I had hoped to achieve some really high velocities, but now it seems that the identification of trends could be of more immediate value. Actually, I am validating some of the ideas that Bob has proposed along the way.
The data in the following table has shots from the past few weeks, and also some of my original hi vel testing of the electronic valve back in 2009. All of the testing correlates surprisingly well. Consider all of the shots to be dump shots from unlimited reservoirs.
The columns with Maximum Theoretical Velocity and Energy are exactly that. Theoretical, with absolutely zero losses accounted for. These Theoretical values are impossible to achieve.
The Actual Values shown in the columns are broken down by barrel length, and then by sectional density of the bullet.
As Bob suggested, it appears easier to achieve a higher percentage of the theoretical values with bullets of higher sectional density. Another way to look at it is, for a given barrel length, the lower the theoretical max velocity, the closer you will be able to get to it.
The max velocity I was able to achieve (so far) was 1517 fps, that was .22 cal, 10.3 grain, 23.3" barrel, 2800 psi.
Lloyd
If you click on the table, it will enlarge so that you can read it.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/Data-07-28-15_zpska88vj2o.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/Data-07-28-15_zpska88vj2o.jpg.html)
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Yes, that certainly shows the trend toward reaching a higher percentage of the possible FPE with bullets of higher Sectional Density (heavier for the caliber).... You are likely seeing some degree of either partial sonic choking (mass flow limiting), or molecular velocity effects at the higher velocities required of the lighter bullets, or rather a reduction in those effect with the heavier ones....
I notice one other trend, and that is that the longer barrel had more difficulty reaching the same percentages as the shorter barrel, with the same bullet and pressure.... Since the tests were done with a virtually unlimited reservoir (ie constant pressure), I think most of that decrease is due to the larger mass of gas required in the longer barrel.... A 3 times longer barrel will contain 3 times the mass of air when the bullet exits.... air that has to be accelerated as well, reducing the theoretical velocity possible to achieve for the bullet.... I wonder if this experimental method might help quantify how much of the mass of the gas needs to be incorporated in the "bullet weight" in your spreadsheet model?.... The two obvious choices are half the mass, or all of it.... You may already have the data to determine that....
There is definitely more friction to be overcome in the longer barrel as well.... both between the bullet and bore, and resistance to the gas flowing down the bore.... but my gut feel is that the mass of the gas is the biggest factor.... Doing the same tests with Helium to see if the percentage drop with a long barrel is similar might tell the tale....
Bob
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I did some more calculations with my spreadsheet and added the increasing weight of the column of air behind the bullet. Adding this additional weight, significantly reduced the "Theoretical" max vel. Dividing the actual velocity by the NEW max theoretical significantly improved the percentage of theoretical velocity achieved.
Now, in the first green column for the 8" barrels, the percentages instead of being 67% to 84%, were 88% to 92%. For the 24" barrels, the percentages instead of being 50% to 73%, were now 84% to 93%. So just adding the column of air behind the bullet greatly reduced the discrepancy between theoretical and actual. The trend of achieving higher percentages with the heavier S.D. bullets continues.
But what I find rather baffling is the fact that the percentages achieved in both the short 8" barrels and the long 24" barrels were very similar. I would have expected the percentages in the shorter barrels to be much better than in the long barrels, but such was not the case.
I believe that the remaining losses (the 16% to 7%) can be accounted for mostly by the expansion of the air behind the bullet not being able to keep completely up with the accelerating bullet, and the force pushing on the bullet therefor slowly dropping off.
It must be remembered that these are ideal circumstances, with no U-turns in the air passages, no valve heads to squeeze past and no T-ports to be accelerated through.
So now, on to designing the next part of the experiment. Suggestions? First, making these shots takes a lot of time, so taking lots of shots with lots of variables is not an option. I do have another 24" .22 barrel that I could cut into into anther length, if that would be useful. Or I could install orifice plates at the breech of the barrel to possibly find that illusive sonic choking velocity. There should be a cusp or break point somewhere where the velocity changes/drops/increases much less/more than it should and I think that will yield some valuable information regarding the modeling of the output from a PCP.
Lloyd
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I thought that accounting for the air in the barrel would bring the longer barrel more in line with the short one, but I am surprised it made them nearly equal.... It shows again just how good your spreadsheet model really is.... BTW, is the progressive addition of the air mass behind the bullet something you have been using all along?.... That does seem like the best way to handle it until the valve closes (which in this case it doesn't)....
As far as additional experiments are concerned, the idea of inserting a series of smaller orifices to see when Sonic Choking occurs would be an excellent idea.... At 2800 psi the speed of sound in air at 70*F is about 1340 fps.... so if you plot efficiency vs. velocity for a given bullet you should see something happening as you approach that number at the orifice.... Perhaps you may need to plot efficiency vs. calculated orifice velocity instead?.... Using multiple weights to do multiple tracks should give you some useful data.... The bullet velocity may continue to increase after that velocity is reached in the orifice, but the mass flow rate should reach a maximum there.... so I would think the efficiency should show a marked decrease....
Using the fourmula I was given for maximum mass flow through an orifice, I get the following for your test conditions:
Mach 1 in air at 70* and 2800 psi = 408 m/s
Air density at 2800 psi = 224 kg/m^3
Orifice diameter of 1 cm; area = 0.785 cm^2 = 0.0000785 m^2
Maximum mass flow = 408 m/s x 224 kg/m^3 x 0.0000785 m^2 = 7.174 kg/s through a 1 cm orifice.... which is also 7.174 g/mS.... This apparently needs to be derated 5-10% for frictional losses, so the maximum should be 6.5-6.8 g/mS through a 1 cm orifice.... and proportional to orifice area....
Bob
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Bob,
OK, given what you have said, it seems like the .22 cal 23.3" lg barrel can serve as a test bed. Max vel with the 10.3 gn projectile was 1517fps and I don't think I can make the projectile any lighter so we are stuck with that as the max Muzzle Velocity. Because this arrangement is strictly a dump valve, the reservoir volume needs to be sized properly. What do you think makes sense? 20 or 30 ccs? Also, I don't know if any efficiency calculations would be valid because there will be no way to tell how much air is being "wasted".
Maybe this is a way to start: We know max vel with unlimited air and max flow passage is 1517fps. Install an orifice plate of full bore dia ( .22 dia orifice) and verify the max vel again. Reduce the reservoir volume until the velocity drops off to about 1500. Permanently fix the reservoir to that volume. Then start reducing the orifice plate and graph the velocities. My guess is that the velocity will drop off linearly (with the area of the orifice) but when the max mass flow is reached, the velocity will fall off much more rapidly. Or as you said, the efficiency will get very bad.
What do you think?
Oh, and the question about the air mass variable in the spreadsheet. The way I do the calculation is to calculate the air mass at each increment along the travel within the barrel, in proportion to the pressure in the barrel at that time. So the air mass continually increases until the valve closes. Once the valve closes, the air mass remains constant.
Lloyd
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I would think you would want the largest possible reservoir volume, so that the pressure was a constant, or nearly so, until after the pellet leaves the barrel.... Your valve is never closing, so the air velocity at the orifice is a function of the pellet velocity at any given instant, by the inverse of the areas (orifice to bore).... If the orifice is half the bore diameter, the velocity should be 4 times the pellet velocity at any given instant....
I'm not sure why you would want to decrease the reservoir volume until you hit any given velocity.... You are obviously thinking of something different than I am.... If you reduce the volume, the pressure will drop as the pellet moves down the bore.... At 1500 fps, you should already be experiencing Sonic Choking by the bore itself, as Mach 1 at 2800 psi is about 1340 fps.... I would think that should mean that the mass flow should be directly proportional to orifice area.... What that means to the velocity I don't know, however.... You may not see any "step" in the efficiency, as you are already choked....
In order to see the test cross the threshold from unchoked to choked flow, I would think that you need to start wayyyyyyyyyy under Mach 1, in fact I see no reason why you couldn't start at, say, 800 fps unchoked, by using a heavier pellet.... Then you should see little reduction in velocity until the orifice chokes, and then a drastic reduction in efficiency.... We need to separate "efficiency" (what we normally think of, in FPE/CI) from the percentage of maximum achieved (per this thread).... as they are quite different....
Bob
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Bob, Yes, we are indeed looking at it a bit differently. First, regarding the reservoir volume and the 1517fps velocity. That velocity was achieved with a reservoir of about 66ccs. For practical reasons (having to refill air tanks) there is no need to have the reservoir any larger than what is needed by everything downstream. so for that pellet 10.3gn pellet and barrel I first want to see if going smaller on the reservoir makes any difference. If it makes no difference why use the extra air? I planned on choking the orifice down even farther, which would use even less air. But after your explanation, i see a couple of experiments. With the 10.3 gn pellet, start with the wide open port, and start reducing it to verify that the vel does indeed drop proportionally to the drop in orifice area. Since we are assuming that sonic choking has already occurred, it will be interesting to see how linear the change is.
For the second experiment, I agree with your suggestion of starting with a heavier pellet, with a full bore size orifice, and muzz vel below, say 1000fps, and then start reducing the orifice to see when choking occurs, and if it indeed agrees with calculations. This continues to be interesting.
Lloyd
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HI Lloyd....
Using your own spreadsheet, and inputting 2800 psi, infinite reservoir, 10.3 gr. in a 23.3" barrel, no drag or transfer port losses, no air mass, 100% efficiency, you get a theoretical maximum of 2896 fps, 204 FPE (not quite sure why it isn't 207?).... Dropping down to a 66 cc reservoir drops it to 2844 fps (185 FPE).... Add in the air mass drops it to 1782 fps (72.6 FPE).... Dropping the efficiency down to 72.5% put you where you are at 1517 fps (52.6 FPE).... with an residual muzzle pressure when the pellet leaves the barrel of 2296 psi.... The lock time is 0.00193 sec (pellet in the barrel this long).... If you could close the valve at a dwell of 0.000193 sec. your efficiency would be 0.38 FPE/CI....
If you cut the reservoir volume in half to 33 cc, you should get the following.... 1500 fps, 51.5 FPE, residual pressure (at pellet exit) of 1945 psi, lock time of 0.00194 sec, efficiency of 0.43 FPE/CI if you closed the valve then.... If you cut it down to 20 cc, you should get.... 1479 fps, 50.0 FPE, residual pressure at pellet exit of 1623 psi, lock time of 0.00196 sec., efficiency of 0.51 FPE/CI if you closed the valve then.... As you can see, the smaller you make the reservoir, the less the maximum theoretical velocity and FPE because you no longer have 2800 psi for the entire shot.... For the last example, the average pressure over the shot is less than 2200 psi.... I think this complicates things, it certainly means that your prediction of 207 FPE is no longer relevant....
Whether or not this makes any difference to trying to figure out what happens with Sonic Choking I don't know.... but because the pressure is less, the speed of sound will also drop some as the pellet moves down the barrel, and the smaller the reservoir, the more it will drop.... I think you will find that reducing the reservoir size has the same effect as using too small a plenum in a regulated gun.... the power drops off.... Because you are wasting so much of the shot to start with, however, it won't be as pronounced.... and I can certainly see the advantage to saving air....
Bob
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HI Lloyd.... Using the formula above, I calculated the Mass Flow Limit for a .22 cal at 2800 psi.... for various port sizes of interest (1/64" increments)....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Mass%20Flow%203_zpsuip5kzrp.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Mass%20Flow%203_zpsuip5kzrp.jpg.html)
The units are grams per millisecond.... The flow has been derated 10% to allow for frictional losses.... Hope you find it useful....
Bob
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Bob,
Changing units of measure on me. That is not nice, LOL. My calculator uses slugs and there are 14,593 grams per slug, so let's do some back figuring. Using the highest velocity sample that I shot, 1517 fps, the lock time is approx .0019 seconds. Mass of the air in the 23.3" barrel at 2550 psi (average for 66 cc reservoir) is .00021 slugs, or 3.06 grams. Lock time was about 1.9 millisec, therefore average mass flow was 1.61 grams/millisec. That is less flow than the limit of 2.0 grams/millisec on your chart. To reach 2.0 grams per millisec, lock time would need to be about 1.5 milli sec. Changing only the grain weight in the spreadsheet, projectile weight would need to be reduced to about 5 grains to get locktime down to 1.5 millisec, and the MV would be about 1781fps. So to reach the mass flow limit, the MV would greatly exceed Mach 1. What do you think? Is the mass flow limit the "hard stop" for velocity?
Lloyd
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Mass flow is how I have based my calculations..... Actually I have kinda gone about it ignorantly, because I calculated the flow in ci's per sec or ms. So, let me organize this line of thought.
establish cal
establish projectile weight
establish desired velocity. This gives a calculated duration that the projectile will be exposed to pressure for accelerating. I do the calculation 1000 times (divide the barrel length by 1000). That leaves me with a final velocity at the muzzle.
establish porting size and pressure
So if I use a established porting, I should then know how much volume I can move in calculated duration as established above. If the velocity isn't as desired, I must increase or decrease port size and/or pressure. There are a lot of back ground calculations that affect the above mentioned such as friction, porting length (dead space) ect. Ultimately the mass flow is the calculation that I use, it is expressed as Volume which in retrospect is confusing. As the psi drops obviously the amount of volume that can flow through the porting will change. For the sake of experiment, a dump valve would seem to me as the best platform to base it all from. as to efficiency, that's a hard one to base line for a dump valve. I suppose using a volume of dump compared to volume of barrel might be a place to start. Bob has done such work already. If we were to move from the test platform to a more typical valve design, we could assume constant psi ( regulated) and a fixed volume plenum. This plenum is essentially your dump valve and the reservoir volume feeding it allows us to use Bob's established efficiency calculations. The hard part there would be getting a set-up that is inline and has no dead space. I suppose it could be done it the rig were designed like one of those quick exhausting potato gun valves. Not sure if you guys have ever seen one but the set up would be pretty sweet for single shot testing.
Lloyd, your test rig is bore diameter porting isn't it? I don't guess I'm seeing how you are going to change the port size. Maybe I should look at the photos a bit closer. Is the barrel you are using a smooth bore?
Bill G
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Lloyd, I'm not sure you can average the pressure and use that to calculate the mass flow, as when the pressure drops, so does the maximum flow rate.... and if you do average the pressure, then the maximum flow rate would not be 2.01 grams/mSec, but about 1.83, and you are at 1.61.... which is 88% of the predicted maximum mass flow rate.... Perhaps the 5-10% derating that I was given was not enough for a "long" orifice like a barrel (more friction)?.... I freely admit to having a poor understanding of sonic choking.... but it appears it is not a sudden event but builds up as the velocity approaches the speed of sound in the system.... Perhaps you can get something useful from post # 132 (and others) in this thread.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.120 (http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.120)
The fact remains that your muzzle velocity of 1517 fps is exceeding the speed of sound at 2800 psi of 1340 fps, so there must be a choke forming in part of all of the barrel, shouldn't there?.... According to the definition of choked flow, the pressure downstream of the choke point cannot be more than 52% of the source pressure.... So much to learn and understand.... ???
Bob
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Bill G, A lot f info in your post. Thank you. It sounds like you have a pretty good data base of ports/calibers/velocities, etc.
My set up does use full bore size porting and a .22 cal Discovery barrel. I planned on modifying the cone-shaped entry into the barrel so that I could use interchangeable ports. A quick exhaust valve (similar to the one described by Ron in Reply# in this topic, or something like the potato guns or paint ball markers could work well and eliminate the need for special projectiles. I have fiddled with some of the QEVs on my prototypes and the difference in solenoid actuation speed is noticeable.
Bob, even though the sonic choking is a progressive phenomenon, if the pressure downstream of the choking can be no more than 52% of the source pressure, I would expect to see some loss of linearity, or change of slope, in the velocity. If indeed my 1517fps shot is already being hampered by sonic choking, maybe just taking a series of shots with progressively lower pressures would produce results that quantified the effect of the choking. I might give that a try. It will be easy to do without changing my set-up.
Lloyd
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Lloyd, I would agree, when choking occurs there should be a change in slope of the velocity vs. pressure curve.... Your suggestion should work.... As the pressure drops so does the speed of sound, but not drastically....
Bob
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I am reviving this post for at least 3 reasons:
1) I m recovering from some surgery :P and I can't work outside, so I can stay in my shop all day and play with airguns, he, he, he. ;D
2) Bill G was taking me to task in another thread http://www.gatewaytoairguns.org/GTA/index.php?topic=74919.60 (http://www.gatewaytoairguns.org/GTA/index.php?topic=74919.60) (see Replys # 76 and 77)
about trying to get high velocities out of itty bitty air reservoirs. Bill, I know you can do this yourself, LOL, but I am going to help you out anyway. ;)
3) I can't stop myself from doing this sort of experimentation.
So, today, I modified the test rig by replacing the way too big reservoir, with an adjustable one: max vol 9.17 cc, but plugged down to 5.08ccs.
I set this series of tests up with the same 23.3" long .22 cal Disco barrel and the same funny bullets.
Look at the pictures starting around Reply # 69 to see what everything looks like.
I only took 3 shots (so far) and here are the results:
.22 cal, 23.3" barrel, zero effective T-port volume,
5.08cc dump reservoir, 2150 psi.
10.3 gn 1180 fps 31.9 fpe
13.6 gn 1065 fps 34.3 fpe
42.7 gn 708 fps 47.5 fpe
Bill, this doesn't answer your original question of whether you can get a .25 cal 25 gn pellet to go 950 fps from a 20" barrel with a 7cc reservoir at 2000 psi, but I am headed in that direction. So just to make you happy, give me a gn weight and volume and velocity for this 23.3" 22 cal barrel and I'll see what I can do. Sorry, I don't have a .25 cal barrel that I want to chop up at this time. :(
I think these numbers show that if you can get rid of all the air constipation associated with valves and T-ports and making U-turns, it doesn't take a lot of air to make a pellet fly pretty fast.
I'm going to try some other configurations.
Lloyd
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Wow, surprising numbers. Supersonic. With 5cc reservoir in .22 is more than I would have expected. Gonna watch this closely...
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Just need a configuration where exit port from valves throat is right at the breech/pellet.
Only losses to volume/pressure within plenum would be that of @valves throat.
You would get the Amplitude of pressure pulse instantly with minimal loss and be quite effective too one would think !
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Just need a configuration where exit port from valves throat is right at the breech/pellet.
Only losses to volume/pressure within plenum would be that of @valves throat.
You would get the Amplitude of pressure pulse instantly with minimal loss and be quite effective too one would think !
Yes, exactly. If the valve were 90 degrees to the breech and maybe the hammer traveled up and down. Maybe use some sort of tap loader for compactness. I think part of the speed to my test setup is that the bullet is more like a cork in a champagne bottle, holding back all the pressure until the bullet is mechanically released.
Lloyd
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HI Lloyd.... Well you know I had to run your numbers through your spreadsheet (I'm sure you already have).... Using zero TP volume, 23.3" barrel, 2150 psi, dump shot, 1 lb. drag, 5 lb. starting friction, air volume included (of course).... here is what I got for the required efficiency....
10.3 gr @ 1180 fps = 68%
13.6 gr. @ 1065 = 68%
42.7 gr. @ 708 fps = 75%
The 75% is on the high side, but it was with a very heavy bullet which helps, but the others are not at all unusual.... If I change only the TP volume, and add 0.02CI (typical), the velocities drop to....
10.3 gr = 1142 fps
13.6 gr = 1039 fps
42.7 gr = 693 fps
It looks like eliminating the TP volume is worth 2-3% in velocity (4-6% in FPE).... significant, but not earth shattering.... Man I love your spreadsheet !!! .... Talk about an invaluable resource !!!
Bob
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I think the significant part of this is getting those velocities and the corresponding muzzle energies of 31.9, 34.3, and 47.5 FPE from a 5cc reservoir at 2150 psi. With those shots you have a reservoir volume range of from 0.16cc/FPE to .11cc/FPE.
Lloyd
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I understand, this is very much pumper territory, not the usual setup for PCPs.... The residual muzzle pressure is about 557 psi in each case, with a dump shot.... Since the valve volume is about 35% of the barrel volume, you are in a good range to get reasonable efficiency with a dump shot.... Your test setup is much more efficient than you would get with most pumpers, of course.... You are using a total of 46 CI of air for each shot, but I realize some of that (26%) is being wasted (blown out the barrel after Elvis has left the building)....
During early testing, with a dump shot, my .25 cal Pumper Carbine was getting 25 FPE (670 fps) with a 25 gr. pellet at 1500 psi from a 20" barrel, with a 5.5 cc valve.... which was 34% of the barrel volume, a reasonable comparison.... That works out to about 57% efficiency using your spreadsheet, not bad for the low pressure and conventional construction.... Residual muzzle pressure would have been about 382 psi.... and wasted air about 25%.... Later versions used more pressure and a longer barrel, but a larger reservoir and were no longer a dump shot.... they were basically a PCP with an onboard pump....
Bob
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I'm still trying to precess all the math and insight in this thread.
But I had a thought of a possible idea that might help maintain pressures a little longer in a dump valve design. What if the dump chamber was also a spring loaded piston chamber that, at full desired pressure the piston was at full stroke and when the dump/shot took place the piston would move to shrink the volume the the chamber. The spring pressure collapsing the chamber should help maintain the pressures for longer, would it not? The energy in the spring should add to the overall energy of the shot correct?
Then you use the motion of the moving piston to drive a semi-auto mechanism. ;)
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Air Snipe,
This thread is going to take a bit of a twist in the next week or so, which might make it more interesting.
The idea of using a spring loaded chamber in a dump valve application is good in theory, but in application is rather difficult. If the piston were 3/4" dia with a fill pressure of 2000 psi, the load on the spring is 884 pounds. It is very difficult to find a spring that is compact enough that will handle that kind of load. Still, if it could be done, you'd be getting the energy from the compressed air AND from the compressed spring. For a single shot. Could be good.
Lloyd
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The Webley Paradigm used that system, and was IIRC a single stroke Pneumatic.... I think it used a stack of Bellevilles against the piston to maintain the pressure in the air chamber during the shot.... Sort of combines a Springer and a Pumper.... The big problem in using the system with large volumes of air is the mass of the piston and the forces required.... This idea has been discussed in this gate (which we call the Geek Gate, for obvious reasons) previously....
Looking forward to where you are taking us, Lloyd.... should be interesting....
Bob
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Bob,
Yes, planning on looking at some things from a different direction. Let's say maybe a little more pragmatic and little less esoteric ;) ?? After all these months off I have forgotten a bit, so I can start fresh.
Lloyd
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pragmatic?.... esoteric?.... ???
where did I put my dickshunery?.... :-[
Bob
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pragmatic?.... esoteric?.... ???
where did I put my dickshunery?.... :-[
Bob
Ha, ha. My wife makes me learn new words every so often. Says it will slow down the progress of my dementia. :o
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HUH?.... WHA?....
My wife looked up them thar fancy words on the internet for me.... (really, she did!).... I'm too busy to get dementia.... DEMENTED, though, I admit to freely.... *LOL*....
Bob
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Air Snipe,
This thread is going to take a bit of a twist in the next week or so, which might make it more interesting.
The idea of using a spring loaded chamber in a dump valve application is good in theory, but in application is rather difficult. If the piston were 3/4" dia with a fill pressure of 2000 psi, the load on the spring is 884 pounds. It is very difficult to find a spring that is compact enough that will handle that kind of load. Still, if it could be done, you'd be getting the energy from the compressed air AND from the compressed spring. For a single shot. Could be good.
Lloyd
Lloyd, you could reduce the piston dia and increase the stroke length. The problem I see is the piston would have to come to an abrupt stop and would put shock into the gun. Would not be near as bad as a springer but I would think, would be noticeable.
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The problem I see is the piston would have to come to an abrupt stop and would put shock into the gun
That was our conclusion in previous discussions.... not only putting shock into the gun, but destroying the piston from the high forces and deceleration involved....
Bob
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This really is an intriguing idea, but making it work is another story. I had wondered if the main air tube on a PCP had a free floating divider piston in the middle and one side of the cylinder was precharged to a certain amount, like a spring would do. Call that the spring side. Then if you filled the active side and it compressed the spring side, like adding a booster spring. I think I did the math and in the end, for all the effort, the amount of usable air was the same. Oh well.
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I think the concept is that the pressure during the shot should stay higher instead of dropping off the way it would without the booster spring.... If you pressurized the booster side to 2000 psi, and then the active side to 1999 psi, the piston would not move (assuming equal diameters).... If you went to 3000 psi, the booster side pressure would have to match, so the volume of the booster side would reduce from full reservoir volume to 2/3rd of that.... while the active reservoir would be the other 1/3.... On firing, the pressure would start at 3000 psi, fall gradually to 2000 psi, and if the pellet was still in the barrel, then the air would continue to expand just as if the valve had closed at 2000 psi.... To put some numbers on it, let's assume the swept reservoir volume is 30cc, full to 2000 psi.... If we pressurize the active side, to 3000 psi, we have 10cc of air available for the shot at 3000 psi.... The air in the booster side is now 20 cc at 3000 psi.... Let's say the barrel volume is 20cc.... At the instant the valve opens, the pressure is ~3000 psi.... By the time the pellet has moved 1/4 of the way down the barrel (5 cc) the total volume is 35 cc, so the pressure is (30/35) x 3000 = 2571 psi.... At half way down the barrel (10 cc), the total volume is now 40 cc, so the pressure is 2250 psi.... At 3/4 travel (15 cc), the pressure would be 2000 psi, and after that expansion would be taking place because the piston has stopped.... At the muzzle (20cc), the total volume is 50 cc, but 30 cc is still at 2000 psi (the booster side).... so we have 10cc of 3000 psi air now occupying the 20cc of barrel, and the residual muzzle pressure is 1500 psi....
If we compare this to a 10 cc dump valve at 3000 psi, same 20 cc barrel volume, we get the following.... At opening ~ 3000 psi.... at 1/4 travel the pressure is (10/15) x 3000 = 2000 psi.... At 1/2 travel, the pressure is (10/20) x 3000 = 1500 psi.... at 3/4 travel, it is (10/25) x 3000 = 1200 psi.... and at the muzzle it is (10/30) x 3000 = 1000 psi.... In both cases, the total amount of air used was 10 cc at 3000 psi (207 bar) = 2070 cc = 126 CI.... However, the pressure profile using the booster chamber at 2000 psi is greater from breech to muzzle, so we would expect a higher velocity from the same amount of air, and hence greater efficiency.... The extra energy is coming from the work done to compress the 30 cc of air at 2000 psi to 20 cc at 3000 psi....
Unfortuntely, using this example, we have a piston being drive at high velocity coming to a crashing halt while there is a huge force behind it.... Let's look at that.... If we have a cylinder of 1/2" diameter, it would take 9.3" of length to store 30 cc of air (plus the length of the piston itself, so at least a 10" reservoir).... The average pellet takes about 1.5 mSec to travel 3/4 of the way down the barrel, at which point the piston hits the end of its travel.... It's average velocity for the trip is (9.3 / 12 / 0.0015) = 517 fps, and it's terminal velocity will definitely be higher than that.... I'm not sure what the piston would weigh, but whatever it is, it's going to hit the end of the reservoir and come to an abrupt halt from over 600 fps.... At that instant, in addition to its own momentum, it still has a force of 393 lbs. pushing it.... Lloyd, you can do the math if you wish, all I can say is OUCH!....
Bob
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Bob,
Just want to let you know that visualizing those piston volumes changing size and pressure as the event unfolds, makes my head hurt. Rocker 1, I see what you mean, now, ha, ha.
If the piston didn't have to come to a halt, or say that it was damped, or that the air could not drain completely from it, so that it was more like a spring, maybe then the movement of the piston would be less violent.
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If the valve closed before the pellet left the muzzle, the pressure left would act as a dampener and slow the piston down. But of course that is not a dump valve.
You could have a piston between two equal force sides connected to a shot side piston. But this would need enough space for the whole system to over travel under momentum and would probably oscillate until reaching equilibrium. Might sound cool.
()-------[------() ]
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If you have a timed valve, just use the entire volume available for the reservoir, I don't think you can do better than that for power and efficiency.... After all, the pressure on both sides of the piston is the same, so why not gain the volume occupied by the piston?....
Bob
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I have one more idea to throw out there to perhaps achieve higher velocities: The Gerlich tapered gun barrel.
A-square made a special .416 caliber rifle (powder burning) with a very light bullet (for caliber) to achieve at least 5280 ft/s (one mile per second). They drew their design from Gerlich's tank gun barrel which has a taper from breech to muzzle. So too did the .416 Gerlich as A-square named the cartridge.
I wonder if a tapered bore and collapsible projectile wouldn't tend to separate the slower from the faster molecules leaving the slower ones behind and pushing the faster ones to the base of the bullet. You would want the collapsible bullet to keep friction down.
Intuitively, I see the air column being extruded longer as the bore reduces. The slower molecules may want to be left behind, while the faster ones move ahead.
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I have no idea if that idea will work with expanding air.... The gasses in a PB are under such pressure and temperature they act completely differently.... not to mention they are already hypersonic, and hyperspeed from the temperature.... I guess the only way to find out would be to try it....
Bob
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hmm air spring chamber that sound like the Quigley wonder if it could be sized up... or just a np piston that reduces size of chamber as shots are taken...
http://www.americanairgunhunter.com/quigley.html (http://www.americanairgunhunter.com/quigley.html)
Me I have been in love with the Idea of a taper bore for a while... .25 paper patched to 30 cal in a taper bore... probably only need 6"-8" of rifle at the muzzle..?
.25 jsb monster with .30 head and tail...
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Just as an aside.... If you were calculating the maximum theoretical velocity in a tapered barrel.... what diameter would you use in the calculation?.... It makes a HUGE difference....
Bob
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limited by the speed of the air molecules
at that temperature
springers have a big advantage since they raise the temperature/speed of the molecules
but you have to cock them-and the springs are heavy long
9.5 lb 45" my 460 with scope
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limited by the speed of the air molecules
at that temperature
If you are saying that that is the max velocity for a PCP on HPA, sorry, but we have left that way in the dust. ;)
Take a look at reply #133 in this thread.
http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.120 (http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.120)
And that velocity isn't going to stand for long.
Lloyd
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Well Bob with LLoyds foray into supersonic flow we are breaking new ground and we need develop an accurate model to know... otherwise its the good old standby of trial and error...
But I do have an Idea of what might be going on in his getting to supersonic velocity and it has to do with the fact that it is the shock wave that destroys supersonic flow is prevented by backpressure and the fact that pressure is dropping as the pellet moves forwards also can be thought of as increasing backpressure...
So as the air charge hits the restriction (throat of the nozzle) with 4500 psi (down to whatever psi supersonic flow can not be achived)it wants to go supersonic may even briefly achieve it until it hits the back of the pellet... from that moment on (for a little while)you have flow that wants to be supersonic but back pressure prevents it...
does the pellet hit supersonic before the pressure falls enough to not support super sonic flow(edit*thru the throat) probably not but maybe?
but in this period there are no supersonic shock waves to destroy/disrupt the supersonic flow at the head of the column of air...
so from there is the two possibility's depending on how fast is the pellet going when the back of the column of air drops below supersonic
allows a supersonic shock wave at the throat of the nozzle and propagating both ways...
one towards the pellet one to the back of the air chamber... the one to the back of the chamber may be cool to wonder about just cause what happens does it disperse or reflect back through the nozzle... what happens when a supersonic shock wave hits a nozzle that causes supersonic flow..? probably scavenges the air chamber so well that it causes vacuum.? ;)
so the other shock wave rides up the column of supersonic air that is collapsing from the rear... so does it catch the pellet and help toss it to super sonic or did the column send the pellet super sonic and out the barrel first...
there may be a further complication as it is possible that weak parallel to the barrel length shock waves form in the eddies along the barrel i.d. ? does that and the shock wave from the rear combine to squeeze the column of air help keeping it supersonic..?
So basically what we have is a tuned nozzle and all its implications....
Bob I have had concentration probs for about ten years(getting slightly worse with time...) so now I need walked thru more complicated math and have a hard time even learning a new song on guitar from tab and sheet music still do ok when shown...
point is I just do not have the math skills any longer (lot of things I would need re-walked thru) to know if there is any usefulness in the applet in the link below about the de Laval/converging diverging (CD) nozzle...
http://www.engapplets.vt.edu/fluids/CDnozzle/cdinfo.html (http://www.engapplets.vt.edu/fluids/CDnozzle/cdinfo.html)
so the things needed are for a given nozzle design/size what is the mass flow max (no backpressure or just ambient) thru the throat at many given pressures 4500 psi and below...
at what point is supersonic flow not supported thru the nozzle throat by the upstream psi... at ambient... that gives an idea of what it wants to do... and the max probable weight of the charge at a given time...
now add the pellet some how (as backpressure?)...
so hopefully I made some sense??? but you can see the barrel taper would depend on what is happening and then projectile capability...
multi layer paper patch that the taper strips rather than embed or other designs...
but can the tapered barrel help support the supersonic flow even longer if designed right or a more sudden squeeze just to reap the benefit of a lighter projectile than the large bore would normally see...
Hope I made some sense cause trying to communicate idea's clearly is a bit rough and tiring for me... I do think I have a semi solid base of understanding, so if I am not clear... :-[
Thanks for you patience Bob and guys... wish I was 19 again I could at least look up stuff to help present things better and come up with some of the math models....
But yep I think it is all in how the shock waves form and do not form..?
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I wonder about converting the psi/ci or cc (Bob) to heat equivalents and modeling that thru a CD nozzle is a valid approach...
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Kirby, I had a hard time following that, and I certainly don't have the depth of Physics or Math to understand, or much less work through, CD nozzles.... My knowledge is limited to a few basic facts regarding them....
1. There are no shock waves upstream of the nozzle, as the flow is subsonic....
2. When and if Mach 1 occurs AT the nozzle, there is a minimum 47% drop in pressure across the nozzle.... This is called "Choked Flow"....
3. Once Mach 1 occurs at the nozzle, there is a mass flow limit for any given pressure.... and no change in the output pressure can increase that....
4. By shape of the Diverging (downstream) part of the nozzle can affect the velocity of the flow, but since the mass flow is fixed, increased velocity must be matched by decreased pressure....
The thread is about the THEORETICAL MAXIMUM velocity that a PCP can produce, and that is a very simple calculation based on pressure (psi) x area (sq.in.) = force (lbs.), acting through a given distance, the length of the barrel in ft.... which results in the maximum possible energy (ft.lb) that can be generated.... Basically, in terms of energy, we are pushing hard to reach 70% of that energy in highly specialized experimental guns, like Lloyd used to reach 1745 fps in the thread he mentioned above.... and even the best of our usable PCPs have great difficulty reaching 50% of the maximum.... There is a thread in the Gate on Choked Flow, perhaps you may find somebody there who has a deep enough understand to help you through that complicated subject.... It would at least be worth your while to go through it as there is a lot of valuable information there.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.0
Bob
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lloyd
Yikes!
1700 fps
I think average air molecule speed at room temp is about 500m/s 1650 fps-
over 1700 fps-well some are much faster obviously- guessing he is funneling those fast molecules-lensing them
Does he use a smooth bore-like our 120mm tank gun?
Yes you have left me behind-1745 fps WOW WOW
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it would be a lot of work but could be proved disproved with a lot of air and projectiles and in stages shorten a sacrificial barrel...
to see what is happening fps wise at each length... and the more shots at each length the better probability of accurate measurement... averaging...
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Kirby, I had a hard time following that, and I certainly don't have the depth of Physics or Math to understand, or much less work through, CD nozzles.... My knowledge is limited to a few basic facts regarding them....
1. There are no shock waves upstream of the nozzle, as the flow is subsonic....
2. When and if Mach 1 occurs AT the nozzle, there is a minimum 47% drop in pressure across the nozzle.... This is called "Choked Flow"....
yes BUT that is only when there is no backpressure both the finite air supply causing an upstream loss of psi and the pellet act to drop the amount of that pressure loss...
Ok there is a 4500 psi pressure vessel of 20cc and the pellet is 2cm down the barrel what is the barrel pressure at that point...
The drop in psi is only caused by the growth in size of the vessel (Boyle's law) when the pellet has traveled to the point the vessel is 40cc you are down to 2250 psi...and the pellet/air is still subsonic... so no sonic choking
with the converging cone feeding the barrel it acts the same way but at a certain point the psi/flow rate/size of the air chamber turn it into a pseudo converging diverging nozzle it happens at a psi that induces supersonic flow through the restriction(throat) and that is when he sonic choking happens producing the supersonic shock wave that since the pellet/and column of air have distance from the source of the shock wave it causes sonic packing behind the pellet but also disrupts flow as it travels up the air column supersonic and crumbling to subsonic and that pressure drop after the shockwave...
The cd nozzle produces a supersonic jet which extends in to the diverging cone and only falls apart past the nozzle when shock waves form.
the fall in pressure does not matter at that point... it is the shock wave that is packing the charge in front of it...
3. Once Mach 1 occurs at the nozzle, there is a mass flow limit for any given pressure.... and no change in the output pressure can increase that....
4. By shape of the Diverging (downstream) part of the nozzle can affect the velocity of the flow, but since the mass flow is fixed, increased velocity must be matched by decreased pressure....
The thread is about the THEORETICAL MAXIMUM velocity that a PCP can produce, and that is a very simple calculation based on pressure (psi) x area (sq.in.) = force (lbs.), acting through a given distance, the length of the barrel in ft.... which results in the maximum possible energy (ft.lb) that can be generated.... Basically, in terms of energy, we are pushing hard to reach 70% of that energy in highly specialized experimental guns, like Lloyd used to reach 1745 fps in the thread he mentioned above.... and even the best of our usable PCPs have great difficulty reaching 50% of the maximum.... There is a thread in the Gate on Choked Flow, perhaps you may find somebody there who has a deep enough understand to help you through that complicated subject.... It would at least be worth your while to go through it as there is a lot of valuable information there.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.0
Bob
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What I am saying is the sonic choke may cause sonic packing and that may move the theoretical max fps up some... so I figured it belonged here...
It has to be happening or Lloyd could not have beat the speed of sound in the 4500 psi original charge...
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It has to be happening or Lloyd could not have beat the speed of sound in the 4500 psi original charge...
This is kind of like arguing about religion, a lot of things have to be taken on faith. ::)
Airguns are science, and I do know as a proven fact, that neither the speed of sound, nor the average molecular speed of the molecules in air, are, in themselves, a limit to the speed that can be obtained from a PCP. Those speed limits are in the dust. 8)
Lloyd-ss
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This is kind of like arguing about religion, a lot of things have to be taken on faith.
Amen, brother Lloyd.... ;)
Bob
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I do see that it has moved thing forwards I just wish I had the $$ to fund the slow shortening of the barrel and the ammo and your time to test...
the velocity curve would be telling I think...
So for now like religion yep
but compression by a shock wave has been proven...
I have TONS OF RESPECT for what you guys have done
but science is also proving why...
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...........
but science is also proving why...
Right you are.
Lloyd
P.S. And shortening the barrel in increments is on the to-do list also. Just not sure when I will get to it, but I certainly hope to.
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The practical application part of this discussion, along with the real-world testing is being continued
in the Sonic Choke, or Sonic Joke, thread in this same gate.
If needed, here is the link.
http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.140 (http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.140)
Lloyd-ss
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Old Physics book
Looks like about 10% of the O2 molecules at 300k(room temp) are above 750m/s
N2 would be maybe 20-30m/s faster- than O2 -
no more like 5m/s than air- since already 80%-my bad
Try helium with longer barrel lighter pellet bigger diameter-
at 1745 his pellet is out running most of his propellent molecules-
Helium is much faster- but lighter-so it will need more impacts-more length to act over or more diameter
1745 FAST
Everyone sure none of that barrel oil is being ignited by friction-tiny boost maybe
Air -equal weight mass-has a BIG 3X momentum advantage and a 7X mass advantage-might have to have a 7X as large "chamber" to use the same weight of He -or a 3x as large to equal the MV advantage-
Stilll 1745 fps-sooo fast
and if I'm backwards on the He- go the other way CO2(but they are slower than air-more MV but slower-for short barrels and lower peak velocity- it might be better-accelerate faster initially)
Why use a rifled barrel? Smoothbore would be faster
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A good percentage of the air (molecules or otherwise) is going much less than 1745fps. The closer to the inner wall of the barrel, the slower they are. The air at center base of the pellet it going 1745fps.
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So, maybe we have some very well organized air molecules?.... The ones on the edge, near the barrel, are on the low side of the velocity distribution curve, while the ones in the middle are the fast ones, at the high end of the velocity distribution.... How very nice of them to co-operate like that, and not have to exceed the 1650 fps RMS velocity!.... J/K guys !!!
or am I?.... ???
Bob
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Maybe I should pre-heat the barrel. :o
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CHEATER !!!
Bob
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CHEATER !!!
Bob
Com'on, Bob, that's the second time you've said that in the past week or so, LOL.
How about we call it "creative solutions"? ;)
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After you get this puppy past 2000 fps with air at room temperature.... I'd love to see what you can get with Helium.... a vacuum on the barrel.... heat it up red hot if you like.... *LOL*....
Bob
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So, maybe we have some very well organized air molecules?.... The ones on the edge, near the barrel, are on the low side of the velocity distribution curve, while the ones in the middle are the fast ones, at the high end of the velocity distribution.... How very nice of them to co-operate like that, and not have to exceed the 1650 fps RMS velocity!.... J/K guys !!!
or am I?.... ???
Bob
This is precisely why I thought that the tapered barrel may have merit. The average temperature is not going to change much if at all. Therefore the average speed of the molecules must remain the same. Those near the barrel walls must be slowed down due to friction effects (which induces some heat, does it not?). Thus the remaining molecules in the center must move faster.
With the tapered bore, you have a progressive reduction in area, and less force per say. However, does this gain more speed possible due to the slowing of more molecules since they are dragging on the walls, which in turn makes those in the middle of the column faster moving?
When observing the extrusion, pultrusion, and wire drawing processes, the material flows much faster in the middle while the material at the walls of the dies moves slower.
Now for figuring out the force on the projectile as it travels down the tapered bore, you may have to apply calculus---a continuing decrease in area for travel. The amount of taper, however, will not be all that great. Tapering a .257" bore to .240" in 36" should be more than sufficient to test this, I would think. Therefore, an average may be a good enough approximation.
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Lloyd if ya really want to cheat/C.S. and since are using aluminum ammo stick with the 19-24 inch barrel but attach a short barrel (8-12 inch) extension that has embedded rails hooked up to a capacitor bank... ;)
Can not help it even my little pumpers are hybrids...
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NASA LIGHT GAS GUN
used H2 or Helium for just the reason I suggested-the heavier molecules run out of speed-just as the physics book diagram showed
velocities were STUNNING- 6000 meters per second-
They are springers -but same idea-air -N2 O2- run out of speed-cut from somewhere-wiki maybe
Try helium and a smooth bore
light-gas gun works on the same principle as a spring piston airgun. A large-diameter piston is used to force a gaseous working fluid through a smaller-diameter barrel containing the projectile to be accelerated. This reduction in diameter acts as a lever, increasing the speed while decreasing the force. In an airgun, the large piston is powered by a spring or compressed air, and the working fluid is atmospheric air.
In a light-gas gun, the piston is powered by a chemical reaction (usually gunpowder), and the working fluid is a lighter gas, such as helium or hydrogen (though helium is much safer to work with, hydrogen offers the best performance [as explained below], and causes less launch-tube erosion). One addition that a light-gas gun adds to the airgun is a rupture disk, which is a carefully calibrated disk (usually metal) designed to act as a valve. When the pressure builds up to the desired level behind the disk, the disk tears open, allowing the high-pressure, light gas to pass into the barrel. This ensures that the maximum amount of energy is available when the projectile begins moving.
Light-gas gun
Diagram of a light gas gun
1 — Breech block
2 — Chamber
3 — Propellant charge (gunpowder)
4 — Piston
5 — Pump tube
6 — Light gas (helium or hydrogen)
7 — Rupture disk
8 — High pressure coupling
9 — Projectile
10 — Gun barrel
One particular light-gas gun used by NASA uses a modified 40 mm cannon for power. The cannon uses gunpowder to propel a plastic (usually HDPE) piston down the cannon barrel, which is filled with high-pressure hydrogen gas. At the end of the cannon barrel is a conical section, leading down to the 5 mm barrel that fires the projectile. In this conical section is a stainless steel disk, approximately 2 mm thick, with an "x" pattern scored into the surface in the middle. When the hydrogen develops sufficient pressure to burst the scored section of the disk, the hydrogen flows through the hole and accelerates the projectile to a velocity of 6 km/s (22,000 km/h) in a distance of about a meter.
NASA also operates light-gas guns with launch tube sizes ranging from 0.170 inches (4.3 mm) to 1.5 in (38 mm) at Ames Research Center. These guns have been used in support of various missions beginning with Apollo reentry studies in the 1960s and most recently for high-speed thermal imaging. Velocities ranging from 1 km/s up to 7 km/s can be achieved. The largest of these involves a 6.25-inch (160 mm) diameter piston weighing more than 46 pounds (21 kg) to compress the hydrogen.
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They are a firearm, for a start....
One particular light-gas gun used by NASA uses a modified 40 mm cannon for power.
This thread is about PCPs, which rely on the EXPANSION of air, not it's rapid, Adiabatic compression by an explosion.... As I've said before, pretty much comparing apples to orange juice....
Bob
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Helium molecules are going faster at room temperature-maybe 3x as fast-at ALL temps-they have a BIG speed advantage-
which is why they used the lightest gas possible-H2-which is too dangerous for home use
at 1745fps his pellet is outrunning more than 70% of his propellant molecules
This isn't my idea-NASA- thought the same thing-everyone would come to the same conclusion
if you want max speed from a gas gun-use the lighest gas
otherwise your projectile will outrun most of your propellant molecules-
DESPITE still having PLENTY of energy and MV
you can't hit what you can't catch
I give up-I'll leave you guys alone
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Actually, you can go ahead and use Helium in a PCP, and you still won't achieve the theoretical maximum discussed at the beginning of this thread.... It is based solely on pressure, barrel length, and caliber.... Read through it and you will (or should) understand....
This thread is not about the highest velocity you can achieve by ANY means.... it is about PCPs.... Hope that clears it up.... Nobody is trying to pretend light gas guns don't work, they do, and extremely well....
but they aren't PCPs... ::)
Bob
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rsterne
Thanks for your polite reply.
I get it room temp just air 14.5 cc volume 4500 psi .22 caliber
so weight friction are about it in respect to improvements
your propellant is just about out of gas
but a why not a smoothbore-and a nod to aero shape for the short chronograph distance -
I will leave you folks alone-no offense meant
Thanks
Charlie
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I would point out that the maximum theoretical FPE with a .22 cal at 4500 psi with a 23.3" barrel is 332 FPE..... Once you subtract the mass of the air that needs to be accelerated, and the pressure loss from a finite reservoir you lose a huge percentage of that.... but even at 1745 fps, with a 7.5 gr. pellet, Lloyd is only at 51 FPE.... Using Helium, with no other changes, might double the FPE.... but that still leaves us a HUGE distance from the theoretical maximum....
Bob
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Yikes
Long thread-parameters-set-air 4500 psi- barrel length-chamber size-rifling not rifling
OP calculated theoretical maximum-and is doggedly shooting nibbling away-
Went thru some of it-noticed helium mentioned way back #25 or so(scotchmo maybe)- plastic bullets too
My apologies- too much water under the bridge a thread to drop in on-
I will just eyeball it occasionally to see how the 1745 changes
Thanks for your patience-
Charlie
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Hey Charlie, Yes, these long threads cover a lot of territory, and wander, but usually come back to the original topic. Like herding cats sometimes. And there is always a ton of information buried within the various replies.
You might want to take a look at this other thread (Sonic Choke, Sonic Joke),
http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.180 (http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.180)
which is an offshoot of this thread you are reading now. (Theoretical Max Vel in a PCP)
The real topic in the other Sonic Choke, Sonic Joke, thread is dispelling existing theories/notions of specific velocity limits in PCPs. Or, to put it more bluntly, if someone is going to state as a fact that there is a velocity limit, they need to back it up with real evidence. If they are going to say they think "there might be a velocity limit," even that needs to be backed up with some amount of credible reference material. None of us here are youngsters :P who just got their first $99 springer at Walmart and can be fooled into swallowing random anecdotal statements. This is a smart, thinking group 8) with commons sense and book and hands-on experience who really love the challenge of these guns. And we see the challenges that most other airgunners don't. This is serious fun, among a great bunch of folks. ;D
I'll get down off my soapbox now. See what I meant about herding cats, LOL. ;)
Lloyd
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Lloyd
Ha,ha-not fair
1) we have 3.5 cats and a retread greyhound-they are about equally un-herdable
2)And I literally JUST(2 hr ago) bought a Crosman phantom NP break barrel $92.74 delivered with a $10 rebate-so $83.24 with the
stamp
This sure is an exotic sub forum-someone designing building a springer cannon?
I will follow this thread-curious just how much over 1745 fps you can get-
Thanks
Charlie
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Here's a simple thought for you to consider.... The maximum FPE potential of a PCP is proportional to the total amount of air you cram into the barrel.... Think about it like uncorking a bottle.... The energy is volume times pressure.... which is ultimately the total volume used at 1 atmosphere.... This is consistent with what we discussed above....
Maximum FPE = Force (lbs) x Distance (ft) = Bore Area (in^2) x Pressure (lb/in^2) x Barrel Length (ft) = Barrel Volume (in^3) x Pressure (lb/in^2) / 12 (in/ft)
In terms of the maximum FPE potential, it doesn't matter if you have a .25 cal barrel that is 4 feet long, or a .50 cal barrel that is 1 foot long.... They both have the same potential to produce energy at the same pressure.... The bottom line is.... how much air are you cramming in the barrel?.... More volume, more power.... More pressure (ie more air), more power.... Multiply the two together, and you just end up with the amount of air at one atmosphere you used tp fill the bottle before you uncorked it.... 8)
Bob
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Bob,
true, but:
The maximum projectile FPE approaches the original FPE of the air volume - as the projectile mass approaches infinity. (highest muzzle-energy efficiency)
The maximum projectile FPS approaches the maximum possible for air - as the projectile mass approaches 0. (lowest muzzle-energy efficiency)
Maximum FPS is at odds with maximum FPE.
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Not really.... because in real PCPs we aren't working with 100% efficiency in either case.... Don't forget, that "Maximum FPE" must include accelerating the mass of air in the barrel as well.... The whole point of this thread, and it's consequent discussion about maximum FPE.... was the THEORETICAL MAXIMUM EXCLUDING LOSSES.... and that's also what I am dealing with above.... In practical terms, the FPE that ends up in the bullet is almost always less than 50% of the theoretical maximum when using air.... Lloyd's last 2035 fps shot with a 5.6 gr. projectile in a .278 cal, 46" barrel at 4500 psi, only achieved 51.5 FPE out of the maximum possible, which was 1047 FPE, if you just look at the projectile.... That's only 5%.... The rest of the energy went into accelerating the air out the muzzle, and losses....
In practical terms, it will be easier to get a given FPE out of a .50 cal with a 1 foot barrel than out of a .25 cal with a 4 foot barrel.... but the theoretical maximum is the same in both cases, at equal pressure....
Bob
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Sorry for dropping out of sight for so long. I hope to get back on this project after things settle down around Thanksgiving.
Scott and Bob, your posts bring out some thoughts that have similarities to the conundrum that both conservation of energy and conservation of momentum within a system must be maintained. But because air is compressible, that sort of comparison really isn’t realistic. And add elastic and inelastic modifiers to the momentum constraints makes it even more confusing.
BUT, just speaking of generalities, I have to agree that Scott’s statement that achieving/approaching ACTUAL maximum velocity is at odds with also achieving maximum energy.
Again, just speaking in generalities, and trying to relate the output to the input, consider this:
For energy, given that KE = ½*mv2
If the input energy is kept the same, to achieve 10 times the velocity, the mass must be reduced to one one one hundredth. But we know empirically that if we use one one hundredth of the mass that we will probably get less than 10 times the velocity. For arguments sake let’s say we get 5 times the velocity and the rest of the energy is transferred to the system.
For conservation of momentum, with input being m1 and v1:
For a perfectly elastic momentum collision, Input m1*v1 = Output m2*v2.
For an inelastic momentum collision, m1*v1 = m2*v2 + losses
Making a leap that the inelastic situation has some relevance to the discussion, and using the thoughts from the energy paragraph above:
For the heavy, slow bullet, Momentum Input m1*v1 = Output m2*v2
For the light, fast bullet, Input m1*v1 = Output m2/100 * 5*v2 + large energy losses
Therefore, in this extreme example, the momentum of the light, fast bullet is only 5% of the momentum of the heavy slow bullet, and a substantial portion of the energy does not go into the KE of the bullet.
Now, everything I said above might be garbage, but it seems that at every turn, the laws of physics predict humbling, diminishing increases as the velocities creep higher and higher.
Lloyd
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I think I follow your reasoning, and that is an excellent explanation of why the "real" velocity cannot keep up with the theoretical as the projectile gets lighter.... I was merely trying to point out that in terms of the maximum theoretical FPE, it can be simplified to barrel volume x pressure.... which simplifies even further to the amount of air (mass, or volume at NTP) the barrel would contain at that pressure before firing....
I agree 100% that heavier projectiles will retain more of this theoretical FPE.... if for no other reason, because there is a considerable mass of air moving down the barrel.... However, this has no effect on the basic calculation of the maximum theoretical FPE.... It just means that the lighter the projectile, relative to the mass of the air driving it, the lower will be the share of the KE given to the bullet....
Bob
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Guys, please check my logic if it makes sense. Energy of pellet and air pushing pellet
(m*v^2)/2 = (M*V^2)/2
m - mass of pellet
v - pellet muzzle velocity
M - mass of air per shot
V - average velocity of air in barrel
V = v *sqrt(m/M)
I'm metric guy.
Air density=0.001225gramms/cc.
Air rifle data from the net.
.25 marauder, data from:
http://www.gatewaytoairguns.org/GTA/index.php?topic=59041.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=59041.0)
25grain Pellet(=1,62gramms), pressure 3000psi(=206bar), muzzle velocity 853fps(=260m/s), cylinder volume 215cc, 62 psi/shot(=4.27bar/shot)
Mass of discharged air per shot = (206*215*0.001225)/(206/62)=1.13gramm
Average air velocity in barrel
V = 260*sqrt (1.62/1.13) = 311m/s
.458 air force texan, data from
pyramydair com /blog/2015/02/airforce-texan-big-bore-rifle-part-3/
(GTA wont let me post external url, I guess I do not post enough)
215 grain pellet(=13.9gramms), pressure 3000psi(=206bar), muzzle velocity 853fps(=260m/s),
cylinder volume 490cc, 256psi/shot(=14.8bar/shot)
Mass of discharged air per shot = (206*490*0.001225)/(206/14.8 )=8.88gramm
Average air velocity in barrel
V = 260*sqrt(13.9/8.88) = 325.29m/s
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So we see that average air velocity in barrel of air rifle is about same 311m/s vs 325m/s. sonic speed is 343m/s. Note barrel length is irrelevant.
Practical max pellet speed (including supersonic) can be calculated by changing m - mass of pellet.
I think there are pretty interesting conclusions can be made, but 1st - do you see any misses in logic above.
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Is your basic assumption that the energy pushing the pellet and the energy pushing the air which is pushing that pellet are equal?.... In other words that the energy produced by the expanding air must somehow be equally divided between the two?.... Your math looks fine, from a quick glance, but I question the initial assumption.... assuming I understood it correctly....
Bob
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...
Practical max pellet speed (including supersonic) can be calculated by changing m - mass of pellet.
I think there are pretty interesting conclusions can be made, but 1st - do you see any misses in logic above.
Practical max pellet speed (including supersonic) can be calculated by changing m - mass of pellet.
True, but it is a very complex calculation once you reach peak mass flux.
That happens when breech velocity of the air reaches mach 1. Any further increase for the pellet above that velocity, is the result of the air expanding inside the barrel.
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All above results are for internal ballistic only. I'm not touching external ballistic - flight outside of barrel.
Based on result that velocity of air in barrel is constant ~311 m/s slightly less than 344m/s (sonic) and does not depend on barrel length/bore. Velocity of pellet leaving barrel
v=311*sqrt(M/m)
so once m mass of pellet is less than 1.06 *M mass of air per discharge - pellet goes supersonic out of barrel. (1.106=344/311).
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Euro2, I looked back through your math in your first post, and I see one small glitch in the calculations.... For the MRod, you calculated the mass of the air from....
Mass of discharged air per shot = (206*215*0.001225)/(206/62)=1.13gramm
while for the Texan you used....
Mass of discharged air per shot = (206*490*0.001225)/(206/14.8 )=8.88gramm
For the MRod, the number in bold (the air pressure) is in psi, while for the Texan it is in bar.... Since your answers are consistent, I assume the 62 in the first equation is just a typo, you actually used 4.27....
I still would like to understand your basic premise that the energy must be equally split between the bullet and the air.... Also, how do you account for the change in velocity along the air column caused by the air expanding, not moving as one solid mass?....
For a moment let's consider two objects touching each other, like two bullets in a barrel.... You apply a force on the back of the one which then pushes on the other, and the two accelerate together, travelling at the same velocity.... At the instant they leave the barrel, they both have the same velocity.... However, the only way they will have the same energy is if they have the same mass.... If one is 10 times the mass of the other, it will also have 10 times the energy, ie 10/11ths of the total.... Now replace the rear one with your air mass.... The only way the mass of air and the projectile can have the same energy as they exit the barrel is if they have the same mass, no?.... Is not your premise that the air and the bullet must have the same energy?.... If so, why?....
Bob
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Bob, thanks. I was typing formulas from piece of paper, and may have mistyped intermidiate results.
Equation is kinetic energy preservation in closed system. To be exact you can add energy of recoil But mass of pcp rifle is so much bigger than air&pellet - it has no measurable effect.
If you use PB gun wih stock loads the only thing that you can vary is bullet weight.
People who do reloading have advantages of varying type and mass of powder. People who do reloading realised long time ago that optimal mass of powder is about 2/3 of the bullet.
Mass of powder burns and converts to mass of gas/fumes at pressure P that pushes bullet out.
PCP rifles are similar to reloading - theres usually way to control mass of air via transfer port & valve diameter and/or hammer spring/discharge duration. Speed of air expansion is pretty much constant.
I dont think that theres anything new in my logic. Except maybe experimental fact that speed of air is constant. It is just gives numerical measure of discharge and it can be correlated to barrel length/bore and exit velocity.
Given all of that - plastic lightweight pellet will probably hit maximum velocity of mach 2 out of optimal lenth/bore PCP. You will need to have just enough pellet mass to hold it from destruction. But how far it will fly and how accurste it will be depends on external ballistics.
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I don't think you can apply the conservation of energy in that way, at least that's not the way I understand it.... You say that is in a experimental fact that the speed of expansion of the air is constant.... Could you please supply a source, and a value for that speed?.... Also, you may be interested in the experimental results in this thread.... http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0)
Bob
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I dont think that starting debates on elementary basics of general physics will be at the right place here:)
Thank you very much for constructive input and thoughtful discussion!
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I dont think that starting debates on elementary basics of general physics will be at the right place here:)
Thank you very much for constructive input and thoughtful discussion!
Euro, it is difficult to avoid some of the debates but we are all still remaining to be friends. I got busy on other projects and drifted away from the maximum velocity/ high velocity project, but will be starting back into it after the first of the year. I am working on a new valve that is less "clunky" than the HV ones I have built so far, and will more closely resemble a valve that could be installed into an actual shoulderable air rifle. I have some very unique lead projectiles that I will be using, which are coming from a GTA source. I am very excited about them and am anxious to see what they will do at very HV.
Lloyd
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to be continued..... :)
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Lloyd. That will be interesting even without shoulderable rifle. Maybe use plastic/acrylic instead of lead?
I'm under impression that something flat/fast and very accurate at 200 yards aka .17 hmr is impossible with air rifles.
Energy is there - 200-300lb/ft is pretty normal for big bores, but most of that energy is coming from projectile mass flying at relatively low velocity. Big bore + big transfer port gives pretty big mass of air at pretty low velocity.
I think that putting .17 barrel on texan will not spill 20g .17hmr bullet at mach 2, unless your barrel length is measured in yards:)
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I think that putting .17 barrel on texan will not spill 20g .17hmr bullet at mach 2, unless your barrel length is measured in yards:)
That is a pretty realistic statement.... In addition, as the velocity goes up, the efficiency goes down, because the mass of air being accelerated increases faster than the weight of the projectile.... Pretty soon you are using huge amounts of air for very small gains in velocity.... Add to that the huge increase in drag in the Transonic region between Mach 0.8 and 1.2 and the bullet slows down very quickly are launch, loosing all that extra energy fast, and ending up with additional wind drift to boot.... In PRACTICAL terms, airguns work the best in the mid 900 fps range for just sooooooooooo many reasons....
However, exploring the limits is fun and educational, which is why we do it.... 8)
Bob
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Glad to see this experiment still in progress. I am just following for the most part as I am lost in the math but the theory and discussion of all the possibilities are very informative and riveting to say the least.
Mike
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I have question. Is that true that none of side injected (aka transfer port is 90 deg to barrel) PCPs are not capable of super sonic projectile velocities? I know that inline injection i.e. AirForce/Huben are capable of supersonic.
My thinking is that 90 deg air injection creates way too much turbulence and there's no sonic choke, so air flow never crosses sonic. Inline injection models have natural air choke that is capable to produce super sonic air flow.
Am I way off?
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Well,
Any of my higher power 90* port PCP's when launching Felt cleaning pellets certainly do .... CRACK !!!
As too launching light lead, alloy or plastic pellets that fast ... why care ???
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Well subject is "Theoretical Maximum Velocity in a PCP" so I think anything counts:)
Can you please chronograph cleaning pellet next time you fire it? Is it almost sonic or way supersonic?
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OK ... here ya go :o
Felts weigh .4 grains
RAW TM-1000 in .177 cal w/16" barrel 1333 fps.
War WarP in .177 w/12" barrel 1365 fps
Elevation 1488 feet , humidity @ 82% , Temp 52*f
Distance to front screen @ 1 foot
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Wow calculated power is 4lbfts based on .4g weight. I just speculate that velocity in barrel was almost sonic, muzzle worked as choke and pushed pellet a bit supersonic at exit?
Is that limit for side injection? Can somebody fire plastic from some big bore to see if it will go any faster?
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Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!!
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Euro.... there is a thread here you may find interesting, although it runs many pages in length.... The post that may answer your question is Reply #490 on this page....
http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.480 (http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.480)
Using a .25 cal Discovery which I built and modified, and a 6mm airsoft bb covered in tinfoil (to increase the diameter to fit the bore better), which weighed 2.2 gr.... I achieved 1752 fps.... Anyone with a .25 cal PCP capable of 100 FPE or more should be able to duplicate these results.... Not only is that supersonic (in fact over Mach 1.5), it is faster than the 1650 fps molecular velocity of air at room temperature, which was previously proposed as the maximum possible speed for a PCP on air.... Other shots in that thread were well over 2000 fps, but mine was done with a side-ported barrel, where the airflow turned 180* before reaching the "pellet".... My barrel, BTW, is NOT choked....
Bob
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Think he might be referring to the barrel choking the flow...or the choke acting as a converging nozzle....
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Lloyd was unable to confirm any of the theoretical effects of "sonic choking".... As I understand it, all that does is create a mass flow limit.... True CD nozzles (converging-diverging) are quite complex in design, I somehow doubt we could be achieving such sophistication by accident, in many varied designs.... but I suppose anything is possible.... I'm just pleased to have been a small part of disproving the 1650 fps "speed limit" for PCPs on air at room temperature....
This thread is not based on any particular design, but on the general concept that there is a theoretical maximum velocity (and energy) for any PCP.... The energy is actually very easy to compute, it is barrel volume (in CI) times pressure (in PSI) / 12.... However, you can never reach that FPE in any given projectile, because the mass of the air propelling it is part of the mass that needs to be used to calculate the FPE.... and it would also require infinite reservoir volume, no friction, and several other factors.... In reality, 50% of the theoretical maximum is pretty good going for even the best PCPs.... and I have not seen that achieved with a pellet weight that ends up with a muzzle velocity of 950 fps (ie half the FPE).... Close, but no cigar....
Bob
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I have question. Is that true that none of side injected (aka transfer port is 90 deg to barrel) PCPs are not capable of super sonic projectile velocities? I know that inline injection i.e. AirForce/Huben are capable of supersonic.
My thinking is that 90 deg air injection creates way too much turbulence and there's no sonic choke, so air flow never crosses sonic. Inline injection models have natural air choke that is capable to produce super sonic air flow.
Am I way off?
The straight inlet has less flow resistance. Either way, straight or angled, the flow out of a pressurized vessel becomes "choked" at mach 1.
A flowing column of air will also undergo expansion in the barrel. The maximum expansion rate is also about mach1. Under the right conditions, the inlet will approach mach 1 relative to the stationary air in the tank. The expansion front, would approach mach 1 relative to the flowing air. The velocity of the expansion front relative to the stationary air is then about mach 2.
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Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!!
Let's say .17 rifle has 15ftlbf energy. By your theory 0.4 g plastic pellet will leave barrel at full blown Mach 4 - 4100ft/s.
And because of REALL BAD BC pellet energy will drop to 2ftlbf and velocity to 1300ft/s in just one ft before it reaches chronograph?
I think to confirm that you can move chronograph one ft further? Should see dramatic drop from 1300 ft/s?
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By your theory 0.4 g plastic pellet will leave barrel at full blown Mach 4 - 4100ft/s.
I don't think anyone suggested that.... If you really want to, you can calculate an approximate BC for the felt pellet.... The SD is 0.4/7000/0.177/0.177 = 0.0018.... Using the rate of velocity decay for a cylinder (Drag Profile GC) from ChairGun, if the BC is 0.018 it would decay from 2000 fps to 1327 in 8 yards.... which means for a BC of 0.0018 the distance for the same deceleration would be 0.0018/0.018 x 8 = 0.8 yards x 36 = about 29".... Therefore, for a measured (average velocity between 12-24 " from the muzzle, the muzzle velocity must be less than 2000 fps.... If we consider the deceleration rate to be uniform, and use an average distance of 18" (0.5 yd), and an average velocity of 1365 fps, my best guess for the MV is 1760 fps....
Bob
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I don't think 2000 ft/s has ground under it. 15lbft will send 0.4 g at 4100ft/s. So speed out of barrel shoul be 4100.
To my understanding losing 3 Mach of speed in 1ft will most probably evoporize plastic pellet:)
But as I said experiment is pretty easy - move crony one more ft away. Bob your calculation should tell speed at 2 and 3 ft.
I'll see if I can order same/similar e plastic pellets to fire from Huben.
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In my experience, as the weight of a projectile goes down, so does the FPE it will be launched at, from a given PCP.... If you are curious why, perhaps you need to look at the mass of the air, compared to the mass of the pellet, as one of the reasons for the drop in efficiency.... Another will likely be that as the pellet moves progressively faster down the bore (because it is lighter and easier to accelerate), the valve (which should have near constant dwell) will be closing later in the pellets travel down the barrel, and at some point, after the pellet exits.... Unless I have a misunderstanding of physics, once the pellet is no longer in the barrel, the air can't accelerate it to your 4100 fps....
I have a copy of Lloyd's Internal Ballistics Spreadsheet, and starting with a .177 cal PCP that shoots an 8 gr. pellet at 15 FPE, on 1500 psi of air from a 16" barrel.... changing ONLY the projectile weight to 0.4 gr predicts 1820 fps and 2.9 FPE.... Any projectile lighter than 1.2 gr (MV = 1615 fps) will be leaving the barrel while the valve is still open.... After that, the losses in FPE are huge, because you have less and less air actually driving the pellet before it leaves the muzzle.... and more and more air blowing out the end after Elvis has left the building....
I see you altered you distances to having the screens at 2 ft. and 3 ft, so the average distance would be 2.5 ft.... If the MV was indeed 1760 fps, and my BC is correct, you should measure an average velocity of about 1170 fps....
Bob
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Oh, I probably was not clear.
We have experimental fact - 0.4 g pellet shows 1300ft/s at chronograph one ft after muzzle from 15lbft rifle,
My speculation was that pellet travels in barrel at sub sonic speed. Muzzle acts as choke and right out of muzzle pushes pellet a bit supersonic.
Motörhead on other hand has his theory;
Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!!
Note that he says that dwell is short - so he speculates that valve closes pretty fast and all mass of air pushes .4 g pellet. This is where I derived theoretical 4100fps. His "MAJORLY slowing down" I read as very bad BC....
But I may have misunderstood him - we can let him explain.
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If you are suggesting that the pellet is accelerated AFTER leaving the barrel, I would ask you to explain how that happens.... If you are saying that the choke at the muzzle is pushing the pellet supersonic, how do you explain my shots from an unchoked barrel at over Mach 1.5 ?
I tried to explain that a gun with a short dwell cycle (with normal pellet weight) no longer has a short dwell cycle with an extremely light pellet, the valve will close after the pellet leaves the muzzle.... I guess I failed....
I wish you luck in your speculations....
Bob
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Oh, I probably was not clear.
We have experimental fact - 0.4 g pellet shows 1300ft/s at chronograph one ft after muzzle from 15lbft rifle,
My speculation was that pellet travels in barrel at sub sonic speed. Muzzle acts as choke and right out of muzzle pushes pellet a bit supersonic.
Motörhead on other hand has his theory;
Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!!
Note that he says that dwell is short - so he speculates that valve closes pretty fast and all mass of air pushes .4 g pellet. This is where I derived theoretical 4100fps. His "MAJORLY slowing down" I read as very bad BC....
But I may have misunderstood him - we can let him explain.
I smell a TROLL who wishes to CREATE conflict among us ... of which quite honestly only responded to Euro2's post in thread because I had easy access to take a few shots over the chrony. Honestly I could care less about the theory & data of perceived or real status quo thinking.
Really could care less being said testing and collected data simply DOES NOT apply to shooting of an air gun with normal pellets in any practical sense.
Indeed I've got my own thoughts on this subject and getting into it as with most outside the box thinking is best left to those persons and places where such application and testing can prove or disprove fact from fiction.
The under lying FACT the speed limitations thought as the speed limit has been dis-proven ... so are those contributing reasons for the original assumption being now questioned beyond the accepted physics involved.
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I smell a TROLL who wishes to CREATE conflict among us ... ... DOES NOT apply to shooting of an air gun with normal pellets in any practical sense.
Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!!
Well if that's all that you have to say to defend your statement quoted above, I'm fine with that. I asked question - none of you guys hanging on forums for years posting same stuff every single day had answer. Cause answer is not written on google and hurts your pride as every day guru here:)
In case if you cool down, please post your best observed "Theoretical Maximum Velocity in a PCP" here and support it with repeatable experiment - it is good subject and wrong place to call people trolls.
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Please excuse my "troll" smelling ... that is just shy of calling someone out.
The internet forums are all subjected to a non stop barrage of those seeking definitive black/white resolve of varied subjects that many times like politics what works for them, does not for you & thus conflict of ones perception to which viewpoint is correct comes into heated debate.
I will say this and then I'm done ...
A pulse of high pressure has a front that bears against the ambient pressure. In a barrel this Pressure as well Amplitude is strongest right at the valve where the HP is subjected to the ambient LP. A Felt pellet of such low mass gets swept up and moved along with the Front of the pressure pulse. As this pulse expands into greater volume of the barrel it's amplitude is diminishing. The felt offers little to no resistance and does not create drag to cause compression pressure behind itself but moves with the pulse energy of the expanding air.
In front of the felt pellet is a column of ambient air that upon the felt getting pushed out barrel is compressed as it gets forced out ahead of the felt ( Pellets too ) This compression of the air column ABSORBS energy and further the felt moves towards muzzle greater is the resistance felt pellet feels. My take is that the Felt pellet having so little weight & mass it SNAPS up to speed near instantly slowing down as the amplitude of the pulse energy driving it falls off as volume is gained while compression losses of the air it is displacing ahead of it is increasing slowing it down. Once felt pellet exits muzzle the column of air it compressed on it's way to muzzle blows clear, but static ambient pressure air is still very effective in slowing it down at very high rate ... Yea the BC is Terrible !!!
JMO ...
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Now my head hurts lol!! whats bad is I understood it. David
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Here is your question....
I have question. Is that true that none of side injected (aka transfer port is 90 deg to barrel) PCPs are not capable of super sonic projectile velocities? I know that inline injection i.e. AirForce/Huben are capable of supersonic.
My thinking is that 90 deg air injection creates way too much turbulence and there's no sonic choke, so air flow never crosses sonic. Inline injection models have natural air choke that is capable to produce super sonic air flow.
Am I way off?
Scott and I both answered it, but apparently you didn't like our answers, which both proved that you can drive something faster than Mach 1 (in fact over Mach 1.5) with a conventional side-ported PCP where the air turns 180*.... Then you made the (very antagonistic) statement....
none of you guys hanging on forums for years posting same stuff every single day had answer
All I see is someone who has their own ideas (and more power to you for that) that is unwilling to accept experimental evidence, or reasoning, that does not agree with you.... I would strongly suggest that when you make a statement, or have a theory, you be prepared to prove it.... Theories are only valid until they are disproved by empirical evidence (just like the 1650 fps limit was).... Then it's time for new theory.... IMO....
In case you don't get it yet.... empirical results will NEVER match theory.... all they can do is prove that the theory is wrong if the number predicted is too low....
Bob
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To take us back to where this thread started.... here is Lloyd's original post, with the numbers changed to reflect the test shot being recently discussed.... ie .177 cal with a 0.4 gr. "pellet" in a 16" barrel, using 1500 psi....
Example of Calculating Maximum THEORETICAL Velocity-
Let’s assume .177 cal, 0.4 gn, 16” (1.33 ft) barrel, and 1500 psi.
We want to solve for “v” in the equation we rearranged above:
v = (F/m) x {sqrt ([2 x d x m]/F)}
Here is one way to solve it:
First, find the force, “F”, that is accelerating the bullet. F is the product of the bullet’s cross sectional area (.0246 sq in for a .177 cal bullet) times the pressure, so the force on the bullet = .0246 sqin x 1500lbs/sqin = 36.9 pounds of force trying to push, i.e., accelerate, the bullet through the barrel.
F = 36.9 pounds
Next, calculate the mass, “m” of the bullet. Mass is the weight of the bullet in pounds, divided by the gravitational constant “g”. (We need the mass of the bullet, not the weight.)
Mass= (0.4 gns/7000 gns per pound)/32.174 = .00000177 slugs ( the slug is the imperial unit of mass, a bit confusing).
mass = .00000177 slugs
Now, plug those calculated values for F and m into the velocity equation:
v = (F/m) x {sqrt ([2 x d x m]/F)}
v= (36.9/.00000177) x {sqrt ([ 2 x 1.333 x .00000177]/36.9}
v = (20,847,457) x {sqrt (.000000127} [note that 20,847,457 is the acceleration in ft/sec2, or 647,960 g’s]
v = 20,847,457 x .000356
v = 7,422 feet/sec MAXIMUM THEORETICAL MUZZLE VELOCITY for this example.
And to take it one step farther, the MAXIMUM THEORETICAL MUZZLE ENERGY for this example is:
FPE = (bullet grains x velocity x velocity ) / 450,240 = 49 ftlbs
By way of double checking the results, we can use the formula for the Maximum FPE that can be produced by 1500 psi in a .177 cal barrel that is 16" long....
FPE = Force (lbs) x Distance (ft.)
= area (sqin) x pressure (psi) x barrel length (in) / 12
= (0.0246 x 1500) x (16 / 12) = 36.9 x 1.333 = 49 FPE
As you can see, achieving a "mere" 1365 fps is nowhere NEAR what the Theoretical Maximum is.... which was the whole point of this thread.... Somehow it got turned into a discussion of what we have "achieved", or that might be "achieveable" in the real world.... rather than how far we are from extracting the theoretical maximums.... which while interesting, is far from the original intent of the thread.... IMO....
Bob
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...please post your best observed "Theoretical Maximum Velocity in a PCP" here and support it with repeatable experiment - it is good subject and wrong place to call people trolls.
"please post your best observed "Theoretical Maximum Velocity in a PCP" here and support it with repeatable experiment"
The maximum observed velocity is about 2160fps per Lloyd's experiments.
"please post your best observed "Theoretical Maximum Velocity in a PCP" here and support it with repeatable experiment"
My best theoretical maximum is about 2500-3300fps depending on the driving pressure.
A repeatable experiment will never exceed the theoretical maximum. It won't even reach it. If it does, the theory is wrong.
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Slight aside
What is the current fastest shot here
The last time i "LOOKED" it was 2300fps or so I think
and the shooter was planning a 2nd or 3nd generation "gun" of bigger diameter-about .27" I think-a smoothbore I think
and maybe it was going to have a different pellet release/trigger-no longer going to use claws to grab the pellet-so the pellet could be lighter
so current max for a PCP?
Thanks
Charlie
ps-I think the builder was a little disappointed with the barrel stock that arrived-it was well off claimed inside diameter
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I believe 2162 is the fastest Lloyd recorded.... The thread is right here in the Geek (R&D) Gate.... http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0)
Bob
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Bob
Thanks-2160-
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Well subject is "Theoretical Maximum Velocity in a PCP" so I think anything counts:)
Can you please chronograph cleaning pellet next time you fire it? Is it almost sonic or way supersonic?
This isn't a cleaning pellet but speed is above mach1 from conventional 180 deg turn valve.
(http://i11.aijaa.com/m/00234/14339087.jpg) (http://aijaa.com/Nnf9Uf)
Marko
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Well subject is "Theoretical Maximum Velocity in a PCP" so I think anything counts:)
Can you please chronograph cleaning pellet next time you fire it? Is it almost sonic or way supersonic?
This isn't a cleaning pellet but speed is above mach1 from conventional 180 deg turn valve.
(http://i11.aijaa.com/m/00234/14339087.jpg) (http://aijaa.com/Nnf9Uf)
Marko
366 m/s (1200fps) is common with alloy pellets.
http://www.gamousa.com/product.aspx?productID=235 (http://www.gamousa.com/product.aspx?productID=235)
Some airguns can even do it with lead pellets.
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Well its a 67 grain lead bullet, I think it counts as a lead pellet.
Marko
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Well its a 67 grain lead bullet, I think it counts as a lead pellet.
Marko
The heavy projectile makes for impressive FPE, but nowhere near the theoretical maximum velocity in a PCP.
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Well its a 67 grain lead bullet, I think it counts as a lead pellet.
Marko
LOL
Not a cleaning pellet either. 50 gn JSB shot from a 308 Slayer . Full U-turn porting...
(http://i1147.photobucket.com/albums/o553/QVTOM/Jsb%2030_zps0fxvqpcu.jpg)
Tom
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WOOF !!
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9mm sabot .224 50gr
(http://i1.aijaa.com/m/00263/14339931.jpg) (http://aijaa.com/2zsAkY)
Just the sabot
(http://i5.aijaa.com/m/00610/14339932.jpg) (http://aijaa.com/o5VaTn)
Marko
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Marko, that is the first time I have ever seen a recorded velocity of OVER MACH 2.... Is this something you have been able to repeat?.... Please post this in the following thread....
http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0)
What is the weight of the sabot used in the above shot at ~ 850 m/s ?.... Also, the pressure and barrel length, please?.... Air or Helium?.... We need to record this information and examine it closely....
Bob
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9mm sabot .224 50gr
(http://i1.aijaa.com/m/00263/14339931.jpg) (http://aijaa.com/2zsAkY)
Just the sabot
(http://i5.aijaa.com/m/00610/14339932.jpg) (http://aijaa.com/o5VaTn)
Marko
WOW! That's amazing.
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...
Just the sabot
(http://i5.aijaa.com/m/00610/14339932.jpg) (http://aijaa.com/o5VaTn)
Marko
2787fps! Almost 2x the SOS.
Waiting for details -
PSI?
conventional valve or dump chamber?
reservoir size?
sabot mass?
air tank temperature?
That's about the maximum possible air velocity predicted by Fanno flow (air flow+expansion).
(http://www.scotthull.us/photos/Misc/fanno-vmax.jpg)
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Actually, the MV is well over Mach 2.... At 70*F, it's about Mach 2.5....
Bob
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Helium inline valve.
I put the info in the other thread, it's repeatable, have shot usually three to five before posting any numbers.
Marko
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Helium inline valve.
I put the info in the other thread, it's repeatable, have shot usually three to five before posting any numbers.
Marko
Helium? ???
Cheater ;)
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Actually, the MV is well over Mach 2.... At 70*F, it's about Mach 2.5....
Bob
Maybe mach 2.5 in relation to the ambient air. But not for 3000+psi driving air. Closer to mach 2.
Besides - it was HELIUM!
SOS is over 3000fps for helium and probably over 4000fps for high pressure helium.
I thought we were talking about maximum theoretical velocity in a PCP? With high pressure AIR. At ROOM TEMPERATURE.
We need to stay withing constraints if we want to test theories.
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Yeah cheating or not, topic says teorethical max on pcp... But anyhow that's what I got and its two years old test. That's it for now.
Marko
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LOL, Helium. I can cancel my appointment with my mental health professional now!
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Actually, the MV is well over Mach 2.... At 70*F, it's about Mach 2.5....
Bob
Maybe mach 2.5 in relation to the ambient air. But not for 3000+psi driving air. Closer to mach 2.
Besides - it was HELIUM!
SOS is over 3000fps for helium and probably over 4000fps for high pressure helium.
I thought we were talking about maximum theoretical velocity in a PCP? With high pressure AIR. At ROOM TEMPERATURE.
We need to stay withing constraints if we want to test theories.
what does it matter what the sos of the gas is? the pellet was moving mach 2 plus.
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LOL, Helium. I can cancel my appointment with my mental health professional now!
That was funny as hel Tom, would be impressive if it was air considering the stub of a barrel I have, only 540mm
Marko
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Actually, THIS thread deals with maximum THEORETICAL velocity, which depends only on pressure, bore area, and barrel length.... The gas won't matter, because the original formula doesn't take into account the mass of the gas, or ANY losses, assumes an infinite reservoir, etc.etc.etc.... The maximum theoretical FPE for Marko's gun (9 mm, 250 bar, 540 mm barrel) would be....
(0.354^2 X PI / 4 ) x (250 x 14.5) x (540 / 25.4 / 12) = 0.0983 sq.in x 3625 psi x 1.77 ft. = 356 lbs. x 1.77 ft. = 631 FPE.... If the sabot weighs 1 g. (15.4 gr.) that works out to a theoretical maximum velocity of 4295 fps.... 54% faster than he achieved.... so no laws of physics have been broken....
Using Lloyds spreadsheet, and including the mass of the Helium in the bore, the efficiency is only 69%, so no magic there.... Changing to air, with no other changes, it predicts 1668 fps....
Bob
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In my experimental experience, it is possible to achieve about 70% of maximun theoretical velocity with Helium. With lead bullets too. I think the reality limit is close to that. Still maybe something more and at least it is something to try for.
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Actually, THIS thread deals with maximum THEORETICAL velocity, which depends only on pressure, bore area, and barrel length.... The gas won't matter, because the original formula doesn't take into account the mass of the gas, or ANY losses, assumes an infinite reservoir, etc.etc.etc.... The maximum theoretical FPE for Marko's gun (9 mm, 250 bar, 540 mm barrel) would be....
(0.354^2 X PI / 4 ) x (250 x 14.5) x (540 / 25.4 / 12) = 0.0983 sq.in x 3625 psi x 1.77 ft. = 356 lbs. x 1.77 ft. = 631 FPE.... If the sabot weighs 1 g. (15.4 gr.) that works out to a theoretical maximum velocity of 4295 fps.... 54% faster than he achieved.... so no laws of physics have been broken....
Using Lloyds spreadsheet, and including the mass of the Helium in the bore, the efficiency is only 69%, so no magic there.... Changing to air, with no other changes, it predicts 1668 fps....
Bob
All you geeks keep pushing the limits is what matters because all this Ivory Tower stuff eventually filters down to the end users that being us lower order AG fanatics ;D ;D
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Actually, the MV is well over Mach 2.... At 70*F, it's about Mach 2.5....
Bob
Maybe mach 2.5 in relation to the ambient air. But not for 3000+psi driving air. Closer to mach 2.
Besides - it was HELIUM!
SOS is over 3000fps for helium and probably over 4000fps for high pressure helium.
I thought we were talking about maximum theoretical velocity in a PCP? With high pressure AIR. At ROOM TEMPERATURE.
We need to stay withing constraints if we want to test theories.
what does it matter what the sos of the gas is? the pellet was moving mach 2 plus.
There are properties of a gas (primarily density and bulk modulus) that will determine the speed of sound. Those same properties also limit the maximum velocity that a gas can achieve when being pushed by it's own pressure.
We don't need the SOS to determine the maximum velocity, but knowing the SOS means that a portion of the math is already done. The same math that is needed to determine the maximum gas velocity.
Mach is a ratio. The mach 2 in this case is meaningless as that is based on the SOS in the ambient air, not the propelling gas. The SOS of the ambient air has almost no affect on the maximum theoretical velocity of the projectile.
The mach ratio that is meaningful when measuring for maximum theoretical velocity is, (final velocity of the gas+projectile)/(initial SOS of the propelling gas).
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okay , im following.. the gas itself never broke its own mach, rather the projectile pushed by the gas never broke the gas mach speed
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You know, there is no such limit for gas flow. There are wind tunnels exceeding many Mach.
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;D I know that at times I know just enough to be dangerous but this time I will ask my foolish question . The pressure equates to thrust pushing the projectile so exceeding MACH is not surprising since we have been exceeding the speed of sound for almost 80 years with various projectiles with expanding gasses just not compressed air out of our air guns or am I all wet??
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You know, there is no such limit for gas flow. There are wind tunnels exceeding many Mach.
True. But, the Speed Of Sound at that point in the tunnel may be low. What velocity in fps does Mach 5 equate to? Mach is a ratio, not a velocity.
High pressure gas becomes choked when the outlet velocity equals the speed of sound of the propelling gas. Expansion in the barrel adds additional velocity. Some of that air (at
the front) is at the highest velocity.
I don't care about the SOS of the ambient air. The velocity limit has nothing to do with that. I'm comparing the actual velocity of the projectile/gas to the SOS of the driving gas.
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okay , im following.. the gas itself never broke its own mach, rather the projectile pushed by the gas never broke the gas mach speed
Its own mach?
It can break Mach 1. And approach Mach 2, with respect to the gas in the tank. With respect to the external SOS (ambient), there is no limit on Mach ratio, so that ratio means nothing since there is no physical tie between them. The velocity limit still holds.
Foget about the SOS of the air outside. Best to look at the muzzle velocity of the gas/air VS the maximum velocity of sound of the gas in the tank. That is the ratio that matters.
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I think you are losing everybody, Scott, including me.... When you start dealing with Fanno Flow, and Thermodynamics, my eyes glaze over....
There is a maximum FPE that any PCP can reach in theory, and that is Force times Distance.... The force (in lbs.) is bore area times pressure, and the distance is the barrel length (in ft.).... Multiply them together, and you get the maximum FPE that can theoretically be achieved.... However, that FPE has to be split between the projectile and the gas propelling it.... With air, you are lucky to hit 50% of that, and with Helium you can hit about 70%.... Until you start exceeding those numbers, we aren't dealing with magic, or witchcraft, and we don't really need to go beyond good ol' Newtonian Physics to find an explanation of what is happening.... IMO....
Bob
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Bob,
FPE?
The topic is the "Theoretical Maximum Velocity in a PCP". You are talking about the theoretical FPE and velocity in a PARTICULAR PCP. Your estimates require caliber, barrel length, projectile mass, etc. For the topic estimate, all those variables drop out of the equation. We are left with maximum flow rate + maximum expansion.
Maximum flow velocity is the SOS of the propelling gas. Maximum theoretical expansion velocity end ups being about that same velocity.
Max velocity = max flow velocity+ max expansion velocity.
That is the velocity that a PCP will never achieve.
Newtonian Physics gives a fairly accurate estimate when modeling, if you account for the flow limit of the inlet. You won't need a fudge factor to account for what appears to be low efficiency.
But for "Theoretical Maximum Velocity in a PCP", I say:
Vmax = SOS x sqrt((2/(k-1))+1)
And I'm sticking to it (at least until proven wrong).
For discussion, we can approximate it and say "about 2xSOS".
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And your point being?
I don't see you making any point, 2 times SOS? In what?
In side the barrel?
Gas speed at the valve throat?
Marko
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OK, Lloyd started this topic based on Newtonian Physics, and gave, in the first post, the formula to determine the maximum possible VELOCITY, for any SPECIFIC PCP, based on nothing more than bore area, pressure, barrel length, and projectile weight.... I added a simplified version to calculate FPE, but if you know one, and the projectile mass, you can calculate the other.... It was the thread on Lloyd's high velocity experiments where we were discussing all the ideas about why the 1650 fps "limit" wasn't a limit at all, etc.etc.etc....
Lloyd's formula, if the mass is low enough, will predict velocities well over 4000 fps, for a SPECIFIC PCP, and while you and I, for different reasons, don't think that is possible, it wasn't what the topic was really about.... I would have preferred that we kept the two topics separate, but that's just my opinion.... As I said, I know nothing about Thermodynamics, so I can't participate in that discussion.... I guess I'll just have to take your word for it, unless somebody manages to go faster (which I doubt)....
I will assume, however, that your "SOS" is the speed of sound at the pressure and temperature of the driving gas present inside the barrel?.... That being the case, using your approximation, then doubling the values in the chart below should be the "limit"....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Speed%20of%20Sound%2020C%20with%20Helium_zps3zw5mksn.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Speed%20of%20Sound%2020C%20with%20Helium_zps3zw5mksn.jpg.html)
Using 4500 psi at 20*C, that gives about 3100 fps with Nitrogen, 3200 fps with Air, and 7450 fps with Helium.... providing you can get your projectile weight down to zero, of course.... Did I get that correct?....
Now, how do I apply that to determine what a PARTICULAR PCP, running a given gas, at a given pressure, with a given barrel caliber and length, can theoretically achieve?.... I ask because that was the question Lloyd was trying to answer in this thread.... as I understood it....
Bob
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Alternative for Newtonian Physics is Quantum Physics. Please keep Newtonian, it is well enough for this.
It's all about energy, not speed. Speed is not limited really but of course going supersonic takes a lot of energy, which we just don't have that much in airgun. You often hear SOS is a limiting factor in AG but it is not, usable energy is.
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And your point being?
I don't see you making any point, 2 times SOS? In what?
In side the barrel?
Gas speed at the valve throat?
Marko
SOS of gas inside the dump chamber. And that dump chamber must be infinite volume, or at least very large in order to maintain pressure.
Gas speed is the maximum velocity at the expansion front. That is at the base of the projectile, if there is to be one.
This equation:
Vmax = SOS x sqrt((2/(k-1))+1)
is a reduction of the following equation (circled in red), with V* (throat velocity) approaching M, the result being V. Throat velocity cannot exceed M.
(http://www.scotthull.us/photos/Misc/fanno-00.jpg)
Fanno flow is the flow (and expansion) of a gas in a constant area duct, with friction. That's basically what we have with an airgun barrel. The same velocity limits will apply.
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OK, Lloyd started this topic based on Newtonian Physics, and gave, in the first post, the formula to determine the maximum possible VELOCITY, for any SPECIFIC PCP, based on nothing more than bore area, pressure, barrel length, and projectile weight.... I added a simplified version to calculate FPE, but if you know one, and the projectile mass, you can calculate the other.... It was the thread on Lloyd's high velocity experiments where we were discussing all the ideas about why the 1650 fps "limit" wasn't a limit at all, etc.etc.etc....
Lloyd's formula, if the mass is low enough, will predict velocities well over 4000 fps, for a SPECIFIC PCP, and while you and I, for different reasons, don't think that is possible, it wasn't what the topic was really about.... I would have preferred that we kept the two topics separate, but that's just my opinion.... As I said, I know nothing about Thermodynamics, so I can't participate in that discussion.... I guess I'll just have to take your word for it, unless somebody manages to go faster (which I doubt)....
I will assume, however, that your "SOS" is the speed of sound at the pressure and temperature of the driving gas present inside the barrel?.... That being the case, using your approximation, then doubling the values in the chart below should be the "limit"....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Speed%20of%20Sound%2020C%20with%20Helium_zps3zw5mksn.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Speed%20of%20Sound%2020C%20with%20Helium_zps3zw5mksn.jpg.html)
Using 4500 psi at 20*C, that gives about 3100 fps with Nitrogen, 3200 fps with Air, and 7450 fps with Helium.... providing you can get your projectile weight down to zero, of course.... Did I get that correct?....
Now, how do I apply that to determine what a PARTICULAR PCP, running a given gas, at a given pressure, with a given barrel caliber and length, can theoretically achieve?.... I ask because that was the question Lloyd was trying to answer in this thread.... as I understood it....
Bob
"I will assume, however, that your "SOS" is the speed of sound at the pressure and temperature of the driving gas present inside the barrel?"
Answer: No, not the barrel, the dump chamber.
"Using 4500 psi at 20*C, that gives about 3100 fps with Nitrogen, 3200 fps with Air, and 7450 fps with Helium.... providing you can get your projectile weight down to zero, of course.... Did I get that correct?...."
Answer: Yes. The equations yields 2970fps. "about 2xSOS" (+/-)
"Now, how do I apply that to determine what a PARTICULAR PCP, running a given gas, at a given pressure, with a given barrel caliber and length, can theoretically achieve?."
Answer: In your spreadsheet, choke the flow at the throat when it reaches Mach 1. And get rid of the efficiency fudge factor.
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"There is a maximum FPE that any PCP can reach in theory, and that is Force times Distance...."
Bob,
That is an incorrect assumption.
That is true only until flow becomes choked. With the choke occurring at Mach 1,
< Mach 1:
energy gain = Force x Distance
> Mach 1 (choked):
energy gain = Power x Time
There is a limit on the power that a "throat" can produce.
Once that power limit is reached, the Force downstream from the point where projectile reaches Mach 1 (choke point), will fall off. Energy gain in the system is then proportional to time, not distance.
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"There is a maximum FPE that any PCP can reach in theory, and that is Force times Distance...."
Bob,
That is an incorrect assumption.
That is true only until flow becomes choked. With the choke occurring at Mach 1,
< Mach 1:
energy gain = Force x Distance
> Mach 1 (choked):
energy gain = Power x Time
There is a limit on the power that a "throat" can produce.
Once that power limit is reached, the Force downstream from the point where projectile reaches Mach 1 (choke point), will fall off. Energy gain in the system is then proportional to time, not distance.
COME'on Bob, everyone knows this ! (-'
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Scott, the THEROETICAL MAXIMUM is as I stated.... you can't get more FPE out than you put in.... HOWEVER, various factors, such as a smaller than infinite reservoir, the fact that the gas actually has mass, friction between the bullet and/or gas and the barrel, and a host of others can REDUCE that.... Your equations, which while elegant theory are unproven (in this context), are just part of that group of things that mean we can never get to the maximums Lloyd predicted in his original post in this thread.... and he freely admits that, and so do I.... If they are correct (and I'm not smart enough to understand them), then would not the velocity (eg. 2970 fps on 4500 psi air@ 20*C) only be achievable with a bullet of zero mass?.... In that case the FPE achieved by the projectile would also be.... zero.... all the energy would have to go into accelerating the gas.... As to your answer to my question....
"Now, how do I apply that to determine what a PARTICULAR PCP, running a given gas, at a given pressure, with a given barrel caliber and length, can theoretically achieve?."
Answer: In your spreadsheet, choke the flow at the throat when it reaches Mach 1. And get rid of the efficiency fudge factor.
I haven't a clue how to do that.... Perhaps you can show us?.... In the meantime, I am getting perfectly satisfactory results by using a "fudge factor" of 50% with air and 70% with Helium, of the theoretical maximum predicted by FPE = barrel volume (in^3) x pressure (psi) / 12 (in/ft).... Exceeding that is difficult, and doing it with a bullet of half the FPE (in gr.) is something I haven't yet seen.... Is it a "limit", no (the limit is the FPE predicted by the equation, with no fudge factor).... but it's a darn good indication of a "lofty goal" that if you accomplish it, you can pat yourself on the back....
Please don't misunderstand me, I'm not saying your method is incorrect, or even flawed.... I'm just saying I don't understand it, and I therefore can't use it....
Bob
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Scott, the THEROETICAL MAXIMUM is as I stated.... you can't get more FPE out than you put in.... HOWEVER, various factors, such as a smaller than infinite reservoir, the fact that the gas actually has mass, friction between the bullet and/or gas and the barrel, and a host of others can REDUCE that.... Your equations, which while elegant theory are unproven (in this context), are just part of that group of things that mean we can never get to the maximums Lloyd predicted in his original post in this thread.... and he freely admits that, and so do I.... If they are correct (and I'm not smart enough to understand them), then would not the velocity (eg. 2970 fps on 4500 psi air@ 20*C) only be achievable with a bullet of zero mass?.... In that case the FPE achieved by the projectile would also be.... zero.... all the energy would have to go into accelerating the gas.... As to your answer to my question....
"Now, how do I apply that to determine what a PARTICULAR PCP, running a given gas, at a given pressure, with a given barrel caliber and length, can theoretically achieve?."
Answer: In your spreadsheet, choke the flow at the throat when it reaches Mach 1. And get rid of the efficiency fudge factor.
I haven't a clue how to do that.... Perhaps you can show us?.... In the meantime, I am getting perfectly satisfactory results by using a "fudge factor" of 50% with air and 70% with Helium, of the theoretical maximum predicted by FPE = barrel volume (in^3) x pressure (psi) / 12 (in/ft).... Exceeding that is difficult, and doing it with a bullet of half the FPE (in gr.) is something I haven't yet seen.... Is it a "limit", no (the limit is the FPE predicted by the equation, with no fudge factor).... but it's a darn good indication of a "lofty goal" that if you accomplish it, you can pat yourself on the back....
Please don't misunderstand me, I'm not saying your method is incorrect, or even flawed.... I'm just saying I don't understand it, and I therefore can't use it....
Bob
Showing is a tall order. We both did spreadsheets that can model Lloyd's tests fairly closely. Yours needs a substantial fudge factor to get close. Mine does not.
I can't tell you exactly what to do as our spreadsheets are different. I use a distance based increment. I think you and Lloyd are using a time based increment. Each approach has it's advantages.
Here is a screen shot of a late version of my spreadsheet modeling one of Lloyd's test shots.
(http://www.scotthull.us/photos/Misc/dump-gun-calc-00.jpg)
Rows 1 thru 4 are user inputs and data needed to run. I should probably move that to another sheet. The main spreadsheet uses row 6 as the column labels. I use a "True" flag to mark if/when the projectile transitions from subsonic to supersonic. See where I drew a green oval around cell N17 to mark that point? Column G is the speed of sound in the driving gas. Column R is the projectile velocity. When column R exceed column G, we have transitioned to the supersonic regime. At that point, the mach-1 cylinder/slug of gas starts to expand. It is not obvious in this model because of the relatively small 55cc dump chamber. In the next screen shot, I increased the dump chamber to 10000cc in order to keep pressure more constant, so you can see what is happening.
(http://www.scotthull.us/photos/Misc/dump-gun-calc-01.jpg)
In that second picture, each cm of barrel in the subsonic regime contains approximately the same mass of air (circled in red). The air flowing in can no longer keep up with the projectile. Subsequent segments of barrel in the supersonic regime contain less and less dense air.
Since you are using a time based increment in your spreadsheet, the air mass per increment will increase until you transition to supersonic. At which point, the air mass, entering the barrel, will be constant for each time increment.
If the fudge factor works for you, use it. But the nice thing about my model is this:
I decrease the pellet mass to 0.1gr
I increase the dump chamber to 100,000cc
remove the fluid friction factor
With a 3000 ft barrel, velocity is over 2900fps and rising very,very slowly with each increase in length.
If I extended out the barrel for miles, I would likely approach the 2972 velocity predicted for 4500psi air.
Vmax = SOS x sqrt((2/(k-1))+1)
That is the absolute limit that you will never reach.
Edit: If you are trying to figure out the rest of the spreadsheet from the pictures, don't bother. Some of the columns in the pictures are from older what/ifs and no longer apply to the supersonic regime. Some of the additional temp K columns are monitors that I used earlier to see if things would adhere to the RMS maximum velocity theory.
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Actually, the only spreadsheet that models Lloyd's tests quite well is Lloyd's, not mine.... and yes, it requires a significant fudge factor.... I won't even pretend to understand your spreadsheet, because I don't.... That doesn't mean it isn't 100% correct, however....
My spreadsheet is far simpler, and is intended to only do what was started in this thread.... predict with some degree of repeatability what can be achieved by real world PCPs.... starting from very few, simple variables.... It deals with FPE, not velocity, and the further the projectile varies from the norm, the poorer the results.... That is where Lloyd's is far superior, because it takes into account the mass of the propelling gas, which is a larger and larger percentage of the total FPE as the projectile gets lighter.... Think of mine as a boiled down, practical, meat and potatoes kind of spreadsheet.... not so good with wine or dessert.... ;)
I don't think I can really offer any more at this time....
Bob
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Wow! Reading this is giving me brain pain!
I don't have a clue! Wish I did but I don't!
Jim - jhm757
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Wow! Reading this is giving me brain pain!
I don't have a clue! Wish I did but I don't!
Jim - jhm757
I enjoy the information and occasionally after reading several times it begins to make some sense but the physics has always made my brain hurt and my eyes cross ;D ;D
I am also married to an RN so I am frequently in way over my head when I sit and listen to her conversations with other nurses and doctors so I am getting used to having a puzzled expression on my face and a dull ache behind my eyes :o ::) ;D ;D
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"There is a maximum FPE that any PCP can reach in theory, and that is Force times Distance.... The force (in lbs.) is bore area times pressure, and the distance is the barrel length (in ft.).... Multiply them together, and you get the maximum FPE that can theoretically be achieved"
Assuming we ignore air mass, that actually works perfectly. But only until flow becomes choked.
Example:
imaginary gas = 2000 psi mass-less gas with a SOS of 1000fps
caliber: .357
projectile mass: 45gr
barrel length: 24"
What is the FPE? velocity?
force = 2000psi x pi x (.357/2)^2 = 200 lb.
FPE = 200 lb. x 24"/12in/ft = 400 ft-lb
In the first foot, the projectile reached 200fpe. In the second foot, it gained another 200fpe.
velocity = sqrt(400/(45gr/450436)) = 2000fps
That would work perfectly, except that the flow becomes choked at SOS of 1000fps.
After 1000fps, the FPE gain is no longer 200 lb. x distance.
The FPE gain after 1000fps is power x time.
power(choked) = ft-lb/s = 200 lb. x 1000fps = 200,000 ft-lb/s
The problem transitions from constant force to constant power: given a constant power, how much time does the projectile take to cover the last 12" of barrel length?
In the first foot, the projectile reached 200fpe. The projectile needs another .001 second in order to gain 200 more ft-lb. At super sonic velocity, it will take less than a .001 second to cover the second foot of barrel. So FPE will be less than 400 ft-lb.
Some calculus or numerical integration is needed to solve that. Numerical integration allows us to incrementally add in the air mass and have a more realistic model.
The whole gist of what I've been trying to get across (here and over on the yellow forum), is that we can look at it as two distinct segments. The subsonic regime (constant force), and the supersonic regime (constant power). And then add them together to get the final solution.
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NT - see next post....
Bob
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Since you have assumed no losses, we will stay with that assumption....
I see what you are getting at.... but with a 45 gr. projectile, 200 FPE is not 1000 fps, it is 1415 fps.... Is the flow choked when the projectile reaches 1000 fps, or is that the velocity of the gas at the throat (or are they the same until the flow chokes)?.... If it is the velocity of the projectile, then at 1000 fps, it only has 100 FPE of energy when the flow chokes, not 200 FPE.... It should achieve that in 6" of barrel travel, not 12", right?.... So the flow chokes when the projectile has travelled 6"....
If we assume your power calculation is correct, 200 lb. x 1000 ft/s = 200,000 ft.lb/s .... then we can turn it around and calculate the FPE gain in a given amount of time, say 1 mSec....
FPE gain in 0.001 sec = 200,000 ft.lb/sec x 0.001 sec = 200 FPE.... but it started with 100 FPE when the flow choked (at 6"), so....
It would then have 300 FPE of energy (ie travelling 1733 fps) once it has travelled for another 1 mSec.... We know it is starting at 1000 fps at 6".... We know that 1 mSec later, it is travelling 1733 fps.... We know that the increase in FPE vs. time (power) is linear, so we know the average energy is 200 FPE, so the average velocity is 1415 fps, so in 0.001 sec. it will have travelled 1415 x 0.001 = 1.415 ft x 12 = 17".... The flow choked at the 6" point, so it has achieved 300 FPE by the time it has travelled 17 + 6 = 23".... It will gain a small amount more in the remaining 1" of barrel, starting from its 1733 fps (300 FPE) point.... If it didn't accelerate at all, it would take (1 / 12 / 1733) = 0.000048 sec. to cover the last bit to the muzzle.... That should add (a bit less than)....
200,000 ft.lb/sec. x 0.000048 sec. = 9.6 FPE for a total of ~309 FPE, which for your 45 gr. projectile would be about 1758 fps at the muzzle.... Did I get that right?....
The classical FPE calculation, without choking, for a 24" barrel, was 400 FPE.... so you got rid of almost 23% of that energy if your choked flow model is correct.... That looks like a pretty good start....
This example is a simple one, as you say.... It doesn't take into account the mass of the gas, or the friction of the projectile and/or the gas in the barrel, but in a spreadsheet, using numerical integration, those could be added in.... However, it can't be that simple, and that is where I get lost.... If the power remained at 200,000 ft.lb/s, then 0.0005 sec. after the projectile got to the 23" point, it will add another 100 FPE and achieve 400 FPE (2000 fps).... The average FPE for that 0.0005 sec. would be 350, so the average velocity would be 1871 fps, so in that 0.0005 sec. it would have travelled an additional (1871 x 0.0005) = 0.936 ft. x 12 = 11.2".... That is a total of 23 + 11.2 = 34.2" of travel to reach 2000 fps, if the power applied is a constant 200,000 ft.lb/s after the flow chokes....
The problem is that you stated that the maximum velocity is under 2 x SOS, which means under 2000 fps.... That means the projectile could never achieve 2000 fps, let alone in 34.2".... Now do you see why I am confused by the "constant power" idea?.... I actually like it, because it is simple, but it seems to be in conflict with your Fanno Flow limit, no?.... I can't see how both concepts can be correct....
NOTE: while I was typing this, Scott sent me a spreadsheet, which uses much more accurate numerical integration, and whereas I got 34" of barrel required to reach 2000 fps, the correct answer is about 45".... His spreadsheet predicted 263 FPE at 24", instead of my roughly 309 FPE.... Since the projectile gets accelerated more quickly than my crude estimate just after the flow chokes, and more slowly the further it goes down the barrel.... this increases it's average velocity sooner.... but the same thing still happens.... just further down the barrel....
Bob
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Bob,
You responded:
"but with a 45 gr. projectile, 200 FPE is not 1000 fps, it is 1415 fps"
True - 1000fps is where flow becomes choked.
"Is the flow choked when the projectile reaches 1000 fps, or is that the velocity of the gas at the throat (or are they the same until the flow chokes)?"
Yes and yes - For simplicity, I use a "hard" transition. I go directly from MAXFLOW to MAXFLOW+EXPANSION. In reality, there is probably significant overlap while in the trans-sonic region, with some expansion occurring before max flow is reached.
"We know that the increase in FPE vs. time (power) is linear, so we know the average energy is 200 FPE, so the average velocity is 1415 fps, so in 0.001 sec. it will have travelled 1415 x 0.001 = 1.415 ft x 12 = 17"
All your subsequent calculations look good. Except not sure about the "average velocity" of 1415fps. Should we be using with respect to time? Or with respect to distance? You can't use it to determine the distance traveled.
Basic word problem example:
You drive 40mph for 90 miles, and then you drive 80mph for the next 90 miles.
What is the average speed with respect to distance? 60mph
What is the average speed with respect to time? 53.3mph
How long did it take to cover the 180 total miles? It was not 3 hrs. It was 2.25hr + 1.125hr = 3.375hr
Either way, we are working on the same page. BTW, I sent you an email earlier today.
Edit: I see that you got the email.
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"The problem is that you stated that the maximum velocity is under 2 x SOS, which means under 2000 fps.... That means the projectile could never achieve 2000 fps, let alone in 34.2".... Now do you see why I am confused by the "constant power" idea?.... I actually like it, because it is simple, but it seems to be in conflict with your Fanno Flow limit, no?.... I can't see how both concepts can be correct.... "
It is not in conflict. It's the same concept, just oversimplified in this case.
I said "about 2xSOS". That is a convenient approximation. The Fanno relation is "SOS x sqrt((2/(k-1))+1)". That is the limit.
But you'll need a more realistic gas. With mass and a specific heat ratio. When you do that, it should clear the confusion. It will also complicate the model. I decided to leave mass out to show the concept that I was attempting to get across. Now that is done, we can get more realistic.
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Like I said, I like the "constant power" idea because it is simple, and I can understand it.... and its even pretty easy to build into a spreadsheet.... Throw in Thermodynamics and that mystical "k" factor, and I'm totally lost.... not so much on the math, but the validity/applicability of the whole concept....
PS, threw a 34 gr. JSB Heavy into my .257 Monocoque today, and hit 1362 fps (140 FPE) at 4000 psi (33" barrel).... It shoots a 113 gr. BBT at 950 fps (227 FPE) at the same pressure....
Bob
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Like I said, I like the "constant power" idea because it is simple, and I can understand it.... and its even pretty easy to build into a spreadsheet.... Throw in Thermodynamics and that mystical "k" factor, and I'm totally lost.... not so much on the math, but the validity/applicability of the whole concept....
Bob
Ignore the "k " factor for now and deal with the air mass.
Speculating: The specific heat ratio will affect the rate of expansion. Not sure if it will have much affect on the maximum-velocity in the spreadsheet. But it should have some affect on the needed barrel length for a specific-velocity.
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Ok now I see the point Scott, it wasn't clear to me just looking at the equation you posted, I'm not a math kind of person, more like try and see what happens.
Not that it would be helpful to have means to calculate and make predictions but making a spreadsheet is way out of my league.
Have you calculated the possible supersonic velocity of gas after the choke point, if there is diverging shape cone?
Marko
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Marko, while it is true that you can use a CD (converging-diverging) nozzle, like in a rocket, to accelerate the gas after the throat.... the mass flow remains constant through the entire system.... In subsonic flow, the mass increases with velocity.... Once any point in the system chokes, which means the velocity at that point is Mach 1 for the gas at the temperature and pressure there.... the mass flow is "locked" at that value, and can no longer increase after that.... Therefore although the velocity downstream of the choke point (throat) can increase, that must be accompanied by a decrease in density and/or pressure....
Lloyd and I were working on modifying his spreadsheet last year to incorporate the mass flow limit, but the calculations are extremely complex.... You have to calculate both the gas density and speed of sound at the pressure at the throat, and then once the velocity through the throat reaches Mach 1 at that point, change the calculations downstream of that to use the now constant mass flow, instead of using a variable mass flow before the flow chokes....
Scott is using a slightly different version of the same idea.... constant "power" instead of constant "mass flow" (which may be the same thing).... but all three of us are trying to improve the modelling of the Internal Ballistics of a PCP so that we can both better understand, and better predict, a guns behaviour.... Since we are interested in getting the maximum possible gas into the barrel to accelerate the bullet, and the bore is of constant size and parallel.... the only way you can introduce a diverging cone before the barrel is to restrict the flow between the reservoir and the barrel.... This smaller throat decreases the diameter of the choke point, raising the velocity through the throat sooner, and limiting the mass flow to a lower amount, limiting the power.... This is one of the reasons smaller transfer ports restrict the power, and the higher the velocity (the closer to the SoS of the driving gas under pressure), the worse a smaller port works....
HTHs....
Bob
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The simple concept: maximum possible velocity is the SOS flow rate + the expansion rate. The maximum expansion rate also happens to be near the SOS.
So "about 2xSOS" for a maximum velocity estimate. That sorta lines up with the Fanno realtions.
I tried to do a spreadsheet starting with that simple concept. To see if I could do a simpler spreadsheet and model any specific dump chamber airgun.
I played all day with it to model the flow+expansion as two distinct regimes, subsonic and supersonic, and hopefully get an accurate result.
No good results.
I still need to deal with the amount of expansion to accurately model a specific airgun. We need to take into account k, SOS, temperature, and changes to each along the way.
It just won't work without them. And as I add them into the "simpler" spreadsheet, it starts to look just as hairy as my old spreadsheet.
I sent rsterne a copy of the simpler spreadsheet. And I think it shows the concept of using a "hard" dividing line between subsonic and supersonic. That concept helps with a simple explanation of the maximum possible velocity predicted by Fanno relations, but it does not help when modeling an actual airgun.
I'll stick with my older, more complex, spreadsheet for now. That was a mind boggling exercise in itself. The thought of trying to recreate it scares me.
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The simple concept: maximum possible velocity is the SOS flow rate + the expansion rate. The maximum expansion rate also happens to be near the SOS.
So "about 2xSOS" for a maximum velocity estimate. That sorta lines up with the Fanno realtions.
I tried to do a spreadsheet starting with that simple concept. To see if I could do a simpler spreadsheet and model any specific dump chamber airgun.
I played all day with it to model the flow+expansion as two distinct regimes, subsonic and supersonic, and hopefully get an accurate result.
No good results.
I still need to deal with the amount of expansion to accurately model a specific airgun. We need to take into account k, SOS, temperature, and changes to each along the way.
It just won't work without them. And as I add them into the "simpler" spreadsheet, it starts to look just as hairy as my old spreadsheet.
I sent rsterne a copy of the simpler spreadsheet. And I think it shows the concept of using a "hard" dividing line between subsonic and supersonic. That concept helps with a simple explanation of the maximum possible velocity predicted by Fanno relations, but it does not help when modeling an actual airgun.
I'll stick with my older, more complex, spreadsheet for now. That was a mind boggling exercise in itself. The thought of trying to recreate it scares me.
;) Not gloating but it does my heart good to see you and Bob giving your selves headaches finally . Keep up the good work guys all this science eventually adds to the body of knowledge that helps in the development of better air guns. Also makes us lesser minds better informed with just what it takes to push the envelope and forge ahead.
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Wow! Reading this is giving me brain pain!
I don't have a clue! Wish I did but I don't!
Jim - jhm757
I enjoy the information and occasionally after reading several times it begins to make some sense but the physics has always made my brain hurt and my eyes cross ;D ;D
I am also married to an RN so I am frequently in way over my head when I sit and listen to her conversations with other nurses and doctors so I am getting used to having a puzzled expression on my face and a dull ache behind my eyes :o ::) ;D ;D
Im in there with both of you, my wife is an RN as well, I also work in the IT department at the hospital and several other medical facilities. As soon as I start feeling bad, my wife or some of the nurses at work will ask me what hurts and when I tell her or them, they start talking to me in some kind of foreign language for about 5 minutes, after they get done jibber jabbering, I make her/them tell me whats wrong in plain ole English language and their reply is ..... you have a cold.... oh great now I have a head-ache as well lol
William
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I think this has been touched on, but the speed of sound has everything to do with max velocity.
However, that does not imply a limit of 1150 FPS:
While many air rifles do seem to top out at around 1150 FPS, it is not the speed of sound at one atmosphere of pressure that matters. Rather, if your air rifle could apply 3000 PSI to your projectile, and sustain that all the way down the barrel, then the projectile should get a bit closer to achieving the much higher speed of sound at 3000 PSI. This assumes a barrel long enough, and a pressurized air volume large enough, coupled via a very short port that is bore diameter.
For max velocity; rather than trying to make a large reservoir sustain flow at lower pressure; it is better to reduce losses by keeping flow distances short. Thus, use a smaller reservoir filled to very high pressure. The reservoir would then be coupled via a very fast acting valve that operates essentially without a transfer port:
This gent achieves 2035 FPS in a purpose built lab airgun: youtube.com/watch?v=qUq4OQqZ2bw
It is the pressure drop across the metering valve that limits typical airguns to about the speed of sound at one ATM. The problem is that the source of gas is not directly behind the projectile - it typically travels through a valve or a transfer port, that has a deliberately small volume to limit air wastage. This pressure drop problem is minimized when gas is generated by burning propellant directly behind the projectile; or when the air is superheated due to the combustion of a drop lubricating oil placed in the hollow base of a pellet:
It is barbaric, but my .177 R9 will shoot 7 grain pistol Meisterkugeln at 950 FPS. Add a drop of CLP oil to just fill the pellet's hollow base, and the same pellets chrony at over 1250 FPS. There is no problem with getting the volume of pressurized gas through the transfer port, because the air has already passed the transfer port, when dieseling occurs. In fact, the transfer port's flow restriction somewhat protects the piston from being blown back and wrecking the spring. At least, compared to what would happen if the same oil was delivered to the piston side of the transfer port...
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Your comments that it is the speed of sound at the ambient pressure of the gas that is important is correct, but we are exceeding that as well.... Here is the speed of sound plotted vs. pressure for a few gasses of interest....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Speed%20of%20Sound%2020C%20with%20Helium_zps3zw5mksn.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Speed%20of%20Sound%2020C%20with%20Helium_zps3zw5mksn.jpg.html)
You will note that at 20*C, the speed of sound in air at 4500 psi is about 1560 fps.... yet Lloyd has achieved 2162 fps using that pressure.... Even with a conventional valve arrangement, with a 180* turn to the airflow, I was able to exceed 1700 fps at 2900 psi with a .25 cal airgun by simply using a very light projectile.... yet the speed of sound at 3000 psi is only 1360 fps.... http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.480 (http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.480) .... see reply #490....
Bob
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Even with a conventional valve arrangement, with a 180* turn to the airflow, I was able to exceed 1700 fps at 2900 psi with a .25 cal airgun by simply using a very light projectile.... yet the speed of sound at 3000 psi is only 1360 fps....
Thanks Bob. Is it possible that you were oxidizing the aluminum foil, and that the heat produced increased the average pressure enough to increase the projectile velocity over the speed of sound at 3000 PSI?
Does a bolus of air slamming into the back of a stationary projectile heat up? I believe it does. If that heat can either cause oxidation of anything that will burn, including aluminum foil; or somehow increase the instantaneous effective pressure acting directly on the base of the projectile (not increase the average pressure in the space behind the projectile). Perhaps, just the collision of the air column into the back of the pellet produces such a pressure spike that can accelerate a light projectile beyond expectations...
Yes; the above sounds like "something for nothing", but I see it as an thermal/pressure energy exchange where force on the projectile is what matters.
If you hammer a nail into a block of wood, is it the energy, momentum or force that matters? Logic suggest that if the force is too low, regardless of how much energy there is in the hammer, the nail will not move. The weight of the hammer should match the size of the nail, or the nail will fail to drive into the wood; or it will buckle.
If we assume that not all the energy contained in the bolus of air meeting the pellet is transferred to the pellet (expected inefficiency), might this make the notion that the instantaneous pressure behind the projectile could exceed that of the bulk supply pressure for an instant more feasible? A light projectile may be accelerated to unexplained high velocities by this transient pressure spike; while a heavier on would not. The latter would require a longer duration push to overcome its higher inertia.
Light, loose fitting pellets may be carried on the stream of air in the barrel, at the speed of the front of that air column; while heavy, close fitting pellets may require to be "pushed" by average pressure, where instantaneous pressure spikes in the bouncing air column behind them have little effect.
Just thinking out loud...
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Recovered pellets showed no such oxidation, but I suppose anything is possible.... When you have a chance, peruse the thread linked above where Lloyd Sikes achieved 2162 fps on air.... It's just over 30 pages.... *LOL*....
Bob
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After doing a lot of perusing, I think the instantaneous pressure behind a super-light-for-caliber projectile theory has merit:
Think of the air rushing in behind the pellet as a coil spring. The closer the coils, the higher the pressure.
Now, as the column of air collides with your stationary light-weight pellet, the "coils of the spring" in the region of contact get stacked closer together. This represents a sub-volume of pressurized air that has been forced to be at a higher pressure than the average pressure in the rest of the column due to the change in flow velocity.
That high pressure region has limited volume; thus it has limited total energy. However, its fraction of energy is enough to accelerate the light pellet to higher than expected velocities (based on the average pressure in the air column). While the light pellet does not exceed the velocity of sound in the temporary high pressure air column front, it exceeds the speed of sound in air at 3000 PSI.
A train that crashes at 10 MPH can still squish a pallet of toothpaste tubes so abruptly that toothpaste flies out radially at more than 10 MPH. The toothpaste comes nowhere close to absorbing all the train's energy; just like your light pellet absorbs only a fraction of the energy contained in the initial air volume at 3000 PSI.
The more familiar model is that a pellet launched by means of only 1000 PSI air produces way more pressure than that, should it impact something rigid close to the muzzle. The air column running into the back of a rigid pellet in the chamber is no different; except that it is the air smacking into the pellet at the speed of sound, rather than the pellet smacking the target that produces the pressure spike that launches your light hyper velocity pellet.
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First of all, the molecules in the air are travelling much faster than the speed of sound.... At room temperature, they have a random RMS speed of ~1650 fps.... with some barely moving, and other moving at many times that speed, and all in random directions.... increasing as the temperature increases.... It was that 1650 fps that has been long proposed as the "speed limit" in PCPs.... and that has been shattered as well....
Here is a calculator for molecular speeds.... http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/kintem.html#c4 (http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/kintem.html#c4)
One proposed theory of how we can exceed the molecular speed is that it is relative to the flow rate, which can itself reach 1650 fps.... making the maximum possible velocity about 3300 fps.... There are many additional theories of how that may be happening, including yours.... If the flow rate is limited by the speed of sound, and then you add the molecular velocity to that, you still end up with about 2770 fps (higher at high pressures and temperatures), and nobody has come close to that yet....
HTHs....
Bob
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After doing a lot of perusing, I think the instantaneous pressure behind a super-light-for-caliber projectile theory has merit:
Think of the air rushing in behind the pellet as a coil spring. The closer the coils, the higher the pressure.
Now, as the column of air collides with your stationary light-weight pellet, the "coils of the spring" in the region of contact get stacked closer together. This represents a sub-volume of pressurized air that has been forced to be at a higher pressure than the average pressure in the rest of the column due to the change in flow velocity.
That high pressure region has limited volume; thus it has limited total energy. However, its fraction of energy is enough to accelerate the light pellet to higher than expected velocities (based on the average pressure in the air column). While the light pellet does not exceed the velocity of sound in the temporary high pressure air column front, it exceeds the speed of sound in air at 3000 PSI.
A train that crashes at 10 MPH can still squish a pallet of toothpaste tubes so abruptly that toothpaste flies out radially at more than 10 MPH. The toothpaste comes nowhere close to absorbing all the train's energy; just like your light pellet absorbs only a fraction of the energy contained in the initial air volume at 3000 PSI.
The more familiar model is that a pellet launched by means of only 1000 PSI air produces way more pressure than that, should it impact something rigid close to the muzzle. The air column running into the back of a rigid pellet in the chamber is no different; except that it is the air smacking into the pellet at the speed of sound, rather than the pellet smacking the target that produces the pressure spike that launches your light hyper velocity pellet.
"column of air collides with your stationary light-weight pellet"
In Lloyds hypergun, that does not happen. The pellet moves before the air can start moving. And the pellet velocity is always equal to, or greater than the bulk air velocity.
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The pellet moves before the air can start moving.
That sounds like magic. Unless pressure builds up behind the pellet, what means is there to drive it faster than the bulk air flow; or at all?
Perhaps you meant that the full pressure of the incoming air does not build up behind the pellet before the pellet starts moving? This sounds like a good case for tight driving bands that hold the pellet still, until a significant pressure has built up behind it.
The principles is not unlike applying the brakes of a jet aircraft, to allow time for the engines to spool up and develop near full thrust, before acceleration starts. Without this practice, takeoff from short runways would not be possible. Similarly, pellet velocity from short barrels would be rather low...
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If you read the thread I linked above, you would realize that the pellet in Lloyd's gun is exposed to the full 4500 psi pressure before it is fired.... This is done by mechanically retaining the pellet, pressurizing the firing chamber, and then tripping the mechanical release.... The air molecules in the chamber are colliding with the base of the pellet, exerting 4500 psi of pressure on it, which provides about 277 lbs. of force to accelerate it.... before the column of air even moves....
Not magic, but the pellet does indeed start to move before the column of air does.... Your analogy of spooling up a jet engine is not too far off, and releasing the brakes is indeed much like firing his gun....
Bob
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If you read the thread I linked above...
Thanks Bob. I guess I didn't read the thread "cover to cover".
I agree that if the pellet is restrained so that it sees full pressure before it moves, then the pellet will move before the bulk of the air column does.
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I am sure most of you have seen a ping-pong ball driven at supersonic velocity by means of only a few ATM pressure: youtube.com/watch?v=YYNCGZCul1Q
For those who state that the air in front of the projectile does not matter; that appears not to be the case, in this instance.
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Totally different situation.... The mass of the air in the extremely long barrel is a much greater percentage of the mass of the projectile, which in itself has an extremely low Sectional Density (and hence very easy to accelerate).... The vacuum is providing a fairly large percentage (typically 10%) of the driving force because the driving air pressure is very low (typically shop air) compared to thousands of psi in a PCP....
I don't blame you for not reading all 30+ pages.... just trying to find individual items is a pain, and I was there while it was current and being written day to day.... ::)
Bob
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I have been following all this with great interest.
I was thinking about how to come to grasp with highspeed low-mass projectiles (lloyds test et all)
Now the theoretical calculations are sound (pun intended) But the one primary factor I either missed (possible) or haven't been addressed since it's too obvious.
The expansion happens in a closed system, that never see equilibrium of atmospheric pressure.
So while speed "rules" might not be breeched under normal circumstances, it might be able to inside the ecosystem created behind the pellet before it leaves the barrel.
A higher "rate" of expansion in high pressure systems might explain some of this.
In my head I see a spring of sorts, as it extends, it doesn't extend equally fast in all places, but rather the one end closer to the source gets to extend first, meaning that the area behind the pellet always have the greatest potential for expansion.
Lets imagine it like this, XXXXX> where the x's are the pressure, the > is the pellet.
As the pellet starts to be pushed down the barrel, it looks something like OOOXX> where the O are extended pressure waves already moving at the speed of sound, the lingering "XX" expanding also, but acting against the O's which in my mind would still only accelerate at the speed of the physical laws, but since the column behind it already pushing it at speed of sound, it expands much faster than speed of sound relative to the ground, but not relative to the column of air behind it.
Addendum, why I feel this is a viable explanation is that the effect of this will drop as the projectile is getting heavier.
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...
Lets imagine it like this, XXXXX> where the x's are the pressure, the > is the pellet.
As the pellet starts to be pushed down the barrel, it looks something like OOOXX> where the O are extended pressure waves already moving at the speed of sound, the lingering "XX" expanding also, but acting against the O's which in my mind would still only accelerate at the speed of the physical laws, but since the column behind it already pushing it at speed of sound, it expands much faster than speed of sound relative to the ground, but not relative to the column of air behind it.
Addendum, why I feel this is a viable explanation is that the effect of this will drop as the projectile is getting heavier.
Exactley
OOO is the flow
XX is the expansion
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...
Lets imagine it like this, XXXXX> where the x's are the pressure, the > is the pellet.
As the pellet starts to be pushed down the barrel, it looks something like OOOXX> where the O are extended pressure waves already moving at the speed of sound, the lingering "XX" expanding also, but acting against the O's which in my mind would still only accelerate at the speed of the physical laws, but since the column behind it already pushing it at speed of sound, it expands much faster than speed of sound relative to the ground, but not relative to the column of air behind it.
Addendum, why I feel this is a viable explanation is that the effect of this will drop as the projectile is getting heavier.
Exactley
OOO is the flow
XX is the expansion
Makes sense to me as I try to picture it. Good visualization imo.
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Been gone-this is my recap-
so 2162 fps is it for now? Lloyd's shot
Well above the 1650 fps that the fellow on the other forum suggested/calculated was the upper limit for a PCP(which caused a fair amount of ill will -claims of fakery etc- back and-forth- before he "recalculated" and produced a new upper limit.
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As far as we know, 2162 fps from Lloyd is the fastest recorded shot with a PCP on air at the present time.... I backed that up with 3 shots averaging 2092 fps with my 6mm, so both of us are solidly over 2000 fps.... on air....
Bob
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And I have shot .357 plain plastic sabot at around 750m/s on helium.
Marko
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Hello, i come from Indonesia.
i have pcp cal.22
length of the barrel 25 inch
bullet weight 38.5grain
muzzle velocity 976fps
what I need to change in order to get more FPE ?
example : i want increase energy to 100fpe with bullet 38.5grain
Thank's
Hendrik
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Generally speaking you need more pressure to increase the velocity and FPE.... However, you also need large enough ports and a heavy enough hammer strike to flow enough air.... I have achieved over 100 FPE with a 41 gr. bullet using 3000 psi and full bore-area porting.... The maximum pressure you can safely run is something only you can determine, based on the strength of everything.... STAY SAFE !!!
Bob
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Thank's for your attention Mr.Bob
my pcp cal .22 use a local barrel.
specifications :
- Throat valve hole diameter 7mm
- Transfer port hole diameter 5mm
- Hammer weight 103grams
- Hammer lift 22mm
- Pressure 3000psi
- Volume air tank 180cc
- Steam valve diameter 10mm from POM material
How optimum hammer lift and port transfer diameter in order to have 100fpe energy with bullet 38.5grain?
or whatever I need to change and please include the size I need to change...
Thank's
Hendrik
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My approach is to increase hammer strike until the velocity no longer increases.... This plateau is the maximum your gun can produce with the current porting, barrel length and pressure.... It will be a real "air hog" at that setting, but if you reduce the hammer strike until the velocity drops about 3-5% you should have acceptable efficiency....
When striving for near maximum power, I use porting which is the same area as the bore.... For the barrel port, this means an oblong port (longer than it is wide) to prevent the bullet from getting damaged when loading.... The barrel port in my .224 Hayabusa is 0.17" wide by 0.27" long, with the transfer and exhaust ports bore size at 0.224".... The valve throat is about 0.266" with a 0.125" stem, and the barrel length is 28".... The hammer is 125 gr. with a 1.20" stroke....
If you reduce the OD of the poppet to 9mm that may make is a bit easier to open.... even then, you may need more hammer travel and/or a stronger hammer spring to max. out the performance....
Bob
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if i increase the hammer travel to 30mm,
the weight of hammer will be reduced to 80 grams.
because i don't have enough space for hammer travel turn back if i use the same hammer.
so hammer will reduce the length about 8mm to add travel to be 30mm.
will the power strike of hammer increase than before?
will the hammer be able to hit the steam valve if I fill the air 3500-4000psi ?
how much hammer energy is required to open the valve ?
i use coil spring with max load 82N, lengh 80mm, OD 12mm
steam 3mm
poppet 10mm
throat 7mm
Hendrik
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If you can get 30mm of hammer travel without compressing the spring to coil bind (or making the gun too hard to cock), you will get more hammer strike with a 30mm stroke and 80 gr. hammer....
If you cannot get to the plateau velocity at 3000 psi, you will never get close at a higher pressure, as the valve opening force required goes up with pressure....
I would try reducing the poppet OD to 9mm to reduce the opening force required....
Bob
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My approach is to increase hammer strike until the velocity no longer increases.... This plateau is the maximum your gun can produce with the current porting, barrel length and pressure....
If the hammer dwell time is past the point of further gains, that would be true. But if the hammer is bottoming on the valve face, increasing the hammer mass could still increase the velocity further by lengthening the dwell time. Is that correct?
Increasing the hammer "strike" can be through increased hammer energy (opening the valve faster/farther), or increased hammer momentum (keep the valve open longer). Higher momentum means that the valve will close slower and have a longer dwell even if the valve is already being opened to it's maximum travel.
103g x 22mm, or 80g x 30mm? If the 103g hammer is already stopping close to the valve face, reducing the hammer mass will just as likely reduce the power. Thinking out loud.
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Generally, once the hammer strikes the valve face it tends to bounce off it, and the velocity tends to drop instead of staying level.... If you increase the hammer mass, it in theory could take longer to close.... but a PCP should never be set up so that the hammer hits the valve anyways, with a couple of exceptions.... one being a Cothran valve which tends to open too far because it has a definite "cycle" where it tends to blow open once cracked... Even in that case, having the hammer hit the back of the valve and tends to bounce and reduce the dwell....
Some hammer energy is used up in "cracking" the valve (opening force x 1/2 poppet compression distance)…. The residual energy governs the lift, while the residual momentum governs the dwell.... This is assuming you aren't "artificially" stopping the hammer.... If you are, then in an unregulated PCP you will end up with a "Korean cliff" because you have set the valve operating conditions, and as the pressure drops, so will the amount of air released, and hence the velocity....
You are correct that if the valve stem is so short that the hammer is stopping near the valve, increasing the hammer energy by increasing the stroke will make it hit the back of the valve, and likely bounce back.... and could even reduce the dwell.... Of course that is a design fault, and really has nothing to do with how increasing stroke increases hammer strike.... Valves don't open very far, and there is really no reason to have such a short valve stem as to further restrict it, and a lot of reasons NOT to do that.... For a valve throat of 7 mm, once the valve opens about 2 mm no further increase in flow occurs (because of the curtain area)…. but the dwell will continue to increase.... My experience has been that PCP valves never need to open more than 1/2 their diameter, even for a dump shot, so if you allow for 4 mm of operating lift, that should be enough to reach the plateau.... I would have the valve stem protrude 5 mm just to make sure the hammer never hits the valve, and you get a good, solid plateau....
Bob
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You are all wrong. All of you. The laws of physics don't truly apply here. We are living in a simulation and that could change at any time....
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You are correct that if the valve stem is so short that the hammer is stopping near the valve, increasing the hammer energy by increasing the stroke will make it hit the back of the valve, and likely bounce back.... and could even reduce the dwell.... Of course that is a design fault...
I tested a low mass hammer in my Gauntlet, and that is what seemed to be happening. No matter how much I increased the spring energy, I could not get as much FPE as I could with the stock higher mass hammer. The Gauntlet has numerous design faults. Though I consider them to be design compromises that were employed in order to keep the costs down on what is otherwise a full featured PCP. The valve is held in by a spacer/retainer that determines the valve stem protrusion. Some tuners have been reducing the thickness of that spacer/retainer in order to get some additional protrusion. For now, I plan on leaving the stock spacer/retainer. I'll pick a target velocity, and reduce the hammer mass as much as possible while still getting my desired velocity. At that point, the hammer should be just nicking (not bouncing) off the face of the valve/spacer.
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Before i modify my air rifle i want to know :
-the formula to calculates hammer momentum and
-the formula to calculates poppet valve force/pressure at a pressure of tank 3000psi
i hope any person to explaining to me because I am confused to find the correct formula
my valve stem protrude only 3 mm, maybe i will change to 5mm for increase in flow if the hammer can strike valve steam until 4mm.
tomorrow i will modify my hammer travel to 30mm and weight change to 80gram
and then we see if there is a significant change to the fps or fpe it.
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Yes, I understand that the Gauntlet has very limited lift due to the stem not projecting far enough behind the retainer block.... This is a design flaw, IMO, and throws all normal attempts at tuning out the window.... That doesn't mean they are incorrect, just will not function with a gun where the design precludes their use....
For the most part, you should be able to achieve a proper tune with the Gauntlet without modifying the block to allow more lift.... Anything you can't achieve in that manner is probably such an inefficient tune it would be out of character with the intent of the gun....
Bob
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Hammer momentum is mass x velocity....
Hammer energy is mass x velocity squared divided by two....
The hammer velocity at impact is determined by the mass of the hammer and the force exerted by the hammer spring on it, and the hammer travel while being accelerated by the spring.... This is quite complex, and depends on the preload and spring rate.... and any frictional losses in the system....
The force holding the valve closed is the diameter of the sealing surface of the poppet, squared, times PI/4, times the air pressure.... If your poppet diameter is 10mm, and the throat is 7 mm, the sealing diameter is likely somewhere around 8.5 mm, but could be 7 or 10.... The area (assuming 8.5mm) is (0.335 x 0.335 x PI/4) = 0.088 sq.in.... so at 3000 psi there is (0.088 x 3000) = about 264 lbf. holding the poppet closed, plus the valve spring force....
The hammer energy lost in lifting the valve off the seat is that force times the distance the poppet material is compressed, divided by two.... If your poppet is compressing 0.010" under that 264 lbf. load, then the energy required to "unstick" it would be (264 x 0.010) / 2 = 1.32 in.lb.... That amount of hammer energy is lost before the valve can flow any air, so only the residual energy and momentum is available to create lift and dwell....
Once the poppet is clear of the seat, the closing force is predominately the stem area time the pressure, plus the spring force.... but there is an additional unknown force caused by the drag of the air passing over the poppet and through the throat.... Since it is virtually impossible to calculate these variable forces, and apply them at the correct point in the poppet travel, it is equally impossible to calculate the total lift of the valve and its dwell.... at least it is well beyond my abilities....
Fortunately, even though the dynamics of the valve are hard to calculate, they are relatively easy to understand, as it their relationship to the hammer strike.... First, find the plateau velocity by increasing the hammer strike until you get no further increase in pellet velocity.... Then back off the velocity about 3-5% to get a reasonable tune....
Bob
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Hi, this is my first post, just a comment on the max velocity of a PCP.
The theoretical max velocity of a PCP is tricky. The formula discussed above, v = F/m..., is an approximation that assumes isothermal expansion and neglects the kinetic energy of the gas behind the pellet (it also assumes infinite reservoir volume and neglects friction and nose work, but that is not fundamental). Notice that, per that formula, the velocity blows up when the pellet mass goes to zero, which is not physically meaningful. It also blows up when the barrel length goes to infinity, same problem.
The reason the max "theoretical" velocity is hard to visualize is that the reservoir discharge into the barrel is a non-stationary problem, and in a "non-stationary" problem the conversion of thermal energy into kinetic energy is counterintuitive (just about every grad student in gas dynamics trips on this one!). To get the right answer, you have to imagine there is an expansion (rarefaction) wave within the barrel, and the pellet is riding the front of that wave. If you do this, you find a well-behaved "theoretical" maximum velocity which depends on the specific heats of the gas. For air, this max velocity corresponds to about Mach 5 (and much higher for lighter gases, such as He, reason why we use light-gas cannons to simulate meteorite impacts etc.) Emphasis on theoretical.
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The intent of my simplified formula is to supply a maximum FPE based on bore area x pressure x barrel length.... and only applies with an infinite reservoir (no difference between isothermal and adiabatic expansion)…. and with NO losses in the system.... As such it is the MAXIMUM energy that can be produced, and a great deal of that goes into accelerating the gas itself, which is why using Helium in a PCP can produce more FPE in the projectile than you can get with air.... Even if the projectile mass goes to zero, since we are still accelerating the gas itself, the formula doesn't "blow up", because there is still a mass that must be accelerated.... Trying to wrap my head around an "infinite barrel length" just makes me dizzy.... ;D ….In practical terms, only the best of PCPs on air approach 50% of the maximum FPE, because of finite reservoirs, friction, and the mass of the air itself.... On Helium, they may approach 70%....
The Mach 5 maximum velocity will never be achieved with EXPANDING air (or Helium), as takes place in a PCP.... Light gas guns rely on rapid COMPRESSION of the gas (with heating), usually by a piston driven by an explosive charge.... so a completely different dynamic than a PCP.... In a PCP, the gas cools as it expands, at least to some degree.... You state that:
To get the right answer, you have to imagine there is an expansion (rarefaction) wave within the barrel, and the pellet is riding the front of that wave. If you do this, you find a well-behaved "theoretical" maximum velocity which depends on the specific heats of the gas.
For a PCP, which relies on expansion of the gas, rather than compression like in a light gas gun.... it had been theorized that the maximum velocity possible was 1650 fps, because that was the average molecular speed of air at room temperature.... and hence the fastest rate at which the air in a parallel tube (barrel) could expand.... This has been left in the dust by both Lloyd and I, we have both recorded velocities using very light projectiles of over 2000 fps.... I agree with you that as the projectile gets very light, it acts like it is simply surfing along the front of the expanding gas.... What the actual "speed limit" is, is currently under debate.... My idea is that each "packet" of air released by the valve is accelerated by the one behind it, which allows the 1650 average molecular velocity to be exceeded.... Others have different theories....
With a very large reservoir, bore size porting, and finite barrel volume, there is little difference between the average effective pressure using adiabatic or isothermal expansion.... in both cases the residual muzzle pressure is not much less than the starting reservoir pressure.... In my 6mm, for the shots I conducted reaching 2092 fps with a 1.8 gr. Airsoft BB.... the calculated muzzle pressure with a 28" barrel and a 500 cc reservoir starting at 4200 psi is 4024 psi using isothermal expansion and 3955 psi using adiabatic.... The average barrel pressure during the shot is 97-98% of the starting pressure....
Welcome to the discussion, we look forward to your input....
Bob
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In your derivation of your formula you made use of the isothermal expansion assumption, even if you didn't state it explicitly. That happened when you assumed the force was equal to P0*A for "any" position of the pellet in the bore.
A formula like yours may in fact give good estimates of max velocity, but that doesn't make it a theoretical maximum. Deriving the theoretical maximum is a lot more complicated because you must take into account the non-stationary of the expansion within the bore, and this is no longer an algebraic problem.
By the way, if I am not mistaken, implicit in your formula is an efficiency equal to [gamma - 1], where gamma is the ratio of specific heats, which in air is 1.4. This means that, per your formula, 40% of the thermal energy of the gas that enters the bore gets converted into kinetic energy of the pellet.
I almost forgot, the reason your formula blows up when the mass of the pellet approaches zero is because, in your formula, vel = srt(2 P0 A x/M), where M is the pellet mass, P0 the reservoir pressure, A the bore area, and x the bore length. As M approaches zero, your velocity goes to infinity like 1/sqr(M), and this is forbidden by the physics of gases (because in that case the gas molecules would not be able to keep up with the pellet!). Same with x, the bore length.
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You are correct, since the reservoir volume was specified as infinite, I used isothermal expansion.... because most people are familiar with that concept and Boyle's Law (but most don't understand adiabatic expansion).... My formula for maximum FPE is just that.... a way to show people that there is a maximum which cannot be exceeded (it can be simplified to pressure x barrel volume).... and in fact "real" PCPs do well to get to 50% of that.... In any "real" PCP, the expansion is somewhere between isothermal and adiabatic.... It cannot be purely adiabatic, because we can reach efficiencies beyond what that would permit.... once you take into account real world losses....
I don't understand what you mean by "must take into account the non-stationary of the expansion within the bore".... In addition, I do not know how to quantify the "thermal energy" of the gas that enters the bore (before the pellet exits the muzzle, after that it doesn't matter)…. so I can't comment on how close we are getting to the accuracy of your 40% assumption.... Thermodynamics is not my strong suit....
Would not the velocity equation you state require the TOTAL mass to be used?.... The gas itself has significant mass, and cannot be ignored in calculating the velocity.... As an example, at 3000 psi air has a mass of 60 grains per CI.... At 3000 psi, the air in a .22 cal barrel that is 24" long weighs 55 gr.... which is heavier than most .22 cal bullets (and all .22 cal pellets).... Therefore, even if the mass of the bullet was zero, the velocity would not be infinite because that 3000 psi needs to accelerate at least half of that 55 gr. of air.... The mass of the air in the barrel therefore must limit the muzzle velocity for any given pressure, would it not?....
Likewise, as the barrel length increases, so does the mass of the air required to fill it.... which puts the conceptualization of that well beyond my mental abilities.... other than to logically and intuitively understand that infinite barrel length will not result in infinite velocity....
You hint that there is a maximum velocity that can be attained with a PCP, based on the gas molecules inability to keep up with the pellet.... We have heard that before (1650 fps at room temperature using air)…. If you have some other number in mind, I would love to hear it, and the reasoning behind it.... as this subject is much debated with no concrete answer so far....
Bob
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In your derivation of your formula you made use of the isothermal expansion assumption, even if you didn't state it explicitly. That happened when you assumed the force was equal to P0*A for "any" position of the pellet in the bore.
A formula like yours may in fact give good estimates of max velocity, but that doesn't make it a theoretical maximum. Deriving the theoretical maximum is a lot more complicated because you must take into account the non-stationary of the expansion within the bore, and this is no longer an algebraic problem.
By the way, if I am not mistaken, implicit in your formula is an efficiency equal to [gamma - 1], where gamma is the ratio of specific heats, which in air is 1.4. This means that, per your formula, 40% of the thermal energy of the gas that enters the bore gets converted into kinetic energy of the pellet.
I almost forgot, the reason your formula blows up when the mass of the pellet approaches zero is because, in your formula, vel = srt(2 P0 A x/M), where M is the pellet mass, P0 the reservoir pressure, A the bore area, and x the bore length. As M approaches zero, your velocity goes to infinity like 1/sqr(M), and this is forbidden by the physics of gases (because in that case the gas molecules would not be able to keep up with the pellet!). Same with x, the bore length.
Mach is a ratio. Mach 5 might be achievable when referencing the wave front. When referencing the reservoir air, that limit is about Mach 2.
The Mach limit at the reservoir-outlet/barrel-inlet is always 1. Couple that resulting flow velocity with the rate of expansion of the gas and that becomes the max velocity.
Based on Fanno flow equations, the absolute velocity limit of compressed air is determined solely by the Speed Of Sound (SOS) of the gas in the reservoir and it's gamma.
I still believe this to be the equation for the absolute velocity limit:
Vmax= SOS x sqrt((2/(k-1))+1)
https://www.gatewaytoairguns.org/GTA/index.php?topic=102604.msg1031163#msg1031163 (https://www.gatewaytoairguns.org/GTA/index.php?topic=102604.msg1031163#msg1031163)
FYI - at the reservoir pressures/temperatures we are dealing with, gamma is considerably greater than 1.4
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You are almost there. The formula v = SOS sqr[2/(gamma -1)] applies to "steady state" flow. This fact is absolutely critical. In a PCP we don't have steady flow.
The correct formula is v = SOS 1/(gamma - 1), which applies to "unsteady" expansions (for gamma = 1.4 this corresponds to Mach about 5.) The speed of sound in this formula is the one in the reservoir.
You may ask, if the first formula represents energy conservation, does this mean the second formula violates energy conservation? What people, even experienced fluid dynamic practitioners, tend to forget is that in unsteady flow the total temperature is NOT preserved. In an "unsteady" rarefaction wave (which is what you have in the bore) the energy of a fluid parcel is not constant (Bernoulli's equation is "not" valid in unsteady flow!)
Unfortunately, you very rarely find any discussion of the difference between these two regimes in fluid dynamic texts.
By the way, although gamma can be significantly higher in a PCP environment, this is not essential to the basic difference between steady and unsteady max velocity.
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v = SOS 2 /(gamma - 1).
How does one edit a post?
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rsterne, your formula is valid for any polytropic process, you are right in this. But just to summarize, the max velocity attained in an expansion (no losses, etc.) when you properly account for unsteadiness is vmax = SOS 2/(gamma - 1), where the speed of sound is calculated at the reservoir temperature. This would only happen in an ideal world where the pellet is able to ride the front of the expansion wave.
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You are almost there. The formula v = SOS sqr[2/(gamma -1)] applies to "steady state" flow. This fact is absolutely critical. In a PCP we don't have steady flow.
The correct formula is v = SOS 1/(gamma - 1), which applies to "unsteady" expansions (for gamma = 1.4 this corresponds to Mach about 5.) The speed of sound in this formula is the one in the reservoir.
You may ask, if the first formula represents energy conservation, does this mean the second formula violates energy conservation? What people, even experienced fluid dynamic practitioners, tend to forget is that in unsteady flow the total temperature is NOT preserved. In an "unsteady" rarefaction wave (which is what you have in the bore) the energy of a fluid parcel is not constant (Bernoulli's equation is "not" valid in unsteady flow!)
Unfortunately, you very rarely find any discussion of the difference between these two regimes in fluid dynamic texts.
By the way, although gamma can be significantly higher in a PCP environment, this is not essential to the basic difference between steady and unsteady max velocity.
I believe that your equation is based on the free expansion of a compressible gas:
Vmax = SOS x 2/(k - 1)
The equation that I'm using is based on Fanno flow which considers the adiabatic flow of a compressible gas through a constant area duct where the effect of friction is considered:
Vmax = SOS x sqrt((2/(k-1))+1)
For now, I'm sticking with that. If that velocity is exceeded in reality, then I'll reconsider.
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Fanno flow is strictly "stationary" flow, this is "not" what you have in a PCP. Think about a situation that would apply to "stationary" 1-D flow and you will see under what conditions your conclusion applies. It is actually interesting that there is a difference between stationary and non-stationary maximum values. This has to do with the transmission of energy between non-stationary fluid parcels, which doesn't happen in stationary flow. It is subtle but important distinction.
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Bob,
To address your questions,
1. Efficiency under isothermal process.
The thermal energy in the bore is TE = cv*T*density*A*x, since you assume isothermal, T = T0 (in the reservoir). You can write this as TE = cv*P0/R*A*x, where R = gas constant.
The kinetic energy of the pellet at position x (the basis of your derivation) is KE = P0*A*x
Efficiency = KE/(TH+KE) = P0*A*x/( cv*P0/R*A*x + P0*A*x)) = 1/(cv/R + 1) = R/(cv+R), now remember R = cp - cv, therefore Efficiency = (cp - cv)/cp = 1 -1/gamma = gamma - 1. Since for air gamma is approx 1.4, your efficiency is 1.4 - 1 = 0.4, or 40%.
2. Energy of the gas in the bore: not taken into account. To include the gas KE, you must account for the pressure change down the bore due to the gas inertia, and doing this invalidates your assumption that the energy imparted to the pellet is P0*A*x.
3. Non-stationary max velocity versus stationary max velocity: In a stationary flow, the total energy of a flow parcel (or particle) stays constant (Bernoulli's equation). In a non-stationary flow, the energy of flow "parcels" changes as they move along. If you convert all the energy of a flow "parcel" into KE, you get the maximum velocity that flow can reach. Since the energy contained in a stationary flow parcel is different than in a non-stationary one, the max velocity will differ. In a PCP airgun, the flow is non-stationary.
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I think I understand at least some of that.... ::) …. Doesn't the value of the gamma of air change with pressure?....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/specific%20heat%20ratio_zpsb7wxxwov.png) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/specific%20heat%20ratio_zpsb7wxxwov.png.html)
Unless I am mistaken gamma is about 1.7 at 70*F and 3000 psi (maybe more as the air cools from expansion? ).... What does that do to the maximum efficiency?.... In addition, I am also confused about one other thing....
If Efficiency = 1 - 1/gamma …. for gamma = 1.4 we have.... Efficiency = 1 - 1/1.4 = 1 - 0.714 = 0.286 …. However you also state....
Efficiency = gamma - 1 …. so for gamma = 1.4 you get.... Efficiency = 1.4 - 1 = 0.4 …. How can you get 28.6% using one equation, and 40% using the other?.... Which one is correct?....
doing this invalidates your assumption that the energy imparted to the pellet is P0*A*x.
I never said that the energy imparted to the PELLET is P0*A*x.... That is the maximum energy that can be released by the expanding air, and INCLUDES that used to accelerate the gas itself.... That is the main reason we cannot get to more than about 50% of that value using air, or 70% using Helium.... Perhaps I should refer to that energy as "Energy In", rather than "Energy Out".... with the ratio of the two being the efficiency....
I am particularly intrigued by your statement #3, as you have put a "name" to a theory I proposed in this thread and others a couple of years ago.... I invisioned "packets" (parcels) of gas, each one being accelerated by the one behind it.... The average molecular speed within each packet may average 1650 fps, but the whole packet is moving down the barrel, and so can still exert force on the pellet even when the velocity exceeds 1650 fps.... Now I know that is called "non-stationary flow", and I sincerely thank you for that.... Can you put a "number" on that for air, starting at 70*F?.... I assume it varies with pressure and barrel length (minus losses)…. but I made a wild guess that at 70*F it was twice the average molecular velocity of 1650 fps.... ie 3300 fps would be the absolute maximum velocity limit in a PCP using air at 70*F.... Any validity to that?....
Bob
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Yes, gamma varies significantly as a function of pressure, but assuming gamma is constant doesn't get in the way of the concepts. In fact, whenever one sets up a framework of analysis, it is best to keep it as simple as possible, and a constant gamma is one of the basic assumptions of simplicity without tearing up the physics.
More important, however, is your statement that P0*A*x includes the KE of the gas behind the pellet. It does NOT. Pressure * Area * distance is the work done by the gas behind the pellet ON THE PELLET ITSELF as it travels from the breech to position x. Because this is work done on the pellet, it turns into the pellet's KE, not the gas KE.
In order for the gas behind the pellet to get accelerated and acquire KE, you need a pressure gradient down the bore (pressure dropping along the bore), to produce the accelerating force. In the isothermal assumption, the pressure is uniform behind the pellet, and there is no pressure gradient - as a result, there is no acceleration of the gas behind the pellet. In the isothermal assumption, all there is behind the pellet is thermal energy, no kinetic energy. If you think there is something off here, you are right, an isothermal model doesn't have the flexibility to accommodate what actually happens.
Neglecting the KE of the gas behind the pellet (in a PCP) makes a difference of a couple of Joules in the pellet energy (for a 12 fpe, 4.5 mm gun).
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Neglecting the KE of the gas behind the pellet (in a PCP) makes a difference of a couple of Joules in the pellet energy (for a 12 fpe, 4.5 mm gun).
This seems to fly in the face of reality when dealing with powerful PCPs, as the mass of air used per shot is huge.... My 6mm produces 173 FPE (starting with 4200 psi in a 300 cc reservoir) with a 73.4 gr. bullet, but only 17.5 FPE with a 1.8 gr. airsoft BB.... The mass of air in the 28" barrel (21 cc vol.) at an average pressure of 4000 psi would be about 100 grains.... greater than the weight of the lead bullet.... and over 50 times the weight of the plastic BB....
I used this calculator for Adiabatic expansion to run the numbers for the above shot (scroll down)....
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html (http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html)
Inputs: Pi = 28958 kPa (4200 psi), Vi - 0.0003 m^3 (300 cc), Vf = 0.000321 M^3 (321 cc), Ti = 294 *K (~70*F), gamma = 1.75 (from chart above).... This gives the following results....
n = 3.5539 moles
W = 573 J (423 FPE)
Pf = 25725 kPa (3731 psi)
Tf = 279.5 *K (a drop of only 14.5*C)
The predicted work done to the bullet is 423 FPE, but it ends up with only 173 FPE of energy for the lead bullet, and only 17.5 FPE for the plastic BB.... If a large portion of that 423 FPE does not go into accelerating the air, where is all the extra energy going?.... Incidently, my simple "back of the napkin" calculation gives a MAXIMUM of 454 FPE, assuming Isothermal expansion and an infinite reservoir.... and 423 is less than 454 (by only 7%)....
Bob
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A great deal of the energy stays behind as heat.
Using the following arbitrary parameters, for illustration only, to get an idea of how the energy gets partitioned.
Pellet weight = 73.4 gr
Pressure = 290 bar
Barrel length = 700 mm
Transfer port diameter = 5 mm
Transfer channel volume = 1.6 cm3 (this is the wasted space between valve and TP)
Gamma = 1.5
Etc.
I get the following,
Muzzle energy = 231 J (170 fpe)
Thermal energy in the barrel = 214 J
Kinetic energy of air in the barrel = 24 J
Energy stuck in the transfer channel = 12 J
About 10% to 20% of the muzzle energy stays in the barrel as kinetic energy of the gas
In this case, about the same amount as the bullet energy stays in the barrel as thermal energy
What is the shot efficiency in the gun you refer to (fpe/in3)?
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I use full bore-area porting, 6mm or equivalent effective area on all ports.... Total port length from valve seat to base of bullet is roughly 1.5", so the total volume would be about 1.1-1.2 cc.... The shots were a "dump shot" as in the valve was still open when the pellet exited the barrel (no additional velocity available no matter how hard you hit the valve).... so no proper FPE/CI can be determined by a simple pressure drop on the reservoir, as some of the air is leaving the valve after Elvis has left the building.... I wasn't particularly fussy about recording the pressure drop, but it was about 300 psi.... That would be about 380 std. CI, so about 0.45 FPE/CI for the bullet, and about 0.045 FPE/CI for the plastic BB....
That 214 J seems like a huge amount of thermal energy left behind.... Would that not increase the temperature of the barrel significantly?.... In reality, PCPs get colder when you shoot them, not hotter.... One of our Forum members with a 20mm gets frost on the barrel after a few shots....
I am wondering about the idea of "packets" of air, each one being accelerated by the air exiting the valve.... Surely that must take energy?.... As the bullet progresses down the barrel, those packets must (somewhat) keep up with the bullet, and by the time it reaches the muzzle, the first packet must be doing the same as the muzzle velocity (1029 fps with the bullet).... In this gun, there is about 100 grains of air in the barrel, so if you divided that into 100 packets, each weighing 1 grain, the front one would have 2.35 FPE of energy.... If they were all going the same velocity, that is 235 FPE.... Even if you only used half the air mass, that works out to 118 FPE, a lot more than 24 J....
I haven't discussed it with you yet, but Lloyd has a PCP Internal Ballistics spreadsheet that adds the mass of the air released by the valve as the bullet moves down the barrel, in increments of 0.00001 sec.... You can toggle that on and off, and when I input the numbers for my 6mm, if I toggle the air mass off, the FPE of the bullet increases from 173 FPE to 289 FPE.... an increase of 116 FPE, pretty close to that guestimate of 118 FPE above.... Without using the air mass being accelerated along with the bullet, the spreadsheet makes NO sense, whether you use Isothermal or Adiabatic expansion (or something in between)…. It has inputs for wasted transfer port volume, bullet sliding and starting friction, barrel caliber and length, reservoir pressure and volume, gas (CO2, air, N2, He), bullet weight, valve dwell, and an "efficiency" (fudge) factor necessary to make it agree with test data.... Once the knowns are input, there is only one combination of dwell and efficiency that will match reality....
For the plastic BB, with a MV of 2092 fps, the first 1 gr. packet of air behind it would have 9.7 FPE of energy.... The last packet leaving the valve could not exceed the SOS at the pressure at the valve throat (~3900 psi), which is about 1470 fps (see chart below), so the maximum FPE of the last packet would be 4.8 FPE (and probably less)…. Some (or all) packets must be expanding as they move from valve to muzzle at these velocities....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Speed%20of%20Sound%2020C%20with%20Helium_zps3zw5mksn.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Speed%20of%20Sound%2020C%20with%20Helium_zps3zw5mksn.jpg.html)
How would your calculation work with the 1.8 gr. plastic BB at 2092 fps?.... Why did you choose a gamma of 1.5 at ~4000 psi, instead of about 1.75?....
I am immensely enjoying this discussion.... Please don't think that my questioning your numbers is a put-down, I merely want to understand the concepts, and make sure that they agree with our observed data.... If not, I need to understand why....
Bob
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Fanno flow is strictly "stationary" flow, this is "not" what you have in a PCP. Think about a situation that would apply to "stationary" 1-D flow and you will see under what conditions your conclusion applies. It is actually interesting that there is a difference between stationary and non-stationary maximum values. This has to do with the transmission of energy between non-stationary fluid parcels, which doesn't happen in stationary flow. It is subtle but important distinction.
"stationary" flow is an oxymoron.
Fanno flow is 2-d flow. It varies radially and along the flow axis.
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Scotchmo,
In fluid dynamics, "stationary" means steady-state, it doesn't mean quiescent - it is part of the jargon. It comes from the idea that if the flow is in steady state and you look at the streamlines, the streamlines don't move, even though the flow itself moves. Like any jargon, the word "stationary" entails a bit of idiomatic abuse.
The flow in an airgun is not steady-state, and that is an essential difference in that total enthalpy behaves very differently in steady and unsteady flows. As I said earlier, I have seen experienced people trip on this one.
Fanno flow is steady-state, "one-dimensional" flow. You may be thinking, I suppose, that it has a radial component because Fanno flow refers to flow in a duct with wall friction, and the wall friction induces a radial component of movement. But Fanno flow refers to a one-dimensional "equivalent" of duct flow with friction - there no radial component. The streamlines of Fanno flow and the streamlines of flow in a duct with friction do NOT coincide - even though both have the same cross-sectional mass, momentum and energy fluxes.
That said, some people may refer to Fanno flow "quasi" one-dimensional, but this is a misnomer; there are no "radial" dependencies in Fanno's relationships.
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Bob, it seems my last reply to your last post dissolved in cyberspace, don't see it anywhere...
The lift and dwell of the valve are the linchpin in capturing the internal dynamics. If you know these, computing the mass and energy transfers is straightforward. From your comments much earlier (which I hadn't fully read when I first started posting), it is clear you have a solid understanding of where the difficulty lies - we don't have a "simple" way to compute the pressure on the poppet downstream face (the face away from the reservoir). And, as it turns out, the whole thing depends crucially on this pressure!
There is something called the instantaneous mixing assumption. If you assume that the gas entering the transfer channel mixes instantaneously with the air that is already stationed there, you can use the pressure in the transfer channel as a proxy for the pressure on the downstream face of the poppet. This assumption is open to criticism, but it allows you to close the problem, and get the dwell and lift as part of the solution.
In addition to this difficulty, there is the issue of the precise mechanism whereby the hammer transfers momentum and energy to the valve. Here again, to make the problem manageable, we have to introduce assumptions. The assumption I use is that the time scale of the elastic deformation of the valve stem (the "give" of the stem) under the impact of the hammer is "much smaller" than the dwell time and the time it takes the poppet to lift itself from its deflected seating area. There is a bit of math in justifying these assumptions, you can find the details in my paper "Internal Ballistics of a PCP Airgun", which I posted a few days ago on Researchgate and Scribd (search "internal ballistics PCP airguns researchgate" and it should pop up) - I don't write the URL in case that was the reason my previous post vanished =)
If I run my calculations with a 1.8 gr pellet (!) I get a velocity of about 2,300 f/sec, but these are just "toy" numbers, really, because I am not using the right parameters for your gun.
One other question: Does your gun experience hammer bounce? I am intrigued by the amount of air you quote.
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I am not aware of hammer bounce, but it's possible, but would not matter, other than for pressure drop in the reservoir.... I am certain that the dwell is enough that the pellet is exiting the muzzle before the valve closes, because I have plotted velocity vs. hammer spring preload, and it is well up on the plateau at 1029 fps with the bullet.... The higher MV of the plastic BB (less time in the bore) would guarantee more than enough dwell to insure the same for it....
I'll delve into your paper when I have the time to properly devote, and a clear head.... thanks for that.... "PHEW".... just had a peek at your paper.... It will take a LOT more than a clear head for me to even BEGIN to understand it.... Perhaps I should just go back to "tinkering" in my shop.... ::) …. Seriously that is a huge amount of work, Dr. Tavella…. thank you so much for sharing it.... 8)
One thing to consider about the pressure rise downstream of the poppet.... It takes a finite time (in this case about 0.00008 sec.) for the air molecules (travelling at about 1650 fps) to get from the valve seat to the base of the pellet, during which time the pellet is either stationary, or has moved only a fraction of an inch.... When you compare the gap between poppet and seat (at 0.00008 sec. after it cracks) to the size of the air molecules travelling through it, there is no reason for the pressure in the transfer port area to not reach "nearly" full reservoir pressure by the time the pellet has moved 0.1" or so.... I think using the full pressure (as expanded into the port volume) is valid at that point in time (say 0.0001 sec. after the poppet cracks off the seat).... Much later in the shot cycle, when the pellet, and the air column behind it, is moving at hundreds of fps, that would not apply, of course.... and there could be a significant drop in pressure across the poppet.... Once the valve starts to close, and the curtain area drops below the bore area, at some point the flow should choke, resulting in a drop in pressure downstream of the valve seat of ~ 47% (choked flow)…. Since the SOS at high pressure is over 1400 fps, however, for most shots with a PCP, that choking would only occur at the seat (assuming full bore-area porting), and only in the very last stages of the valve cycle.... The result is that the mass flow through the valve would drop off rapidly just before the valve slams shut.... squaring off the last portion of the flow cycle.... If the valve is open until after the pellet leaves the muzzle (and assuming full bore-area porting) that choking should not be an issue for shots with a MV of less than Mach 1 (outside the barrel)….
Bob
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What you say makes sense. Things would be a lot simpler if the empty space between valve and TP didn't exist!
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I have read through your paper, without so much as looking at the equations.... You did an excellent job of describing what happens inside a PCP, from hammer strike to bullet exit.... The math is beyond me, unfortunately, despite my B.Sc. in Organic Chemistry.... I took Physical Chemistry 3 times, and the Calculus was my downfall.... Conceptualizing orbitals I got, but the math left me far behind.... ::) …. My Physics is limited to 2nd year, and I was in over my head, math-wise, at that.... :-[
Your descriptions and assumptions are great for a typical PCP, but I wonder what would happen if you apply them to some of the more "far out" guns we are experimenting with.... When I build a PCP to shoot bullets (instead of pellets), I use full bore-area porting throughout.... The valve exhaust port and transfer port are caliber diameter, the annular valve throat area exceeds that by about 10%, the inlet area into the valve is at least as large as the throat diameter (sometimes much larger), and the barrel port is typically about 80% of the caliber wide x 120% long, so the area is again equal to the bore.... I use a flat-nosed, retracting bolt that after loading the bullet ahead of the barrel port, retracts to level with the back of it.... With this arrangement, all the passages are bore area, so effectively I am starting with the bullet part way along the barrel (about 1.5" from the valve would be typical)….
I have found that if you increase the hammer strike far enough, at whatever pressure, you will reach a velocity plateau where additional hammer strike only wastes air, because the pellet has left the muzzle....
(http://i378.photobucket.com/albums/oo221/rsterne/Flying%20Dragon%20PCP/Grizzly%20Hammer%20Preload_zpsgcucivpj.jpg) (http://s378.photobucket.com/user/rsterne/media/Flying%20Dragon%20PCP/Grizzly%20Hammer%20Preload_zpsgcucivpj.jpg.html)
Increased pressure, or to a lesser degree increased projectile weight, requires more hammer strike (preload) to get to the plateau, of course.... For a regulated PCP, tuning to a velocity 3-5% below the plateau velocity (which I call the "knee" of the curve) yields the best balance between power and efficiency.... Here is a plot of efficiency vs. hammer spring preload for a typical regulated PCP....
(http://i378.photobucket.com/albums/oo221/rsterne/QB%20on%20HPA/QB79NinjaDelrin1200_zps999456be.jpg) (http://s378.photobucket.com/user/rsterne/media/QB%20on%20HPA/QB79NinjaDelrin1200_zps999456be.jpg.html)
The other thing I would be curious about is how your formulae would work for predicting hammer bounce for the SSG (Stopping Spring Guide) I have championed over the last couple of years.... The concept is not mine, but I brought it into the mainstream in this thread.... https://www.gatewaytoairguns.org/GTA/index.php?topic=102095.0 (https://www.gatewaytoairguns.org/GTA/index.php?topic=102095.0) …. The idea is that the hammer spring is installed on a spring guide which stops the spring travel just before the hammer strikes the valve stem.... Here is one of several versions possible....
(http://i378.photobucket.com/albums/oo221/rsterne/Parts%20for%20Sale/SSG%20Original_zpsc7o9n5b6.jpg) (http://s378.photobucket.com/user/rsterne/media/Parts%20for%20Sale/SSG%20Original_zpsc7o9n5b6.jpg.html)
A typical setup would use a longer than normal spring with a lower spring rate, set with about 3-5 lbs. of preload.... The gap between the hammer and the end of the spring guide is adjustable via the (red) hollow bolt, which basically changes the cocking distance, and hence the hammer velocity when it leaves contact with the spring and flies "free" before hitting the valve stem.... Properly designed and set up, this is easier to cock than a preloaded spring, and when the hammer is thrown back by the closing valve, it hits the end of the spring guide, which requires that 3-5 lbs. of force before moving and storing any energy in the hammer spring.... The result is an almost complete elimination of hammer bounce that is strong enough to open the valve a second (or third) time.... and hence a great savings in wasted air.... Basically, the hammer just rattles around between the end of the spring guide and the valve stem on rebound....
I have many more questions, but this is a start.... BTW, for simplicity, we model the hammer as travelling with the valve stem (instead of repeated collisions with it)…. With the new MDS (impregnated nylon) hammers I wonder if that may actually be the case?....
Lloyd Sikes, co-owner of this "Workshop Gate" has built some very unique PCPs and test guns, the most unusual is the gun which he used to first break 2000 fps, found in this thread.... https://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0 (https://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0) …. The gun he used in that testing has no "transfer chamber", there is full pressure against the "pellet" before and at the instant of firing.... You may find it interesting.... When I built my 6mm over the winter, I just had to try it with an airsoft BB, and was pleasantly surprised that with a conventional layout I averaged 2092 fps for 3 shots.... https://www.gatewaytoairguns.org/GTA/index.php?topic=128036.320 (https://www.gatewaytoairguns.org/GTA/index.php?topic=128036.320) …. Reply #324....
Lloyd is the author of the Internal Ballistics spreadsheet we use to model PCP performance.... He is just in the process of rewriting it, to take into account gas Density (VanDerWaals correction) and mass flow.... The goal is to try and get the "fudge factor" currently required as close to 100% as possible.... I have a feeling your paper will send him scurrying back to the drawing board.... ;D
Bob
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Scotchmo,
In fluid dynamics, "stationary" means steady-state, it doesn't mean quiescent - it is part of the jargon. It comes from the idea that if the flow is in steady state and you look at the streamlines, the streamlines don't move, even though the flow itself moves. Like any jargon, the word "stationary" entails a bit of idiomatic abuse.
The flow in an airgun is not steady-state, and that is an essential difference in that total enthalpy behaves very differently in steady and unsteady flows. As I said earlier, I have seen experienced people trip on this one.
Fanno flow is steady-state, "one-dimensional" flow. You may be thinking, I suppose, that it has a radial component because Fanno flow refers to flow in a duct with wall friction, and the wall friction induces a radial component of movement. But Fanno flow refers to a one-dimensional "equivalent" of duct flow with friction - there no radial component. The streamlines of Fanno flow and the streamlines of flow in a duct with friction do NOT coincide - even though both have the same cross-sectional mass, momentum and energy fluxes.
That said, some people may refer to Fanno flow "quasi" one-dimensional, but this is a misnomer; there are no "radial" dependencies in Fanno's relationships.
Understood, so the next points of concern with your velocity limit equations:
You said that the velocity limit is determined by:
Vmax = SOS x 2/(k - 1)
For 500 psi air at 70F, SOS = 1142fps, and k(gamma) = 1.461
Vmax = 4995fps
For 4500psi air at 70F, SOS = 1548fps, and k(gamma) = 1.744
Vmax = 4161fps
Those are very high numbers, even exceeding the highest velocity powder cartridges. And it seems counterintuitive to say that the higher pressures will have a lower velocity limit.
For the Fanno derived equations, we get velocity limits that seem more reasonable:
500psi, 70F
Vmax = 2639fps
4500psi, 70F
Vmax = 2972fps
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The theoretical limit is what would happen under ideal conditions, which cannot be implemented in real life. The fact that another formula yields a more realistic value doesn't make it right. If you divided your formula by the cubic root of 2, for example, you would get an even more realistic value.
Some people assume the max velocity is what you would get if you converted the stagnation enthalpy of the gas in the reservoir into kinetic energy of the gas. For air, this would give you about 2,500 ft/s as the limit. This value "looks" very reasonable, but is incorrect.
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Bob, if I understand your sketch correctly, you want the guide+spring to dissipate the hammer energy on the rebound. For this to happen you need friction or material that dissipates, rather than store, energy on impact. I am not familiar with the impregnated nylon material you mention. Aluminum and copper have low restitution coefficient.
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More of a theoretical type of guy?
The spring slows the hammer down on rebound and not exerting enough force to open the valve second time.
I'm a little confused on your maximum velocity theory, how can less pressure have greater theoretical maximum?
Doesn't that go against everything that is teached at school?
Marko
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I'm a little confused on your maximum velocity theory, how can less pressure have greater theoretical maximum?
Doesn't that go against everything that is teached at school?
Marko
The max velocity theory that shows higher pressures giving lower max velocities is not mine and I don't currently accept that theory, but - I see how variation in k(gamma) with respect to the starting/ending temperature and pressure might give what seems like a counterintuitive result. When k is not constant (and maybe not even linear), strange things happen.
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The comment was more directed to Domingo. You just pointed it out Scott.
Marko
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Domingo, the SSG works just fine with a steel hammer and steel spring guide.... although I do think that the small 70D O-ring between the back of the spring guide and the gap adjusting nut (red) helps absorb the hammer rebound.... That wasn't it's purpose, it was to quiet the stopping of the guide, and reduce the "shock load" on the parts, but may have a beneficial effect on reducing the hammer bounce as well.... I know it isn't essential, however, because lots of these have been made, and work fine, without it....
The MDS hammer is a separate device, and can be used with or without an SSG.... Some have a metal (steel or brass) nose that strikes the valve stem, others are all MDS.... still others have a metal core to add weight, but the nose of the striker is MDS.... If the point where the sear latches the hammer is MDS, you must be using a trigger with a "drop sear" where the sear falls away on release.... If the sear gradually creeps down the face of the hammer, and drags on the side of the hammer at release, it will quickly destroy the reliable latching of the sear, and the gun may eventually misfire.... Here is a photo of an MDS hammer with steel core, in this case the core extends through to strike the valve, but the sear latches only on the MDS....
Rear view showing steel core, and the recess in the back where the Delrin spring guide pushes... and the clearance hole for the stop rod....
(http://i378.photobucket.com/albums/oo221/rsterne/6mm%20Sporter/Hammer%20Rear_zpsp3kq4ear.jpg) (http://s378.photobucket.com/user/rsterne/media/6mm%20Sporter/Hammer%20Rear_zpsp3kq4ear.jpg.html)
Top/front view.... The sear catches on the slightly tapered front of the MDS filled Nylon sleeve.... Here are the properties of MDS....
http://kmac-plastics.net/data/technical/mds.htm#.W1Y9CeSWyUk (http://kmac-plastics.net/data/technical/mds.htm#.W1Y9CeSWyUk)
(http://i378.photobucket.com/albums/oo221/rsterne/6mm%20Sporter/Hammer%20Front_zps7fbtqj35.jpg) (http://s378.photobucket.com/user/rsterne/media/6mm%20Sporter/Hammer%20Front_zps7fbtqj35.jpg.html)
SSG from the same PCP (my 6mm)…. Small threads adjust spring preload, large threads adjust the gap from guide to hammer.... both 28 TPI.... The white Delrin guide slides back to compress the spring, and drives the hammer.... The steel rod is stationary when firing or cocking.... The threaded gap adjuster is drilled to allow room for the 3" long hammer spring inside it.... In this style of SSG, the small O-ring bumper is at the front, between the white Delrin spring guide and the head on the front of the stop rod....
(http://i378.photobucket.com/albums/oo221/rsterne/6mm%20Sporter/Spring%20Guide%20and%20Longer%20Rod_zps8a3kpkm9.jpg) (http://s378.photobucket.com/user/rsterne/media/6mm%20Sporter/Spring%20Guide%20and%20Longer%20Rod_zps8a3kpkm9.jpg.html)
The hammer has its own cocking handle, it is not cocked by withdrawing the bolt.... It weighs about 1/3 what a steel hammer would.... The grooves in the sides of the hammer are to allow air to move past it, to prevent a positive pressure in front, or a partial vacuum behind, on firing.... That can cause you fits (inconsistent velocity and increased preload required) if you don't realize it's happening.... ::)
Bob
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Stimulating conversation! Domingo, your use of the terms stationary and non-stationary flow, and your additional associated descriptions and comments have shed new light on the discussion of internal ballistics of PCPs. The fact that a steady state is never reached, that is, the air is always in a dynamic "entry length" and never becomes "fully developed," is what seems to complicate the math of the PCP. I have always (well, almost always) know that the the pressure, temperature, and velocity, at all points within the PCP pressure system are always changing..... a continuum of changes. There are never any steady state, fully developed regions within the system. The changes occur both axially and radially within the system.
My spreadsheet, due to my lack of expertise in several areas, treats the calculations as a series of snapshots of "stationary flow", along the axial length of the flow path. Despite the spreadsheet's lack of sophistication, it does provides an approximation of what might be occurring inside the system. I appreciate your sharing your research paper and hopefully will use your presentation to see what areas of my spreadsheet might be improved upon.
I have a few questions about your early statement of the pellet riding the front of the expansion wave in the barrel. For there to be air expansion, there must be a pressure differential in the length of the barrel, with the lowest pressure at the back of the pellet, and air flowing toward that low pressure. Is the air velocity the greatest at the back of the pellet? Since this is non-stationary flow, i.e., always in transition, is it true to say that the average air velocity immediately at the back of the pellet is equal to the velocity of the pellet?
I will digress a little here, but I have often envisioned the pellet as analogous to a piston being driven in a cylinder by air pressure.... a piston air motor. Similar to a single cylinder piston steam engine, without the additional thermodynamics (and power) of the heat energy in the steam. Is that piston air motor analogy reasonable? Thank you.
Lloyd
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Jeez!!!! there is more than 2 of them. David
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stationary and non-stationary flow
Interesting how terminology varies. My old schooling used "steady flow" for time invariant conditions.
is it true to say that the average air velocity immediately at the back of the pellet is equal to the velocity of the pellet?
The back of the pellet forms a boundary condition. The axial velocity of the air contacting the back of the pellet has the velocity of the pellet.
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is it true to say that the average air velocity immediately at the back of the pellet is equal to the velocity of the pellet?
The back of the pellet forms a boundary condition. The axial velocity of the air contacting the back of the pellet has the velocity of the pellet.
Then might we also say that inside the barrel, the pressure VELOCITY (edit) in the barrel the instant before the pellet exits the muzzle is lowest at the breech end and highest at the muzzle, and the pressure is highest at the breech end and lowest at the muzzle, with no pressure or velocity reversal anomalies along the length of travel?
Can this also be taken a step farther and stated that throughout the entire pressure system, the air velocity increases toward the muzzle, and the pressure decreases toward the muzzle, except for localized regions that have physically constricted air passages?
Just trying to nail down some basics.
Thanks,
Lloyd
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Lloyd,
The back of the pellet boundary condition is a constraint on the gas behavior at that location and does not in itself imply anything about the rest of the flow. The two statements you make are conclusions to be evaluated. While they both sound reasonable, there may be conditions where there are pulses in the flow that may affect them. The breech pressure measurements George made with the CP-2 CO2 gun show a generally smooth gross pressure profile.
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...
Just trying to nail down some basics.
Thanks,
Lloyd
"...is it true to say that the average center air velocity immediately at the back of the pellet is equal to the velocity of the pellet?"
"Then might we also say that inside the barrel, the pressure velocity in the barrel the instant before the pellet exits the muzzle is lowest at the breech end and highest at the muzzle, and the pressure is highest at the breech end and lowest at the muzzle, with no pressure or velocity reversal anomalies along the length of travel?"
That is what I would say is more correct.
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I think Lloyd was testing us to see if we can actually read and comprehend. LOL
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Just trying to nail down some basics.
Thanks,
Lloyd
"...is it true to say that the average center air velocity immediately at the back of the pellet is equal to the velocity of the pellet?"
"Then might we also say that inside the barrel, the pressure velocity in the barrel the instant before the pellet exits the muzzle is lowest at the breech end and highest at the muzzle, and the pressure is highest at the breech end and lowest at the muzzle, with no pressure or velocity reversal anomalies along the length of travel?"
That is what I would say is more correct.
.
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^X2....
Bob
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Scott, Thank you catching my using pressure where I should have used velocity. My mistake, and I did go back and edit that in reply 313 to correct it. I am still leaning toward average velocity at the back of the pellet as opposed to center of the pellet. It is arguable either way, I guess.
Stan, yes, the 2 statements might be conclusions, but if you were a gambling man, what kind of odds would you put on them if we assumed PCPs that did not have any unusually odd or restrictive passageways or characteristics.
Tom and Bob, I was trying to see if I could get down on paper (ok, computer screen) what was in my head. At work I would always print out any of my important emails/documents and give them a final read on paper to catch those last few silly mistakes. Not getting any younger, so I guess I still need to do that, LOL.
Lloyd
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... I am still leaning toward average velocity at the back of the pellet as opposed to center of the pellet. It is arguable either way, I guess....
Lloyd
For what purpose are you using that assumption?
"average" implies that there is greater and lesser. None of the air that is behind the pellet will be at a greater velocity than the pellet. The average velocity of the air behind the pellet will be less than the velocity of the pellet.
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We knew what you meant, Lloyd.... even if it's not what you typed.... *chuckle*….
I think that the concept of a large, parabolic velocity gradient radially across the bore may be overrated.... While that occurs (2:1) for laminar flow, it is almost a flat gradient until you reach within a few thou of the bore for turbulent flow.... Since the flow would be tripped to turbulent right at the valve, and once turbulent never again becomes laminar.... I think the velocity gradient would look more like the lower one in this diagram than the upper one....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Turbulent_Laminar%20Flow_zpssbzges0q.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Turbulent_Laminar%20Flow_zpssbzges0q.jpg.html)
Note that the velocity at the center is not a lot greater than the average flow velocity, like it is in laminar flow.... Yes, it is greater right at the center.... but the much flatter profile across the bore, radially, would mean that the pressure distribution across the pellet would be much more even.... After all, pressure is only the force on the surface (in this case the moving pellet) caused by the collision of the molecules of air against it.... The pressure gradient should follow the velocity gradient, no?....
Bob
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Lloyd,
I don't have any issue with using engineering estimates to aid in understanding what is going on in the flow, I just try to keep the boundary conditions separate, since those tend not to change as the engineering estimates mature.
Bob,
I'm not sure the velocity profiles you show are applicable. The pellet obstruction flattens the velocity profile. Between the wall where the boundary condition is zero velocity, and the outer edge of the pellet where the velocity should be of the pellet, there is a complex transition. Might be worth searching to see if it has been modeled for other applications.
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We knew what you meant, Lloyd.... even if it's not what you typed.... *chuckle*….
I think that the concept of a large, parabolic velocity gradient radially across the bore may be overrated.... While that occurs (2:1) for laminar flow, it is almost a flat gradient until you reach within a few thou of the bore for turbulent flow.... Since the flow would be tripped to turbulent right at the valve, and once turbulent never again becomes laminar.... I think the velocity gradient would look more like the lower one in this diagram than the upper one....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Turbulent_Laminar%20Flow_zpssbzges0q.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Turbulent_Laminar%20Flow_zpssbzges0q.jpg.html)
Note that the velocity at the center is not a lot greater than the average flow velocity, like it is in laminar flow.... Yes, it is greater right at the center.... but the much flatter profile across the bore, radially, would mean that the pressure distribution across the pellet would be much more even.... After all, pressure is only the force on the surface (in this case the moving pellet) caused by the collision of the molecules of air against it.... The pressure gradient should follow the velocity gradient, no?....
Bob
"...Yes, it is greater right at the center...."
Here is that diagram with both (laminar and turbulent) scaled to have the same pellet velocity.
(http://www.scotthull.us/photos/Misc/laminar-vs-turbulent.jpg)
Hardly flat. And assuming that the pressure variation follows, we should remember that as you move toward the barrel axis center-line, the area of each subsequent pressure annulus is decreasing. The larger area outer annuli do not get the benefit of the highest pressures. If you assume that the pressure at the outer annulus is the same as the inner, does it matter? It probably does not make much difference for lower velocities (subsonic?).
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Sorry, I just noticed the other replies as I was getting ready to post this, so some of my response might seem redundant.
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What about the possibility of turbulent flow, which will have higher and lower velocities? The air that is immediately exiting the Valve > T-Port > Barrel Port, will be turbulent. That should be a valid assumption, I think. Will the air then be able to transition from turbulent flow to a laminar flow before it reaches the muzzle? Because this is a closed system, with one of the boundaries (the pellet) accelerating away from the pressure, how similar to an open flow pipe is the gun barrel?
I go back to the air piston/cylinder analogy. With a slow moving air piston, there is very little pressure or velocity differential throughout the system. As the resistance of the piston decreases and the velocity of the piston increases, the differentials chance rapidly in the matter of a few milliseconds.
If we were talking about a slow moving air piston I would be firm in a commitment that the velocity of the air immediately behind the piston was uniform, and the same as the piston. When talking about a pellet moving at 1000 fps, I am not sure at all.
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I agree, Lloyd.... I am not aware of any mechanism whereby turbulent flow can revert to laminar, but that doesn't mean there isn't one.... IMO the shape of the leading edge of the velocity profile in subsonic flow behind a pellet will be exactly the same shape as the base of the pellet.... Further back along the barrel, I have no idea, but would bet it is something like that shown for turbulent flow....
Bob
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Jeez!!!! there is more than 2 of them. David
What did you expect ?? ;D Every time I read these "Geek Squad " threads I spend several hours doing Google research to better understand what these guys are saying and sometimes I scare myself when it starts to make sense
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Jeez!!!! there is more than 2 of them. David
What did you expect ?? ;D Every time I read these "Geek Squad " threads I spend several hours doing Google research to better understand what these guys are saying and sometimes I scare myself when it starts to make sense
You got that right! There is so much info on the internet that I can pretend like i know something, LOL. But a serious filter is needed to separate out the "good" info.
Lloyd
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So.....
There are powder burners that see 40,000 psi or more, don't know what the highest pressure is. Anyway, I was wondering what is the highest pressure that air can be compressed to?
Would the barrel know the difference between 40,000 psi of hot, burning gas, or super pressurized air?
Steve
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So.....
There are powder burners that see 40,000 psi or more, don't know what the highest pressure is. Anyway, I was wondering what is the highest pressure that air can be compressed to?
Would the barrel know the difference between 40,000 psi of hot, burning gas, or super pressurized air?
Steve
The expanding gases in a powder burner are very hot (high temperatures). The stored air for an airgun is assumed to be at room temperature.
Aside for the challenges of building a 40kpsi vessel with a sufficient volume - 40kpsi would likely allow for more FPE in a subsonic rifle. But I'm not sure it would be any benefit when trying to approach the theorhetical maximum velocity of air. You would be well into the supercrictical region. Adiabatic expansion of the 40kpsi air beyond a couple of multiples would cause a significant drop in temperature. Would the temperature drop be enough to initiate condesation of the air into liquid oxygen or liquid nitrogen? Wouldn't that limit any further expansion in an adiabatic process? I don't know - just thinking of some possible outcomes.
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There are numerous PB calibers that have a MAP of 60,000+ psi values,
the max psi for a standard 25-06 is right at 62,000+ psi,
the standard 06 runs at 60,000 psi,
the standard 30-30 is right at 42,000 psi.
Standard 357 Mag pistol runs at 35,000 psi,
the lowly 22 LR runs at 29,700 psi.
Just to name a few,
but we are an Airgun site and have to deal with less than 35/4000 psi, sadly ::) etc.
Wouldn't it be nice, if we could get into the 20,000 psi realm?
Just think of what we do................Lloyd & Bob would be unstoppable. LOL
Tia,
Don
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Here comes a dumb questions, for you enablers/geeks.
I have read this post and don't remember see any info on it,
What effect does the the air column, inside the bore, ahead of the pellet/bullet,
have or come into play, with the maximum fps etc. :-\
This air column has weight and provides resistance when shooting the pellet, correct?
Tia,
Don
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I addition, with air that densely packed, the simple Boyle's law relationship between pressure and density goes out the window.... If you take air at 6,500 psi and compress it into half the volume, instead of the pressure being 13,000 psi, it is over 40,000.... When you expand it, the opposite occurs, the pressure drops extremely rapidly as it expands, reducing the power available to drive a projectile.... Simply put, 40Ksi air is not going to give twice the power of 20Ksi air.... you are working with (quickly) diminishing returns at such high pressures....
Bob
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17 pages of this. My head exploded about 14 pages ago.... ;D
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Don, that air creates what is called the "nose pressure", which is only a very small factor in the overall performance.... This is because you have hundreds or thousands of psi behind the bullet, and only 15 psi in front to start with, and maybe several times that just before the bullet exits the muzzle.... The mass of the air in front of the bullet that must be pushed out of the way is tiny, so little energy is expended overcoming it....
Bob
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"Wouldn't it be nice, if we could get into the 20,000 psi realm?"
That kind of pressure wouldn't worry me at all...… as long as I'm in New York and the gun is in Nevada.
Steve
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Since the discussion is hovering about "pressure"...
More pressure, more max velocity? This is a wonderful example of how intuition doesn't always take you to the right place.
Several posts earlier, I posted the max theoretical velocity a pellet can achieve, as
2 * Speed of sound in reservoir / (gamma -1)
This formula is an unconstrained limit that can never ever by surpassed. It is also very hard to come close to, at least on Earth.
If you look at this formula carefully, you may find it disturbing. The reason is that the pressure doesn't appear in it. You may argue that the pressure appears indirectly, because for a "real" gas, gamma depends on the pressure. But even if gamma didn't change with pressure ("ideal" gas), you would expect the formula for the max velocity of an air gun to have the pressure in it. But it doesn't. Why?
Imagine a barrel with a volume of compressed gas at the breech end, and a pellet keeping the gas in place. Now you release the pellet, and the pellet accelerates down the barrel. Assume the pellet weighs almost nothing, and the outside environment is vacuum. Assume there is no friction, the gas has no viscosity, and there is no heat transfer. Under these conditions, the pellet is pushed down the barrel by an expansion wave. Behind the pellet, there is a column of gas that is expanding, with the front end expanding more quickly than the rear end. The pellet will travel, therefore, with the velocity of the front of this expanding wave. This velocity is given by the formula above. The gas cannot move any faster (the front of the expanding wave is the fastest it can go, that is why it is the FRONT of the wave!), therefore, the pellet cannot be accelerated to a velocity higher than the one I quote.
Why is it that the front of this wave will NOT move any faster if you RAISE the pressure of the volume of gas BEFORE you release the pellet? The higher the pressure (keeping the same temperature), the more dense the gas is. Nature has arranged things in a way that no matter how much you raise the pressure, the kinetic energy tied to the higher density behind the wave front compensates for any increment in velocity the front end of the wave could have due to the higher pressure. The speed of the front end of the wave reaches a limit - that limit is the formula I indicated above.
If you impose constraints, such as the barrel having a given length, the pellet a given weight, etc., things change. The formula for the max theoretical velocity "under those constraints" becomes a bit more complicated and depends explicitly on the pressure.
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So according to your formula for the maximum velocity, which is typically about Mach 5, the pressure, caliber and barrel length are all unimportant (they aren't after all, in the formula).... All that matters is that the pellet have zero mass and surf along the front of the expansion wave, and the whole thing be surrounded by a vacuum.... This is the maximum velocity that can be achieved by a "gas gun", and that depends on the speed of sound for the gas used.... Hydrogen, having the highest speed of sound, can produce the highest velocity, which is why it (or Helium) is used in "light gas guns" to reach near orbital velocities for testing micrometeorite impacts, etc.... They additionally use compression of that gas to raise the temperature and pressure, using a piston typically driven by a "controlled explosion"....
Let's backtrack to the title of the thread, where we are considering Pre-Charged Pneumatic airguns.... Typically we are using these on Earth, surrounded by an atmosphere and gravity, and therefore constrained by the practicalities of materials science which limits pressure, caliber and barrel length in some way.... Respectfully, pressure, caliber and barrel length all enter into the potential energy the PCP can produce.... and for a given FPE the velocity is then inversely proportional to the square root of the mass of the pellet.... If you get the pellet light enough, and with minimum bore drag, it is virtually "surfing" down the barrel on the leading edge of the expanding column of gas supplied by the reservoir.... That gas itself has mass as well, and absorbs some energy from the system....
Given the above constraints, can you give us a more realistic formula or number for the maximum velocity of a PCP ?.... because we all know that Mach 5 is simply out of the question.... Further, if you personally wanted to test that maximum, how would you build a PCP to produce the maximum possible velocity using compressed air at room temperature as your power source, and no vacuum applied to the barrel?....
Bob
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Domingo,
I have taken a first pass at reading your paper, Internal Ballistics of PCP Airguns, and found it quite fascinating. Several more readings will be needed to become comfortable with the information. A few of the stand-out points for myself were the mass flow discussion regarding the controlling/limiting of mass flow through the restriction points at either end of the transfer port; the concept of uniform air density in the barrel behind the pellet; the quantifying method for dealing with the acceleration of the air mass behind the pellet; and the temperature gradients and "hot spots" in the barrel and ports. I had not considered that there could be hot spots within the system, but it does indeed make sense.
A lot to absorb! Thank you for sharing this information.
Lloyd
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If the Generals could calculate and predict were the shells would land and hit, they wouldn't need forward Artillery spotters!
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@ Bob,
It isn't that pellet mass and barrel length don't matter. They must be viewed as "constraints", such that the velocity is "bounded" by the theoretical limit. In a way, the theoretical limit is like the speed of light, which has its greatest value in vacuum. It doesn't mean the medium the light travels through doesn't matter, it just means the vacuum value is a reference that can never be surpassed. A theoretical limit is valuable because a transgression would mean you violated at least one the laws of nature.
I am looking into getting a more general formula in a friendly format :)
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Domingo.... agreed, theoretical limits are extremely useful, which is why I find my simple FPE(max) = Pressure x Bore Area x Barrel Length so valuable.... When used as intended, with no constraints (reservoir volume, bullet friction, thermal losses, etc.etc) it produces the intended result from a simple "back of the napkin" calculation.... "Real" PCPs will never reach that number, but that is what theoretical maximums are all about....
Like Lloyd, I find your paper interesting and educational, although much of it is beyond my math skills.... In particular I want to understand the concept quoted below....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Effect%20Gas%20Mass%20on%20Acceleration%20of%20Pellet_zps4kydhbrq.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Effect%20Gas%20Mass%20on%20Acceleration%20of%20Pellet_zps4kydhbrq.jpg.html)
The idea of including 1/3 of the gas mass to be accelerated with the pellet I understand.... but what about "decreasing the force by 1/6 of the inertia of the gas mass".... Could you explain that, I don't get how to do that.... In Lloyd's spreadsheet, he includes the air mass moving through the valve during a time increment of 0.01 mSec. with the mass of the pellet to be accelerated in the following increment.... He then uses a=F/m to calculate the acceleration, and from that the velocity and position down the barrel.... The process then repeats for the next time increment.... The force is degraded by pellet friction, and an "efficiency factor".... I am wondering if the proper way to do this is to include only 1/3 of the mass of gas moving through the valve (and why)…. and how would you incorporate that "1/6th decrease" into the force available?....
Bob
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There are intermediate steps in the derivation which I didn't include. The 1/6 term is changing during the time the valve is open, and it is affected not only by the dwell of the valve, but by the rate of change of the dwell. In order to capture this term, you have to solve the full problem, tracking the valve opening and closing. Since you currently aren't doing this, you won't be able to evaluate this term. However, this term is not as important as the pressure term and you can leave it out, it won't make a serious difference.
For guns where the valve opens and closes before the pellet moves significantly down the bore, to take care of the gas column behind the pellet, all you need is the 1/3 correction in the denominator.
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Looking at the big picture....
Lloyd is getting close to mach 2.5 in the real world.
Domingo believes that in theory, in a vaccume, with a pellet that weighs almost nothing, with no losses of any kind, mach 5 is the absolute limit. He is not suggesting that mach 5 is possible in the real world.
Who knows, Lloyd or Bob might get a little closer to mach 3 ?
Steve
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Looking at the big picture....
Lloyd is getting close to mach 2.5 in the real world.
...
Based on the the 4600psi charge used, Lloyd's highest velocity shot of 2162fps works out to mach 1.36, not mach 2.5. If someone actually exceeds mach 2, then I would take a serious look at changing over to Domingo's limit.
When discussing "Theoretical Maximum Velocity in a PCP", there is no relationship with maximum FPE. Maximum velocity occurs as the pellet mass approaches zero. Not very practical.
FWIW - maximum FPE is just the opposite. We approach maximum FPE as pellet mass approaches infinity.
In a real world design, we settle on a compromise somewhere between the two (zero and infinity).
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Sorry,
I thought Lloyd was up to approx 2,500 fps.
Steve
speed of sound 1,126 fps in dry air 68 deg 768 mph
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Sorry,
I thought Lloyd was up to approx 2,500 fps.
Steve
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Domingo, thanks for that.... I had a feeling that the 1/3 of the air mass was for a shot where the valve closes before the pellet had moved very far down the barrel.... much like a coil spring, where you include 1/3 of the mass as accelerating, correct?....
I would assume that in a shot where the valve is open until the pellet exits.... or for that portion of the shot while the valve is open.... the percentage of mass to be included with the pellet in the calculation of the acceleration would be much larger?.... Lloyd is currently using 100% of the incremental mass while the valve is open, with the sum of the mass of air released added to the pellet mass for the next incremental calculation.... Is that close to correct?....
Machinist, Lloyd has not yet reached Mach 2, using the speed of sound of the air at the muzzle.... Domingo's formula gives a maximum of about Mach 5, based on the air in the reservoir, and as Scott points out, the speed of sound at 4600 psi is much higher, so the Mach number is even lower....
Bob
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Sorry,
I thought Lloyd was up to approx 2,500 fps.
Steve
speed of sound 1,126 fps in dry air 68 deg 768 mph
That might be useful for external ballistics. For this exercise, we are concerned with what is happening inside the barrel. When doing calculations used to predict what velocity the air can achieve, we start with the speed of sound in the propelling air:
http://www.wolframalpha.com/input/?i=air+4600psi+70F+speed+of+sound+fps (http://www.wolframalpha.com/input/?i=air+4600psi+70F+speed+of+sound+fps)
which is 1561fps in this case.
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Bob, the comparison with the compressed spring, where you add 1/3 of the spring mass to the mass of the object attached to the spring, is "exactly" right. The reason is that the air column inside the barrel behaves like a "gas" spring. Nice analogy.
If the valve is open and air is being pumped through the transfer port, you don't change the 1/3 into a 1, but rather change the numerator, by adding the 1/6 term, as EQ (40) shows. I know this is counter intuitive, but this is what momentum balance tells us. If air were pumped at a steady rate the 1/6 term would be zero, but the "1/3 * mg" term in the denominator would steadily grow, so this formula would still capture the "increasing" inertia of the gas behind the pellet. When air comes through the TP, the gas behind the pellet is like a spring that gets longer by adding more coils, the correction is still 1/3 of the spring mass, but that mass grows.
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So if we added 1/3 of the mass of the air moving through the transfer port, in each time increment, to the mass of the pellet to get the (ever increasing) mass being accelerated, that would be correct?.... and while the valve is open, we can ignore the 1/6 inertia term, right?....
That will work for us I think....
Bob
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"So if we added 1/3 of the mass of the air .."
Correct. :)
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There have been some things going on behind the scenes regarding understanding how Domingo's calculations reflect empirical data. Personally, with the way my brain works, until real world numbers are run through the calculations, my mind hits a point where it glazes over and comprehension hits a ceiling. Domingo was kind enough to run the numbers from four of the many high velocity shots I made with my high velocity bench test PCPs. His calculations take all of the possible system losses into account, and reflect the practical maximum, not the theoretical maximum. Two of those shots are video documented and on the airgun lab channel on youtube.
These 4 shots were made with a gun that clamped a special o-ring gasketed pellet in place in the breech. There was no valve, just a fixed amount of air in a conical/cylindrical reservoir directly behind the pellet. When the pellet was mechanically released (rather than a valve opening), the air followed directly behind the pellet, as if coming in through a funnel, necking down from the reservoir to full bore diameter. All of the air was exhausted with a single shot.
Here is the data from the 4 shots. Given the fact that Domingo and I only met on this forum a few weeks ago, the correlation of his calculations with these shots from 2 years ago, is quite remarkable.
Info for shot 52 (1745 fps)(2/18/16), which is NOT one of the videos:
23.3" Barrel length
.22 Caliber (rifled bore)
7.5gn Pellet weight
26cc Reservoir size
4,500psi Reservoir initial pressure
0 psi Reservoir final pressure (dump shots)
1745fps Measured muzzle velocity
Domingo's calculation of max possible vel given these parameters: 1884 fps.
Actual shot was 93% of calculated maximum.
Info for shot 56 (2031 fps)(3/21/16) which IS one of the videos:
46" Barrel length
.278 Caliber (smooth bore)
9.1gn Pellet weight
55cc Reservoir size
4,000psi Reservoir initial pressure
0 Reservoir final pressure (dump shots)
2031fps Measured muzzle velocity
Domingo's calculation of max possible vel given these parameters: 2105 fps.
Actual shot was 96% of calculated maximum.
Info for shot 60 (2162fps)(3/31/16), which is NOT one of the videos:
46" Barrel length
.278 Caliber (smooth bore)
7.7gn Pellet weight
55cc Reservoir size
4,500psi Reservoir initial pressure
0 Reservoir final pressure (dump shots)
2162fps Measured muzzle velocity
Domingo's calculation of max possible vel given these parameters: 2173 fps.
Actual shot was 99% of calculated maximum.
Info for shot 64 (2035fps)(4/19/16) which IS one of the videos:
46" Barrel length
.278 Caliber (smooth bore)
5.6gn Pellet weight
55cc Reservoir size
4,500psi Reservoir initial pressure
0 Reservoir final pressure (dump shots)
2035fps Measured muzzle velocity
Domingo's calculation of max possible vel given these parameters: 2232 fps.
Actual shot was 91% of calculated maximum.
Here is a picture of the path from the air reservoir toward the barrel, with the clamping cams fully opened for pellet release.
The second picture is of the breech end of the barrel and the special pellet with o-ring. The openings in the side of the barrel are for the clamping cams that pinch the waist of the pellet.
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Was bored today and not quite up to speed working on any customer guns ... Just getting over the flu bug after 4 days down.
So I thought it would be fun to take the most powerful PCP I own and make a Delrin pellet for it and see how well it does against theoretical data ? .... So hopefully Bob sees this and can give comment.
WAR Warp .25 cal with 20" barrel 1-19 twist. Regulated at @1870 psi. Outside air temp 52*f & 22% rh. 1500' elevation.
Full .250 porting threwout, SS valve in "Python configuration"
Shooting the JSB 33.95 grain lead pellet = 870 fps making 57 ft lbs
Shooting a slightly lighter than shown 2.2 grain pellet= 1553 fps ( 2.5 gn as shown on scale shot 1488 fps )
Not a math guy ... comments welcome.
Scott
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Not unlike what I did with my .25 Disco.... https://www.gatewaytoairguns.org/GTA/index.php?topic=102604.480 (https://www.gatewaytoairguns.org/GTA/index.php?topic=102604.480) …. Reply # 490.... Took a PCP shooting 104 FPE and with no changes drove a 2.2 gr. projectile at 1752 fps....
Note, a 2.2 gr. at 1553 fps is only 11.8 FPE, not 26.7.... 2.5 gr. @ 1488 fps is 12.3 FPE.... The loss in FPE is huge with such a light projectile because the HPA being blasted out the muzzle is much heavier than the projectile.... The air in your barrel at 1870 psi would weigh about 37 gr....
If you are asking what the theoretical maximum FPE is for your gun, you would use (0.25 x 0.25 x PI/4) x 1870 x 20/12 = 152 FPE.... For a 2.2 gr. projectile, that works out to a ridiculous 5577 fps (this thread has discussed why).... Of course your gun doesn't have an infinite reservoir and it has a few losses along the way.... the largest of which is that huge mass of air being accelerated along with the projectile.... Using my "lofty goal" calculation for your gun would yield 152 / 2 = 76 FPE.... so at 57 you are quite a ways from that....
Bob
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Lol took the energy numbers from chairgun ... oups
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Chairgun has a minimum pellet weight of 5.0 gr.... If you put in anything lighter, it defaults to that weight.... hence the 26.7 FPE number....
Bob
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Scott, I think that the 1553fps is pretty reasonable and about what might be expected from a 57fpe .25 cal. The 1870 psi, and 20" barrel both limit the velocity quite a bit.
I looked back at my records from the 2016 hi vel tests and found that had only one similar shot, a shot with a .278 smooth bore barrel, 46" long, and the conical air chamber flowing right into the back of the pellet. There was a shot with a plastic pellet, where the pellet broke as the chamber was being filled, and it fired at about 1500 psi. That velocity was 1777 fps, but, as I said, the gun had a a 46" long barrel.
If your gun got 1553fps with the 20" barrel, the calcs show that it could do about 1752fps with a 46" long barrel, so very similar to what I got. It is reassuring when different people in different places doing the same types of tests get similar results.
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Thank you gentlemen !!
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OK, so what I think we need is a short length chrony. Put sensors and lasers every 2 cm for some tens of cm...I suspect the MV across the first two/three sensors will show some radical velocity indeed. Using a 4 channel scope to read the sensors right at the muzzle should be adequate...:)
cheers,
Douglas
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Douglas, Lloyd has instrumented a barrel to read the time between several sensors inside the bore, and hence the average velocity per segment.... I presume your idea is to eliminate the velocity loss between the Chrony and the muzzle?.... While that is considerable for a very lightweight projectile, it can be estimated by using the SD of the projectile and a drag model for the approximate shape.... For example, my fastest recorded velocity was a 1.8 gr. Airsoft BB from my 6 mm at 2092 fps.... The drag model for a sphere at those velocities is well known.... so it would be a simple matter to calculate backwards from my Chrony to the muzzle to get what it actually was.... From the thread where I made those shots, is this quote....
The BC, however, will be VERY low, on the order of about 0.003, so it will lose velocity and energy very quickly.... It should fall subsonic in about 8 yards, and at 40 yards be down to under 400 fps.... In fact with my Chrony at about 1 yard, the MV would likely be around 2300 fps
Bob
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I am trying to improve on the sensors for that lab setup, and adding something just beyond the muzzle could be helpful. Seeing the acceleration plunge from thousands of g's to very negative would be educational, to say the least.
What about using some of these self contained photo detectors to add to the setup? They have some with gaps big enough to shoot thru. Maybe coupled with an Arduino?
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Lloyd,
In the middle of George's Hacking the CP-2 thread, there is some discussion on this. Page 9 https://www.gatewaytoairguns.org/GTA/index.php?topic=137566.160 (https://www.gatewaytoairguns.org/GTA/index.php?topic=137566.160)
I ended up using a laser detector module and a pointer laser diode. Both are set up to run off of 5V so hook-up is trivial. The cost is minimal (~$3 for both).
Cindi suggested using the photointerruptor. I don't know if she actually implemented it. Looking at the parts, the response time varies.
There are some Arduino based chrony projects out there. The impression I get is that you need to use the interrupts to get timing that is fast enough. I am not an Arduino expert.
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You guys got me thinking about this again, and how to instrument a barrel to read travel time at numerous locations along the inside of the barrel. I had been doing some fiddling with home built alternators for wind and water power. Ah ha! Magnets and coils!
This looks like it will work, and it is much simpler and MUCH more reliable than the previous methods I was using. However, it does require attaching a small rare earth magnet, probably spherical or cylindrical, to the front of each pellet that is tested. The neodymium magnets are itty bitty, and cheap. Shouldn't be a big deal.
The best thing about this is that you don't have to drill any holes into the barrel, with the associated miserable deburring that is required. But you do still have to sacrifice a barrel.
The magnet, attached to the front of the pellet, will be fired thru the barrel. At each location that you want to read a pulse as the pellet/magnet passes by, a groove is machined in the O.D. of the barrel. Each groove creates 2 perpendicular surfaces in the steel barrel that will interrupt and amplify (kind of) the flux lines of the magnet as it passes by. There is a coil of very fine wire (a coil salvaged from a relay) that slides over the barrel. The coil is positioned over top of one of the grooves that are machined in the barrel. The 2 wires from the coil are attached to the input of a single channel of the o-scope. A voltage blip (sine wave, kind of) shows on the o-scope as the magnet passes thru the coil, or surprisingly, when it passes thru any of the other machined O.D. grooves.
I set up an experimental barrel, coil, and magnet. as shown in this picture. The magnet is the tiny thing taped to the front of the 3/16" wooden dowel.
The barrel has 3 grooves machined in it, all located near the muzzle end of the barrel. The coil is positioned over the center groove.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/MagnetTest-2_zpsjibyi3wk.jpg)
For the experiment, the magnet on the end of the dowel was pushed into the barrel about 12". To simulate the magnet being fired out, I just pulled the dowel out of the barrel as fast as I could.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/MagnetTest-3_zpsztni4wod.jpg)
Here is the scope trace. You can see 4 distinct events in the trace. The first three are the magnet passing from left to right thru the 3 O.D. grooves. The 4th event, on the left, is where the magnet left the barrel.
One very nice feature of this arrangement is the precise timing on the events on the trace. You can see the vertical line at each event, where it drops straight down from maximum plus voltage to minimum negative voltage. That is where the magnet is passing thru the center of the groove. You can see where the magnet comes out of the end of the barrel, that the trace is distinctly different on the negative (bottom) side.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/MagnetTest-1_zpsnnky6vou.jpg)
I am not sure if a separate coil will be needed at each groove or not. More experimentation is needed, but this looks very promising.
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Cool idea, Lloyd.... *looking at my watch*…. and BTW, Happy New Year (almost)…. *LOL*….
How sad is it that we are on the Forum right now?.... *eyeroll*….
Bob
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Lloyd - This is an interesting experiment, but Faraday's law and Lenz's law will be working against you if you're planning to use this for anything quantitative relating to ballistics. It would make an interesting braking system, though.
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Lloyd - This is an interesting experiment, but Faraday's law and Lenz's law will be working against you if you're planning to use this for anything quantitative relating to ballistics. It would make an interesting braking system, though.
George, I agree that a braking effect will be induced in the magnet as it is propelled thru the barrel, but that force will be orders of magnitude less that the propelling force of the air pressure on the pellet. For a crude comparison of the braking force, pushing the wooden dowel with its attached magnet thru the barrel offers much less resistance than pushing just a plain pellet thru the barrel. I tried pushing the magnet both fast and slow and resistance was only slightly perceptible in both cases.
It will be easy to quantify the actual resistance that the magnet adds by by firing the pellet with magnet thru the barrel and measuring its MV, and comparing that to the MV of a plain lead pellet of the same weight and configuration. I doubt that the difference in velocity will be consistently measurable, but the experiment will show the answer.
But back to point of the experiment, it is just another way to measure the acceleration of a pellet thru a barrel.
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the braking force is a function of power taken away. With a large monitoring load( Mega-Ohm+ ), the system will just about only create voltage. This will cause a negligible drag. Now if you short the coils, there will be non-trivial braking...:)
cheers,
Douglas
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The coil in the setup is 80 ohms, so lots of turns of small gage wire, but the coil does produce pretty spikes, from the groove it is directly over, and from the grooves that are nearby. That makes connecting to the o-scope very easy. But I am wondering if just hand winding a tiny coil in each groove along the barrel might work? But how would they be connected? Since the idea is to just produce a clean indication at each groove, I could see the numerous coils interfering with each other.
The only magnet wire I have is 20 gage and I was able to get about a dozen wraps in one groove. By pulling the magnet thru the barrel with a stretched bungee, I could barely detect some sort of event on the scope from the 20 gage coil. Also, I am not sure what passing the magnet thru at pellet velocities will do, but I think it will improve the indications.
Lloyd
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Looking forward to the results.
The rare earth magnets are brittle and I don't think the resulting dust is all that great. A dedicated soft pellet trap full of old clothes should help keep them intact.
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Good thoughts gentleman. Thank you.
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Sort of an odd question on determining losses over the short distance a light test pellet travels.
Could you not start with say the rearmost sensor @ 2 feet from muzzle & take velocity shot.
Then move the Chrony backwards so the Front screen as at the 2 foot position & take a velocity shot.
* Both figures added & divided by 2 should give a accurate average if the CENTER between screens was a 1.5 feet from muzzle.
Then do the test again at say 6 to 10 feet and come up with DECELERATION figure over distance. * As in FPS per inch of loss
Knowing that you should be able to now add back the speed into the 1.5 foot distance to muzzle and be close to exit velocity.
Or something like this ???
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Scott,
Very good idea, but my guess is that the shot to shot velocity variation would be too great to get any sort of repeatability.
BUT, if you had two chronys that read the same (or within a few fps of each other), then your idea would work great getting 2 measurements from each shot.
Lloyd
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I am pretty sure this way of measuring internal velocities will work, so I am getting excited.
I wound coils in the 3 grooves I had machined in the .25 cal barrel. I'm still just pulling the magnet thru the barrel by hand. And believe me, the hand is NOT quicker than the eye, LOL.
Each coil is approx 90 turns of 32 gage magnet wire. The grooves are just randomly placed to see if I could get some readings.
Here's a pic of the 3 small coils on the barrel.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/3-small-coils-1a_zps0hx9fo1r.jpg)
Here are pics of the o-scope pics with the coils connected in series, and with them connected in parallel. I am a little surprised that each groove shows up very distinctly, with no type of cross talk. The voltage spikes are a bit taller with the coils connected in series, so that is how I will try it installed ona gun. I am anxious to see what happens at airgun velocities, seeing that the calcs show that i pulled the magnet thru the barrel at a blazing 12.8 fps. Doh! :-[
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/3-small-coils-in-parallel-1a_zpspaisboxo.jpg)
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/3-small-coils-in-series-1a_zpsuuky5pov.jpg)
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Great stuff Lloyd!
Tom
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One more coil over the valve stem and / or hammer and you'll have complete monitoring over the shot cycle.
Marko
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Not sure what your scope has in terms of input voltage tolerance, but since voltage is a function of speed, do make sure that your first shot does not burn out input circuitry...:) The old tube Tek's I use for preliminary investigations don't have this issue...they also don't have Record the trace capability either...LOL
cheers,
Douglas
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Tom, Thanks for commenting. It is fun working with the electronics and actually making progress.
Marko, I was definitely thinking about how to use the other channel in the scope. The coil winding is easier than I thought it was going to be, and hopefully, there is a combination of coil arrangement and magnet that will yield both velocity and displacement for a valve stem with a single trace. Maybe?
Douglas, The scope is a PC based Velleman PCSU200 2 channel rig. About $120 and I am just scratching the surface with it. I am a novice at this, but managing to fumble along. Your comment about the voltage from the coils when the magnet is actually fired is well taken. The magnet velocity could be 100 times as fast as the demo, and the coil output voltage is supposed to be proportional to the speed of the magnet. The scope also has a high impedance probe with a 10x setting. Maybe I should take the first shots with that probe and the voltage set to the max setting on the scope. Would that be prudent? Right now, the coils only have 90 turns, maybe fewer will be needed. I don't know.
Lloyd
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Lloyd fewer turns might be prudent otherwise there is definitely a strong possibility of overloading the scope input. Even if the input is has over limit protection the result would be useless data
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Don, I read your post just as I was getting ready to post this one. You've made a good suggestion. Fewer turns in narrower grooves sounds like a safer way to go.
Lloyd
----------------------------------
This is from last night's experimentation:
I was wondering if the coils could be made as pre-wound bobbins that just slipped onto the barrel, eliminating the need to machine grooves into the O.D. of the barrel.
Here are 2 coils that I made and tried.
The one on the low carbon steel bobbin was a complete fail. It has about 100 turns of 32 gage wire, but thinking about it now, the steel bobbin seems to have shielded the coil from the magnetic lines from the passing magnet. There was basically no indication from this magnet on the scope. The coil checked out ok: good continuity and no shorts, but no output. Oh well.
The other coil is about 300 turns on a nylon bobbin. This coil definitely showed a trace on the scope, but it needs improvement. This coil is twice as wide as the coils in the grooves in barrel. This extra width makes a trace with longer duration rise and fall on the scope. And despite having 3 times as many turns as the coils in the grooves, the voltage level was much lower. Overall, the coil worked, but it's trace was not as precise as the narrower coils in the grooves.
Since I've basically already ruined this .25 cal barrel, I will continue working with it and machining additional grooves into it to get more coil locations. But first I have to machine the breech end and add the barrel port, and see what kind of output I get from the 3 coils that are already there.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/2-different-coils-1_zpsdoifkwkb.jpg)
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I as you know am a tech geek lol and I have probably 3 working scopes and a few more for parts and have dabbled a bit in building pic up sensors for ignition systems so I have a few pointers that I can share. The closer the magnet is to the pick up or in your case coil spool the better a signal you will see now I have a feeling that at speed you will most likely not see any spike at all or just a bump in the signal ( I hope I’m wrong). When building the pick ups for a high reving Seadoo engine (10k rpm) if the gap got more than .030 the signal was lost at speed so I wonder how the barrel thickness will play into this at speed. I would in this case thin the barrel as much as possible where the pick ups go on or even better thin the barrel and put down a thin insulation barrier and wrap directly to the barrel and epoxy over it you don’t want any wire movement it will show up on the scope. Do this every 6 inches and run the pick ups in series with insulation tape between them to help prevent any bleed over. Even going to this extreme I’m not sure at Speed you will see a good strong signal
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Travis, You're up bright and early this morning, but I think that's standard for you, LOL.
Thanks for those thoughts, I had been pondering what might happen when i actually fire the magnet thru barrel. That is going to happen within the next few days. Right now, the barrel has a .437 O.D., and the grooves where the coils are wound directly on the barrel are .327 dia. That leaves a wall thickness of .038"..... about as thin as I am willing to go. The only magnet I have is 6mm dia x 3mm long. So that is a total gap of .045" to the coil, per side. I doubt I can get the magnet any closer to the coil than that. Your thought of the voltage spike degrading to an indistinct "bump" when the magnet passes by at high speed sounds realistic. We'll see when I fire the magnet. But if the spike does disappear, the backup plan is to try a longer magnet. Instead of 6mm dia x 3mm long, maybe 6x6 or 6x10. Too bad I don't have a handy "Magnet Store" down the street, LOL.
Lloyd
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I can see it now Lloyd casting magnet/epoxy mix Bullets!!! That just might work! LOL The older I get the less I sleep so I just get up and start working. I’m tinkering with a program to tune my Subaru ecm right now. Nothing I own is unmodified 😂
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...............................................................
I’m tinkering with a program to tune my Subaru ecm right now. Nothing I own is unmodified 😂
Do you ever look at it from your wife's perspective? "What the heck is that crazy @#x%* doing now. I am just going to turn around and pretend like I never saw that." ::)
My wife has a tag line she uses on facebook called "Married to an engineer." She uses it for "Guess what this is," and good natured laughs. Yes, she puts up with a lot. But not everyone has a silent exhaust fan under the kitchen sink so that the whole kitchen doesn't smell like a trashcan full of mashed garlic and old shrimp." She didn't even know she needed it, but she loves it. Right? ::);)
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Could you use your test barrel and existing probe with shop air (blowgun) to explore the response at higher (moderate) velocities?
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Yes, I will creep up on the velocity and hopefully not loose my only magnet in the process. The catch can for the pellet/magnet is filled with plastic grocery bags. They exhibit tremendous elongation when hit with a pellet, spreading the deceleration over a distance of 6 or more inches.
I am anxious to see how it goes.
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Keeping with the cautionary note of creeping up on the task, I managed to successfully record some 400psi, 350 fps shots. They all went well, but a few tweaks will be done before the velocity is bumped up.
I won't be able to give full documentation until later tonight, but here are pics of the test setup.
This is the overall setup.
The .25 cal Disco-based gun is strapped into place. It shoots thru the birdhouse muffler. The metal rod above the gun barrel is an alignment bar for the hole thru the birdhouse. If the gun's barrel is parallel to that rod, the pellet should pass thru without hitting anything. Beyond the birdhouse is the chronograph with light bar above it, and then the bullet trap. For this exercise a 6x6x6 open-fronted cardboard box is filled with grocery bags, and placed in front of the normal trap, to catch the fired pellet. To the right side is the trusty laptop with the PC based o-scope program ready to go. It has 2 channels. One channel records the valve stem movement, and the other channel records the pellet/magnet movement past the sensor coils.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Setup-3-1a_zpscwxthgg5.jpg)
Here is the pick-up for the valve stem movement. As Rube Goldbergish as it looks, it is about the 20th attempt at a reliable (ha ha) valve stem movement pickup. But, it does work! Sticking out of the window in the side of the air tube is a 1/4" steel rod that is threaded ontothe end of a special valve stem. It travels in unison with the valve stem as a single entity. Sticking out of the top of that valve stem bar is a short length of .050 hex key. The hex key pivots where the little set screw is visible, and the end of the hex key swings an arc across a portion of carbon track from a trim pot. The white bead on the end of the hex key is a teflon ring that helps the wiper maintain a proper pressure ont eh carbon throughout its swing of travel. There is about a 3 to 1 travel increase ratio of the wiper across the carbon track. A 1-1/2 volt battery and a resistors plus the carbon track, make a voltage divider circuit to provide a voltage to the o-scope that is proportional to the travel of the valve stem. There is a torsion spring wound around the hex key pivot point to remove any backlash from the setup. The voltage seems to track well with the movement, although I am sure there is some lag and overshoot at the extremes of travel. But again, it does work.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Setup-3-3a_zpspjktole9.jpg)
This is the front end of the barrel with the 3 coils in place in grooves on the barrel. More grooves and coils will be added after the bugs from these are worked out. The 3 coils are wired in series and connected to the second channel on the o-scope. They work well, but the inter-connecting wiring of the coils needs to be done in a neater manner to reduce unwanted indications on the scope. But, it works, too. The patient is ready for the experiment to begin. :(
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Setup-3-2a_zpsdtrfj2rj.jpg)
REAL results tonight. 8)
Lloyd
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Hey, Rube.... nice setup !!!!
Can't wait to see the results.... *grin*….
Bob
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What Bob just said. You can't help but smile when you see a setup like that gets the job done ;D ;D ;D
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Ok I’m excited!!! Popcorn at the ready
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Looks a bit like my ecu bench setup at times. Wires soldered to the ecu board, going to open programmer with changed components hanging on ribbon cables.
But if it gets the job done it's enough. ;D
Good job Lloyd!
Marko
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Thanks guys. When you can do it with stuff from your junk.... uh, project material collections. so much the better.
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Ohhhhhhhhhh man.... I just KNEW your junk was bigger than my junk.... ::)
Bob
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Bob, and I just spent today putting more flooring in the attic to store MORE junk. :P
----------------------------------------
First internal velocity data.
There were some good recordings of 3 different shots, so far, but I have only annotated the 3rd one.
The platform was a modified (do ya think, LOL) Discovery, .25 caliber, with 128cc of reservoir. All shots were low pressure and low speed.
The pellet was a Beeman wadcutter pellet with a neodymium magnet attached with 2 faced tape to the flat front end. Total weight of the pellet and magnet was 32.6 gn.
This shot was fired at 386 psi, and the pressure after the shot was 354 psi.
Velocity across the chrony was 309 fps. Distance from muzzle to the first eye of the chrony was 30 inches.
After you get oriented with the graphs from the oscilloscope, they are pretty easy to follow. There are 2 channels, red, and blue. They read as voltage in the vertical axis and time in the horizontal axis. The time scale for both channels is the same, and the total time across the ENTIRE graph is 11.5 milliseconds, or 1/2 millisecond per horizontal division line. The vertical voltage scales are different for each channel, and are set to appropriate scales for the inputs.
For the blue channel, which is travel of the valve stem, the scale is 1 volt per large vertical division line. For the red channel, the output of the coils that are excited by the magnet, the scale is 30 milli volts per large vertical division line.
The blue trace is for the valve stem starts moving at time = 0. You can see it rise to max height at about 1.4 milli sec and then return down to its seat at about 3.4 millisec. The overshoot, or the poppet reseeding into the seat is probably just a function of over travel of the mecahnical indicator attached to the valve stem. Maximum stem height is about .12 inches, but I need to investigate that further.
However, I do think that the valve open time of approx 3.4 msec is reasonably accurate.
For the red trace, the travel of the pellet/magnet combo, the first real indication is where the magnet passes thru the first coil, at 17.7" down the barrel. That occurs at 6.2 msec after the valve stem starts to move. At 6.7 msec the pellet is at 20.15", at 7.0 sec the pellet is at 21.3", and at 7.5 msec, the pellet passes out the muzzle at 23.5".
(Note- this picture is from 2 screen captures of the same shot that were combined to make a single, complete timeline of the shot. You have to scroll thru the o-scope screen to see the entire shot, so knitting the 2 together was necessary.)
Click on the picture to make it larger.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Third-Shot-1-2a_zpsavnlfa0a.jpg)
The extra humps and bumps in the red trace are due to a number of things that need to be cleaned up. The hose clamp at the front end makes the extra blip at the muzzle. The way the extra lengths of coil wires are soldered together and taped to the barrel also cause funny bumps near the coil indications. But a little bit of house keeping will fix all of that.
There is some definite overtravel in the valve stem indicator, and it might actually be running out of travel.... I am not sure, but it will be looked at. For the time being, it is functional.
Once this set up is functioning at real airgun velocities, more coils will be added, including, probably, a couple just past the muzzle.
This seems to be working. Fingers crossed! ;)
Lloyd
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Very neat stuff, my friend.... watching with continued fascination....
Bob
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I was studying the data from the shot in the graph in post # 392 and ran into a few things that surfaced some questions.
There are 3 magnetic coils near the muzzle end of the barrel. The o-scope indications of these 3 coils, plus the indication of the muzzle of the barrel, provide 3 segments along the barrel where average velocities can be calculated. The first attempt at calculating velocities yielded questionable results.
The results were, starting with the one closest to the breech, 374fps, 342 fps, and 364 fps. And finally, velocity across the chronograph was 309 fps, although interestingly enough velocities across the chrony for the previous 2 shots (at very slightly higher pressures) were 366fps and 376 fps.
So, I remeasured, more accurately, the distances along the barrel, and also enlarged the o-scope trace so that calipers could be used to measure the time more accurately (fractions of the 1/2 msec time divisions).
The final results that I got were, again, starting closest to the breech, 366fps, 361fps, and 369fps. Still a bit odd with the slower velocity in the middle of the 3 segments. So, there are some possible explanations for the anomalies. One is that the velocities are correct. Another is that I need to remeasure everything for accuracy again. Another is that the magnetic center of the coils might not be where I think they are. Another is George's comment about the magnetic resistance of the magnet passing thru the barrel. Another is the affect of the muzzle crown on the magnetic end of the barrel.
The bottom line is that the setup is working, but we are down to splitting hairs on the velocity measurements, and that requires more accurate work on my part to reduce the tolerances wherever that can be done. The work continues.
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Here are a few pictures of the method I used to retrieve the pellet and magnet after each shot. I've show this before, so please forgive my repetition.
This is a picture of pellet hole in the "catcher". The catcher is a 6" square box, with no cardboard on the front end ,just 5 sides to the box, not six. Plastic grocery bags are layered loosely in the box to stuff it slightly tight, but still soft, and then a single bag is tightly tied around the entire box to hold everything in place. The plastic grocery bags have tremendous elongation and slow the pellet very gently.
Here is a pic of the catcher with the pellet hole in it.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Retrival-1a_zpsrnkzathr.jpg)
In this pic, the outer bag has been removed and you can see the funnel shaped hole into the bags. The nice thing is that the pellet stretches the first bags deep down into the bottom of the hole just like you were trying to push your foot out thru the toe of a sock.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Retrival-2a_zpsnil77fwn.jpg)
Here is everything peeled back and you can see the pellet with the magnet attached with 2-faced tape. Also note that there is a single layer of shiny packaging tape wrapped around the magnet to stop it from making direct contact with the bore of the barrel. BTW, the magnet is a plain cylinder even though it doesn't look like it in the picture.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Retrival-3a_zpsl5waxfbp.jpg)
I've used this grocery bag method to catch everything up to 50 caliber. One thing to keep in mind is that the bags need to be re-fluffed after each shot because the stretched portions loose their elasticity and don't stretch for the next shot.
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You might be able to corroborate the muzzle signal with a broken wire (or probe wire) approach using your magnet wire. You would lose the valve info for those shots but that would be OK.
One thought that would take more work would be to add the coils a small precise distance from the probe positions on your .22 test barrel.
Looks like for the shorter distances you need to pick the trigger point to about 5 micro-sec. When you expand the timescale on the scope, is that doable?
This is all great stuff, thanks for doing this.
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Stan, I like those ideas and will give them a try, in particular, about verifying exactly when the magnet leaves the muzzle.
The trigger point can be adjusted on the scope, but the scope is constantly storing data until the trigger is triggered, LOL. So even if the trigger voltage has to be set a little high to avoid false triggering, the before-trigger data will be displayed on the graph. Is that what you were asking about? Sorry, but I don't know much of the proper terminology for o-scopes.
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Lloyd, Sorry bad wording on my part. My question was whether the trace produced by the pellet exciting the coils has a sharp enough peak to allow resolving down to about 5 micro-seconds
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Stan, I am not sure but I am about to find out. ;)
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The bounce on the valve stem indicator could be the hammer hitting the stem after the valve closes but not enough energy to open it.
So its frame harmonics probably?
Nice looking data.
Marko
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Hi Marko, Thank you for the comments. The mechanical setup for the valve stem, because of its mass, might be introducing some false movement, or lag, or over-travel, that is being recorded. But I am not sure. Also, right now, the air pressure is only 400 psi, so the hammer strike is opening the valve much farther than if the air pressure was higher. I need to experiment more to figure out what is actually happening.
Hi Stan, The recording time on the scope is 4000 samples, and the sampling frequency is variable (but not user-adjustable) based on the time scale chosen. And I am just figuring this out, LOL. It appears that if the time scale is adjusted to 0.2msec per division, that the sampling frequency produces a recording length of about 8msec. At 4000 samples, that is 2microsec per sample. And that is the resolution that you were asking about, I think.
What I need to figure out now is how to set the horizontal slider control on the scope that determines how much pre-trigger data is recorded along with the post-trigger data. Right now, I am getting too much pre-trigger data such that only the second half of the recording is the actual post-trigger event. So basically, the first half of the recording is useless. It is just something I haven't set correctly and I need to improvise a fake trigger to experiment with because firing a shot multiple times to learn how to set the trigger isn't practical.
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Lloyd,
The sampling resolution limit is one part of it. The other part is whether when you zoom in on the signal, does it have a distinct feature or is it a lumpy plateau with some noise on it, making it hard to define a specific signal timing event. It is hard to tell from the 0.5 msec trace you posted. That is something slot dimensions and coil characteristics may optimize.
For optimizing your use of the limited sample size, a couple of questions:
1. Can you set the slider so that all 4000 samples are pre-trigger and then trigger on muzzle exit, using a probe wire? Maybe combine it with your valve potentiometer in a voltage divider?
2. For experimenting with the scope settings, you could use plain pellets and just use the muzzle exit probe wire or broken wire as the trigger.
Great work. I really like the innovative measurement being applied to AG testing
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Stan, Those are some excellent ideas and I will try them out, hopefully tonight. I am still building a climate controlled store age room in the attic, so I only get computer time when I come down to take a break. The progress on the room is going well and it is the kind of project I enjoy, so everything else is taking a back seat for the next few days.
Back to the resolution of the recording, from the little experimenting I have done, it seems that you can zoom in a couple of clicks and the sharpness improves, but after that, there is no more "hidden" accuracy. The pictures of the scope screen that I am posting are just screen captures via Microsoft Paint, so the resolution looks worse in the pictures than it actually is. I know there must be a way to save the recordings, but I haven't gotten there yet. Too bad we are on opposite sides of the country because I bet a one hour visit by you or onee of the other electronics gurus would yield solutions to all the learning inadequacies on my end.
Lloyd
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One thing that would be interesting to measure is the time that is between valve opening and start of pellet movement.
Most of the gains can be made at the get go, somewhere in the first quarter of the barrel where acceleration is greatest.
I would space out coils so that there are many at the start.
Just a thought.
Marko
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Keeping with the cautionary note of creeping up on the task, I managed to successfully record some 400psi, 350 fps shots. They all went well, but a few tweaks will be done before the velocity is bumped up.
I won't be able to give full documentation until later tonight, but here are pics of the test setup.
This is the overall setup.
The .25 cal Disco-based gun is strapped into place. It shoots thru the birdhouse muffler. The metal rod above the gun barrel is an alignment bar for the hole thru the birdhouse. If the gun's barrel is parallel to that rod, the pellet should pass thru without hitting anything. Beyond the birdhouse is the chronograph with light bar above it, and then the bullet trap. For this exercise a 6x6x6 open-fronted cardboard box is filled with grocery bags, and placed in front of the normal trap, to catch the fired pellet. To the right side is the trusty laptop with the PC based o-scope program ready to go. It has 2 channels. One channel records the valve stem movement, and the other channel records the pellet/magnet movement past the sensor coils.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Setup-3-1a_zpscwxthgg5.jpg)
Here is the pick-up for the valve stem movement. As Rube Goldbergish as it looks, it is about the 20th attempt at a reliable (ha ha) valve stem movement pickup. But, it does work! Sticking out of the window in the side of the air tube is a 1/4" steel rod that is threaded ontothe end of a special valve stem. It travels in unison with the valve stem as a single entity. Sticking out of the top of that valve stem bar is a short length of .050 hex key. The hex key pivots where the little set screw is visible, and the end of the hex key swings an arc across a portion of carbon track from a trim pot. The white bead on the end of the hex key is a teflon ring that helps the wiper maintain a proper pressure ont eh carbon throughout its swing of travel. There is about a 3 to 1 travel increase ratio of the wiper across the carbon track. A 1-1/2 volt battery and a resistors plus the carbon track, make a voltage divider circuit to provide a voltage to the o-scope that is proportional to the travel of the valve stem. There is a torsion spring wound around the hex key pivot point to remove any backlash from the setup. The voltage seems to track well with the movement, although I am sure there is some lag and overshoot at the extremes of travel. But again, it does work.
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Setup-3-3a_zpspjktole9.jpg)
This is the front end of the barrel with the 3 coils in place in grooves on the barrel. More grooves and coils will be added after the bugs from these are worked out. The 3 coils are wired in series and connected to the second channel on the o-scope. They work well, but the inter-connecting wiring of the coils needs to be done in a neater manner to reduce unwanted indications on the scope. But, it works, too. The patient is ready for the experiment to begin. :(
(http://i226.photobucket.com/albums/dd79/loyd500/Velocity%20GTA/Setup-3-2a_zpsdtrfj2rj.jpg)
REAL results tonight. 8)
Lloyd
Lloyd use this software to screen record and document its the best out there. https://www.youtube.com/watch?v=ObiYYSgvmmk (https://www.youtube.com/watch?v=ObiYYSgvmmk)
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Travis, That looks a whole lot better for capturing images than what I've been doing. Thanks you! I will give it a try.
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Travis, That looks a whole lot better for capturing images than what I've been doing. Thanks you! I will give it a try.
For me Lloyd this thread is pure bliss and I wish I had time to experiment more and get back to doing what I love(R&D) but Im just swamped with gun builds and working on a new valve design (SS valve 2) but nothing like what your doing, Im jealous and proud of your efforts at the same time. Back to my cave LOL
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Travis,
Thank you, that means a lot. It is great to be surrounded by like minded people, and I mean all of us, who can share this passion with each other even though we are thousands of miles apart.
Did you see the you tube video by MrTeslonian with a vacuum pump on the muzzle of a Texan? 2900 fps? Darn, looks like another project.
Lloyd
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the you tube video by MrTeslonian with a vacuum pump on the muzzle of a Texan? 2900 fps?
Any time the claimed energy output exceeds the energy input.... I have my doubts.... ::)
Bob
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the you tube video by MrTeslonian with a vacuum pump on the muzzle of a Texan? 2900 fps?
Any time the claimed energy output exceeds the energy input.... I have my doubts.... ::)
Bob
Bob, I agree, but I am still very curious about what he has going on there.
His fastest shot was 2904fps, .45 cal, 144gn, assume 38" barrel and 4500 psi. If he pulled a vacuum on the muzzle, that would make the relative pressure 4515psi.
You've presented your math, which I agree with, but I'd like to present a different calculation that leads us to the same conclusion (confusion?)
So here is my math that calculates the absolute maximum theoretical velocity if there are zero losses of system limitations.
Force on bullet = .159 sqin x 4515 psi = 718 pounds force
mass of the 144 gn bullet = (144 gns/7000 gns/lb)/32.174 ft/s/s = .000639 slugs
barrel length is 38/12 = 3.167 feet
a=F/m a=718/.000639 = 1,123,630 ft/sec/sec
Final velocity (given a zero starting velocity) = square root of (2 x a x d)
V = sqrt (2 x 1,123,630 x 3.167 ) = 2,668 ft/sec
The absolute maximum velocity I calculate, given zero losses, is 2,668 fps, but he got 2,904 fps.
Hmmm. I must be missing something. I would love for his velocities to be real because that would mean there is more to learn.
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Yeah, but what about the mass of the air used to accelerate the bullet?.... Include that and the velocity goes wayyyyyyyy down....
Bob
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Yeah, but what about the mass of the air used to accelerate the bullet?.... Include that and the velocity goes wayyyyyyyy down....
Bob
Agreed it falls off the map. If you calculate the needed vacuum to accelerate the bullet even a tiny bit its huge and with his equipment its not possible I call this MYTH busted.
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Darn, do i have to find a vacuum pump? >:(
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Darn, do i have to find a vacuum pump? >:(
I have and AC vacuum pump but that’s not going to be good enough but I’ll send it to you if you need it.
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Darn, do i have to find a vacuum pump? >:(
I have and AC vacuum pump but that’s not going to be good enough but I’ll send it to you if you need it.
A 2 stage 7cfm vacuum pump should be more than adaquite it will pull a 20 ton A/C system down to 50 microns in about 2 hours.
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Heres some more math.
38" barrel 45 cal = 99 cc barrel volume
Full barrel volume at 4500 psi is roughly 35 grams of air.
35 grams of air has 10570 fpe ar that psi.
28 percent of 10570 is 2959 fpe.....
His obtained figure is 25% of what that barrel length could theoretically do at that psi
So in theory it's possible?
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Darn, do i have to find a vacuum pump? >:(
I have and AC vacuum pump but that’s not going to be good enough but I’ll send it to you if you need it.
A 2 stage 7cfm vacuum pump should be more than adaquite it will pull a 20 ton A/C system down to 50 microns in about 2 hours.
Its and automotive AC pump
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I also want to add I'm skeptical of the 2904 fps with 144 gr out of a Texan but wanted to present a different theoretical view point, however the muzzle blast difference between 700 and 2904 fps want much more negligible than what I'd expect, an aluminum chunk from his vacuum seal weighing next to nothing moving those speeds seems more likely than him achieving what hes leading people into believe. Leaving out any chronograph errors still makes the 2904 shot impressive regardless of what was recorded..
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More math for you....
Bore area = 0.458^2 x PI/4 = 0.165 in^2 …. x Pressure = 4500 psi.... Force = 742 lbs....
Barrel length = 38" (including 4" for the muzzle brake) / 12 = 3.167 ft....
Maximum theoretical FPE = 742 x 3.167 = 2350 FPE....
That must accelerate not only the 144 gr. roundball, but also the mass of air in the barrel....
Air density at 4500 psi = 331 kg/m^3 = 83.7 gr/in^3.... Barrel volume is 0.165 x 38 = 6.27 CI.... Mass of air = 83.7 x 6.27 = 525 gr....
So the air in the barrel is over 3.6 times the weight of the roundball…. The total energy available to accelerate both, plus overcome all other losses is 2350 FPE.... Tell me again how anything close to that FPE can end up in the roundball?....
He claimed 2904 fps with 144 gr. = 2696 FPE.... more than the maximum possible from F=ma.... Not possible....
Bob
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Lloyd,
I was doing a little web searching on the speed measurement and came across this https://magnetospeed.com/pages/how-it-works (https://magnetospeed.com/pages/how-it-works) The comments on Amazon imply people get it to work with AG pellets https://www.amazon.com/ask/questions/Tx39M6R6R8DVSAT/ref=ask_ql_ql_al_hza (https://www.amazon.com/ask/questions/Tx39M6R6R8DVSAT/ref=ask_ql_ql_al_hza). Here is a discussion that started with how to get an Arduino to read fast enough but drifted into making magnet based sensors for lead pellet measurement https://forum.arduino.cc/index.php?topic=473669.0 (https://forum.arduino.cc/index.php?topic=473669.0).
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2900 fps through a 38 inch barrel would be terminal at muzzle in under 3ms without question..which we can calculate the flow potential of a full bore .45 port...which I estimate at 13.3~ g/ms. To flow the required 35 grams of air you would need 2.6 ms of full flow valve dwell to achieve the release of 35 grams of air from a .45" port at 4500 psi.
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That makes perfect sense.... When a PCP is operating at maximum velocity the valve is open until the pellet exits the muzzle.... That is why the efficiency is so low, on the order of 0.3-0.5 FPE/CI with normal weight bullets and velocities.... With my 2092 fps shot with a 6mm Airsoft BB weighing 1.8 gr. it was about 0.05 FPE/CI.... :o
Bob
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the you tube video by MrTeslonian with a vacuum pump on the muzzle of a Texan? 2900 fps?
Any time the claimed energy output exceeds the energy input.... I have my doubts.... ::)
Bob
Exactly! Perpetual motion time machine that happens to expel projectiles.
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En.wikipedia.org/wiki/vacuum_engineering is quite an interesting read, although I dont give merit into introducing vacuum into the consumer market I do think it may warrant testing with theoretical maximum velocities. I was not aware particle accelerators make use of ultrahigh vacuum systems to achieve their velocities.
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En.wikipedia.org/wiki/vacuum_engineering is quite an interesting read, although I dont give merit into introducing vacuum into the consumer market I do think it may warrant testing with theoretical maximum velocities. I was not aware particle accelerators make use of ultrahigh vacuum systems to achieve their velocities.
Atmospheric pressure is only about 14.7psi. When dealing with HPA, that 14.7psi is mostly lost in the noise. In a particle accelerator, I suspect that they would want a vacuum in order to remove all traces of molecules that the particles might collide with. A pellet will hardly be disturbed when it plows through a low density (14.7psi) air column.
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I wonder what his Al foil chaff does to the chrony measurements
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Very well could be what the Chrony is picking up....
Bob
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Yeah, debris and vapor.
Marko
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While I concur it's much more likely some other than a 144 gr projectile triggered the reading ...its still impressive..even more so if it's a piece of aluminum foil ejecting with only inches to accelerate...I dont think I can trigger my chronograph to read my dry fires however...or wouldnt we all be here trying to measure who has the fastest air parcel? Idk..
Lloyd's and Bob's experiments with high velocity recordings from a pcp utilize the lightest ammo feasibly possible to keep the mass under the average weight of air. If we could use chronographs to read air parcels would we just use the air parcel itself as a projectile to verify our data?
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Mike, you CAN get erroneous velocity reading (way faster than true) if you are too close to the Chrony…. I don't know if it is a plume of water vapour, or something in the airstream triggering the Chrony, but when developing my .457 Hayabusa I had some readings of 1300 fps with a 336 gr. bullet that only does 820ish....
Those shots I made with the 1.8 gr. Airsoft BB in my 6mm PCP, it was basically surfing along the front of the air column.... The FPE dropped from 173 FPE with a 73 gr. bullet to 17 FPE with the 1.8 gr BB.... Both shots at 4200 psi, no changes to the tune, just changed the projectile.... BTW, I got a 3 shot average of 2092, with an ES of only about 10 fps, so the Chrony wasn't lying....
Bob
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the you tube video by MrTeslonian with a vacuum pump on the muzzle of a Texan? 2900 fps?
Any time the claimed energy output exceeds the energy input.... I have my doubts.... ::)
Bob
Exactly! Perpetual motion time machine that happens to expel projectiles.
++++++++++++++++++++++++++++++++++
I watched 2 or 3 of this guys videos about a year ago. A complete waste of time in my opinion. I cringed when I saw his channel name here.
Steve
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He took around 4 shots in fairly short time with minimal light change. Not trying to give the guy credit but let's say 2700 fps was his average over 3 shots...that's traveling from sensor 1 to sensor 2 in .37ms...still interesting whatever its picking up..
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Sounds like he’s getting the famiilure double reading caused by 1 light source normally or poor lighting. I’d bet he’s half of the actual reading. Double speed readings can be very consistent I have had it happen myself
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Just like dirt e harry in his texan advertising, he got some way off readings from stock tex.
Marko
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If we assume double readings then that suggests the vacuum still took the 700 fps moving projectile up to 1400~ which still doesn't give a clear answer but more within reason..I hope Lloyd gets around to debunking or confirming the benefit of adding vacuum to the barrel during the shot, and if there is benefit..how much?
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The Myth Busters TV show did a segment on a ping pong ball shooting air powered AG and in their experiment they were able to achieve improved velocities with with a vacuum in their barrel. I don't know if that would make a major difference with a more aerodynamic projectile.
On the other hand I'm not a card carrying member of the "Geek Squad" just a curious sideline occasional commenter ;D ;D
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The Myth Busters TV show did a segment on a ping pong ball shooting air powered AG and in their experiment they were able to achieve improved velocities with with a vacuum in their barrel. I don't know if that would make a major difference with a more aerodynamic projectile.
This guy got speeds in excess of Mach 1 with his ping pong ball setup using an evacuated barrel and only modest pressure in the order of 80 psi in his air chamber:
https://www.youtube.com/watch?v=rF9HuU7vMpg (https://www.youtube.com/watch?v=rF9HuU7vMpg)
Impressive stuff:
(https://i.imgur.com/keAz3XV.gif)
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;) On the Myth Busters segment they only measured the projectile speed after it exited the barrel
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;) On the Myth Busters segment they only measured the projectile speed after it exited the barrel
The Myth Busters also miss stuff...
cheers,
Douglas
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We aren't talking a low-mass, large diameter projectile here.... Look at the SD of a .45 cal lead ball compared to that of a ping-pong ball.... Comparing apples and lizards.... ::)
Removing the mass of the air from the barrel of a ping-pong ball cannon, and adding 15 psi to 80 (a 19% increase in pressure differential and therefore force)…. is a whole lot difference to removing the mass of air from the barrel of a Texan and increasing the pressure differential by 0.3%.... ;)
Bob
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Removing the mass of the air from the barrel of a ping-pong ball cannon, and adding 15 psi to 80 (a 19% increase in pressure differential and therefore force)…. is a whole lot difference to removing the mass of air from the barrel of a Texan and increasing the pressure differential by 0.3%.... ;)
No doubt about that, but my understanding is that it has more to do with removing the air drag that the pressure differential, not sure if this has been mentioned before as I have not read through the whole thread.
If we look at Light Gas Guns (https://ares.jsc.nasa.gov/orbital_debris/hvit/impact/light-gas-guns.html) used for hypervelocity impact testing, they use a powder charge to compress a cylinder of hydrogen or similar light gas to hundreds of thousands of pounds of pressure, and yet they still bother to evacuate the barrel even though the pressure differential is infinitesimal.
There are other reasons to do this of course, if you're simulating an impact in outer space then you want it to happen in a vacuum to be as close as possible to the actual conditions. Also at velocities of 7 kilometers per second (almost 23000 fps :o ) then your projectile heating up with air friction also becomes an issue.
I did however dig up a report on "TWO STAGE LIGHT-GAS GUN INSTALLATION FOR HYPERVELOCITY IMPACT STUDIES" (https://apps.dtic.mil/dtic/tr/fulltext/u2/766810.pdf) and it clearly states on page 6 of the report (page 14 of the pdf):
The launch tube is evacuated to minimize air resistance during acceleration of the projectile.
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Ping bong ball is a whole different matter, look at the surface area for the pressure to push on considering the weight. Remove the atmospheric pressure from one side you have a lot of energy right there.
And hyper velocity studies is another thing entirely, they want all the speed they can get and effort or money is not the problem. Velocity is the key there, and air resistance becomes a major effect at those speeds.
Marko
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:D My mentioning the Ping Pong ball AG was only because they did use a vacuum in the front of the ball to help achieve higher FPS not to compare apples to walnuts
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But it was a good idea, unfortunately for us the heavy and small projectile kind of kills the idea.
Marko
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Light gas guns, which use an explosive charge to fire a piston to Adiabatically compress a light gas (H or He) and achieve velocities up to Mach 5 of that gas at those elevated temperatures and pressures are NOT a PCP.... This thread has been sidetracked there before, please start a thread on light gas guns if you wish to discuss them.... The "Back Room" might be a suitable Gate?....
The ability to accelerate a projectile with a limited pressure differential is closely tied to the Sectional Density.... The SD of a 144 gr. .457 cal roundball is 0.098.... A ping-pong ball weighs 2.7 grams (41.7 gr.) and has a diameter (caliber) of 40 mm (1.57")…. Therefore the SD is 0.0024.... making it 41 times easier to accelerate.... Without the mass of the air in front of it, a pressure differential of just 110 psi will provide the same "g" of acceleration as would 4500 psi in the Texan.... :o …. No wonder ping-pong ball cannons, with a barrel many feet long, can drive a ping-pong ball supersonic.... 8)
Bob
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This thread has been sidetracked there before, please start a thread on light gas guns if you wish to discuss them...
That was not my intention, I just wanted to make the point that they are "prior art" in the field of gas based acceleration and they incorporate evacuated barrels not for the purposes of creating a pressure differential but to prevent acceleration being limited by the atmosphere.
Since the vacuum apparatus adds a complex and expensive element to the device, then including it must mean that the dividends are significant in terms of increased acceleration, beyond what is gained by simply removing the mass of the air in the barrel.
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With AG velocities there is absolutely very small effect due to air in front of the projectile. Maybe in light gas guns their purpose of vacuuming is decreasing barrel stress to minimum yet I haven't seen nor didn't even know it has done. Still atmospheric air pressure is there right after muzzle.
Anyway that video claims barrel vacuuming produces 13.6 times the energy. That's well enough to me to skip the whole statement as BS. Actually I would be sceptic with 10% increase.
Besides, this guy is an expert in vacuuming: ;D
https://www.youtube.com/watch?v=ERNlSDqeiTg (https://www.youtube.com/watch?v=ERNlSDqeiTg)
I'm a bit disappointed for not to see the result of that experiment.
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Anyway that video claims barrel vacuuming produces 13.6 times the energy. That's well enough to me to skip the whole statement as BS.
If that's what's being claimed then the statement can be dismissed out of hand.
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I think we all know how to do it. Place your muzzle touching chono and there it is, a world record of a kind you would like to achieve. No matter of error message, it is not that important when we are doing a WR. :P
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I was digging though some patents and found one from 1891 (https://patentimages.storage.googleapis.com/a6/df/f4/b4de0262ede848/US458329.pdf) for a "valveless" pneumatic launcher where the projectile is locked in the barrel then released by a lever mechanism:
(https://i.imgur.com/1SagyG7.png)
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Lloyd's 2162 fps shot used such a system.... The projectile had a notch, released by a cam (rod with a flat, turned to fire)…. Full pressure on the base of the bullet before, during and after release.... Still, I got within 70 fps of him with a conventional PCP firing a 1.8 gr. airsoft BB....
Bob
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Lloyd's 2162 fps shot used such a system
That's why I posted it :)
Still, I got within 70 fps of him with a conventional PCP firing a 1.8 gr. airsoft BB....
When you consider how quickly such a light projectile accelerates, that's no mean feat and a testament to a hammer valve's rapid opening time.
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Yeah, with such a light projectile, basically the plastic BB is just surfing along the front of the air column.... Air at 4050 psi (the average pressure during the shot) weighs about 77 gr. per CI.... That 6mm x 29" long barrel is 1.34 CI, so that air had a mass of about 103 gr. out of a total of about 105 gr. with the BB.... :o …. Most of the energy (95% or so) went into accelerating the air....
The FPE in the BB was only about 17.5, compared to 175 FPE with the same gun shooting a 73 gr. bullet....
Bob
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comparing apples to lizards (roaring laughter)
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I have not read 18+ pages of replies so maybe this has been mentioned!
Has anyone googled: Light gas gun?
Not 100% what OP did but none the less an compressed gas gun that reaches @20000fps (yes twenty thousand!)
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Yes, it was mentioned many times.... A light gas gun is not a PCP.... It uses an explosion to drive a piston to compress and heat Hydrogen or Helium.... compared to a PCP that starts with a pressure reservoir at room temperature and the pressure drops as the gas expands and cools.... It is a completely different situation....
Bob
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LOL ... been a spell and just had to try it again.
This go around my .22 caliber Warp with 24" barrel ( 6 groove HW with no choke )
Manufactured an Acetal AF pellet at .218" that weighted 1.4 grains.
Fired @ 1 foot from the first chrony screen ( barrel is shrouded so a LOT of the pulse energy absorbed within it so it should not get a reading on air or debris following the pellet out )
Fired at 2200 psi ( Air ) the little pellet sailed threw the chrony at 1790 fps
* This gun as set fires @ 25 grains of lead @ 970 fps making 60 ft-lbs.
Just giggles (https://www.bmwlt.com/forums/images/smilies/snork.gif)
Scott S
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Yep, it's great for the giggle factor.... much like I did with my Disco.... 8)
Bob
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Hey I'm new...
... so please forgive my ignorance, if so.
I think also there might be a mistake in OP post.
Aren't we overthinking this?
1. a=f/m
2. t=sqrt (2d/a)
3. v=at
4. e=0.5mv^2
thus, substituting only for var a in equation 3:
v=at:
v=(f/m)(sqrt ((2d)/(f/m)))
then substituting var v in equation 4:
e=0.5m((f/m)(sqrt ((2d)/(f/m))))^2
or, simplified in Wolfram|Alpha, because I'm lazy.
e=df
in other words, mass has no effect on muzzle energy, and barrel length linearly correlates:
thus, in caveman terms *gruffly* : heavy rock go slow, light rock go fast, power same
also, estimating energy, as the final equation shows, is very simple
e = (barrel length in feet)(psi acting)
so 1 ft x 3000 pounds per square inch x pi r^2 on the 50 cal = 1x3000x0.196 = 588.8 ft lbs.
THUS: a 1/2 inch diameter slug, with 3ksi pushing it, REGARDLESS of mass, will achieve ~580 ft lbs, regardless of mass, regardless of mass... see caveman terms.
Also you should be able to pull 9mm data in 2 sufficiently distinct masses, like 100 and 150gr, but with identical powders/charge loads, and see the same energy despite delta v.
looks like OP missed the 0.5 on mv^2 for m.e., its 0.5, which explains why he estimated efficiency at 50% with question marks.
efficiency in terms of isolated m.e. should be high, because we're not talking about shots-per-bottle or wasted gas coming out end of barrel... just internal ballistics or basically pressure/friction.
Hope I'm right, hope that helps.
if faster is your goal, pressure, longer, or lighter will help.
if energy is your goal, mass change will NOT help, pressure or longer does.
a side note from gun design, and for whatever reason, is that mass seems exponentially correlated to impulse of felt recoil, so trading mass for speed is good for max energy/charge without hurting shoulder. (12g slugs hurts shoulder more than 308, despite similar energy). you would think spreading out the joules over time would hurt shoulder less, but the opposite seems true.
I know gun guys chase fps for simplicity of ignoring holdovers, so deciding on design depends I think mostly on absolute range and terminal ballistic goals.
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Your calculations for the maximum FPE agree exactly with Lloyd's.... For the .50 cal (area 0.196 in^2) with a 1 ft. barrel with 3000 psi you get 588 FPE and Lloyd, with 3500 psi, got 686 FPE.... the only difference being the pressure used....
The reason for the "50%?" remark at the end of the first post is that REAL PCPs have many losses, so can never approach the theoretical maximum, there was no "missed 0.5 factor".... For a start, the bullet is not the only mass being accelerated, the air itself has significant mass.... That 1 ft. long .50 cal barrel-full of 3000 psi air would weigh 142 grains.... in a 24" barrel, twice that, or about the same weight as the bullet.... In addition, the maximum FPE would require constant pressure over the entire 1 ft. of barrel travel, which would require an infinite reservoir volume.... When the reservoir is of limited volume, you get a pressure drop during the shot, and then the pressure drops even more from adiabatic cooling.... It also ignores barrel friction and other losses.... In fact, only the very best of our PCPs even approach 50% of the theoretical FPE.... most fall far short....
Bob
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...THUS: a 1/2 inch diameter slug, with 3ksi pushing it, REGARDLESS of mass, will achieve ~580 ft lbs, regardless of mass, regardless of mass... see caveman terms.
...
That sort of works up to a point. But the air itself has mass. When trying for very high velocities, the air mass required to propel the pellet becomes a significant part of the equation. And there are limitations in the rate of flow and rate of expansion for air at room temperature.
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...THUS: a 1/2 inch diameter slug, with 3ksi pushing it, REGARDLESS of mass, will achieve ~580 ft lbs, regardless of mass, regardless of mass... see caveman terms.
...
That sort of works up to a point. But the air itself has mass. When trying for very high velocities, the air mass required to propel the pellet becomes a significant part of the equation. And there are limitations in the rate of flow and rate of expansion for air at room temperature.
Noah,
To understand why projectile mass matters; return to reality: With a real airgun, you are stuck with a finite air supply of, where the pressure drops as the projectile accelerates down the barrel. Now; lighter projectiles mean higher acceleration. Higher acceleration to higher velocities mean much more of the system energy is spent accelerating the air in the barrel up to that higher velocity; because Kinetic Energy = V x V x 1/2 X mass.
So, in real PCPs, heavier projectiles are more efficient and carry more energy than light ones, because less energy is wasted accelerating the air column in the barrel behind them. End of story.
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A perfect example is my 6mm PCP.... With a 73.4 gr. lead bullet, and tuned for maximum power, it shoots at 1029 fps, which is 172.6 FPE....With no changes, other than using an airsoft BB which only weighs 1.8 gr. I get 2092 fps, but that is only 17.5 FPE.... Incidently, the theoretical maximum FPE for this gun is (0.243 x 0.243 x PI/4) x 4200 x (28 / 12) = 454 FPE.... A large percentage of the lost FPE (only 38% ended up in the lead bullet, and less than 4% in the plastic one) went into accelerating the 250 cc of 4200 psi air released by the valve, which weighed 78.6 grams, or 1212 grains.... and yes, most of that left the muzzle long after Elvis had left the building....
Bob
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Just curious if anyone with access to welding gases has taken shots with argon (38% denser than air) at the same pressure to see the drop off of FPE, might be able to get an idea of what the average velocity of the gas column is.
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Okay, good, I didn't see the 0.5 on the equation posted, didn't double check the exact numbers.
Re air mass, I remember years ago some science on paintball markers with ported barrels, the porting was found to substantively reduce pressure and turbulence in front of the ball, and acceleration actually increased, even compared to the exact barrel prior to drilling holes through it.
The point on e=df is just to bring it down to earth for considering that its all linear.
Extrapolating to eliminate air acceleration in favor of max M.E. per charge e just means increasing mass, perhaps to the point of being a harpoon gun...
Can someone make a heavy "harpoon" and measure M.E. compared to lead?
I'm curious in seeing it taken to the limit.
Barrel length is also linearly equivalent to force... could double length.
Also: Bumping pressure to 10ksi should be pretty easy within the gun.
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Eventually, long barrels become too awkward to deal with.... High powered PCPs are typically running 28" to 34" barrels....
Using higher pressures, while technically possible, means heavier (stronger) guns, and difficulty finding a way to fill them.... This thread is not so much about how fast you can go, but what those limits are, based on barrel volume times pressure.... If you haven't checked the math already, you can use the barrel volume, since a .50 cal barrel a foot long has the same potential FPE as a .25 cal barrel 4 feet long.... so you can simply use this formula for the theoretical maximum FPE....
Maximum FPE = Barrel Volume (cu.in) x Pressure (psi) / 12 (in/ft)
In reality, approaching half that is difficult, so I often use a formula to predict a "lofty goal" for PCPs, with the proviso that the weight of the bullet is half the FPE goal (so the velocity is 950 fps)....
Lofty Goal FPE = Barrel Volume (cu.in) x Pressure (psi) / 24
I have never quite made it, I usually need about a 10% longer barrel, or 10% higher pressure, to get there.... If you use a heavier bullet, getting to, or even surpassing, that 50% goal is easier to accomplish (but still rarely done)…. Most production PCPs don't even reach half of the "lofty goal" FPE....
Bob
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Eventually, long barrels become too awkward to deal with.... High powered PCPs are typically running 28" to 34" barrels....
Using higher pressures, while technically possible, means heavier (stronger) guns, and difficulty finding a way to fill them....
A simple pressure booster is just a couple rods and tubes, it can be machined from steel and integrated into the action.
We're talking about a handful of in^3?
It might be a 4 lbs piston & volume assembly... although I suppose you might as well have it charge via battery at that point.
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I suppose, if what you are talking about is what is possible vs practical.... then just about anything is possible.... Don't forget, if you only have a reservoir consisting of a "handful of in^3", you will get a significant pressure drop during the shot.... particularly if you are in search of high FPE, which means lots of barrel volume for the reservoir air to expand into.... For example, for a .50 cal with a 24" barrel, starting with 10,000 psi, to maintain 9,000 psi at the muzzle, you will need a reservoir of about 111 CI (1820 cc).... The VanDerWaals effect rears its ugly head above 3000 psi, and by the time you get to 10,000 psi, dropping to 9,000 only reduces the air density by 4% instead of 10%.... This requires reservoirs to be more than twice as large as predicted by Boyle's Law for a given pressure drop.... This also affects shot count, of course, something we already see when using 4500 psi instead of 3000.... the shot count is noticeably less than you would calculate using Boyle's law....
May I ask if you have ever built a PCP, or a pressure booster?.... If not, then doing that to understand what is "simple" or even practical might be a good idea.... If you have, then please share some of your projects and results, we would all love to see them....
A much easier way to greatly increase the FPE of a given PCP is to use Helium instead of air.... Since the primary power loss is from accelerating the gas, using a gas that is 1/7th the density has a huge advantage.... For a PCP shooting a bullet at about 950 fps, Helium will usually drive that same bullet Supersonic, with about a 50% increase in FPE.... The gains in FPE are even greater for lighter bullets, because the losses with air are higher, so the FPE gains shifting to Helium are larger....
Bob
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...
Also: Bumping pressure to 10ksi should be pretty easy within the gun.
10ksi air?
At some point, compressability of a supercritical fluid becomes nearly flat, almost non-existent.
Why not 100ksi vs 50ksi? No benefit, because at those pressures, it would make zero difference in FPE.
For air, I wouldn't go above 6000psi (for a number of reasons).
https://www.researchgate.net/figure/The-temperature-pressure-phase-diagram-for-nitrogen_fig1_315888614 (https://www.researchgate.net/figure/The-temperature-pressure-phase-diagram-for-nitrogen_fig1_315888614)
(https://www.researchgate.net/profile/Wieslaw_Fracz/publication/315888614/figure/fig1/AS:570481125801984@1513024707771/The-temperature-pressure-phase-diagram-for-nitrogen.png)
It sounds like you might be talking about compressing air on the fly after pulling the trigger), with a booster. If so, then you are really talking about an air powered spring gun. Temperatures of the propelling gas would be higher than room temperature, so velocity limits would also be higher.
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Not sure I understand, Scott.... The critical pressure for air is 550 psi.... above that we are dealing with a supercritical fluid anyways, providing the temperature is above -140*C.... Yes, eventually only a small change in density requires a huge change in pressure.... no doubt about that.... and VanDerWaals equations deal with that.... Here is a very good calculator showing the relationship between pressure and density for air, up to 1000 bar (14,500 psi)....
https://www.peacesoftware.de/einigewerte/luft_e.html (https://www.peacesoftware.de/einigewerte/luft_e.html)
As an example, a 100% increase in pressure from 500 bar to 1000 bar only requires a 37% increase in air density....
Bob
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Not sure I understand, Scott.... The critical pressure for air is 550 psi.... above that we are dealing with a supercritical fluid anyways, providing the temperature is above -140*C.... Yes, eventually only a small change in density requires a huge change in pressure.... no doubt about that.... and VanDerWaals equations deal with that.... Here is a very good calculator showing the relationship between pressure and density for air, up to 1000 bar (14,500 psi)....
https://www.peacesoftware.de/einigewerte/luft_e.html (https://www.peacesoftware.de/einigewerte/luft_e.html)
As an example, a 100% increase in pressure from 500 bar to 1000 bar only requires a 37% increase in air density....
Bob
"As an example, a 100% increase in pressure from 500 bar to 1000 bar only requires a 37% increase in air density...."
It looks like you understand the problem -
As you increase the pressure of a supercritical fluid, the change in density/pressure becomes less and less. At some point, the increase in pressure produces no more usable energy in the air. It behaves more like a liquid as far as increasing pressure.
I guess 10ksi is doable (though not really easy). At that pressure, any additional gains are only 1/2 what you would expect from an ideal gas.
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so 6000 psi is an ideal working pressure if you can compress it .. very interesting .
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In my opinion, 6000 psi is the maximum pressure I would consider.... but the losses in shot count are already significant.... In practical terms, with current portable bottles at 4500 psi, anything much over 3600 psi leave you with difficulty filling in the field.... unless you use a portable compressor or booster.... Air boosters, while they can be made capable of over 4500 psi, waste far more air than they can cram into a tank or gun....
Bob
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yes.. i was thinking in terms of msp/ssp designs ... the one working design over 6000 psi was 10 yrs ago on the green forum by a brillant designer named Ron.. It was a dual stage MSP pistol.. The main issue as i recall was melting seals on the way to 6000
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In my opinion, 6000 psi is the maximum pressure I would consider.... but the losses in shot count are already significant.... In practical terms, with current portable bottles at 4500 psi, anything much over 3600 psi leave you with difficulty filling in the field.... unless you use a portable compressor or booster.... Air boosters, while they can be made capable of over 4500 psi, waste far more air than they can cram into a tank or gun....
Bob
The thread is discussing several variables simultaneously... so everything I've said could be right or wrong depending on the project goals.
Efficiency, practicality, capacity, fps, energy, etc.
But for max-fps I'm glad we decided on small-caliber miniature electric 10ksi booster. ;)
And you can feed it helium. 8)
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Can't wait until you build one.... 8)
Bob
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Eventually, long barrels become too awkward to deal with.... High powered PCPs are typically running 28" to 34" barrels....
Using higher pressures, while technically possible, means heavier (stronger) guns, and difficulty finding a way to fill them....
A simple pressure booster is just a couple rods and tubes, it can be machined from steel and integrated into the action.
We're talking about a handful of in^3?
It might be a 4 lbs piston & volume assembly... although I suppose you might as well have it charge via battery at that point.
Topic of thread:
"Theoretical Maximum Velocity in a PCP"
If it involves adiabatic compression and expansion, it is not a pre-charged gun. You are really talking about a piston gun, not a PCP. Many of the limiting factors for a true PCP will not apply to a piston gun.
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I think Noah is talking about using a (4 lb.) booster pump, mounted on/in the gun, to raise the pressure in the reservoir to 10 Ksi…. He referred to only having to compress a "handful of in^3s", which is why I pointed out the need for a large reservoir to prevent severe pressure loss during the shot.... Perhaps he can explain whether that is what he means (in which case it is a PCP)…. or if the compression piston is driven by expanding air DURING the shot, in which case you are correct, it is an "air driven boosted springer", using adiabatic compression of the firing air, and not a PCP at all.... They operate under quite different conditions....
Bob
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I think Noah is talking about using a (4 lb.) booster pump, mounted on/in the gun, to raise the pressure in the reservoir to 10 Ksi…. He referred to only having to compress a "handful of in^3s", which is why I pointed out the need for a large reservoir to prevent severe pressure loss during the shot.... Perhaps he can explain whether that is what he means (in which case it is a PCP)…. or if the compression piston is driven by expanding air DURING the shot, in which case you are correct, it is an "air driven boosted springer", using adiabatic compression of the firing air, and not a PCP at all.... They operate under quite different conditions....
Bob
I think you've got it.
I would just try to work backwards from terminal ballistics goals.
If the goal is FPS you should go as lightweight as possible, whereas if the goal is energy you should go as large bore as possible, yes?
These are more or less opposites, for lets say mass or chamber volume, so its easy to say I'm right or wrong, depending on the project goal.
Originally most people seemed to be discussing energy, but after I mentioned that y'all were overthinking it, the conversation switched back to fps, then someone brought up practicality...
... so there's no consensus on what to solve for.
If the premise of the thread is FPS and definitely NOT energy, efficiency, or practicality, then the math is easier.
Practicality is pretty abstract, and efficiency is more complicated math.
Ignoring those two variables, yes, I was referring to a booster to bump to 10ksi, in the gun or off the gun, prior to the shot... so no reason to charge with air, just plug it in and let it waste air to charge itself to 10ksi.
If you want to solve for energy, then it would get very large and heavy, sure.
Helium and 10ksi are each probably good choices for both energy and fps, but probably not for either practicality and/or efficiency.
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Helium and 10ksi are each probably good choices for both energy and fps, but probably not for either practicality and/or efficiency.
The theoretical maximum velocity in a PCP helium-gun will be significantly higher than that of a PCP air-gun, regardless of how you fill the reservoir.
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Actually, the THEORETICAL maximum FPE is exactly the same, regardless of the gas chosen, because it is only a result of the force applied in lbs. (pressure times area) and the length of the barrel in feet.... What Helium does is allow more of that potential FPE to end up in the bullet, because less is wasted in accelerating the propellant gas....
When it comes to velocity, this is even more true, because you can use a lighter projectile before the mass of the gas becomes a serious factor.... and also the speed of sound in Helium is higher, increasing the efficiency at high velocities....
When it comes to the maximum theoretical FPE, however, they are the same....
Bob
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There is no THEORETICAL maximum FPE limit. Unless we are talking about a particular PCP gun, which is ultimately limited by the size/duration of the valve, and the amount of air that it can deliver. FPE is scalable, FPS is not. A bigger PCP system will always give more FPE, but not more FPS.
True, the FPE of the system is the same, regardless of gas density (helium vs air).
FPE(system) = FPE(gas) + FPE(projectile)
Everything else being equal, the FPE(projectile) is never exactly the same for Helium vs air. For ideal gases, the lighter gas gun will always have slightly more FPE in the projectile. As the mass(gas)/mass(projectile) ratio increases, the difference in projectile FPE increases.
So if you want the FPE(projectile) to be the same for both, the mass(gas)/mass(projectile) ratio must be the same. The air_gun will need a heavier projectile to keep FPE(projectile) the same as in the helium_gun.
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You are correct, of course, FPE is scalable, and depends on pressure and barrel volume.... It is also the thing that we can calculate.... whereas the velocity depends on the weight of the projectile.... For a given FPE, as the mass of the projectile approaches zero, then IN THEORY the velocity approaches infinity, but we all know that is a crock of doo-doo.... because of the mass of the propelling gas.... Ultimately we then enter a circular argument and end up back at Mach 5 for the gas and temperature in question as the ULTIMATE velocity limit at the pressure and temperature in question.... We also know that is NEVER going to happen in a PCP....
Lloyd started this thread trying to quantify what velocity could be calculated for a PCP of specified parameters.... bore, pressure and barrel length.... It then became a discussion about the theoretical maximum FPE for a PCP of specified parameters.... Where it went after that was something we know little about, and cannot quantify in any meaningful way, IMO.... I see no point in personally going there again, I would be just as lost as the last time.... Probably the best arguments about maximum velocity in PCPs are those presented by DomingoT, starting with Reply #281....
https://www.gatewaytoairguns.org/GTA/index.php?topic=94054.280 (https://www.gatewaytoairguns.org/GTA/index.php?topic=94054.280)
He is a Professor of Thermodynamics, and has written several papers on airguns published on ResearchGate.... While the concepts are very complex, he does make it somewhat easier to understand.... ALMOST to where I can get what he is talking about.... :-[
Bob
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.... whereas the velocity depends on the weight of the projectile....
... Mach 5 for the gas and temperature in question as the ULTIMATE velocity limit at the pressure and temperature in question....
I understand that velocity does depend on the "weight" (mass) of the projectile. And less projectile mass will give a higher velocity. But the velocity limit depends on the propelling gas. My research says that it is approximately MACH 2 (relative to the propelling gas being air at 70F), up to 10,000psi. I don't see it getting to MACH 5, even in theory, though I've only taken the calculations to 10ksi for air. Bulk modulus (k) is needed for the determination at higher pressures, and I can't find any k data for air above 10ksi.
(http://www.scotthull.us/photos/Misc/vmaxfps-01.jpg)
PS - I did think the thread was about THEORETICAL maximum velocity, in general for a PCP, and not for a specific PCP - sorry if that's not the case.
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While I think that in practice we will never see Mach 2.... I have my own theory where I can "justify in my mind" the possibility of (1650 fps x 2) = 3300 fps for room temperature air.... When you consider that the speed of sound increases with pressure, our ideas agree at about 6000 psi....
BTW, I notice that the value for "k" peaks at about 5000 psi, any significance to that?.... I also note that the SoS at that pressure is close to the average molecular speed at 20*C of 1650 fps.... Just observations, is all....
However, I am not a thermodynamics expert.... and I certainly won't argue with a guy who lives and breathes it, and teaches it for a living.... ;)
Bob
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BTW, I notice that the value for "k" peaks at about 5000 psi, any significance to that?....
Bob
It means we should start discussing max fps of hydraulic guns