GTA
All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: rsterne on December 13, 2013, 04:09:43 PM
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I've been thinking about this for a while.... What makes sense trying to accomplish with PCPs and what is basically a waste of time tryng to accomplish with any hope of doing so efficiently?.... There are a couple of things that, while they don't present HARD limits, seem to me to be the point where pushing beyond them is prone to a (sometimes severe) loss of efficiency in the energy delivered to the target for the amount of air expended....
1. Velocities over Mach 0.9.... Bullet drag increases drastically once you are over 900-1000 fps.... therefore less FPE delivered downrange....
2. Port velocities over Mach 1.... Shock waves inside the ports drastically increase the drag, dropping the efficiency in FPE/CI....
RE #1, I realized some time ago that the BC of waisted pellets dropped significantly in that velocity range.... What I found out recently was that bullets suffer the same fate.... The velocity at which the drag suddenly increases varies between Mach 0.75 and Mach 0.9 depending on bullet shape.... My point is, why bother trying to go supersonic when our source of power is so limited (compared to a PB) when the bullet tends to give it all back in the first few yards?....
RE #2, this was recently brought into clearer focus by Steve in NC where he set out a formula for "optimum transfer port sizes" based on the point where the flow goes supersonic.... It is based on the idea that if you know the velocity of the air in the barrel (the bullet velocity) you can calculate the velocity in the transfer port, and when it goes supersonic, the drag takes a big jump.... It's not that you CAN'T push past that point, it's just that doing so EFFICIENTLY is extremely difficult.... In a carefully design, axial flow gun (like the Condor) in theory it MAY be possible to design a convergent-divergent nozzle (think rocket nozzle) that would accelerate the airflow past Mach 1.... but until the CFD types figure that out, we are left with trying to keep all of the flow under Mach 1 to keep the efficiency up, IMO.... Steve's formula is very simple:
Port diameter = Caliber (Muzzle Velocity / Speed of Sound) ^0.5 .... ie take the muzzle velocity, divide by 1130 fps, take the square root of the result, and multiply by the bore size.... When the muzzle velocity equals Mach 1, you need ports that are bore-size.... For CO2, use 917 fps, and for Helium use 3200 fps (all at 20*C).... Here are some other values....
Mach 0.8 (904 fps) : Port 90% of caliber
Mach 0.85 (961 fps) : 92% of caliber
Mach 0.9 (1017 fps) : 95% of cailber (valve throat = caliber)
Mach 0.95 (1074 fps) : 98% of caliber
Incidently, in my testing I have found that having the throat slightly (10%) larger in area than the remainder of the ports seems to help the efficiency.... I'm thinking that since the critical part of the flow that starts the pellet acceleration occurs before the 1/4 diameter "curtain limit" on the lift, that larger throat helps keep shock waves from forming at that critical time as the pellet acceleration is beginning.... but I can't prove it.... I digress....
So, let's assume for a moment that we use bore area porting and limit the velocity to around 950 fps, where the FPE is easy to calculate, it's twice the weight of the projectile.... So that we don't push the ports too close to Mach 1 (as I'm sure the drag starts increasing well below that anyway), let's use bore-size porting.... If the gun was 100% efficient, we could calculate the maximum FPE we can get per foot of acceleration once we know the force on the base of the pellet.... That force is the bore area times the pressure....
(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)
OK, so we know the force, what else do we need to calculate the acceleration, and the velocity after a foot of travel?.... Well, we need the mass, but not just of the bullet, but of the air in the barrel that is accelerating as well, which is considerable.... How about if we use the barrel volume of air at that pressure, assuming a foot of barrel?.... At 21*C, that is 1.2 kg/cu.m. at 1 bar.... let's convert that to grains per cu.in.... We get (7000 x 2.204 x 1.2) / 61023 = 18514/61023 = 0.303 grains / cu.in times the pressure in bar.... We can calculate the weight of air inside the barrel at various pressures, from the cailber and the barrel length.... For a 12" long slug of air (you'll see why later), this works out to:
Wt. (gr.) = 0.303 x (cal ^2 x PI / 4) x 12 x pressure (bar) = 2.86 x P x C^2
Here is what that works out to, in the same format as above....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/AirWeightperFoot_zpsb4339983.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/AirWeightperFoot_zpsb4339983.jpg.html)
Now we need the weight of the projectile.... For a high performance PCP, a roundball isn't heavy enough, IMO, so here is a graph, again in the same format, giving similar bullet weights graphed against the caliber....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/BulletWeightvsCaliber_zpsf853667f.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/BulletWeightvsCaliber_zpsf853667f.jpg.html)
I left off the 4x roundball weight over .357 cal because the bullet weights just seemed unreasonably heavy.... Really all the lines are just to give you some examples.... Can you see where I'm going with this?.... Good, because my train of thought has left the station and it's time for me to stop for a while and regroup.... *LOL*.... I think I was getting off track (in fact I know I was) but I'll leave the graphs here anyway just because some may find them useful....
Bob
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OK, fresh start.... Back to the basic math, I hope I've got it right.... Sorry I hit the "post" button before I was done.... Starting with the equations for constant linear acceleration:
F = ma .... Force F = mass m x acceleration a .... solve for a you get .... a = F/m
E = 1/2 m v^2 .... Energy E = one half the mass m times the velocity v squared....
v^2 = 2as .... starting at rest, the velocity v = twice the acceleration a times the distance s .... substitute 2as for v^2 in the energy equation above....
E = 1/2 m (2as) .... the 1/2 and the 2 cancel and we get E = mas .... now substitute F/m for a....
E = m (F/m) s .... the m's cancel out, and you are left with E = Fs .... the energy E in Ft.lb equals the force F in lbs. times the distance s in ft.
Now, let the distance be 1 ft., and we get E = F.... so, going back to the original graph of Force vs. Caliber, if we apply that force over one foot of travel, we now have FPE vs. Caliber....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/FPEvsCaliber2_zps83b05893.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/FPEvsCaliber2_zps83b05893.jpg.html)
I feel that this represents a reasonable goal for modern PCPs.... Now you may say that our barrels are more than a foot long, but remember that to get any reasonable efficiency we have to close the valve before the pellet/bullet travels more than half the length of the barrel.... Then you will point out that the air keeps expanding after the valve closes, adding more energy, to which my answer is that makes up for the less than 100% efficiency assumed in my calculations.... Well, what about barrels longer than two feet?.... OK, you got me there, in a three foot barrel maybe you should be able to get 50% more FPE than the graph suggests.... You can lug around something that long if you wish....
I know this is going to be controversial, and that's fine.... This is, after all, the Geek Gate, and I expect to have you guys be tough on me.... So, have at it !!!
Bob
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Very well detailed...had to put it on a seperate document to be able to make clear thoughts
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and you are left with E = Fs .... the energy E in Ft.lb equals the force F in lbs. times the distance s in ft.
Now, let the distance be 1 ft., and we get E = F....
It has been a while since I've had to put my old physics degree to use, Bob: but Energy = Force X Distance is pretty much a definitive equation for energy (a force exerted across a distance), "aka the ability to do work".
So - yep, you're right. But I don't' think you needed to derive that all over again from the basic Newtonian equations ;D
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Not everyone is a math whiz (and I'm certainly not) so I figure if it helped me to work through it and have to explain it to others I would make sure I didn't make any glaring error.... The fact that the units worked out in the end was the validation I was looking for.... Yes, you're completely correct, Energy is force x distance, so maybe it should have been obvious, but hopefully my explanation was slightly clearer than a muddy pond....
Bob
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It was very well explained. I really enjoy reading your posts, graphs, data, etc. Seems you've achieved some pretty groundbreaking results translating this stuff into actual real-world shot strings, etc. Very cool stuff. Makes me want to send you my Rainstorm .357 for a tune.
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Just a few interesting data points for my Hayabusa.... All the below have 28-29" barrels, running at 3000 psi....
.224 cal maxed out at 106 FPE.... full boresize porting.... right on the blue line
.257 cal maxed out at 160 FPE.... full boresize porting.... right on the blue line
.308 cal maxed out at 207 FPE.... 92% porting.... about 5% below the blue line
.357 cal maxed out at 257 FPE.... 80% porting.... about 13% below the blue line
Based on that data, I feel the chart above is pretty good as a goal.... and to achieve it you likely have to go with pretty much boresize porting and a barrel over 24"....
Bob
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Yes, very interesting data points. The combination of shot count, performance, ES and efficiency you squeeze out of the .308 and .357 seems to beat a lot that's out there in the market.
The stock barrel on the Rainstorm .357 is is 21.5". The stock shroud doesn't project much more than 2 inches over that. But if you're willing to give re-barreling, re-porting, etc a shot - I think this would be a worthy platform to try them on. I'd honestly pay to see what could be done with some of your techniques on this very nice Rainstorm platform :D I don't hunt, but I do enjoy long-range target - so that rapidly sloping shot string isn't ideal - which is why I like the fine balance of ES consistency and performance that you're able to achieve in your projects without a regulator.
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Where is the like button when you need one ;D. Some very useful information you put there Bob and I think is pretty helpful to modders and DIYers
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IFF force is not constant...E=integral(force x distance)...but we seem to have it relatively constant...:)
I was pleased to see my .224 with bore area porting running quite efficiently at 80 FPE. Which validated the experiment on opening both sides of the valve up...inlet at ~5x port area, and outlet at bore area at the smallest. Now to get it to put one on top of the other...tried many different shape pellets; all the way to 47 gr weight and still no joy. Next thing is to examine the barrel harmonics.
If it were easy everybody would be doing it.
cheers,
Douglas
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They promised me there would not be any algebra on this forum.......
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They promised me there would not be any algebra on this forum.......
Where is that written? ;D This is the GEEK Gate. ;D ;D ;D
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Where is that written? ;D This is the GEEK Gate. ;D ;D ;D
[/quote]
Oh, I am a geek, and a nerd.
I have been working on computers since the TRS-80 came out
And still do today for a living..
(Not working on the TRS 80's, but mostly pc's)
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Nice work. I see so much start to happen in the Transitional velocity range from Mach .82 to 1 but it is hard to say what is happening in the ports. You can induce supersonic flow to help a valve shut quicker. There is always a point of max restriction which will be your highest air speed. It will normally be at a port restrictor if you are using that to throttle it.
Convergence on a contoured bolt probe where I like to accelerate the flow so it scavenges the air through the TP. That's my theory. If you can create the point of max restriction at a point other than the port redirection in the valve or barrel it creates the most fluid flow. What I consider a pop rather than a belch or bark rather than a burp is what the ear hears when the charge value is dead on
THE MASS OF OUR PELLETS AND THE SMALL MASS OF OUR CHARGE is why we need to be so efficient and not play with the supersonic thing. We can do it but it is a massive energy zapper. We find efficientcy and accuracy holding hands so often they are a harmony you see a lot in good Airguns. Standing on it will cost you in General. More sometimes than others.
TimmyMac1
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Oh, I am a geek, and a nerd.
I have been working on computers since the TRS-80 came out
And still do today for a living..
(Not working on the TRS 80's, but mostly pc's)
Ha ha, that picture's a blast from the past. I do software today too. Even before high school I was sneaking upstairs while the family slept to code on my brother's TRS-80 Level II 16 K "microcomputer" (older than the one in your pic). Brother told me he'd kill me if he ever caught me touching his computer - but I guess he never caught me.
That TRS-80 and my old rock-solid Chinese break-barrel .177 were my two things. Tinkering with computers is a lot like tinkering with airguns. OK - back to airguns...
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Since I am nearly at 3x roundball weight in .224, I think I should get a few; that would make for a neat close-in chipmunk killer...or squirrels, or...:) which BTW is one way to establish power plant capability---put more light boolits in and examine delivered velocity.
cheers,
Douglas
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If you want to look at what bullet weight does, check this out.... Gun settings maxed out, starting at 3000 psi for all strings....
(http://i378.photobucket.com/albums/oo221/rsterne/Discovery/25DiscoPEEKMaximums_zpsfdaeaeca.jpg) (http://s378.photobucket.com/user/rsterne/media/Discovery/25DiscoPEEKMaximums_zpsfdaeaeca.jpg.html)
(http://i378.photobucket.com/albums/oo221/rsterne/Discovery/25DiscoPelletWeightPEEK_zps9cc5f532.jpg) (http://s378.photobucket.com/user/rsterne/media/Discovery/25DiscoPelletWeightPEEK_zps9cc5f532.jpg.html)
Note that I didn't have quite enough hammer strike to max out the velocity with the heavier bullets, so their maximum FPE should have been even higher....
Bob
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;D Every time I do this (read your Geek Posts) I end up talking to myself and wishing I had taken mechanical engineering rather than electronics. Then I would not have to think so hard ;D
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;D Every time I do this (read your Geek Posts) I end up talking to myself and wishing I had taken mechanical engineering rather than electronics. Then I would not have to think so hard ;D
Yeah...riiiight. Variable gate-drain capacitance based on drain-source voltage? No thanks. I am quite happy with the easy ME stuff...LOL
cheers,
Douglas
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rsterne-"The fact that the units worked out in the end was the validation"
It always feels good, doesn't it? The first thing they try to beat into your head in physics class is to be sure to use dimensions throughout your calculations, and the last thing a student wants to do.
The courses I took used both English and metric units. So, you could have a problem where 5 of the units were metric, and one English unit snuck in. Always screwed you if you were not paying attention to the units.
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rsterne-"The fact that the units worked out in the end was the validation"
It always feels good, doesn't it? The first thing they try to beat into your head in physics class is to be sure to use dimensions throughout your calculations, and the last thing a student wants to do.
The courses I took used both English and metric units. So, you could have a problem where 5 of the units were metric, and one English unit snuck in. Always screwed you if you were not paying attention to the units.
LOL...slugs
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yes, the one unit I never understood.... *LOL*....
Bob
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yes, the one unit I never understood.... *LOL*....
Bob
ha! slug-cubit/fortnight-squared...not going to cause a headache...back to metric...:)
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OK, I've been thinking about this stuff over the past couple of days, tried some stuff in my spreadsheet, some of which worked and some didn't.... I knew intuitively that there had to be an "optimum" bullet weight (or rather Sectional Density) and that it likely varied with pressure, where higher pressures would be able to handle heavier bullets.... The first chart I did above on Bullet Weight just gave what bullets of different SD's would weight in various calibers.... What I wanted was a way to decide what range of bullet weights made sense for different calibers and pressures.... It turned out to be a LOT simpler than the first few trials I made....
You remember that at 950 fps, the FPE is twice the bullet weight in grains?.... Well, I used that for the basis for the following graphs.... They are basically the FPE (for a 1 foot push) from above, divided by two.... As such, they represent what a bullet would weigh to achieve 950 fps while meeting the FPE possible from that graph, which I view as a "goal" for a high powered PCP....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/BulletWeightvsCaliberfor950fps_zps00e63184.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/BulletWeightvsCaliberfor950fps_zps00e63184.jpg.html)
You can use heavier bullets, but you will be less likely to achieve 950 fps, and if you use lighter bullets, they are likely to go faster in a really powerful PCP.... When I was doing this graph, I also calculated the Sectional Density for each combination, and it turned out that the SD was a constant for each pressure curve.... When I plotted that vs. the pressure I got the following:
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/SectionalDensityvsPressure_zpse91f1e93.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/SectionalDensityvsPressure_zpse91f1e93.jpg.html)
Obviously, this is a linear trend.... The graph shows that as the pressure increases you can increase the Sectional Density.... and in fact you have to, to keep the same velocity.... Since I started this thread with an argument for using about 950 fps, it makes sense to bring the argument full circle.... One other thing I might mention.... For a given "shape" (ie length/diameter ratio) the SD increases in proportion to the caliber.... Here is an example, using roundball.... The BC is the SD divided by a "Form Factor", which for a sphere is 1.55, so the SD is also proportional to the caliber (ie linear)....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/BCofSpheres-1_zps7161580b.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/BCofSpheres-1_zps7161580b.jpg.html)
While we're on a roll here, this brings about one more relationship to ponder.... If the SD to achieve a given velocity (eg. 950 fps) is proportional to the pressure, and the SD for a given shape is also proportional to the caliber, then it follows that as the caliber increases, you need to increase the pressure to drive a given shape to that velocity....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/PressurevsCaliber_zps613d11ed.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/PressurevsCaliber_zps613d11ed.jpg.html)
The net result of this is that large calibers, because we currently can't use past about 4500 psi, can't drive bullets of high sectional density at our goal of 950 fps.... This makes them more practical for delivering lots of power at close range.... while the smaller calibers will tend to be better shooting bullets of high SD over long ranges, because the Ballistics Coefficient and the Sectional Density, for the most part, go hand in hand.... So that you can relate the above graph to actual bullet weights, here is an updated version of the graph offered in the first post....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/BulletWeightvsCaliber2_zps2464d1a7.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/BulletWeightvsCaliber2_zps2464d1a7.jpg.html)
I hope this information helps you to understand what is practical with the present state of the art for PCPs, and what makes sense to try and accomplish and what doesn't.... I've learned a lot developing these graphs, and hopefully they will prevent me from chasing unrealistic goals.... As an example, it would appear that bullets about 5x Roundball weight are only practical up to about .25 cal (eg. 117 gr. @ .257 cal).... those of 4 x Roundball to about .30 cal (eg. 170 gr. @ .308 cal).... and in .357 cal about the heaviest practical would be just over 3 x Roundball weight (roughly 220 gr.).... That is because we are currently limited to about 4500 psi.... If you drop the pressure to 3000 psi (much more common), that gives you the following maximum bullet weights to acheive roughly 950 fps.... This is the data from the blue line on the graph at the beginning of this post....
Maximum Bullet Weight at 3000 psi to achieve ~950 fps
.177 cal - 35 gr. = 70 FPE
.224 cal - 55 gr. = 110 FPE
.257 cal - 75 gr. = 150 FPE
.308 cal - 115 gr. = 230 FPE
.357 cal - 150 gr. = 300 FPE
.408 cal - 200 gr. = 400 FPE
.457 cal - 250 gr. = 500 FPE
.510 cal - 300 gr. = 600 FPE
.580 cal - 400 gr. = 800 FPE
.720 cal - 600 gr. = 1200 FPE
I'm not saying that these are the absolute maximum bullet weights you can use to achieve 950 fps with those calibers at 3000 psi.... You can probably do a bit better with a long enough barrel and good efficiency.... It goes without saying that to achieve the above you will need bore-size porting or close to it.... as any ports less than 92% of the bore diameter will be subject to sonic throttling at that velocity.... However, it should be a pretty good guide to assess your goals by....
Bob
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Is that So?
:P Man I'm tellin ya. There is more useful information in this one post than NASA published in the 70's
Awesome stuff Bob.....rather amazed no one else has chimed in here.
How much would it take to convince you to publish this to our share drive?
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Oh, you noticed I added more to the spreadsheet I sent you.... *LOL*....
Consider it done, my friend....
Bob
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Here is just one way you can use the above information.... Let's say you want to find out the maximum bullet weight you can launch at 950 fps in a .457 cal PCP at two different pressures, to help you decide what to build.... On the top graph, find .457 cal on the bottom, and your pressures on the side.... Where those lines intersect is the bullet type.... In the case of 3500 psi, it's a bullet that weighs twice as much as a Roundball.... for 3000 psi,it would be about 1.7 times RB weight....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/BulletFinder_zpsaf342439.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/BulletFinder_zpsaf342439.jpg.html)
Then using the bottom graph, on the vertical line for .457 cal, find those corresponding spots on the graph, and read the bullet weight on the left.... For 3500 psi, about 280 gr., and for 3000 psi about 240 gr.... If you do a good job designing and building your PCP, you should be able to get about 950 fps with those combinations....
OK, how about you have a caliber and bullet weight in mind and you want to know how much pressure it will take to hit 950ish fps.... Using the graphs in the opposite order, this time for .300 cal and an 80 gr. bullet, on the top graph find .300 cal along the bottom, and 80 gr. on the left.... Where they intersect is the bullet type, which in this case is twice Roundball weight (the red line)....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/PressureFinder_zpse6259744.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/PressureFinder_zpse6259744.jpg.html)
Then on the bottom graph, you find where the red line (twice RB) intersects .300 cal, and read the pressure on the left, in this case 2300 psi.... If you are using a regulator, you would need to have it set for at least that pressure.... For an unregulated PCP, you will need that pressure at the BOTTOM of the shot string to get 950 fps at that point.... If you only want 950 at the peak, then you could use that for the mid-point of your fill range....
Remember, this information is only a guide.... but it does give you an idea about how to use just SOME of the above data....
Bob
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Sometimes I do my best work between 6-7 AM before I'm fully awake.... I know that sounds weird, maybe my mind is just relaxed and clear as I'm just waking up, but often that is when things suddenly become clear to me.... This morning I woke up thinking about the relationship between barrel length and pressure, and how increasing both allow you to push heavier bullets to a given velocity.... My brain then tied that in with the graph above showing how the Sectional Density of a bullet can increase with pressure, and I wondered if it might also increase with barrel length.... After breakfast I sat down and plunked some numbers into my spreadsheet and came up with the following graph....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/SecDensvsPresvsLength_zps152829e8.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/SecDensvsPresvsLength_zps152829e8.jpg.html)
As you can see, the trends are linear, going through zero as would be expected.... It shows an interchangeabilty between pressure and barrel length in their ability to push a given weight (actually SD) of bullet.... For example, look at a 36" barrel at 3000 psi and a 24" barrel at 4500 psi, and they should both be able to push a bullet with an SD of 0.252 to 950 fps.... Another example would be an 18" barrel at 2000 and a 12" barrel at 3000, pushing a bullet with an SD of 0.084.... Both combinations should in theory be able to produce about 950 fps.... Now my brain doesn't readily relate bullet weights in grains to the SD, so here are a couple of graphs to help with that....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/WeightvsSectionalDensity_zps6c1a8dfe.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/WeightvsSectionalDensity_zps6c1a8dfe.jpg.html)
To make an exact calculation of the weight if you know the SD and the caliber, the formula is: Weight (gr.) = Sec.Dens. x Cal.^2 x 7000
Let's do an example, for my .257 Hayabusa, which runs on 3000 psi and has a 28" barrel.... That says I should be able to push a bullet with an SD of 0.196 at 950 fps.... That works out to a weight of 0.196 x 0.257 x 0.257 x 7000 = 90.6 gr (181 FPE) .... The best I've ever done is an 88 gr. bullet at 908 fps (161 FPE) not too far off (89% of target).... Another example would be the Haley Scandalous .257 with a 36" barrel running 4500 psi.... The SD is 0.379, which works out to a bullet weight of 175 gr. at 950 fps (350 FPE).... and Haley has reported that he has managed over 300 FPE (~86% of target).... but I don't actually know what bullet weight and pressure was used to acheive that.... If anything, it would appear that driving the weights produced by this method to 950 fps is a very lofty goal, and very difficult to achieve.... but that's a good thing, because the whole point of this thread was "what makes sense for a PCP".... I think using the weights predicted by this system as an absolute maximum if you want to try and achieve 950 fps (2 FPE/gr.) is a pretty good guide.... For a 24" barrel and 3000 psi, that works out to a maximum SD of 0.168, which gives the following bullet weights....
.177 cal: 37 gr.
.217 cal: 55 gr.
.250 cal: 74 gr.
.308 cal: 112 gr.
.357 cal: 150 gr.
.408 cal: 196 gr.
.457 cal: 246 gr.
.508 cal: 304 gr.
.580 cal: 396 gr.
.720 cal: 611 gr.
Using heavier bullets than the above, IMO you are pretty much conceding that you won't acheive 950 fps unless you use more pressure or a longer barrel.... In fact, achieving 900 fps in a 24" barrel with the above at 3000 psi would be excellent results.... At 900 fps, the FPE is 1.8 times the bullet weight in gr....
Bob
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Great insights and info....
Using your graphs and formula, would the way to calculate the maximum .357 yield for an 18" barrel at 3000 PSI be like the following?
0.120 x 0.357 x 0.357 x 7000 = 107 grain bullet at 950 fps, or 214 FPE?
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Close, the maximum SD is actually 0.126 (I have the benefit of the numbers, not reading the SD from a graph, where it's just over 0.12), so it's actually:
0.126 x 0.357 x 0.357 x 7000 = 112 gr. @ 950 = 224 FPE.... Getting over 200 FPE, in reality, will be quite a challenge, however.... The most useful result, IMO, is that if you want to approach 950 fps, I wouldn't use a bullet heavier than 112 gr....
Bob
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Every time I read your posts I develope a massive headache then reread and begin to understand. When I was young all I did was shoot and hit what I aimed at no science . Now I am learning what should work best before I pull the trigger. Sometimes trial and error is ok but knowledge is a better way to achieve good results ;D ;D ;D
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I love your charts Bob, If I just knew what I was looking at LOL. Na I am beginning to understand some of them. Not really much difference that the standard deviation charts back when I was in the concrete testing business.
Love your work and explanations.
Bob
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It seems that supersonic velocities were eliminated at the beginning of this discussion because of the low efficiency and turbulence above mach .9, but... Those efficiencies and turbulence significantly improve once you get above mach 1.2. It seems it might be possible to build a PCP gun that shoots above mach 1.2 for the duration of the flight?
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The turbulence and stability problems lessen about Mach 1.2 or so, as you say, but the drag is still some 5-6 times as great as it is below Mach 0.8-0.9, even with bullets.... so they will still lose their velocity quite quickly.... In addition, once the air velocity inside the porting and barrel exceed Mach 1, you start getting a sonic choking effect which drastically affects the efficiency.... While it is possible to drive pellets (or bullets) supersonic with a PCP, unless you start using Helium, you run into another "limit" at about 1650 fps due to the RMS velocity of the air molecules at 70*F.... If you actually experiment with achieving high velocities in a PCP (using air) you will find a huge drop in efficiency (FPE/CI) at around Mach 1 (or below if the ports are smaller than the boresize) and what amounts to a brick wall at around 1500 fps, with the efficiency going essentially to zero at 1650 fps (about Mach 1.46).... I have seen one recorded shot at 1706 fps on air, using a Condor in .177 drivng a 1.4 gr. plastic sabot, but the efficiency was about 3%.... Since by definition, the RMS velocity is part of a curve, I guess there are a few molecules moving fast enough to break the theoretical limit of 1650 fps.... The nitrogen in the air actually has an RMS molecular velocity of 1680, so it's not that surprising.... but who wants a PCP that dumps 500 psi to produce a very loud shot of only 9 FPE?....
Therefore, even if you were willing to accept a very low effiiciency (ie extremely low shot count) you have a very narrow window of velocities that are fast enough to get the bullet to still be travelling at Mach 1.2 (which is 1350 fps) at, say, 100 yards.... Since the title of this thread is "What Makes Sense for PCPs" I feel that eliminating velocities over about Mach 0.9 is logical....
Bob
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Good job teacher. Very articulate way of saying "you don't need to go fast to get-r done". Quite the opposite actually. We have a relatively limited FPE window in each caliber. Going from 500-900 .177 can deliver from 4-20 FPE, .20 can deliver 6-40 FPE, .22 can deliver from 7-50FPE or .25 cal can deliver 10-60+ FPE and stay both accurate and efficient.
TimmyMac1
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I figure the maximum FPE to be 2X the pellet weight in grains, which occurs at 950 fps.... so yes, those numbers are about it, unless you go to bullets.... You can now add to the list, with pellets, .30 cal 25-100 FPE, and .35 cal 48-156 FPE, using 500-950 fps....
Bob
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They promised me there would not be any algebra on this forum.......
Every time I re-read this thread I see another reason I need to go back to school for Mech Engineering classes . Fortunately there is a SUNY 5 miles away that has an excellent engineering program and I have a Geek buddy to help me hone up my math skills they also have an old fart program
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so I was thinking about a post I read where the problem was an entirely down sloping velocity plot, a couple of fixes were discussed in the post but I wondered if increasing the projectile weight would raise the far end of the curve...
then I reread this thread and in the second post ( correct fourth post from the bottom of the first page) there is a graph showing that happening as the projectile weight gets heavy enough to drop the velocity below 1100fps...
hmmmmmm...more feud for thought....
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;D Thank you Bob this thread has been a huge PIA (learning experience ;) ) but it has enlightened this relative newbie to the potential and limitations of AG's in general and the very valid reason why for longer range repeatable accuracy bigger is better. So again thanks for all your hard work this info needs to find its way int the library . PS: now I need a .357 or .45 possibly a Recluse and molds and lead bars and a melting pot ladle and more STUFF as my wife is fond of calling my new obsession ;D ;D ;D
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Do you think that pellets in general are over stabilized when shot from a barrel that has enough spin to stabilize bullets? (and thus loosing some accuracy) After looking over some calculations for model rocket stability, It seems to me that the diabolo shaped pellets are far closer to being stable than bullets before you add spin. Model rockets don't spin so they rely on their shape and tail fins for stability. So it seems logical that pellets must be over stabilized when you add the same amount of spin, of course this assumes "geometric stability" and "spin stability" are additive or multiplicative and not just different?
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"Overstabilzed" is a relative term, there really is no such thing as too fast a spin for the "tumble resistance" of a projectile.... What it really means is that other factors, such as spin-induced rise and fall in a crosswind due to the "Magnus Effect" and precession caused by an out of balance bullet (CG not aligned with center of form) increase to the point of opening up the group size.... These would not exist in a bullet that is not spinning, and increase as the spin rate increases.... However a bullet not spinning will tumble.... It's about finding the "best" balance between the two....
Bob
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I'm wondering how atmospheric conditions effect an air rifle / pellets accuracy. I just saw a consistently 1 1/2 moa rifle shoot 25 continuous sub moa shots at 75 yards and the only difference from past shooting sessions is that today it was considerably cooler and more humid than normal. 48 degrees F, 64% RH, 2400 ft msl, 27.81 in Hg, 25 cal, BT65, 910 fps. Would a slightly different tune yield these or better results more regularly?
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Since I don't want to be the guy who killed this thread, let me ask a different question:
If I understand it correctly, the LASSO competition shoots at steel animal targets at 100 to 300 yards with big bore air rifles. A year or two back the competition was won with a 257 Haley but the rules have been clarified to require at least a 308 now. Using Chairgun a 357 158 gr bullet at 950 FPS would have a 1 MOA vertical change for a 10 FPS spread and a 16 foot vertical drop. So does 300 yards make sense for PCPs?
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No reason why not.... I recently saw a video of a guy with a Haley Scandalous killing a Pop Can at 615 yards.... took him 3 shots, but he got it!....
Bob
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I suspect we'd have a significantly better idea of the capability of the Scandalous/Charlie ROach combination if that vid was about a half hour long, and there were several pop cans to shoot as well as a sighter target and a target to receive 3-5 shots after the last can. I don't recall if the set up/sighting in was covered or not, or IFF those three shots included ranging/sighting shots too. The only thing I am certain of is that it would take me more than 3 shots to connect...and I have lit a match at 25 yards...:)
cheers,
Douglas
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Let's do an example, for my .257 Hayabusa, which runs on 3000 psi and has a 28" barrel.... That says I should be able to push a bullet with an SD of 0.196 at 950 fps.... That works out to a weight of 0.196 x 0.257 x 0.257 x 7000 = 90.6 gr (181 FPE) .... The best I've ever done is an 88 gr. bullet at 908 fps (161 FPE) not too far off (89% of target).... Another example would be the Haley Scandalous .257 with a 36" barrel running 4500 psi.... The SD is 0.379, which works out to a bullet weight of 175 gr. at 950 fps (350 FPE).... and Haley has reported that he has managed over 300 FPE (~86% of target).... but I don't actually know what bullet weight and pressure was used to acheive that.... If anything, it would appear that driving the weights produced by this method to 950 fps is a very lofty goal, and very difficult to achieve.... but that's a good thing, because the whole point of this thread was "what makes sense for a PCP".... I think using the weights predicted by this system as an absolute maximum if you want to try and achieve 950 fps (2 FPE/gr.) is a pretty good guide.... For a 24" barrel and 3000 psi, that works out to a maximum SD of 0.168, which gives the following bullet weights....
Bob, perhaps the missing component to meeting your calculated/ theoretical FPE is in fact the energy used to induce spin. I would think that if the examples where done with a smooth boer, that the fpe would be much closer to theory. Also, look at the % difference of the 88gr and the 175gr examples. the heavier projectile had deminished % and I'll bet the required twist to stabilize the 175gr was more enery than the 88gr. heavier require more twist and more twist requires more energy and that results in more deviation from theorectical fpe. Just a thought as to where the energy/efficiency went.
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Bill...sonds like a proper math quest. I from the tables of a disc of boolit mass, w( omega ) calculated by speed and twist rate and then E=1/2I* w^2...and I'll get back wid a number soon...:)
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I did not understand very much of this but i read every word
Tommy
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so, for a 5 gram, 25 cal boolit, the rotational inertia 1/2mR^2 gives us .00000003 kg-m^2. Lets assume 12" twist so 950 fps gives us 950 rev/sec for total energy of ~0,45 Joule spent spinning it up.
cheers,
Douglas
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How does that correlate to Bobs example, or do we have enough info to asses that?
BTW Douglas. DUDE YOU ARE A NERD! ;D. An awsome nerd i might add.
Bill
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So, not a lot of energy lost to spinning it up, really.... ~ 0.3 FPE
Bob
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Much lower than I imagined.
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Just had a few more thoughts about the Maximum SD vs Pressure concept.... I'm referring to this graph, which is basically what is the heaviest bullet you could launch at ~ 950 fps for a 24" barrel....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/SectionalDensityvsPressure_zpse91f1e93.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/SectionalDensityvsPressure_zpse91f1e93.jpg.html)
It recently occurred to me that you can also use the chart the other way around, to predict how much pressure you need for a given bullet SD (from that 24" barrel).... This might be of some interest if you are curious about what pressures are required for the heaviest pellets in various calibers (as distinct from bullets).... Here are the SDs for those, and the corresponding pressures....
.177 cal - 16.4 gr. - 0.075 - 1400 psi
.22 cal - 32.4 gr. - 0.098 - 1800 psi
.25 cal - 42.7 gr. - 0.098 - 1800 psi
.30 cal - 51.2 gr. - 0.081 - 1500 psi
.35 cal - 77.8 gr. - 0.087 - 1600 psi
Since I am interested in the answer, I also did the calculation for my Bob's Boattail's....
.250 cal - 50.6 gr. - 0.116 - 2100 psi
.300 cal - 70.0 gr. - 0.111 - 2000 psi
.308 cal - 79.0 gr. - 0.119 - 2100 psi
.357 cal - 127 gr. - 0.142 - 2600 psi
This information will come in useful if you are designing, for example, a regulated PCP to shoot pellets (or BBT's) as it will give you the MINIMUM pressure you should consider, assuming you want to be able to use the heaviest pellets available today.... As I think it likely that heavier pellets in .30 and .35 cal will eventually be available, it seems that 1800 psi would be a reasonable pressure to use for the heaviest of pellets.... Remember, these results are not easy to achieve, you will likely need full boresize porting, and it might well be that you may need more pressure or a longer barrel to get to the mid 900s with the heaviest pellets in those lists....
Bob
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;D I cannot read this thread when tired. I intend to show it to my math nerd computer friend/geek for an English translation, then maybe the math will make more sense as it is just when I think I'm beginning to understand some other bright light adds a new "twist" (slight pun intended) ;) ;D
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It seems like there is a never-ending way that these estimates can be used.... Before I give you my latest however, I need to stress that these are only estimates of what MAY be possible.... Although I have come close with my Hayabusa, it took a slightly longer than 24" barrel to get there.... One of our GTA members, dyotat100, who builds high-powered Condors, has likewise come very close.... I should remind you of the basis for the math behind this....
I started with the bore area, which is caliber (in inches) squared times PI/4.... Then I multiplied by the pressure (in psi) to get the force (in lbs) available to accelerate the pellet/bullet.... I then assumed a 24" barrel, with that push happening over half its length (ie 1 ft.) and that force then became ft.lb. of energy (FPE) that could be produced.... That is where the "estimate" part comes in.... It assumes an equal push over that 1 ft. of distance, at an efficiency of 100%, and then no force for the rest of that 24" barrel.... As it turns out, even with bore-sized porting and the best efficiency I am aware of anybody achieving, this is a lofty goal, but not an unreasonable one.... At least, IMO, it points out what may be a maximum for (at least current) PCPs using air (ie not Helium).... As an example, we can get to these goals for a 24" barrel by using a 28" barrel, (even exceed them slightly) so we're not that far off....
As I worked through this thread (and let me point out that it was a learning and development process), I realized that there were a whole bunch of related things going on.... Since when you push a projectile to 950 fps, the FPE is twice the weight (in grains), it became obvious that if there was a maximum FPE we could reach (for a given pressure in a 24" barrel) then there had to be a maximum weight that could be pushed to 950 fps, and a corresponding Sectional Density (SD).... That led to the graph relating SD to pressure.... Then I realized that it was the product of the pressure and (half) the barrel length (in ft.) that affected the FPE, so for a given pressure you could use a heavier bullet in a longer barrel.... Therefore, any combination of pressure and barrel length (as the product) would have a maximum SD that would have a decent chance of reaching 950 fps.... In the last couple of days, I decided that this could be put into a simple formula in which the pressure, caliber and barrel length could be used to calculate the maximum bullet weight that has a decent chance of reaching 950 fps in a PCP running on HPA.... Here is what I came up with....
W =( P x L/24 x B x B X 3.14159/4 ) / 2
W = P x L x B x B / 61.1
W = P x BV / 48
where W = weight in grains
P = pressure in psi
B = bore in inches
L = length in inches
BV = bore volume in cu.in. (which is L x B x B X PI/4 with all dimensions in inches)
If I may just make a comment about the last formula.... I find it interesting that the weight is proportional to the amount of air.... pressure times barrel volume.... In other words, you can only ask a certain weight of air to do a certain amount of work.... Makes perfect sense to me.... Here are some example cacluations, with their real-life comparisons:
.257 cal, 28" barrel, 3000 psi.... W = 3000 x 28 x 0.257 x 0.257 / 61.1 = 91 gr.... which works out to 182 FPE.... My Hayabusa has reached 908 fps (160 FPE) with a bullet weighing 87.6 gr....
.257 cal, 24" barrel, 3300 psi.... W = 3300 x 24 x 0.257 x 0.257 / 61.1 = 85.6 gr.... which works out to 171 FPE.... dyotat100 managed 170 FPE (925 fps) with an 89.5 gr. bullet....
.257 cal, 32" barrel, 4000 psi.... W = 4000 x 32 x 0.257 x 0.257 / 61.6 = 138 gr.... which works out to 276 FPE.... dyotat100 got 1083 fps (245 FPE) with a 94 gr. bullet....
As you can see, we're not far off the mark.... Heavier bullets can, of course be used, and will likely increase the FPE above estimates, at the expense of not reaching 950 fps.... Conversely, lighter bullets will be able to exceed 950 fps, but likely at reduced FPE, and particularly downrange as transonic drag starts taking it's toll.... As a final, simple formula, here is a good goal for FPE for your next PCP project (on air)....
FPE = P x L x B x B / 30.5 .... With a 30" barrel you can simplify it even further.... FPE = P x B x B (pressure times caliber squared).... For my new 7mm project, that works out to FPE = 3000 x 28 x 0.284 x 0.284 / 30.5 = 222 FPE.... If I can get to 200 FPE with the 95 gr. Bob's Boattail I have designed, and end up with a short string at 950 fps, I'll be a happy camper....
Bob
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:D Thanks Bob now I have another headache
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Quite possibly the remaining energy is taken by the friction between the barrel walls and the pellet/bullet. This page (http://www.engineershandbook.com/Tables/frictioncoefficients.htm)has the coefficient at .95 for dry, sliding contact.
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The Coefficient of friction is the ratio between the force between the objects and the force required to overcome friction.... If it is 1.0, it means that a 1 lb. object will take 1 lb. of force to slide it.... If it is 0.5, it means that a 1 lb. object will take 1/2 lb. to slide it.... It is really only useful if you had a bullet sitting on a plate of steel, and if the bullet weighed 100 grains, with a coefficient of friction of 0.43, it would take 43 grains of force to slide it.... Lead to cast iron is 0.43 on that chart....
This doesn't really apply to a bullet in a barrel, what you need to know is the force it takes to slide it through the barrel, and also the force it takes to break it loose and start it moving.... You can actually measure these, and when I'm using Lloyd's spreadsheet he has inputs for both values.... What those values are depends on how tight the bullet fits in the bore.... If the bullet is not larger than the groove diameter, the force to keep it sliding is in the 3-10 lb. range, and to start it maybe twice that, depending on the leade angle.... Since in a .308 cal gun running 3000 psi we are dealing with a force of 223 lbs. that is available, we are talking about a measureable amount, but nothing like 50%.... Pellets are more like 2 lbs to start and 1 lb. to keep it moving....
If you want to measure the sliding force required, simply stand your gun on a scale, muzzle down, and push the pellet/bullet with a rod from the breech.... To get the starting force, add weight to the rod until it starts to move and record the weight.... You will be surprised how little force it takes to move a .22 cal or even a .25 cal pellet.... Bullets do take more, and if they are TOO tight, can take a LOT....
Bob
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Once again I lay in bed thinking about this stuff just before arising and came up with yet another way this information can be used.... I made the observation a few days ago that bullets of similar Sectional Density (SD) had very similar lengths, regardless of caliber.... I thought about that this morning, and realized that the weight W of a cylindrical bullet is, of course W= PI x (C^2 / 4) x L x D where C = caliber, L = length, D = density.... and the SD, which is the "weight per unit area" is SD = W / C^2 / 7000.... Both formulas use the square of the caliber, so it ends up that for a cylindrical bullet, the length is proportional to the SD.... Therefore if the SD is fixed (or determined as in the graph above), then the length of a cylindrical bullet having that SD will be a constant, regardless of caliber....
Now for the most part, we don't use cylindrical bullets, as they are very "draggy", so I used the Kolbe Bullet Design Calculator to figure out how much longer our "typical" bullets are than a cylinder of the same weight.... I worked with round-nosed designs and with tangent ogive designs with a decent size Meplat, and found that many bullet designs we use in airguns are about 15% longer than a cylinder of the same weight.... So, I incorporated that as a "fudge factor" into the graph below....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/BulletLength_zps130ba617.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/BulletLength_zps130ba617.jpg.html)
A few important notes here.... This graph is NOT intended for Spitzer bullets, as they will be longer (and yet not much heavier) than a tangent ogive design with a good sized (50-60%) Meplat.... Nor is it intended for roundball.... However, the data is consistent with a lot of the results I have obtained in high-performance PCPs like my Hayabusa and DAQ.... I'm sure you can find bullets that are longer that you can drive at 950+ fps than with the barrel/pressure combinations shown above.... The overall governing factor as to the suitability of a given bullet in a given barrel length and pressure combination will still be its weight.... The above graph will just give you some idea of whether or not a bullet of a given length may be able to be driven close to that 950 fps target velocity....
The interesting data point for a lot of guns in the chart above is for a 24" barrel at 3000 psi.... which suggests a maximum bullet length of 0.60" to reach ~950 fps.... I think you will find that is a pretty challenging, but reachable, target for a high-performance PCP....
Bob
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..........Well, what about barrels longer than two feet?.... OK, you got me there, in a three foot barrel maybe you should be able to get 50% more FPE than the graph suggests.... You can lug around something that long if you wish....
I know this is going to be controversial, and that's fine.... This is, after all, the Geek Gate, and I expect to have you guys be tough on me.... So, have at it !!!
Bob
Fascinating thread, Bob - Seriously, THANKS!
But - who says you have to want to "lug it around" all that much?
I'm just suggesting that, for instance at my age and newly limited mobility,
(and possibly at whatever point where one begins to consider truly long range shooting, just for grins)
one does begin to consider there are other ways to acquire a target than to chase it around the woods, across the countryside, or wherever.
There are even truly stationary targets one might consider best approached
from as great a distance as possible, as an advantage.
In such circumstances, a SUPER long range might be the predominant consideration, certainly over mobility - just as shot count, and even efficiency, might not be paramount..
I know I don't get around much anymore (as the song goes) and thus my budding fascination with the possibilities of super long rifles, with 3-4 foot barrels. Then there's that black powder crowd (numerous enough to have their own hunting season,) whose ancestors didn't mind schlepping a five foot rifle even through the woods hunting squirrels... or redcoats....
Rod
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Even a 5 foot rifle won't have a barrel much more than 3 feet.... If you want to build a rifle with a 4 foot barrel, then you can double all the FPE levels I based this post on originally....
Bob
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Even a 5 foot rifle won't have a barrel much more than 3 feet.... If you want to build a rifle with a 4 foot barrel, then you can double all the FPE levels I based this post on originally....
Bob
And with enough plenum to half- fill them, right?
Tubing is cheap... Now where do I get the fattest commercially made valve?
(No lathe...)
Rod
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Even a 5 foot rifle won't have a barrel much more than 3 feet.... If you want to build a rifle with a 4 foot barrel, then you can double all the FPE levels I based this post on originally....
Bob
And with enough plenum to half- fill them, right?
Tubing is cheap... Now where do I get the fattest commercially made valve?
(No lathe...)
Rod
'Fattest'? There is no single one. There are effectively two ways, one balanced to reduce the opening strike, and the other w/o balance. The latter suffers a quadratically increasing energy to kick open as its flow potential increases, the other suffers internal friction form the seals on the balancing parts. I suspect the balance point lies somewhere around the .357 bore area port area...
cheers,
Douglas
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Plenum volume still needs to be at least 1cc per FPE you want for a regulated gun.... much more than that unregulated unless you only want one shot....
Bob
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I thought it might be time to revisit this thread with the idea of coming up with a range of maximum bullet weights that make sense for different PCPs.... In particular, I'm thinking about relatively common guns like the MRod, Condor, even the DAQ, where you are dealing with a 3000 psi fill and a barrel of about 24", and unregulated.... In practical terms, this means that the last shot of a usable high power shot string occurs at about 2400 psi.... In other words, looking at how heavy the bullet can be using 3000 psi isn't really practical for these guns, unless you want just one maxed out shot.... So, what kind of maximum bullet weight are we looking at using 2500 psi and a 24" barrel, to achieve 950 fps?.... Here is what I get for the various calibers.... The Sectional Density works out to 0.140 for all of these bullets....
.177 cal - 31 gr.
.217 cal - 46 gr.
.224 cal - 49 gr.
.250 cal - 61 gr.
.257 cal - 65 gr.
.284 cal - 79 gr.
.300 cal - 88 gr.
.308 cal - 93 gr.
.357 cal - 125 gr.
.408 cal - 163 gr.
.457 cal - 205 gr.
.508 cal - 253 gr.
.580 cal - 330 gr.
.720 cal - 509 gr.
This doesn't mean you can't use heavier bullets than the above.... just that you are unlikely to achieve 950 fps unless you tune for just 1-2 shots, using a decreasing style shot string.... If you increase the pressure or the barrel length, you can use a heavier bullet, of course.... but if you want to hit about 950 with a usable shot string and a 3000 psi fill these are about as heavy as you can go.... To achieve this performance, of course, will require a very high-performance PCP with large ports and enough hammer strike to make use of the potential pressure and barrel length available.... in other words a lofty, but achievable goal....
Bob
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That matches well with my experience Bob( limited as it is ). I have slightly more barrel ( 27" ), but lower weight in .224 ( 46 gr ), and have hit nearly 1000 fps around 25-2600 psi. More hammer is clearly needed. The 3k6 psi bottles leave a reasonable bit of headroom in terms of velocity curve pressure; kick the valve open well at higher pressure, but don't hit it so hard you get the Korean cliff velocity profile, and you're off to the races.
Doing it accurately means managing the barrel harmonics...and perhaps living with a smaller than usual velocity spread. Can't help wondering if the pressure-variable hammer hit excites the system differently enough to make it even more troublesome...LOL Which ov course is perhaps one reason the pellet energy stuff is easier to tune well.
cheers,
Douglas
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Douglas, between the extra 3" of barrel and 100 psi, plus 3 gr. lighter weight, you could easily hit 1000 fps.... as all three of those fudge the numbers to greater FPE.... Nothing is written in stone, this is just intended to be a guideline anyway.... Increase the hammer strike to take advantage of the 3600 psi you have available and all bets are off.... but you will find that at 2500 psi the velocity won't increase, just use more air....
Bob
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;D Every time I do this (read your Geek Posts) I end up talking to myself and wishing I had taken mechanical engineering rather than electronics. Then I would not have to think so hard ;D
+1 on that... once I realized every calculation had been done by someone (and studied Heisenberg;) I gave it up, having acquired the gut feeling by doing them in school and designing systems IRL (where the math is at best a rough guide and never works out perfectly on imperfect conditions and materials.) And then the bean counters, time misers, and cost cutters attack....
Rod
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.... So, what kind of maximum bullet weight are we looking at using 2500 psi and a 24" barrel, to achieve 950 fps?.... Here is what I get for the various calibers.... The Sectional Density works out to 0.140 for all of these bullets....
This doesn't mean you can't use heavier bullets than the above.... just that you are unlikely to achieve 950 fps unless you tune for just 1-2 shots, using a decreasing style shot string.... If you increase the pressure or the barrel length, you can use a heavier bullet, of course.... but if you want to hit about 950 with a usable shot string and a 3000 psi fill these are about as heavy as you can go.... To achieve this performance, of course, will require a very high-performance PCP with large ports and enough hammer strike to make use of the potential pressure and barrel length available.... in other words a lofty, but achievable goal....
Bob
If we're using "bullets" rather than diabolo pellets, why the subsonic MV limitation at all?
-without getting into a discussion of time to fill the barrel, or valve port speed limitations-
which seem to me a little too academic given the myriad added parameters and unpredictabilities
(like machining precision, friction and wear) when approaching that level of analysis.
Still fascinated by that Xs/FDPCP GenII concept of multiple barrel ports...
Rod
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If we're using "bullets" rather than diabolo pellets, why the subsonic MV limitation at all?
Airgun barrels have riflings that make the pellet rotate but not as fast as a "powder" barrel.
Diabolos stabilize due to their skirt,some barrels make them rotate slightly (smooth twist) and still have exc. accuracy.
Using bullets on a barrel designed for pellets? Then better go subsonic or go hypersonic all the way from gun to target,
so that the bullet won't have to deal with it's own sonic blast.
My 2 cents
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If we're using "bullets" rather than diabolo pellets, why the subsonic MV limitation at all?
-without getting into a discussion of time to fill the barrel, or valve port speed limitations-
which seem to me a little too academic given the myriad added parameters and unpredictabilities
(like machining precision, friction and wear) when approaching that level of analysis.
Still fascinated by that Xs/FDPCP GenII concept of multiple barrel ports...
Rod
Because it becomes increasingly wastfull of stored air as you pass 950 FPS( not to mention projectile drag sky-rockets around that point). The push available is diminishing then too...the porting starts suffering from the sonic choke, and the gas will only expand so quickly...stored energy has to be put into a faster and faster column of air in the barrel....
On a relatively powerful .224 boolit shooter, I have managed a 1174 fps shot with a 28 gr E-J pellet...I got the 'crack' indicating SS travel. Then went back to more sensible testing speeds.
cheers,
Douglas
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The same reasons exist for staying subsonic with bullets as with pellets, with one exception, diabolo pellets have even greater instability than bullets when transitioning from supersonic to below.... However, the drag on bullets also skyrockets as you pass about Mach 0.8-0.85 (900-950 fps).... and the efficiency of the air accelerating the pellet inside the barrel takes a dump as well, unless the ports are bore-sized.... Even with bore-sized ports and high pressures there are sonic limitations to be considered.... Even though they aren't hard limits, who need to use ten times the amount of air to try and get to 1200 fps?.... If you start looking at wind drift, you will find that it reaches a minimum at somewhere around 950 fps even with bullets, because as you drive them faster the drag, and hence the drift, increases rapidly....
Bob
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Given those numbers, I have a 50 gr, .224 boolit mold on the way( 22596 ). With more barrel, and slightly more pressure I think it will go fast enough. That particular Marauder is slightly short on hammer energy; it is going to get the hammer energy stretched as far as I can go...slide the trigger backwards a bit, lengthen the cocking lug slot in the air tube and breech and modify the stock's inletting. I think an extry .125" hammer travel is possible this way. If I can shoot a 940-960-940 string from 3k starting pressure I think I am going to be OK with it...:) ( yeah, right...as long as it is accurate )
cheers,
Douglas
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Great discussion. Relatively low pressure is fairly hard to make speed with and our breech pressure averages are in the hundreds not thousands like firearms. We definitely have to work within a narrow envelope before inefficientcy spikes and accuracy plummets. I stay below Mach .8 but for sure don't toy with .82 as it has been a huge disappointment for decades. For 4 years now I've played at 815 FPS in .22 as I have a 20 FPE performance max to stay under in both FT and HV Bench Rest. I think it is a better solution in conditions and my results speak for themselves. I've rarely shot better. I wish I could go 865-875 but there are no accurate .22 pellets that weigh that little. I use RS JSB 13.43 grain at Mach .72. Since resistance goes up @ the square of the speed going faster has its consequences and there are some real advantages to going even slower like .22 Pistols at Mach .52-55. The slower you start out the less you lose because you are dealing with higher BC and lower resistance. Wind drift and trajectory aside you just don't lose as much.
I've always thought going fast was highly over rated.
Supersonic is out of the practical envelope for Airguns when the discussion is about accuracy at distance.
The best work so far has been done sub-transonic and I believe that will always be the case.
TimmyMac1
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Seems that the reality is that unless you can have an avg barrel psi of 2000+psi, supersonic isn't going to happen on a shot string. IMO, it's not worth chasing. More efficient projectiles(better BC) at 950 fps is the best route. Bobs study on the connection with SD vs PSI is priceless. This information gives a wealth of info for those who want to establish a shot string with an acceptable ES% deviation. It also hints to the possibilities of what to shoot to get a declining fps string.. This is a real decision tool in a nut shell. Each of us have personal likes as far performance. None of them are wrong, they're just prefernces. This will allow us to asses a platform for a window of performance and apply the best weight projectile for that preformance. Or..... Let us know we need a new platform ;)
Bill G
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I just had a look through the data on some of my wilder PCPs, and the lowest pressure I saw supersonic with was 2200 psi, but to be truthful I never tested down to 2000 with the lightest pellets.... However, I can assure you that the efficiency takes a dump past Mach 1, and is declining much before that.... Add to that the fact that no projectiles have a "drag discontinuity Mach number" (the speed at which the drag increases drastically) higher than Mach 0.9 (and most are 0.8-0.85, some as low as 0.7) and I really see no point in trying to push to Mach 1, let alone beyond, with an airgun.... Here is a graph of the drag of the standard G1 projectile....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/ChairGunG1Model_zps44a89ca4.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/ChairGunG1Model_zps44a89ca4.jpg.html)
Note that the Drag Coefficient is below 0.25 up to Mach 0.8 (900 fps), double that at Mach 1, and peaking at 0.65 at Mach 1.3.... The wind drift will follow a similar curve.... doubling at Mach 1 compared to at Mach 0.8....
Bob
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Bobs study on the connection with SD vs PSI is priceless.
Bill G
That and many others reside in a 'Best of Bob' favourites folder...:D
cheers,
Douglas
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I'm gonna have to start one of those. It would be easier to buy his Book ;) ;)
Having fun Bob
Bill
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Check this out, Bob-
http://bulletin.accurateshooter.com/2009/04/us-army-team-tests-radical-new-dimpled-bullet/ (http://bulletin.accurateshooter.com/2009/04/us-army-team-tests-radical-new-dimpled-bullet/)
I actually envisioned this a long time ago but didn't know how to act upon it. Now someone else is collecting all the money. Ain't that always how it goes.
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I'm pretty close to Bobs projected number for a 357. 24" barrel, 3400 psi, 138 gns, barrel port 100%, valve area at poppet 110% and now getting an average of 967 fps. Still on a regulated tether while trying to sort out some valve/hammer issues.
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Interesting about the "dimpled" bullet, not easy to make I'm sure....
Projected FPE in .357 with 24" barrel and 3000 psi is 302 FPE (goal).... at 3400 psi, 342 FPE.... Maximum SD to achieve 950 fps would be 0.168 (150 gr.) at 3000 psi and 0.190 (170 gr.) at 3400 psi....
Bob
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I read the dimpled bullet thing, as I got further into it, I started to say ,huh..........what?really...........i dont know?
at the bottom it says its a april first deal
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I read the dimpled bullet thing, as I got further into it, I started to say ,huh..........what?really...........i dont know?
at the bottom it says its a april first deal
I didn't get to the bottom, because when they brought out the golf ball thingie I concluded it was BS. The dimpling works on the golf ball cause it is moving so close to the turbulent Reynolds number...bullets are of similar dimensions and moving considerably faster...LOL
cheers,
Douglas
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DUH!.... that'll teach me not to read something before I comment !!! .... I thought it sounded unlikely.... *LMBO*....
Bob
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Even a 5 foot rifle won't have a barrel much more than 3 feet.... If you want to build a rifle with a 4 foot barrel, then you can double all the FPE levels I based this post on originally....
Bob
And with enough plenum to half- fill them, right?
Tubing is cheap... Now where do I get the fattest commercially made valve?
(No lathe...)
Rod
'Fattest'? There is no single one. There are effectively two ways, one balanced to reduce the opening strike, and the other w/o balance. The latter suffers a quadratically increasing energy to kick open as its flow potential increases, the other suffers internal friction form the seals on the balancing parts. I suspect the balance point lies somewhere around the .357 bore area port area...
cheers,
Douglas
Thanks. I meant biggest throat for the tube ID, in this case, FDPCP (about .745")
Rod
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Maximum throat size in that ID will be about 5/16" but I don't think there is one that big available commercially.... Perhaps the new Cothran with "Force Reduction" that lowers the hammer strike?.... No idea how (or how well) it works.... but he's talking up to 300 FPE in .45 cal....
Bob
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I don't have anything like an understanding of the FR design yet, but it does suggest an answer to my forming questions about how the FX Revolution could possibly work...
Has anyone experimented with homebuilt semi-auto airgunning yet?
Rod
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I don't have anything like an understanding of the FR design yet, but it does suggest an answer to my forming questions about how the FX Revolution could possibly work...
Has anyone experimented with homebuilt semi-auto airgunning yet?
Rod
The experiment would be worth doing if it was for somebody that would pay for it. Semi-Auto is harder than Auto. Select fire is what people want. Very doable but getting paid has always proven to be fruitless. I no longer experiment because it has led to most of my grief, when I've done development for others. Trusting people is bad business. Licensing arrangements are invariably broken and lead to lawsuit and legal battles. Rich people(lawyers win and plantiffs pay) win, film at 11.
TimmyMac1
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I always have a soft spot in my heart for people like Tim who devote their life to airgunning, and try to make a living from it.... It must be one of the hardest things in the World to do, and I speak from the experience of someone who was self-employed nearly all my life.... Like I was told recently, if you work for yourself, you only have to work half days.... just 12 hours out of 24.... *LOL*.... Of course development time comes on top of that.... *grin*....
When I retired and went back to airguns (after nearly 40 years away) I decided I would never try and get paid for my ideas, and would freely share them.... Refusing to build guns or parts for others has given me the freedom to do what I enjoy.... test old ideas, develop new ones, and share the results with everyone here.... My hat's off to those who try and make a living doing it.... as without them 90% (or more) of airgunners would still be shooting BB guns....
Bob
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I always have a soft spot in my heart for people like Tim who devote their life to airgunning, and try to make a living from it.... It must be one of the hardest things in the World to do, and I speak from the experience of someone who was self-employed nearly all my life.... Like I was told recently, if you work for yourself, you only have to work half days.... just 12 hours out of 24.... *LOL*.... Of course development time comes on top of that.... *grin*....
When I retired and went back to airguns (after nearly 40 years away) I decided I would never try and get paid for my ideas, and would freely share them.... Refusing to build guns or parts for others has given me the freedom to do what I enjoy.... test old ideas, develop new ones, and share the results with everyone here.... My hat's off to those who try and make a living doing it.... as without them 90% (or more) of airgunners would still be shooting BB guns....
Bob
;) ;D Without people like you , Tim, Scott, Doug and many others with the passion and skills to develop those ideas beyond the concept you're right it would still be Red Ryders and 880's
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I always have a soft spot in my heart for people like Tim who devote their life to airgunning, and try to make a living from it.... It must be one of the hardest things in the World to do, and I speak from the experience of someone who was self-employed nearly all my life.... Like I was told recently, if you work for yourself, you only have to work half days.... just 12 hours out of 24.... *LOL*.... Of course development time comes on top of that.... *grin*....
When I retired and went back to airguns (after nearly 40 years away) I decided I would never try and get paid for my ideas, and would freely share them.... Refusing to build guns or parts for others has given me the freedom to do what I enjoy.... test old ideas, develop new ones, and share the results with everyone here.... My hat's off to those who try and make a living doing it.... as without them 90% (or more) of airgunners would still be shooting BB guns....
Bob
;) ;D Without people like you , Tim, Scott, Doug and many others with the passion and skills to develop those ideas beyond the concept you're right it would still be Red Ryders and 880's
You forget Bob Kraus and Ed Wackerhagen...they if nobody else saved us from Red Ryders in the form of the Supergrade A&B and for me, the Blue Streak( even if I wanted Silver ).
cheers,
Douglas
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I don't have anything like an understanding of the FR design yet, but it does suggest an answer to my forming questions about how the FX Revolution could possibly work...
Has anyone experimented with homebuilt semi-auto airgunning yet?
Rod
Tim sums it up best. Once you commit to earning a living off of it, there is no in between, unless you like being taken advantage of or seen as someone who takes advantage of. Nature of product based business I suppose. Semi is a challenging engineering feat for a PCP. Use of air either robs power from the shot or shortens number of shots, too few shots make semiauto needless. Good topic for another thread though.
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This topic has a lot of useful (and some useless) information.... but a while back I did a summary over on the NOE Moulds Forum.... It is directed at making an intelligent decision on what bullet weight and length makes sense.... but it takes into account most of what was discussed here.... Rather than type it out all over again, I am just going to provide a link.... It is a locked sticky over there.... http://noebulletmolds.com/smf/index.php/topic,1137.0.html (http://noebulletmolds.com/smf/index.php/topic,1137.0.html)
Bob