Sonic Choke? Maybe not. 2162 FPS

[Privateer]

Well. I tossed a FPCP into the 'Let's blow it up thing'
Send me your PayPal info by PM and I'm in for a few bucks myself.

[Scotchmo]

Lloyd,

You are heading up these groundbreaking experiments. I would like to ask your permission:

I was told of the limit of 1640fps some time ago on another forum where it seems to be accepted as fact. I accepted the reasoning given for it at the time, without too much thought. I would like to present a little info on your results, to that forum, prior to the Nitrogen tests. Are you OK with that?

[Buldawg76]

I meant the 2nd stage on the ShoeBox, which of course is the 3rd stage in the system.... input directly into the block after the larger cylinder on the Shoebox, and only use the smaller, HP cylinder to boost the pressure to 4500.... Should be very little load on the motor that way, you may even be able to run a bit higher pressure than the peak during operation (which would occur at 4500 psi output).... subject to the strength of the lines, fittings, and check valve between the stages, of course.... If the two stages both have about the same compression ratio, and we are going from 125 psi to 4500, which is 36:1, it is reasonable to assume each stage is 6:1, which could mean you might be able to feed the 3rd stage directly with 750 psi.... possibly just use an 850 psi paintball regulator with a shim removed?....

Of course dropping the pressure down to 125 psi would allow you to use more of the pressure in the N2 tank that you are paying for.... so I guess that would be more cost effective....

Bob

Bob
Ok I misunderstood what you were referring to as the second stage so yes that would be the way to do it and you can do the math ( not my forte at all ) to determine what would be capable pressure wise of being fed into it to speed thing up.

Using only 125 psi out of the tank means more cost for the regulator to control the tanks output pressure but being able to use most all of the nitrogen in the tank is more cost effective as well so I guess to some extent its a 50/50 toss up.

Lloyd
I believe if in a freedom 8 or max shoebox over pressurizing the first (2nd) stage of it will add to the strain on the motor and increase the heat and wear on the o rings that seal the shafts as well as the plastic shaft bushing and if over pressurized enough likely would stall the shoebox completely. In any event it would not be a good idea at all as the cylinders are only held in the block by circlips and they can become projectiles in themselves if stalled at 4500 plus psi. It would IMO be better to be safe and use 125 psi fed into the shoebox as it was designed than risk damage or injury by redesigning its operation that is already a proven concept.

Mike

[rsterne]

Interestingly, you don't gain much at extreme pressures with such a light projectile.... I guess the mass of the air is overwhelming the total mass.... The mass of a 9.1 gr. pellet is only 0.00004 slugs.... A 47.5" barrel full of 1600 psi air (that is what it is, starting at 3000 psi with a 55cc chamber and 47 cc barrel) is over 10 times greater, at 0.00043 slugs.... Here is what I get with Lloyd's spreadsheet using the inputs for his recent 2031 fps shot, at 70% efficiency.... pressures are before shot....

3000 psi = 1928 fps  (75 FPE)
3500 psi = 1980 fps
4000 psi = 2024 fps
4500 psi = 2063 fps
5000 psi = 2097 fps
5500 psi = 2128 fps
6000 psi = 2156 fps  (94 FPE, an increase of 25%)

Lloyd's current calculator uses Boyle's Law for air density, and once you go above 3000 psi the density actually drops off compared to an Ideal gas.... If I understand this correctly, this results in a greater pressure drop during the shot, the higher the starting pressure.... but the density will be less, which is a plus.... I don't know how those opposing factors will effect the spreadsheet results.... On the plus side, 6000 psi Nitrogen should add about 30 fps because it is ~4% less dense than air....

Interestingly, if we increase the weight of the pellet by a factor of ten, to 91 gr. (typical bullet weight for that caliber), we see a lot different situation....

3000 psi = 1083 fps (237 FPE)
6000 psi = 1349 fps (368 FPE, an increase of 55%)

It appears that in regards to barrel lengths and pressures, while we can still make small gains, they are no longer in proportion to the gains a "normal" PCP sees.....

Bob

[lloyd-ss]

Lloyd,

You are heading up these groundbreaking experiments. I would like to ask your permission:

I was told of the limit of 1640fps some time ago on another forum where it seems to be accepted as fact. I accepted the reasoning given for it at the time, without too much thought. I would like to present a little info on your results, to that forum, prior to the Nitrogen tests. Are you OK with that?

Scott,
Please do. 
This is all in the interest of learning, and sharing knowledge with the entire airgun community.  There are a lot of very smart airgunners out there with provocative ideas and theories.  Sometimes we get it right; sometimes we don't.  Nothing ventured, nothing gained.  But if the theories are proven wrong, give them a dignified burial and move forward.
Lloyd

[lloyd-ss]

Buldawg,  With yours and Bobs discussion on the shoebox, I think if I use one  to boost the nitrogen pressure, I will just reduce it to approx 120 psi first and dump it into the input in the normal fashion.  Sounds like there are too many unknowns (at this time) to do it safely any other way with the shoebox.
Lloyd

[Buldawg76]

Lloyd
I would tend to agree with you on the use of the shoebox to boost the pressure of the nitrogen since there are unknowns in trying to bypass its normal operation for the sake of saving a little bit of time versus risking damaged equipment or worse injury.

If you can get the 6000 psi nitrogen tank though then there should be no need for boosting pressure since you will have 190 shots worth of pressure with just the turn of a knob with the CGA677 fitting and your current fill setup.

Mike

[lloyd-ss]

Interestingly, you don't gain much at extreme pressures with such a light projectile.... I guess the mass of the air is overwhelming the total mass.... The mass of a 9.1 gr. pellet is only 0.00004 slugs.... A 47.5" barrel full of 1600 psi air (that is what it is, starting at 3000 psi with a 55cc chamber and 47 cc barrel) is over 10 times greater, at 0.00043 slugs.... Here is what I get with Lloyd's spreadsheet using the inputs for his recent 2031 fps shot, at 70% efficiency.... pressures are before shot....

3000 psi = 1928 fps  (75 FPE)
3500 psi = 1980 fps
4000 psi = 2024 fps
4500 psi = 2063 fps
5000 psi = 2097 fps
5500 psi = 2128 fps
6000 psi = 2156 fps  (94 FPE, an increase of 25%)

Lloyd's current calculator uses Boyle's Law for air density, and once you go above 3000 psi the density actually drops off compared to an Ideal gas.... If I understand this correctly, this results in a greater pressure drop during the shot, the higher the starting pressure.... but the density will be less, which is a plus.... I don't know how those opposing factors will effect the spreadsheet results.... On the plus side, 6000 psi Nitrogen should add about 30 fps because it is ~4% less dense than air....

Interestingly, if we increase the weight of the pellet by a factor of ten, to 91 gr. (typical bullet weight for that caliber), we see a lot different situation....

3000 psi = 1083 fps (237 FPE)
6000 psi = 1349 fps (368 FPE, an increase of 55%)

It appears that in regards to barrel lengths and pressures, while we can still make small gains, they are no longer in proportion to the gains a "normal" PCP sees.....

Bob

Bob, you said a lot in that post.   The variables are so interrelated that the calculated (and actual) results sometimes are not what you would expect.  Seems like a lighter projectile is the fastest way to higher velocity.  But as you pointed out, with a light projectile and a long barrel, the mass of the column of air (nitrogen) can exceed the mass of the projectile by an order of magnitude and much of the energy is spent just accelerating the air.  With heavier pellets, where the pellet is a much larger percentage of the total mass that must be accelerated, the Energy gains are more substantial.  The variables that you change for a particular test shot need to be relevant to what the goal of each unique experiment or shot really is.

Regarding the spreadsheet, I started incorporating the VanderWaals pressure vs volume vs density and got stalled half way through.  It was more difficult than I anticipated.  I need to take a fresh stab at it and complete the task, because it is one of those tasks that just needs to done.  Boyles law isn't applicable in our situation, so we will stop hanging onto it, and give it a dignified burial, and move forward.
Lloyd

[rsterne]

I was pretty shocked when I found that the velocity increase going from 4000 psi to 4500 with your current setup is only predicted to be on the order of ~ 40 fps.... It would take a full 1 gr. reduction in the weight of the bullet to get that as well.... or about 7" more barrel length.... Interestingly, even an infinite reservoir would never get us that 40 fps if we change nothing else.... We really are getting to the point of (severely) diminishing returns.... Mach 2 (2250 fps) is looking a long way away right now, without Helium, IMO.... but with it, we would be flirting with Mach 3....

It will be interesting to see which way applying the VanDerWaals corrections takes us.... ie which is more important the lower density at high pressure, or greater pressure loss during the shot, compared to an Ideal gas.... or if they pretty much cancel out?....

Bob

[lloyd-ss]

Bob,
I will see if I can finish up the VanDerWaals corrections, and then a fresh look at caliber,  SD, barrel length, etc, will be in order. 

[Scotchmo]

...
It will be interesting to see which way applying the VanDerWaals corrections takes us.... ie which is more important the lower density at high pressure, or greater pressure loss during the shot, compared to an Ideal gas.... or if they pretty much cancel out?....

Bob

Bob,

Isn't that backwards once you get over about 2000psi?

Looking at your earlier graph:


It will result in the model showing a higher than expected air mass at pressures over 3500psi. So that reduces the velocity estimate.

However, with the correction, air at 2000psi is wanting to take up a larger volume than an ideal gas. As the 4500psi dump chamber depletes, the pressure will not be falling off as fast as we originally predicted. So that increases the velocity estimate.

As you suggested, maybe it will still be a wash. It could end up balancing out to be the same with or without VanDerWaals correction.

Guessing what happens with an infinite or very large dump chamber should be easy:

An infinite dump of 2000psi could use an air mass multiplier of about 93%. - higher velocity than ideal gas.

An infinite dump chamber of 3500psi air needs no correction. - velocity as predicted

An infinite dump of 4500psi might need an air mass multiplier of about 109%. - velocity lower than ideal gas

An infinite dump of 6000psi might need an air mass multiplier of about 125%. - not good for performance

[rsterne]

That graph is labelled incorrectly, and is pretty confusing.... I was having Nitrogen and an Ideal gas intersect at 3000 psi when I drew it, to compare what happens at 4500 psi.... In addition, the air density I used was based on the geometric average of Oxygen and Nitrogen because I couldn't find the data for air.... Here is the correct data....



As you can see, for an Ideal gas (as per Boyle's Law), the relationship between density and pressure is linear.... Air and Nitrogen are almost perfectly linear up to 2000 psi, and the deviation at 3000 psi is only about 4%.... However at 4500 psi, the density is about 13% less, and at 6000 psi (not shown), it is about 20% less than predicted by Boyle's Law....

Bob

[madeInLV]

Loyd,

congratulations! Boy it's great to see when metal comes to life!

The o-ring contraversy is BS...i think. Yes, it will cause frictiona and yes it will heat up. Will it BURN and aid the expansion by increasing the mean pressure...NO. After all, the air behinf it is expanding and COOLING. The heat generated on the o-ring surface due to friction will mess up the O-ring and won't even heat up the barrel.

Still, there will be nay sayers. Do a test with NO lube and a tefon ring (making them is real easy and they can stretch and pushed back into shape). Since you are in the US (the land of e-bay) you cold try and get some PTFE coverad O-rings. Still...making a TEFLON ring is easy.

Boy, i wish i didn't have this cold/running nose...would write more clearly:)

What's more important is what do you plan on doing with the rig?

Ok...you'll make another pellet (as light as you possibly can) with a teflon ring an hopefully get it to seal, give it 4500psi and fire it, which hopefully gets to M=2.

Say the projectile end up being 6 grains. But what if it were 3 grains? Would it go twice as fast? But you can't test it....3 grain pellet won't hold up structurally.

You could make a graph : Vmax vs SD  (SD=sectional density) where you fire heavy to light and record Vmax and EXTRAPOLATE to Vmax when SD->0. Now that would be more valuable IMHO. Then you could perfrom the same set of shots and varry the pressure. The graph would then have a bunch of pressure lines representing Vmax at that partilucalar pressrue. Increase of P and it's affect on Vmax (linear, exponensial....) woul then be visible.

Stupid cold....god i feel awfull.

Ok, what I'm getting at is practical application. This rig will show us V max attainable on air which is cool. In reality when constructing a PCP we deal with other issue though...

we are limited to 300m/s (you don't wan't to be in the transonic region) which is a lot if you think about it. NOW....we can change: caliber, barrel length, pressure ,firing cahmber volume.

At what point having a longer barrel is meaningless?
How many CALIBERS long should my barrel be?
WHY do bigger caliber systems are more efficient rather than small caliber counterparts. (efficiency vs caliber)
How big should my firing chamber be? Is the a golden rule? As in V_chamber=4*V_barrel There has to be a limit.
..............................
Is the inline configuration of the vavle that much more efficient than the traditional with 2*90deg bends? If so, how much? How about the Gyrardony style port?

In an inline valve....how steep should the angle of the cone be? 45...30 deg?

I could go on and on:)

You are doing a great job. Keep it up:)

[rsterne]

Scott, I see the responses over on the Yellow, completely predictable.... One thing mentioned is the cooling effect of Abiabatic expansion, to as low at 150*K.... This of course lowers the molecular velocity.... Here is the calculator for that (air is 29 AMU)....  http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c4

At 150*K, the molecular velocity of air is a paltry 1177 fps, which leaves the concept of that providing a limit to the velocity of an airgun even further in the dust.... Incidently, I think that 150*K is greatly flawed.... Here is a calculator that gives the temperature (and available energy) in expanding air, for both Isothermal and Adiabatic expansion.... http://www.tribology-abc.com/abc/thermodynamics.htm

Starting at 20*C (293*K) with 55 cc (0.055x10^-3 m^3) at 4000 psi (27.6 MPa), and ending at 2160 psi (14.9 MPa) that calculator gives a final temperature when the pellet exits the muzzle of 245*K, although it could drop much lower than that once the pellet exits and the pressure goes to 1 atm.... At 245*K, the molecular velocity of air is 1506 fps.... Incidently, there would be 0.6 kJ (442 FPE) of energy released by that expansion, so we are only getting about 19% of that....

Bob

[Buldawg76]

Ok well totally lost in the math again as usual but my gut tells me if the pellet is light enough and the pressure high enough it will reach Mach 2 given the right barrel length and firing chamber volume and pressure.

It has been said to many times in history that it cannot be done only to be proven wrong later on by someone that is not willing to take the theory and math numbers at their face values. So I say let the nay sayers be darned and let the impossible be proven like it always is by those who refuse to stand by convention.

Mike

[lloyd-ss]

....................................
Starting at 20*C (293*K) with 55 cc (0.055x10^-3 m^3) at 4000 psi (27.6 MPa), and ending at 2160 psi (14.9 MPa) that calculator gives a final temperature when the pellet exits the muzzle of 245*K, although it could drop much lower than that once the pellet exits and the pressure goes to 1 atm.... At 245*K, the molecular velocity of air is 1506 fps.... Incidently, there would be 0.6 kJ (442 FPE) of energy released by that expansion, so we are only getting about 19% of that....
Bob

Bob, I quoted just part of your previous post regarding temperature drop resulting from the expansion of the air during the shot, and as you pointed out, up to the point that the projectile leaves the muzzle. Expanding from 55cc to approx 102cc in 2.5 milliseconds. So your calcs show a total drop of 48*K, or 86*F? As we have previously discussed, there is a continuum of velocities and pressures and now,  temperatures, inside the system.  Hard to say where most of the temperature changes are localized, but I would guess at the entrance into the barrel, for what its worth. Anyway, it doesn't seem that the temperature drop will have much affect on the velocity, in the same way that the slight heating of the air from a rapid fill won't have much affect.

In upcoming shots, I will pay attention to the before and after temperatures of the breech block and barrel, even if just by hand touch, to see if anything extraordinary is happening, despite its effect, or lack of effect, on the velocity.
Lloyd 

[lloyd-ss]

New projectiles.
I just received some correct dia 7075 aluminum rod and some Teflon to make some new projectiles and seals for the upcoming Nitrogen shots. 
With the way the clam shell grips the conical rear end of the projectile, I think I can make the clamping O.D. slightly smaller (.230 dia)  than the front end (.274 dia) of the projectile.  If I also make the extreme rear end of the projectile pointed, I hopefully will be able to force the Teflon seals on from the rear of the projectile, over the .230 dia, without damaging them.  The I.D.  of the Teflon seal will be about .170, so it ought to work.

Another thought on the projectiles is to eliminate the clamshell clamping and instead have a skinny aluminum stem extending from the rear of the projectile that is secured just outside the entrance of the barrel so that it effective holds the projectile in place as the reservoir is filled.  The skinny stem would have a necked down area that would break under tension when the correct pressure is reached.   Using, as an example, a 4500 psi fill and 60ksi break for the 7075 (will have to experiment to find out), the projectile will have 277 pounds force on it. If the stem were necked to .071, break would occur at 4500 psi.  With a .070 dia stem the break would be at 4400psi.    I should be able to hold the dia (and finish) of the necked area to a .001 tolerance and a 100 psi variation is as good as I can read on the gauge anyway.  So that design is a possibility.  The problem is figuring out a retention method that doesn't interfere with the air flow.

Lloyd

[I_like_Irons]

The breaking rod idea is a pretty good one, but there will be a bit of variability at which pressure it actually breaks.  I'd suggest making a recording pressure gauge on the receiver block so you know exactly what the pressure is when the rod lets go.   Even one of the "old school" Bordon pressure gauges with the recording needle will work.  A camera trained on the gauge should also work.  I think you want a fairly high frame rate so that you don't "blink" just before peak pressure.

One thing that happens when a rod is put into tension but before it breaks is that it necks down.  If you look at stress strain charts you will see the ultimate strength occurs at the peak of the curve while the break point is at a lower force level.  This latter half of the curve is due to the cross sectional area being reduced though the strength of the material remains pretty much constant.  Brittle materials have a very short extension to the curve, while ductile (like aluminum) have a longer curve.

The necking aspect may be put to good use, however.  If you can design the rod's  break point a bit behind the barrel opening, then you have a fairly pointed smoothly tapered "needle" which shouldn't affect the flow too much.   The actual break on the point of the "needle" will also be ~45 degrees which helps with reducing the point gradually a bit.

[Buldawg76]

That's what was used in the auto industry to install ignition switches so that they could not be easily removed was break away fasteners in which the head was necked down to shear at a predetermined torque thereby leaving a fastener without any means to remove except a hammer and chisel. Then of course it was located so that the chisel had to be custom ground to even reach the head to drive it loose to be removed, I hated those screws with a passion.

Luckily in your application removal will be supersonic and instant with no need for a hammer and chisel. LOL

Mike

[rsterne]

I take the idea of Adiabatic expansion in PCPs with a bit of a grain of salt.... The reason is, that I have never seen an fog of ice in front of the muzzle, even though air temperature drops of over 100*C are predicted when the valve closes early in the shot cycle.... If we start at 2000 psi, and have a residual muzzle pressure of 400 psi (not unusual for a PCP), the resulting air temperature at the muzzle should be 185*K (-126*F).... In addition, if the expansion is purely Adiabatic, the maximum achievable efficiency seems too low to me, ie we are getting too close to the theoretical maximums....




I got the numbers for the above graphs (and the temperatures above) from this calculator.... http://www.tribology-abc.com/abc/thermodynamics.htm

With a SSG installed, we are seeing some PCPs with efficiencies of over 2.0 FPE/CI at pressure under 2000 psi.... that seems too efficient (only 15% total losses) for the expansion to be purely Adiabatic, IMO.... Remember, part of the FPE released by the expansion of the air goes into accelerating its own mass.... The reasons why the expansion are nearly Isothermal may be escaping us.... but reality, to me, shows that Adiabatic isn't the best model to use.... Does some cooling occur?.... Yep, you can feel the temperature of the reservoir drop a bit with continued shooting.... However, I have never felt the barrel get as cold as the reservoir, even though that is where the majority of the expansion is taking place....

Bob