Theoretical Maximum Velocity in a PCP

[rsterne]

HI Douglas.... Good questions, please supply the answers.... The "simple" answer that the pressure is zero is the wrong one, because some of the molecules are moving much faster, or we wouldn't be able to achieve more than ~1650 fps using air, and that has definitely been done.... To answer the second part, we need to know if the speed of the molecules is relative to the moving mass of the gas, or the barrel.... All I can tell you is that the idea that you can't exceed 1650 fps in a barrel using air is wrong....

Once again, all of these things are reasons that we cannot achieve the calculated maximum FPE for (bore area) x (pressure) x (length)....

Bob

[rgb1]

A few more details for Lloyd.
Chamber D has a fixed charge pressure of ~ 900 psi. Initially, before
the gun is pumped, the valve will be closed by moving it all the way
to the left and the piston will be against wall A. Pressurized air from
the pump is introduced thru a transfer passage in corner B. The
additional ~ 12 cu. in. of air will move the piston to the right approximately
.2 in. and the pressure in both C and D will rise to ~ 1000 psi. The valve
is self opening because of the larger diameter at E. The discharge
part should be self explanatory.

                                                                          Ron

[wwonka]

If there is a projectile moving away from a volume of gas at its mean molecule velocity...what happens to the pressure? Take this over a dx long bit of travel and a dt long time period so we won't have to worry about replenishing the volume behind it... Better still answer this at any particular velocity and find out what this available pressure v. projectile speed plot looks like.
cheers,
Douglas

I hear you. But whatever that answer is, the absolute ceiling for any given starting pressure is going to be the simple formula that has already been calculated in this thread. That is the beauty of that formula. It's not trying to predict what the actual performance will be, it's giving you a quick back-of-the-envelope limit on the performance. And that limit is useful for a lot of things.

If someone with TOO much time on their hands wanted to, they could go full-blown calculus on this thing, but that would just give lower ceilings based on the attenuation of pressure as the bullet travels, and the effects of friction, etc. But then, you're doing something else - and it's not as useful as the simple formula.

[PakProtector]

Yes Wonka, I am quite familiar with the 'neglecting air resistance' answer... The better means of figuring out what the real ceiling is would require knowing what the pressure v. delivered velocity is. At least we would know how close the first approximation is....or, how big is the effect at less than 2/3 mean molecular velocity?

If I am going to discount something, I want to know how big it really is...LOL
cheers,
Douglas

Bob, I have no idea what the answer is...I have a suspicion but no proof.

[Cal]

Well,  As the moderator discourages the introduction of elements that may cast reality on a theoretical model, I will "interject" instead of "derail".  That is,  no reply comments expected.  ;-)

When I look at theoretical calculations and models,  I look to the extreme conditions and see how things hold up.
In this thread,  one extreme might be  a zero mass projectile or one of "point Oh so small" mass anyway .  Think of it as the propelling gas mass velocity limit.
Another extreme might be a <1 psi propelling force (think blow gun).  Viscosity must come to play,  but that is definetly OT,  so no sense to bring that up (even if the mere mention of hydrogen implies as much)
Combinations of any and all does tend to get confusing.  If it could only be as simple as the math implies.

[Hanabata808]

Here’s an example of working backwards from a theoretical max velocity to what we might actually get from a real PCP.

...
3) Add the mass of the column of air that must be accelerated in the barrel behind the pellet:
1562 fps,  136 FPE  (major reduction ! )

Would using helium improve these results?

[wwonka]

Here’s an example of working backwards from a theoretical max velocity to what we might actually get from a real PCP.

...
3) Add the mass of the column of air that must be accelerated in the barrel behind the pellet:
1562 fps,  136 FPE  (major reduction ! )

Would using helium improve these results?

Yes, there is less energy spent on accelerating the column because helium is a lighter gas than either Nitrogen (which is mostly what we call "air"), or Oxygen (which is a small part of what we call "air"). 7 times lighter than Nitrogen, 8 times lighter than Oxygen.

[rsterne]

To be clear, the gas makes no difference to the MAXIMUM FPE, that is dependent only on pressure, caliber (bore area), and barrel length.... However, the reduction in power that occurs from including the mass of the gas in the calculations is greater with Air than with Helium.... ie Helium can come closer to the theoretical maximum than air can.... The loss of power with Air is 7.2 times as much as the loss with Helium.... 

Bob

[rsterne]

Here is a graph I published a while back showing the force on a bullet for various pressures and calibers....



If you multiply by the barrel length in feet, that will give you the maximum FPE possible for that combination, as per the simple Physics discussed in this thread.... I have found that for air, if you use 50% of that figure you will have a lofty goal to try and achieve.... I've never quite made it.... As an example, if you look at 3000 psi with a .357 cal and a 24" barrel (2 feet), the maximum is about 600 FPE.... A good goal would be 300 FPE.... Anybody ever done that with a 24" barrel on air?....

Bob

[lloyd-ss]

I have been absent (online) from the thread for a few days but have been diligently working on this topic.  A lot of theory and questions being passed around, mostly with more questions than answers. But that is the nature of this subject. 
And as has been stated here by several of us, there is nothing like hard data to bounce against the theory.  rgb1 Ron posted a sketch of a test set-up and that got me back to thinking of making an apparatus strictly for max velocity testing.  So for the past few days (my wife keeps asking, What have you got going in the shop?) I have been building a "Max Velocity" gun. Or more like a barrel with a tank. I think I have taken a different approach to the actual firing than anyone else has.  Very different from Ron's, and probably not practical for a field gun, but who knows?

I might start a new thread with the actual gun and testing, not sure yet. I built it strictly for .25 cal barrels, because I have a bunch of those on hand.  The first set-up uses a short barrel with an effective length of only 8".  I figured I would see if my idea worked before continuing with other barrel lengths, pressures, grain weights, ports, etc.

I took the first shots last night.  Technical details will follow.  I first tried some 9 grain plastic projectiles and they didn't function very well in the gun.     So I resorted to making a brass projectile, which is re-useable, but it is hefty 54 grains (.25 cal).  It worked decently for a first try, but I only got one good shot before I had an equipment malfunction.      (The wooden filler plugs I was using inside the tube to reduce the shot volume kind of exploded     ). More work will be needed in the next few days as this gun evolves. But anyway, the good shot is as follows:
.25 cal
8" barrel
54 gn brass "bullet"
20 cc air
2800 psi
Actual velocity 707 fps
Actual energy 60 fpe

Theoretical Maximum Velocity 874 fps (for this gn wt, psi, barrel cal and length)
Percent of Theoretical Maximum Velocity achieved  81% 

I am pleased with the result for a first try, but there is much more work to be done with lighter projectiles and longer barrels.
Here are a couple of pics.

Lloyd

View of the straight shot through the 8" barrel.


The test set-up


 

[rsterne]

Pretty interesting, Lloyd.... I'm actually pretty shocked you got to over 80% on air.... Got any Helium?.... 

EDIT: Did I do the math right?.... .25 cal.... area = (.25^2) x PI/4 = 0.0491 sq.in.... times 2800 psi = 137 lb.f.... time 8/12 ft. = 91.6 FPE.... 60 FPE is 66% of that.... If the barrel is .257 cal, the max. would be 96.8 FPE, and you would be at 62%.... Oh, wait a minute, you are talking velocity, not energy, we got the same thing.... 



Bob

[lloyd-ss]

Bob, The set-up needs some tweaks, but the method is solid.  I hope to exceed 80%.
Helium?  I have been thinking about that. 
Lloyd

[rsterne]

See Edit above....

Ran the numbers through your spreadsheet, using 20cc, no TP volume, 1 lb. drag, 2 lb. breakaway, air mass included, isothermal, got 89% efficiency.... Changed to Helium, got 753 fps at the same efficiency.... Overall efficiency of your one "good" shot is 60 FPE / 235 CI = 0.26 FPE/CI....

Bob

[lloyd-ss]

See Edit above....

Ran the numbers through your spreadsheet, using 20cc, no TP volume, 1 lb. drag, 2 lb. breakaway, air mass included, isothermal, got 89% efficiency.... Changed to Helium, got 753 fps at the same efficiency.... Overall efficiency of your one "good" shot is 60 FPE / 235 CI = 0.26 FPE/CI....

Bob

Bob,
For this exercise, a test set-up that can only make dump shots, efficiency in FPE/stdcuin based only on reservoir volume is irrelevant and misleading.  "IF" the valve could have been closed when the bullet left the muzzle, efficiency would have been about 1.02 FPE/cuin, which gives the relevant information about the actual flow characteristics and efficiency of valve and barrel.

I chose to compare the actual shot results against the theoretical maximum velocity rather than FPE for a particular reason.
I think the linear change in velocity represents a more realistic perspective on the changes made in the airgun performance, when the performance is judged against the THEORETICAL maximum.  For instance, your velocity might be at 60% of the max theoretical, but the FPE would only be at 36%.     The FPE comparison shows an unnecessarily  bleak and  discouraging comparison to what really is rather good performance.  This not trying to sugar coat the results, it is just choosing a more realistic perspective, IMHO.
 
EDIT: Bob, I re-read some of your previous posts about theoretical maximums and see how you have been referring to percent of max theoretical FPE, not FPS. Either approach will work, obviously, it is just which one do you decide to use and the purpose of the testing or the goal of the project.   So lets try it both ways in this thread.  For the one "good" shot that I managed to take, it achieved 81% of max theoretical velocity and 65% of max theoretical energy.  More work to be done!      Lloyd
Lloyd

[sixshootertexan]

Lloyd that looks like something Mythbusters. Way cool. Maybe hook up a vacuum like they did to shoot a ping pong ball at over Mach.

[rsterne]

Lloyd, the FPE approach is independent of bullet weight, that is why I prefer it.... and it is much simpler to calculate.... However, stating both is probably a good idea.... Either way, I think heavy bullets will be favoured, don't you?.... particularly if it makes a difference between pushing Mach or not....

Bob

[lloyd-ss]

Bob, Yes, the heavy bullets should favor approaching the max theo FPE, but as the title of this thread indicates, chasing that illusive "Maximum Velocity" of a projectile propelled by compressed air (or nitrogen or helium) is one of the driving factors of this experiment.  That will require a very light projectile, and my 54 grain brass one certainly isn't a lightweight, 
I am making some aluminum projectiles right now.
Lloyd

Sixshootertexan, mentioning me in the same breath as Mythbusters is quite flattering.     I will see if I can live up to that "myth"!   

[rsterne]

My gut feel is that you will be able to more easily reach a higher percentage of the "maximum theoretical velocity" with a heavy bullet than a light one.... particularly once you start pushing supersonic.... but that is what experiments are for is to find out, right?.... 

Bob

[lloyd-ss]

I made a 17gn, 25 cal aluminum projectile to try in the test set-up.  Managed to get one shot tonight and here are the results.
Specs:
25 cal, 8 inch barrel, 30ccs, 17gn,  2900 psi.
Results:
1110 fps, (70 %of theo max)  46.5fpe (49% of theo max.)
The results were a little disappointing compared to the heavier pellet, but still, for an 8" barrel, not too bad.

Here are a few pics of the test.

The aluminum bullet and the barrel


The bullet loaded into the barrel.


1110FPS from an 8" barrel.


Retrieving the bullet, unscathed, from the box of plastic grocery bags.

[QVTom]

Lloyd, do you just rotate a half moon rod and off goes the projectile?

Tom