Measuring internal ballistics- first attempt ** NEW SET_UP in Reply #51

[rsterne]

If I understand correctly, Lloyd plans more than 3 sensors, in order to plot acceleration curves along the barrel with different pressures and bullet weights.... The goal is to confirm how accurate the modelling done by his Internal Ballistics Spreadsheet is.... It already takes into account friction (starting and sliding), pressure drop due to finite reservoir volume and wasted port volume, and the biggest loss which is the mass of the air being accelerated (though the model for that is imperfect)…. but still we need a "fudge factor" for that missing ~30% and that is what he is trying to figure out....

Bob

[Scotchmo]

If I understand correctly, Lloyd plans more than 3 sensors, in order to plot acceleration curves along the barrel with different pressures and bullet weights.... The goal is to confirm how accurate the modelling done by his Internal Ballistics Spreadsheet is.... It already takes into account friction (starting and sliding), pressure drop due to finite reservoir volume and wasted port volume, and the biggest loss which is the mass of the air being accelerated (though the model for that is imperfect)…. but still we need a "fudge factor" for that missing ~30% and that is what he is trying to figure out....

Bob

There is also the adiabatic nature of the expansion that you must account for.

Based on Lloyd's earlier experiments with the super-sonic dump gun, we know where the "losses" are not.

I did a spreadsheet that accounted for all energy in the dump gun model (no fudge factors). If you are talking about pellet-FPE/air-energy, than 70% is about the expected "efficiency" at typical airgun velocities. And that efficiency falls off quickly as you attempt to push for higher velocities. Most of those so-called losses are not missing, they just don't end up in the pellet.

I would not expect any better "efficiency" than about 70%, even with a perfect valve/port design.

[CraigH]

The more sensors the better.   Bu with whatever data, a differential equation can be developed to plot the precise curve of acceleration with calculus.   Or so I was long ago lead to believe - quite well beyond current capabilities.

[TPL]

Scott, I think these guys have considered adiabatic nature of process but how much it really is adiabatic and how much diabatic? In which time period? That we really don't know. I would like to see measurement method that gives us exact temperature and pressure gradient inside barrel over shot cycle but I think we never will. What comes to pressure it is possible but temperature real time measurement would be even more than rocket sciense. Not possible with low budget if at all.

Please don't tell me air is cooling as pressure drops as if I wouldn't know it. Our barrels can have thin ice coating after shooting in cool moist conditions but what we see is long time result. We still have no good idea what happens inside barrell over one small time period of shot cycle.

However, it would be possible reasoning it all by only having pressure gradient but it takes pressure should be measured based on time. Not just indicate when bullet bypasses certain point. That is the reason why I mentioned strain gauges.

[rsterne]

The shot cycle in our PCPs is neither purely isothermal, nor purely adiabatic.... and I am quite convinced that the type of expansion is different while the valve is open (and the reservoir is part of the system) or closed (when only the air in the barrel is expanding)…. Timo is correct, Lloyd's spreadsheet has the ability to use either (or in fact something between the two) for each part of the shot cycle, separately....

It is not a matter of trying to achieve 100% efficiency, we all know that is impossible.... it is a matter of trying to figure out WHERE that "missing" ~30% of the energy is going.... IMO....

Bob

[TPL]

Yes, isothermal is the term I tried to recall..    It is the matter of understanding.

[subscriber]

It is not a matter of trying to achieve 100% efficiency, we all know that is impossible.... it is a matter of trying to figure out WHERE that "missing" ~30% of the energy is going.... IMO....

Hi Bob,

Excuse my ignorance, but how is the 100% baseline energy calculated?

I have seen a rule of thumb of 16.5 CC.BAR per ft.lb PCP airgun pellet energy values, but this already accounts for losses.  Also, the energy content of air surely depend on the starting pressure.  The higher the pressure, the greater the energy content:

In playing around with a P17 (single stroke pneumatic pistol with a dump valve), increasing the compression pressure by reducing the residual volume boosts pellet velocity.  The extra energy comes from the extra force required to compress that air.  The scavenging efficiency is no doubt also improved in the manner that an air compressor's efficiency is improved when the residual air space above the piston is minimized.

While PCPs do not burn fuel, it may be interesting to note that the best diesel engines convert only 50% of the chemical potential energy in the fuel into power available at the crankshaft.  So, getting 70% of the energy in the compressed air into a pellet would seem spectacular in comparison.

The energy content of fuel is measured by capturing the temperature increase of a container full of a working fluid, having a known specific heat capacity; when a specific volume of that fuel is fully burnt.  How do you measure or calculate the full energy content of compressed air?

As for pellet friction; if it takes 4 lb of force on average to drive a pellet down a two foot long barrel, then that represents an 8 ft.lb loss.  If the pellet still achieved 40 ft.lb, then that loss is 4/44; thus 9%. 

If you look at the compression volumes of springer air rifles for their pellet ft.lb, and compare that to equivalently power PCP, that my help quantify adiabatic cooling losses in PCPs.  The unknown here is how much a springer loses due to piston bounce. 

If piston bounce losses are significant, and yet springers achieve perhaps twice the power of PCPs from the same swept volume, as measured at one atmosphere, that might suggest cooling of air on expansion in PCP barrels  is significant.  Yes; I realize there is a difference between cooling, and the absence of heating.

I notice a lot of videos of PCPs being fired show a vapor cloud "exiting the muzzle".  Considering how many of these videos are made by people using dried aqualung air, that cloud may be moisture in the surrounding air, condensed by contact with the much colder exhaust air from the barrel.  Perhaps Lloyd can find a way to measure that temperature drop and quantify the energy involved.

[Scotchmo]

The shot cycle in our PCPs is neither purely isothermal, nor purely adiabatic.... and I am quite convinced that the type of expansion is different while the valve is open (and the reservoir is part of the system) or closed (when only the air in the barrel is expanding)…. Timo is correct, Lloyd's spreadsheet has the ability to use either (or in fact something between the two) for each part of the shot cycle, separately....

It is not a matter of trying to achieve 100% efficiency, we all know that is impossible.... it is a matter of trying to figure out WHERE that "missing" ~30% of the energy is going.... IMO....

Bob

Assuming a large enough reservoir and no constrictions: While the valve is open you have flow only. Once the valve closes you have expansion only and are now in the adiabatic phase.

Knowing that the 30% losses are not in the valve, we know that we will never be able to improve on that figure, even if we are able to measure where all the "missing" energy is.

For a given gas type, pressure, reservoir, temperature, bore, barrel length, pellet mass, etc, there is a predetermined efficiency that is possible. Regardless of the port/valve/dwell system, we cannot improve on that efficiency, we can only be worse than that.

I know where the majority of the "missing" energy is. It's still in the gas (air).

[rsterne]

Subscriber, the "maximum" FPE is of course bore area x pressure (ie force) x barrel length, but will never be achieved because that includes the FPE imparted to the air exiting the barrel as well as the bullet.... In actual fact, if we reach 50% of that number, using air in a PCP, we have done a spectacular job.... However, most of the losses are incorporated into Lloyd's spreadsheet, and we are still "missing" some energy.... Some is undoubtedly lost due to adiabatic cooling of the air, but if you assume Scott is correct, and use a huge reservoir and keep the valve open until the bullet exits, then cooling should not occur.... yet we are still "missing" that energy....

All Lloyd is trying to do, I think, is help us understand where that lost energy is going.... In a "perfect" model, no "fudge factor" would be required, all losses would be known and quantified.... The 70% efficiency includes the energy lost to the air, to the pellet we are nearly always under 50%....

Bob

[subscriber]

"maximum" FPE is of course bore area x pressure (ie force) x barrel length

Makes sense.  Thanks, Bob.

I wonder what the hysteresis is for air compression and re-expansion.  Even a steel spring takes a bit more force while being compressed,  compared to the force it delivers when allowed to re-expand.  Air molecules would not seem to have much friction against each other, but has anyone measured the efficiency of air springs, compared to steel?

[subscriber]

Air spring hysteresis: 

https://www.degruyter.com/downloadpdf/j/ijame.2015.20.issue-1/ijame-2015-0009/ijame-2015-0009.pdf

[lloyd-ss]

Great discussion!
Let me throw in a few comments. As Bob said, we are not trying to achieve 100% efficiency (impossible), just trying to determine where the energy is going.
For Scott, I agree that the "missing" energy is in the air that is exhausted out the muzzle of the barrel. My latest spreadsheet, that incorporates Van der Waals equation of state, and some other thermodynamic adjustments (all legit) for the higher pressures used in PCPs, have reduced this "unaccounted for" energy to around 10%.  That's quite an improvement from the previously unaccounted for 30%.

For subscriber, I agree with much of what you say, but springers and PCPs cannot be compared. The energy from the heat of compression is tremendous, and that does not occur in a PCP. But adiabatic cooling definitely occurs in a PCP.

Here is the direction I am still headed in as far as explaining the PCP process. I could be all wrong, but I am getting closer to being able to model what the empirical data demonstrates.

For the sake of illustration, we'll use a .357 cal, 100 gn, 20" barrel, 55cc tank, 3000 psi, zero T-port volume. The valve opens fully, and closes exactly when the bullet leaves the muzzle.
Bear with me on this, but let's say that this PCP actually shot that 100 gn bullet at 925 fps (190 fpe), and because the tank was only 55cc, the final pressure in the tank was 1559 psi. (the final pressure is important because it IS THE measure of how much air was used.) That would mean an air efficiency of .57 FPE/std-cuin of air. This efficiency should not be confused with the actual system efficiency. This number is a simple calculation of how much energy the bullet had compared to the energy used.

So where does the system efficiency come from?  First off, try and visualize the gun barrel like a cylinder with the piston at bottom dead center. The bullet is the piston, and it resists the expansion of the air. The air has to do work to move the piston/bullet. If you do a plain P1V1=P2V2 of the system you are starting with 55cc at 3000 psi and ending with 88cc of air at 1879 psi when the bullet reaches the muzzle (piston is at the top of the stroke).
Unfortunately, if you do proper calculations of the acceleration of the mass of the bullet based on the pressure acting upon it (the pressure is dropping as the air expands), the final velocity (MV) calculates to be 1327 fps with an efficiency of 1.51 FPE/std-cuin. And we know that is not a reasonable number.
So why does the calculation show 1327fps and the actual measured velocity is only 925fps?
Let's start deducting the losses (actually energy conversions).
Pellet breakaway friction. (heat)
Pellet dynamic friction. (heat)
Accelerating the air mass behind the bullet (65 grains of air added to the 100 gns of the bullet). (work done)
Making those deductions, the MV is still an unreasonable 1125 fps.
Let's call this a purely adiabatic process (the air cools as it expands but no heat is transferred to or from the gun). That makes the estimate 1093 fps. This is because as the air expands, it cools, and because it is cooler, it has less pressure to push the bullet.

So, at this point the calcs show 1093fps, but actual MV is only 925fps. If, within the program, you do a blanket reduction of the force on the bullet of 28%, the calculation becomes 925fps, to match the real world.

OK, even if that 28% reduction is indeed due to real losses or conversions, and it obviously has to be, what has happened to that 28%?

At Bob's prodding, I totally revamped the excel spreadsheet. Switched to metric.... long overdue. The basic calculation procedure is the same, but the volumes and masses, and temperatures are now calculated per Van der Waals equation of state for gas mixtures, specifically air, and proper adjustment have been made for temperature and mass of air and the laws of thermodynamics.

Here is how the calculation is done now.
Given the starting pressure, temperature, and volume, the actual mass of the air in the system is calculated. (Scott- this makes mass flow calculations possible). 
Here are some things that are different now, that fall more in line with "proper" thermodynamics. The specific heat of air at 3000 psi is higher than at standard temp and pressure. The ideal gas law and p1v1=p2v2 is no longer true at higher pressures with the air mixture,and, air is not an ideal gas. When that 55cc of air expands almost instantaneously (3 millisecs) to 88cc, its temperature drops by 48 degrees C!! By definition, this is almost a true adiabatic process. That is 77F down to -10F, but with the exit velocity of the air, the extreme temperature is not obvious.  To make a long story short, the calculation is now closer to 975 fps, which isn't to far from the 925 real world example. I think to put it more precisely, losses have not occurred, but energy conversions have been made. Heat from friction has occurred, air has been expanded and cooled, work has been done on the bullet (which now has kenetic energy), and some energy has been converted by the  turbulent flow within the system. The high pressure and the convoluted  path of the air guarantee turbulent flow for much, if not all, of the travel down the barrel.

Honestly guys, this is just my take on the process (along with Bob's input) and what MIGHT be happening inside a PCP. There could be holes in my approach, but this is what I have for now.  I think the calculation is getting closer all the time but it still does not (and can not) compensate for gun-specific characteristics of operation and air flow.

Lloyd-ss

edits-6-24-18 8:16AM, made a couple of corrections in the numbers; added turbulent flow comment.

[rsterne]

Great explanation, Lloyd.... I'm delighted that the new version of the spreadsheet has reduced the missing energy to only 10%.... WELL DONE !!!

Bob

[lloyd-ss]

Thank you Bob. It is still a little rough around the edges and needs some visual refinements. Also, with all the calculations being done in metric (which is actually so much easier!), I have to add conversions for the final outputs so that comparing them to previous data is painless.  I should have a copy for you in the next several days. Then a consultation or several and more refinements and such.
Lloyd

[Mole2017]

Air spring hysteresis: 

https://www.degruyter.com/downloadpdf/j/ijame.2015.20.issue-1/ijame-2015-0009/ijame-2015-0009.pdf

Wow, that brings back memories...in grad school I modeled race car shocks using a similar model (the hydraulic damper has a compressed gas charge, so that part acts as a gas spring). It is so simple, yet it gets the results, especially when you use a nonlinear damping characteristic. I think his results in figure 8 would have looked better if he modeled that stiffness change at 15 mm deflection, but his linear model is enough to show the effect.

Back to the topic, somewhere I've read about fiber optic sensors for this sort of thing. There are two versions. First would be a photogate--drill completely through the barrel and use fiber optics to get the light in one hole and then to the receiver from the other hole. You might have to work at keeping it clean and you'd have to address the difficulties of keeping a hole plugged at high pressures, but that seems doable.

The other that I remembered while writing this is fiber optic pressure sensors. The idea is simple and far out at the same time. Just one hole now, with a light source (laser, I think) and a receiver piggy backed somewhere so it can detect the change in the light signal as the pressure deforms the flat end of the fiber optic. $$$. I think I've seen that used in cylinder pressure measurements in internal combustion engines. While the nice sensors cost money (and give you calibrated pressure measurements), perhaps a DIY version could at least detect the passing of a pellet.

[Scotchmo]

Not sure what exact radial point your sensors are measuring pressure. While at speed, there should be a radial pressure gradient in the bore. Most drastic near the wall. If measured near the bore center-line, the pressure might be close to what is otherwise expected, but it will be higher than at the perimeter. And the reverse for temperature. That is the nature of Fanno flow.

The shear friction ends up as heat in the propelling gas. The propelling gas will end up at a lower pressure and higher temperature than otherwise expected.

This is the same mechanism that determines the upper velocity limit of a PCP airgun.

The energy that we expected to be transferred to the projectile as KE, ends up in the propelling gas as additional heat. If that could be measured, it might account for the "missing" energy.

Then again, I could be wrong.

[WhatUPSbox?]

Thank you for the descriptions of the energy accounting and many of the loss terms.

I'm new to this topic so I just wanted to clarify my understanding of the overall performance measures.

There is comparison against the ideal maximum pellet energy at the muzzle which is, as Bob described simply the source pressure x barrel bore cross section area x barrel length. This comparison is not so much a shot efficiency but rather a comparison against theoretical max pellet velocity

Then there is shot efficiency which is the pellet energy at the muzzle divided by the change in the stored energy in the source tank. For HPA the source tank energy change would be roughly (I realize the actual calc is more complex) a V x delta P change, For CO2, it is roughly proportional to the change in the liquid/vapor mass fraction in the tank, but is probably easiest to tie back to CO2 mass and shot count, and for the springers, it is the compressed energy (1/2 KX²) of the spring.

Am I understanding the performance terminology definitions as they are used in this thread?

Thanks, sorry for the sidetrack into basics

[Scotchmo]

...There is comparison against the ideal maximum pellet energy at the muzzle which is, as Bob described simply the source pressure x barrel bore cross section area x barrel length ...

That would be a more valid statement.

[WhatUPSbox?]

Thanks Scott,

I guess I misunderstood, I thought Bob was describing the ideal barrel where the pellet is pushed by a non-varying source tank pressure for the entire length of the barrel without losses. In that case the energy imparted into the pellet simplifies to the PxAxL and should be the ideal upper limit for those conditions. I'm not sure I understand what maximum energy means if it does not apply to the pellet at the muzzle. I need to re read some of the discussion. Glad I asked

[rsterne]

Stan, the P x A x L term is the maximum energy available for the shot, indeed the "upper limit for those conditions".... Part of that goes into accelerating the air itself, so is not available to accelerate the pellet.... At 3000 psi a .22 cal. barrel 24" long contains 55 grains of air.... This is why the very best of our PCPs on air have great difficulty approaching 50% of the P x A x L theoretical number.... In fact, I use P x A x L / 2 as a "lofty goal" for PCPs running on air....

The ~ 30% loss in the spreadsheet (now about 10% in the latest version) is after you take into account all the known losses.... If you ask me, getting within 10% is quite a feat, Lloyd should be very proud of that result.... I'm looking forward to seeing the latest version of his spreadsheet....

Bob