Spring Piston Simulator Project

[WhatUPSbox?]

The holding force is what enables full air pressure to be reached before the pellet breaks free. 

I think the pellet motion starts long before full pressure. George Schmermund's pressure transducer based data on a .22 CO2 barrel had motion start at about 232 psi. My Accelerometer based data for a .22 gas ram gun showed the pellet motion start as early in the pressure rise.

[WhatUPSbox?]

Nice work Marty.
It may be interesting to plot pressure vs. pellet position and or velocity. It would show the break free pressure as well as the rise and fall of the friction term as the pellet moves down the barrel.

I my head, the pellet/barrel interaction partitions more clearly into skirt effects and body/head effects. The skirt effects include the pressure term and cover friction including the rifling. I don't think you can separate that out. The body/head effects would be pressure independent (though velocity dependent) and may be dimensionally driven. You may be able to capture some of this in testing by pellet head size.
The pellet elastic (and actually plastic) deformation energy may need an FEM analysis. I don't think Tavella's suggestion of pushing a pellet down the barrel will capture the effect.

Like I said earlier, great work!

[subscriber]

I think that if you had a test bed where could ramp the air pressure slowly,, the pellet would stat moving at lower pressure than in an actual air rifle.  This would be in part due to pellet inertia and friction.

As for pellet friction down the barrel, that should be a lot lower than while pellet is being swaged down into the bore.  After the rifling is fully engraved and the air pressure starts to drop due to the enlarging expansion volume, friction should drop off and remain near constant until the pellet reaches the choke.  Am aggressive choke probably uses up significant pellet energy.

As long as the air pressure is high enough to force hard contact between pellet  skirt and barrel, friction is likely to be significant.  If the barrel has constrictions in the diameter anywhere a long the length, friction there is likely to reduce efficiency.

A  soft or thin pellet skirt is likely to reduce breech cone pressure, but if the skirt balloons a lot it increases friction in part due to the length of skirt contact down the rest of the barrel.  Both breech cone pressure and barrel friction would be affected by the diameter of the skirt before the pellet is fired.  To some degree a more expandible pellet skirt will increase friction, as the air pressure in the skirt forces hard skirt to breech cone and barrel contact. 

This is a bit like drum brakes, where wheel rotation draws the brake shoes in on a wedge or pivot, making them self actuating to a significant degree.  Also the reason why drum brakes tend to lock the wheels and not allow them to start turning again when the brakes are released.  Although that may be problem associated with early designs, before vacuum brake boosters were common.

So, with a springer, either side of the point where the pellet starts to move, building air pressure feeds friction; and increasing friction feeds the build up of air pressure - until the piston stops moving forwards.  This is due to the very abrupt "crash" of the piston into the air ahead of itself, being stuffed into a tiny space.  Not what would happen if you fed air to the base of the pellet more gently and ramped the pressure slowly.  At least in the model in my head

[subscriber]

I am not sure what the breech looks like on the CO2 airgun used by George, but any probe loaded PCP that pushes the pellet into the bore to some degree is not a good model for a spring piston airgun.  The latter have a breech cone that has the pellet finger loaded to just make contact with the cone.  A probe loaded PCP would be similar to deep seating the pellet in a springer's breech cone.  The PCP' air is pre-compressed and does not need a breech cone to build the air pressure on firing the way a spinger does.

At one time pellet loading tools were popular. All well and good for uniformity, but some people thought they were helping by overcoming the breech cone force, by deep seating pellets.  If they ran their pellets over a chrono and observed lower velocities, they might consider that the lost pellet energy went into slamming the piston harder.

The holding force is what enables full air pressure to be reached before the pellet breaks free. 

I think the pellet motion starts long before full pressure. George Schmermund's pressure transducer based data on a .22 CO2 barrel had motion start at about 232 psi. My Accelerometer based data for a .22 gas ram gun showed the pellet motion start as early in the pressure rise.

[WhatUPSbox?]

I don't think the pellet knows (or cares) what is causing the pressure on its rear end to rise. Once its fingernails can't cling to the barrel wall anymore, off it goes.  Geometric tolerances and pellet material probable drive this, but it happened well before peak pressure.
I think I remember Lloyd did some of his high velocity tests with a pellet equivalent that was restrained until peak pressure was achieved.

[MartyMcFly]

Nice work Marty.
It may be interesting to plot pressure vs. pellet position and or velocity. It would show the break free pressure as well as the rise and fall of the friction term as the pellet moves down the barrel.

I my head, the pellet/barrel interaction partitions more clearly into skirt effects and body/head effects. The skirt effects include the pressure term and cover friction including the rifling. I don't think you can separate that out. The body/head effects would be pressure independent (though velocity dependent) and may be dimensionally driven. You may be able to capture some of this in testing by pellet head size.
The pellet elastic (and actually plastic) deformation energy may need an FEM analysis. I don't think Tavella's suggestion of pushing a pellet down the barrel will capture the effect.

Like I said earlier, great work!

Thanks Stan! I’m working on adding some nicer graphs that should show the timings and positions a bit better. But I gotta work to pay for eggs first , wish I had more time.

-Marty

[WhatUPSbox?]

One interesting parameter that you may be able to extract from your analysis is the net force on the rifle. This would be the pressure times the compression head area minus the force between the aft end of the spring and the wall. This is in essence the acceleration of the unconstrained rifle. It is also what I attempted to measure with accelerometers in this graph. It shows the acceleration as a function of time and also includes (overlayed from a number of shots) the pellet position in the same timeframe. It is an external measurement beyond just muzzle velocity that one could compare to modeling results.
https://www.gatewaytoairguns.org/GTA/index.php?action=dlattach;topic=176445.0;attach=360073;image
https://www.gatewaytoairguns.org/GTA/index.php?topic=176445.msg156155029#msg156155029

[ballisticboy]

I wrote a program about 10 years ago which was able to predict the effects of changes to a spring gun, but not until it had been calibrated against known measured characteristics for the gun in its original state. There are just too many variables at work.

Take pellet release pressure, there is a difference in the release pressures depending on the rate of increase of the pressure. The pellet will move at a lower pressure for a slow increase in pressure than it does for a rapid increase. Also, the gas specific heat factor gamma will be different at the high temperatures and pressures in the rifle which will affect the speed of sound in the gas and thus the flow through the transfer port.

The friction coefficients for the various parts are all mostly unknown, and measuring them under the correct conditions is difficult. The pellet has a different friction coefficient when it is sliding than it does when stationery, and the pellet velocity also has an effect on the friction value. There is in addition the mechanical interactions as the pellet deposits lead in the barrel. Friction plays a major part in the gun efficiency and is difficult to get right. The most efficient spring gun I have come across was a 12 FPE rifle with a small diameter piston, sealed with O rings, which had an efficiency of just over 60% as measured by the pellet energy as a fraction of the available spring energy.

So you can get useful information from the models, but it takes a lot of effort to develop the model and to calibrate all the separate parts. The Cardew book is useful for the initial development.

[subscriber]

Thanks, Miles

60 percent efficiency is very impressive.  Perhaps double the typical springer efficiency?

Can you remember the piston diameter of the efficient air rifle you mentioned? 

I wonder if smaller bore pistons experience less bounce at usefully high pressures...

[MartyMcFly]

I wrote a program about 10 years ago which was able to predict the effects of changes to a spring gun, but not until it had been calibrated against known measured characteristics for the gun in its original state. There are just too many variables at work.

Take pellet release pressure, there is a difference in the release pressures depending on the rate of increase of the pressure. The pellet will move at a lower pressure for a slow increase in pressure than it does for a rapid increase. Also, the gas specific heat factor gamma will be different at the high temperatures and pressures in the rifle which will affect the speed of sound in the gas and thus the flow through the transfer port.

The friction coefficients for the various parts are all mostly unknown, and measuring them under the correct conditions is difficult. The pellet has a different friction coefficient when it is sliding than it does when stationery, and the pellet velocity also has an effect on the friction value. There is in addition the mechanical interactions as the pellet deposits lead in the barrel. Friction plays a major part in the gun efficiency and is difficult to get right. The most efficient spring gun I have come across was a 12 FPE rifle with a small diameter piston, sealed with O rings, which had an efficiency of just over 60% as measured by the pellet energy as a fraction of the available spring energy.

So you can get useful information from the models, but it takes a lot of effort to develop the model and to calibrate all the separate parts. The Cardew book is useful for the initial development.

Miles, the current simulation is only calibrated to my TX200 in the sense that I took some quick spring and dimensional measurements. I have not calibrated any of the other frictions based on my rifle. I took the friction coefficients as given in Tavella's paper, which are based on a different gun. Either I got extremely lucky and Tavella's friction measurements are very close to my TX200 or his friction measurements don't vary too much from one rifle type to another. I sincerely hope that it is the latter, but future testing should confirm what is happening in real life.

That said, my long-term intent is to get some force gauges and to check how close my rifle matches the friction figures from the paper. Lastly, I am skeptical about the 60% efficiency of reduced piston size designs. The Tony Leach kits, which shrink the piston down to 22mm, are said to be up to 40% efficient. I'm in possession of one of these kits and intend to test the real-world performance. I'd love to get my hands on one of the titanium kits form the UK to compare too... If 60% efficiency is possible that would be outstanding.

-Marty

PS. Miles, If you happen to have access to the rifle that is 60% efficient it would be great if you could share the rifle's internal dimensions, spring measurements, etc. I can plug it into the sim and see what comes out.

[ballisticboy]

The 60% efficiency gun was one of Tony Leach's development guns using, as I said, o rings and not parachute seals. It makes a large difference while they are sealing. I was running some early development numbers through the model for him at the time. I don't have any details of the gun any more. Jim Tyler was also carrying out experiments with a full length HW77 at the time and getting efficiencies of 40% with a conventional layout using different types of springs.

[MartyMcFly]

The 60% efficiency gun was one of Tony Leach's development guns using, as I said, o rings and not parachute seals. It makes a large difference while they are sealing. I was running some early development numbers through the model for him at the time. I don't have any details of the gun any more. Jim Tyler was also carrying out experiments with a full length HW77 at the time and getting efficiencies of 40% with a conventional layout using different types of springs.

Thanks for the additional color. I love my TL kit and its one of the reasons why I decided to finally do this project. I'm very curious to see how the Tony Leach specs square up against the simulator, but I don't want to jump the gun. First, I want to be sure that the predictions I'm getting for the unmodified TX aren't a fluke. For the TL kit my best guess is that the faster compression due the lighter and reduced diameter piston is overcoming the loss from the additional piston mass.

I hope that Jim will chime in too. I've seen him around GTA a few times before, so I know he's lurking around

-Marty

[JPSAXNC]

Something else to consider, there's often a restriction where the barrel is forced into the breech block, and then there's the choke. Both usually harder for the pellet to get through than the release at the breech.

[MartyMcFly]

Something else to consider, there's often a restriction where the barrel is forced into the breech block, and then there's the choke. Both usually harder for the pellet to get through than the release at the breech.

Good points. I think the breech restriction can be largely captured by the pellet's initial stiction. I haven't given the choke much thought. Although choke does slow down the pellet, my guess is that it's probably by no more than 10-15 fps. Only way to know for sure would be to take a rifle and either cut off the barrel end or enlarge it. For now, these effects will be netted into the pellet stiction and deformation frictions. I might come back to them later for more detailed handling.

-Marty

[MartyMcFly]

Nice work Marty.
It may be interesting to plot pressure vs. pellet position and or velocity. It would show the break free pressure as well as the rise and fall of the friction term as the pellet moves down the barrel.

I my head, the pellet/barrel interaction partitions more clearly into skirt effects and body/head effects. The skirt effects include the pressure term and cover friction including the rifling. I don't think you can separate that out. The body/head effects would be pressure independent (though velocity dependent) and may be dimensionally driven. You may be able to capture some of this in testing by pellet head size.
The pellet elastic (and actually plastic) deformation energy may need an FEM analysis. I don't think Tavella's suggestion of pushing a pellet down the barrel will capture the effect.

Like I said earlier, great work!

Stan, here is the graph you were interested in. It shows that the pellet starts moving before max pressure is reached, but it's very hard to see due to the scaling so I added a vertical line to show exactly when this happens. I would be very cautious in accepting this data without further testing. The model has stiction friction on the pellet, but the force might be set too low and thus result in the pellet moving too early. The movement looks plausible, with the pellet taking off like a rocket near max pressure. Take this output with a grain of salt...

PS. I've been looking at the pellet acceleration graphs. The change in acceleration is incredible, which makes me think that most of the friction force would come not from the barrel lands or stiction, but from the pellet deforming due to the high Gs.



-Marty

[WhatUPSbox?]

Marty, Thank you for posting the curve.
It was interesting to compare your model results to the test results I posted the link to.
In both cases the pellet passes through 200 mm pretty much towards the end of the pressure spike. In your model, it looks like it takes about 1.4 ms to get there. In my tests it was about 1.8 ms. I was shooting a .22, 14.7 gr pellet, so the slower start make sense. It is also a gas ram which has a different pressure rise curve. It may be that your friction model is not that far off. How does it compare to the bounding "no pellet friction" case?

[MartyMcFly]

Marty, Thank you for posting the curve.
It was interesting to compare your model results to the test results I posted the link to.
In both cases the pellet passes through 200 mm pretty much towards the end of the pressure spike. In your model, it looks like it takes about 1.4 ms to get there. In my tests it was about 1.8 ms. I was shooting a .22, 14.7 gr pellet, so the slower start make sense. It is also a gas ram which has a different pressure rise curve. It may be that your friction model is not that far off. How does it compare to the bounding "no pellet friction" case?

Stan, I'll see what I can do with getting additional data points. BTW, you just gave me an idea to add a gas ram option in the future. I'll have to do some research on how to implement it but I'm very curious as to how efficient gas rams are versus springers. I believe that gas rams accelerate the piston faster than a traditional spring which undoubtably results in their faster lock times. But what is less spoken about is that with faster lock times you get higher pressures and temperatures over a shorter time interval. To me that means there is a possibility that gas rams are more efficient than springers. I say 'possibility' because as I stated before I also believe that elastic deformation of the pellet is a large friction component, which means that faster acceleration may lead to more radial friction than you would get with a slower lock time.

This is just a thought, but maybe we can couple a gas ram with a transfer port and breech cone designed to spread out the pressure force on the pellet over a longer period of time (more like a PCP). I still need to verify this, but it's my assumption that most of a springer's pellet velocity is generated over a 2ms period near the max pressure point, which results in almost instantaneous acceleration and therefore higher deformation friction. If you can spread out the acceleration to 4ms we might be able to reduce the total friction and increase efficiency.

That said, we should not forget that this might also be achieved with clever pellet design and twist rates. Pellet deformation is not only driven by acceleration but also on the mechanical properties of the material it's made of and the centrifugal force from its spin. For example, a pure lead pellet will have a lower Young's modulus than an alloy pellet. This means that it compresses more during acceleration and thus creates more friction. Furthermore, the timing and magnitude of pellet spin can also have an impact on friction. Centrifugal expansion from pellet spin creates radial forces that add to elastic deformation friction. Therefore, it would make sense to have a twist only at the end of the barrel and to use materials that have high Young's modulus, or which have a very small contact area with the barrel. 

Anyways, these are just my musings. I hope I haven't put you guys to sleep.

-Marty

[WhatUPSbox?]

Marty,
I'm not sure what you mean by faster lock times.
George Schermund measured the Gas ram force in the Titan. He got 140 lbs preload and 213 lbs compressed 4 in. So the gas ram has a much flatter force curve than the metal spring's Kx with a smaller preload.
https://www.gatewaytoairguns.org/GTA/index.php?topic=176445.msg156015839#msg156015839
In my testing, at one point I compared the gas ram Titan against the spring driven Quest. The first was .22 and the latter .177 but overall they put out similar FPE.
https://www.gatewaytoairguns.org/GTA/index.php?action=dlattach;topic=176445.0;attach=348841;image
In the image, the yellow traces are accelerometer measurements at the scope mount. Positive is forward. It shows the springer with a much higher initial rearward recoil (more negative) due to higher spring force and then falling off as Kx ( and eventually the seal friction and pressure rise) The gas ram has a much more constant recoil until the seal/pressure rise.

[MartyMcFly]

Stan, by faster lock time I mean that the piston completes the full stroke in a shorter amount of time.

Yes, you are correct. The gas ram has a flatter force curve than a metal spring. Assuming that there is no dampening force acting on the spring, it will have its peak acceleration at the very beginning of its motion and slow down linearly. On the other hand, the gas ram applies its peak force across the entire travel, thus its acceleration (assuming no dampening) remains constant until its full extension. However, this difference results in the gas ram completing its full stroke faster than the metal spring, because on average the gas ram is accelerating more, even if the metal spring has a higher peak acceleration at the beginning. In fact, as you stated the metal spring's higher initial acceleration lines up well with the bigger rearward recoil. This also implies that in a springer the pellet might experience higher elastic deformation, at least initially.

Lastly, not taking into account the friction from the seal, the gas ram may generate more force over the same stroke length because it is sustaining the acceleration for longer (i.e. F=ma * t). I'd like to hedge this statement by saying that this is in theory only. Right now, we don't know the scale/impact of the friction from the ram seal nor whether choke conditions in the transfer port become a limiter before the peak air pressure is reached.

PS. If anyone knows the physics better, please jump in and correct me. I not a physics major, but I stayed in a Holiday Inn last year

-Marty

[mikeyb]

...add a gas ram option in the future. I'll have to do some research on how to implement it but I'm very curious as to how efficient gas rams are versus springers. I believe that gas rams accelerate the piston faster than a traditional spring which undoubtedly results in their faster lock times. But what is less spoken about is that with faster lock times you get higher pressures and temperatures over a shorter time interval. To me that means there is a possibility that gas rams are more efficient than springers. I say 'possibility' because as I stated before I also believe that elastic deformation of the pellet is a large friction component, which means that faster acceleration may lead to more radial friction than you would get with a slower lock time.

Shorter "lock time" is a myth you should be able to disprove once your gas spring simulation is running. My sim showed a gas spring WITH THE SAME STORED ENERGY as a coil spring has a slightly LONGER lock time. The gas spring is about 8%-10% SLOWER than the equivalent coil spring. The "perceived" quicker lock time may be due to the lack of lingering spring vibrations? The FORCE profiles are different with the gas spring "initial force" being LOWER and "end force" being HIGHER than a coil spring. This does lead to a larger perceived 2nd recoil force. Some confirmation of the hypothesis that gas springs kill more scopes.

I've tested airguns that are the same model where one has a coil spring and the other has an air spring. Except for the different force profiles FELT during the cocking cycle, the shot cycles seemed identical. If you handed me either rifle already cocked I could NOT feel any difference between the 2 different springs during the shot. Chronograph data and pellet group size at 30' (open sights, no scope) were the same. IMO there is NO REAL SIGNIFICANT PERFORMANCE ADVANTAGE to using a gas spring. The big difference is that it is EASIER for the manufacturer to charge more money for and "claim" better performance on a rifle that shoots the SAME as a properly lubed coil springer with a fitted spring guide. That being said, gas spring rifles do shoot well right out of the box... no rework/tuning needed. Except for the high rate of leaky Vortex AIR springs there is no real NEGATIVE performance from gas(N2) spring rifles.

This is just a thought, but maybe we can couple a gas ram with a transfer port and breech cone designed to spread out the pressure force on the pellet over a longer period of time (more like a PCP). I still need to verify this, but it's my assumption that most of a springer's pellet velocity is generated over a 2ms period near the max pressure point, which results in almost instantaneous acceleration and therefore higher deformation friction. If you can spread out the acceleration to 4ms we might be able to reduce the total friction and increase efficiency.

That said, we should not forget that this might also be achieved with clever pellet design and twist rates. Pellet deformation is not only driven by acceleration but also on the mechanical properties of the material it's made of and the centrifugal force from its spin. For example, a pure lead pellet will have a lower Young's modulus than an alloy pellet. This means that it compresses more during acceleration and thus creates more friction. Furthermore, the timing and magnitude of pellet spin can also have an impact on friction. Centrifugal expansion from pellet spin creates radial forces that add to elastic deformation friction. Therefore, it would make sense to have a twist only at the end of the barrel and to use materials that have high Young's modulus, or which have a very small contact area with the barrel. 

Anyways, these are just my musings. I hope I haven't put you guys to sleep.

-Marty

BTW ;-) It's the Holiday Inn Express www.youtube.com/watch?v=8dOHEw8izno