Air rifle max velocity vs. tank pressure

[Mark44]

I wasn't sure if this was an engineering question or a physics question, but decided to pose it here in the general engineering section.

A friend of mine, Blake, has a high-end air rifle that exhibits some puzzling behavior. The highest velocity for the pellet doesn't occur when the internal air tank is at its highest pressure, but instead occurs after the pressure has dropped a fair amount.

The Excel chart below shows a bunch of data that Blake has captured, with the velocity, in fps, along the vertical axis, and the internal tank pressure, in bars (1 bar = 14.7 lb/in², if memory serves) along the horizontal axis.

We're most interested in the lowest graph, in black. In this graph, the peak velocity is about 900 fps, when the tank pressure has dropped from 190 bars to 120 bars (from about 2800 psi to about 1800 psi). Obviouly, this is not a Daisy BB gun. The internal tank can be filled using a foot pump, but Blake uses a scuba tank to fill the tank on the rifle.

When Blake asked me why this might be happening, my first thought was that at the higher pressures, some of the pressure might be escaping past O-rings, resulting in less pressure to fire the pellet. He replied that if you start off at the lower pressure, you still get the same sort of concave-down graph, so my theory went down in flames.

My next and final thought was that the peak came after 25 to 30 pellets had been fired, so possibly the friction of the pellets passing through the rifled barrel was causing it to heat up and shrink to make a tighter fit for the pellet, with less air passing around the pellet, and more air propelling the pellet out the barrel.

Does anyone have any ideas about what could be causing the max velocity to peak after the tank pressure has decreased (and after several pellets have been fired)? I don't have any other ideas to offer.

Notes:
1. The velocities are measured with a photo chronograph -- I think that's what it's called.
2. The four graphs come from tests different numbers of turns of the linkage between the trigger and a gizmo that releases air from the internal tank to the chamber behind the pellet. More turns increase (I think) the amount of air that is vented.
3.

 

[Bystander]

First two lines of investigation: 1) Joule-Thomson coefficient for air as a function of P; 2) mass of air behind the pellet being accelerated. Guess there's a third to look at, the drag on the pellet "skirt" at the higher pressures.

Joule-Thomson could be examined best by playing with CO₂; mass of propellant gas is going to be tough to pin down; "skirt drag" could be ruled in/out with a string of solid pellets (less subject to deformation).

 

[256bits]

Looking at the Hatsan site,
http://www.hatsan.com.tr/en_at44_10.html
I could not find the gizmo referred, that is supposed to regulate the air.

Her, by the way is the shot pellet,
http://www.airgundepot.com/jsb-546287.html

 

[Mark44]

Looking at the Hatsan site,
http://www.hatsan.com.tr/en_at44_10.html
I could not find the gizmo referred, that is supposed to regulate the air.

The user manual in the link you provided doesn't show the internal parts. The "gizmo" I described threads into the back of the air tank, and has a needle valve that is actuated by the trigger.

Her, by the way is the shot pellet,
http://www.airgundepot.com/jsb-546287.html

 

[Mark44]

Anyone else want to weigh in?

 

[Doug Huffman]

Locally choked flow?

 

[montoyas7940]

You might be seeing the effects of pellet tumble which would become less severe as the pressure decreases.

How far from the muzzle are you measuring the velocity?

 

[montoyas7940]

He replied that if you start off at the lower pressure, you still get the same sort of concave-down graph, so my theory went down in flames.

Even if you start at the peak velocity pressure or is it true for any lower pressure?

My next and final thought was that the peak came after 25 to 30 pellets had been fired, so possibly the friction of the pellets passing through the rifled barrel was causing it to heat up and shrink to make a tighter fit for the pellet, with less air passing around the pellet, and more air propelling the pellet out the barrel.

Heating the barrel should cause it to expand.

 

[Mark44]

You might be seeing the effects of pellet tumble which would become less severe as the pressure decreases.

That's an interesting thought.

How far from the muzzle are you measuring the velocity?

Say about 2 to 3 feet.

 

[Mark44]

Even if you start at the peak velocity pressure or is it true for any lower pressure?

If he starts out at a lower pressure (where the peak is), he still sees the velocity increase and then decrease.

Heating the barrel should cause it to expand.

I should know better, but apparently that's not firmly etched in my mind. I was thinking, incorrectly, that if you heat a tube, the metal expands in all directions, with the inner wall moving toward the center of the tube's axis. Apparently that's not what happens, so there goes my theory.

 

[berkeman]

Has he tried different shape pellets? It would be interesting to see if pointed pellets and blunt pellets show the same curve.

Sorry if you mentioned it, but has he tried slowly increasing the pressure for single shots? It sounds like he can charge the cylinder to whatever pressure he wants, right? Start low for a couple shots, add a bit of pressure for the next couple shots, and so on up to a couple shots at the highest pressure...

 

[256bits]

Does this make sense ?
The pressurized cylinder is sealed with a valve.
The valve must be spring loaded, so that once opened it will close shut again, with pressuzized air also helping the closure ( and hindering the opening )
The trigger releases a bolt, also spring loaded, that strikes the valve mechanism and temporarily opens the valve releasing air into the pellet chamber accelerating the pellet.
Each firing drops the pressure in the tank, subsequentially less air should be released each time to fire the pellet.

But, the bolt mementum hitting the valve has to overcome the valve spring force and the force from the pressurized air on some area of the valve.
After each firing, less force from the pressurized air will resist the valve opening, and the valve will open up just a bit more and remain open just a little bit longer before closure.

Thus with a high pressure in the tank, the strike of the bolt opens the valve a small value, and closes quickly, so less air can escape, even at high pressure.
( At some high enough pressure, the bolt striking action would not open the valve)
Less air available to accelerate the pellet to less than optimal.
With a low pressure tank, the valve opens to a greater value, and stays open longer for air to escape.
At less pressure, the air can accelerate the pellet to less than optimal.

At some tank pressure, the valve opening and time open, will allow the maximum amount of air mass to escape, accelerating the pellet to its maximum speed.

The gizmo, with the number of turns, sets the bolt striking force - ie. zero being less of a force than turned.

I envision that if the tank pressure was increased beyong 200 bar, curves for 2 and 2.5 turns would follow the same curved pattern as 0 and 1 turn.

 

[Simon Bridge]

If he starts out at a lower pressure (where the peak is), he still sees the velocity increase and then decrease.

... I'd suggest waiting a while between shots, let things settle down, see if the effect disappears. It looks like there are (a least) two competing processes happening.

Some models may help the investigation:
http://www.kiledjian.elac.org/phys 001/Ballistics of Air Gun.pdf
http://home2.fvcc.edu/~dhicketh/DiffEqns/spring07projects/StephenCompton/SpringAirModel.pdf
http://arxiv.org/pdf/1106.2803.pdf

 

[256bits]

You can query some of the air gun sites with question as the users seem to know their guns, since it seems from perusal of their sites that for pre-charged pneumatic guns, the hammer force, the valve mechanics, pressure in the tank, and barrel length will have an influence on the velocity of the pellet.

Here someone does explain the valve operation. It seems to be in agreement with what I wrote earlier.

http://www.pyramydair.com/blog/2006/10/diagram-of-a-pneumatic-valve/
This is a knock-open valveThe most commonly used air valve in airguns today is the knock-open valve. To operate it, a valve stem is struck by a weight called a hammer that is driven by a spring. The inertia of the impact moves the valve stem in the same direction. There is a synthetic valve face on the valve stem that holds the high-pressure air (or CO2) inside a reservoir until the valve is open. A valve-return spring behind the valve face starts the valve moving back toward the closed position after the valve has opened as far as it can. Once the valve stem starts to return to the closed position, the pressure of the air or gas in the reservoir also pushes on it. That’s because the pressure inside the channel of the valve body is always a little lower than the pressure in the reservoir. If it weren’t, the valve would remain open longer, dumping a lot of the air in one shot. The little valve-return spring exerts a huge controlling force over the valve because of this pressure differential.http://www.gunnersden.com/index.htm.airguns.html
During the discharge cycle, the hammer of the rifle is released by the sear to strike the valve. This usually involves the hammer moving toward the rear of the rifle, unlike firearms where the hammer normally moves forward. Prior to being struck by the hammer, the valve is held closed by a spring and the pressure of the air in the air gun's tank. The pressure of the spring is constant, and the pressure of the air changes with each successive shot. As a result, when the tank pressure is at its peak, the valve permits passage of less total volume of air than when the tank pressure has been reduced by a series of shots. This results in a somewhat greater consistency of velocity from shot to shot than would otherwise be expected, and accuracy with a rifle is mainly dependent on consistency.

 

[JakeBrodskyPE]

Doug Huffman suggested the possibility of locally choked flow. I tend to agree with that notion. Remember that you're dealing with a gas flow that is approaching Mach 1 --which at sea level should be around 1150 fps at the muzzle of the air-gun at standard atmosphere temperature and pressure.

My question is whether there is a sonic orifice after the needle valve that might limit the flow of gas into the breech of the gun. I don't know this specific model of airgun, but It seems to me that there ought to be such an orifice so as to keep the mass flow and velocity as consistent as possible.

My guess is that the gas flow from the tank will initially cause the tank and its gas to cool. This chilled gas will then admit more flow through the sonic orifice, until the pressure starts to drop. I suggest you try chilling the cylinder and filling it with cold gas and then compare that to a room temperature cylinder. I'm willing to bet that chilling the cylinder and gas will shoot the pellet faster than room temperature gas at the same pressure.

 

[Mark44]

Thank you all for weighing in. You have given me something to think about that I can report to my friend, Blake.

 

[Mark44]

Has he tried different shape pellets? It would be interesting to see if pointed pellets and blunt pellets show the same curve.

I didn't get much of a look at the pellets, but as I recall, they are blunt rather than pointed, and have skirts. A quick search on Amazon shows a variety of pellet shapes - https://www.amazon.com/s/?ie=UTF8&keywords=22+caliber+pellets&tag=pfamazon01-20

Sorry if you mentioned it, but has he tried slowly increasing the pressure for single shots? It sounds like he can charge the cylinder to whatever pressure he wants, right? Start low for a couple shots, add a bit of pressure for the next couple shots, and so on up to a couple shots at the highest pressure...

He can alter the pressure in the internal take, up to a point. There's a gauge at the tank end, but the dial covers only about 120° or so, and the increments are pretty large. Still, I think this is a good idea.

 

[Doug Huffman]

Competition pellets, high value pellets, have an extremely precise shape, weight and density. PV=nRT extrapolate from known volume strokes of the foot pump.

 

[Mark44]

You can query some of the air gun sites with question as the users seem to know their guns, since it seems from perusal of their sites that for pre-charged pneumatic guns, the hammer force, the valve mechanics, pressure in the tank, and barrel length will have an influence on the velocity of the pellet.

Here someone does explain the valve operation. It seems to be in agreement with what I wrote earlier.

http://www.pyramydair.com/blog/2006/10/diagram-of-a-pneumatic-valve/
This is a knock-open valveThe most commonly used air valve in airguns today is the knock-open valve. To operate it, a valve stem is struck by a weight called a hammer that is driven by a spring. The inertia of the impact moves the valve stem in the same direction. There is a synthetic valve face on the valve stem that holds the high-pressure air (or CO2) inside a reservoir until the valve is open. A valve-return spring behind the valve face starts the valve moving back toward the closed position after the valve has opened as far as it can. Once the valve stem starts to return to the closed position, the pressure of the air or gas in the reservoir also pushes on it. That’s because the pressure inside the channel of the valve body is always a little lower than the pressure in the reservoir. If it weren’t, the valve would remain open longer, dumping a lot of the air in one shot. The little valve-return spring exerts a huge controlling force over the valve because of this pressure differential.http://www.gunnersden.com/index.htm.airguns.html
During the discharge cycle, the hammer of the rifle is released by the sear to strike the valve. This usually involves the hammer moving toward the rear of the rifle, unlike firearms where the hammer normally moves forward. Prior to being struck by the hammer, the valve is held closed by a spring and the pressure of the air in the air gun's tank. The pressure of the spring is constant, and the pressure of the air changes with each successive shot. As a result, when the tank pressure is at its peak, the valve permits passage of less total volume of air than when the tank pressure has been reduced by a series of shots. This results in a somewhat greater consistency of velocity from shot to shot than would otherwise be expected, and accuracy with a rifle is mainly dependent on consistency.

I believe the air rifle in question has an air valve as described in the first paragraph above, where the hammer moves in the direction toward the muzzle end. It's possible that higher air pressures in the tank cause the air valve to shut sooner than it does at lower pressures, and the higher pressure causes a shorter duration for air to flow into the chamber behind the pellet. So here we have the competing factors of higher pressure (and higher flow rate) vs. shorter duration for the flow. If this is a reasonable explanation, it would seem that the shorter duration has more of an effect on the pellet velocity, based on my friend's data.

 

[Doug Huffman]

I used to service high pressure (=<3ksi) spring loaded stop valves that had an adjustable blowdown by way of a reaction nozzle ring that could be adjusted closer or farther away from the seat. The lift pressure was set by the spring tension (and hammer knock in your case), the reset shut pressure was controlled by the falling reaction of the blowdown ring.

Might there be a similar shape in you knock-open valve?

 

[mr166]

Well here is my guess. It is a temperature issue with the air valve. The fact that it happens at high and lower tank pressures makes me think this is possible. Compressed air gets cold when the pressure is released and after a few shots something in the metering system gets cold and allows more air to pass. To test this, fire shots until the pellet velocity starts to increase and then let the gun rest for a couple of hours and test again. I bet that you see the same increasing velocity after a few shots.

 

[mfb]

He replied that if you start off at the lower pressure, you still get the same sort of concave-down graph, so my theory went down in flames.

I think that rules out all urely pressure-based explanations.

Simon Bridges suggestion of waiting a while after each shot should help: if the effect vanishes, it is related to heat or other temporary effects, if it is still there, this cannot be the main reason.
If there is a long time between those series, there could be dust or similar effects reducing the performance of the rifle for the first shots. That leads to another possible test: make two of those test series quickly after each other. If the second series sees the same increase, then something odd is going on (it rules out dust/similar things and temperature).

I should know better, but apparently that's not firmly etched in my mind. I was thinking, incorrectly, that if you heat a tube, the metal expands in all directions, with the inner wall moving toward the center of the tube's axis. Apparently that's not what happens, so there goes my theory.

The metal does expand "in all directions", all distances scale in the same way (assuming uniform material and heating).

 

[Tatersoup]

On the other hand, the higher pressures may obdurate the bullet more, pressing the bullet more tightly against the barrel and rifling and increasing friction.

So, it might be that a harder lead alloy would perform better as it would not expand as much. If the air gun can accept BBs as well as pellets, try those and see if you get the same plot of pressure vs. velocity. I bet it will be a very different plot. Or even with those darts that go in air guns.

 

[Mark44]

I just talked to my friend Blake on the phone, and he has had a chance to look at all of the responses in this thread. He expressed his thanks to you all for taking the time to respond. He thought there were a lot of good ideas here.

 

[Tatersoup]

There is another possibility as well.

Let's assume there's nothing really complicated going on with bullet design or friction or valves.

Could it be that the velocity peaks at a lower pressure because, at the higher pressure, the bullet leaves the barrel more quickly and therefore doesn't have as much dwell time inside the barrel to develop full velocity? This would mean that these results only indicate the optimum pressure to obtain maximum velocity. Nothing more, nothing less.

This idea is testable, I believe.

I'd also be interested to see if all the parameters remained the same except the barrel length, if the peak velocity will occur at a different point on the pressure scale.

Time to get out the hack saw!

 

[mfb]

How can a bullet leave the barrel faster if it is slower?

 

[Tatersoup]

That's not quite what I meant. Sorry for being sloppy.

There are three things that I was envisioning in that statement. The pressure behind the pellet, the volume of air injected behind the pellet, and the volume of the barrel itself to the muzzle. With these parameters (plus friction loss and many other factors as well), there will be an optimum pressure/volume combination that will yield the maximum velocity.

The volume of air expelled by the valve may be less with higher pressure for example.

I'd love to know what the difference is between the plots. Are they different pellet weights or designs?

 

[jim mcnamara]

Power curve. This discusses the power curve of a pre-charged airgun.
http://www.pyramydair.com/blog/2008/12/understanding-the-performancepower-curve-of-a-pcp/

There is an optimal velocity (power) curve as a function of the internal pressure in the air chamber. At pressures above and below that range of optimal pressure values velocity is reduced. Which is exactly what you reported. Short answer: You are "over charging" the pressure chamber. Since this affects external ballstics (accuracy) competitive target shooter folks are picky about chamber charge pressures.

 

[HuskyNamedNala]

Is the air expanding more rapidly inside the muzzle?
Does the pellet velocity have a component in a direction the measurement device cannot detect (IE, if you are using 2D particle tracking, you can't measure into the plane of the camera)?
Drag might work out funny where the muzzle velocity is actually higher, but slows down rapidly. 3 feet seems kind of short, but you never know. Recall drag = f(shape, Re, M,V^2)
I don't know about the Joule-Thompson effect. These pressures don't seem high enough to have that be a major player. If anything the valve would feel noticeably cold, but I am not an expert on compressible flow.

Also: How many measurements did you take at the anomalous values?

I personally think the air inside the barrel prior to projectile exit might be expanding at a different rate for different pressures. That would be a fun project to get that data! If you were using combustion you could get an infrared camera and measure the change in heat with time. I think a cool idea might be to get some strain gauges and measure their value at various points along the barrel simultaneously.

 

[Electrifieddriver]

Maybe the factory have intentionally made the trigger mechanism to compensate for variable pressure. That will make a relatively flat area to make the speed constant for a variable pressure, With a higher pressure it will overcompensate and slow down the pellet too much.

 

[JBA]

Doug Huffman suggested the possibility of locally choked flow. I tend to agree with that notion. Remember that you're dealing with a gas flow that is approaching Mach 1 --which at sea level should be around 1150 fps at the muzzle of the air-gun at standard atmosphere temperature and pressure.

My question is whether there is a sonic orifice after the needle valve that might limit the flow of gas into the breech of the gun. I don't know this specific model of airgun, but It seems to me that there ought to be such an orifice so as to keep the mass flow and velocity as consistent as possible.

My guess is that the gas flow from the tank will initially cause the tank and its gas to cool. This chilled gas will then admit more flow through the sonic orifice, until the pressure starts to drop. I suggest you try chilling the cylinder and filling it with cold gas and then compare that to a room temperature cylinder. I'm willing to bet that chilling the cylinder and gas will shoot the pellet faster than room temperature gas at the same pressure.

The problem with that concept is that the gas mass flow still increases essentially linearly with pressure after choked flow is achieved. Only the throat discharge velocity remains constant.