# Compressed air, heat and pressure?

Yes compressing air increase its temperature but does that necessarily increase pressure? In an pellet gun a spring driven piston compresses the air which increases the temperature but wouldn't any increasing pressure simply retard the piston's advance? Because the chamber volume is not fixed shouldn't the pressure be equal to the spring's force but not greater? So my question is, does the resulting higher temperature increase the pressure in this situation?
I'm not an engineer let alone a physicist so please explain the answer in layman's terms.
Thank you,
Ed.

Bystander
Homework Helper
Gold Member
Thank you Bystander. I know about airgun energy with different bore diameters vs pressure and discharge volume.
Does anyone understand the pressure/heat relationship in a sprung piston condition?
Ed.

jrmichler
Mentor
Start by reading The Airgun from Trigger to Target, by Cardew and Cardew that was referenced in the thread that @Bystander linked. It's an excellent book, especially for somebody who has not been through engineering school. This will probably answer your questions, but if you want to get deeper into what happens when air is compressed suddenly, study this link: https://www.engineeringtoolbox.com/compression-expansion-gases-d_605.html. If that's not enough, search using search terms air compression isothermal adiabatic polytropic.

If you get through all of that, and want to dig deeper, come on back, and we will walk you through how to set up a numerical simulation using a spreadsheet.

russ_watters
Mentor
Yes compressing air increase its temperature but does that necessarily increase pressure?
Somehow you have twisted the issue around in your head into the suggestion that increasing pressure doesn't increase pressure. Um, what?
In an pellet gun a spring driven piston compresses the air which increases the temperature but wouldn't any increasing pressure simply retard the piston's advance?
Same thing here. Compressing the piston stops the piston from compressing. Well, in a way that's true: as the pressure rises, obviously it applies a higher force and you feel that when you are moving the pump arm.
Because the chamber volume is not fixed shouldn't the pressure be equal to the spring's force but not greater? So my question is, does the resulting higher temperature increase the pressure in this situation?
Yes to the first: the pressure if the force you apply divided by the cross sectional area of the piston. Period. Everything else that happens - such as the temperature rising - still gets manifested as part of that force. So I think you are making this more complicated than necessary.

jrmichler and Tom.G
This question came to mind after reading a recent article in 'Hard Air Magazine' entitled 'Ham Airgun Technical'. This quote is from the first paragraph.

"Broadly, there are two types of airguns; springers (including gas rams), and pneumatics. The former compresses the air during the shot, creating heat and pressure, with the heat further increasing the pressure and efficiency." I'm assuming that by efficiency he's implying greater pellet velocity.

That highlighted part of the line is what I have a problem with. jrmichler reminded me of a book I read years ago on line at https://www.scribd.com/doc/124074201/CARDEW-The-Air-Gun-From-Trigger-To-Target. I reread chapter 7-The Air, pages 57 to 60.
There the author explains how the forward moving piston stops and rebounds once the chamber's air pressure is equal to the force it can apply.
So, hypothetically if no heat were produced the piston would simply advance further until that same chamber pressure was reached causeing it to rebound. To me this means the final pressure would be the same either way and the heat doesn't further increasing the pressure on the projectile.
The author is a friend of mine on another forum and I'd like to tell him of my concerns, but only if I had a valid point.

cjl
Even if you achieve the same pressure though, the projectile will achieve a higher velocity if the gas propelling it is hotter

Yes the lower density of the hotter air will accelerate a little more quickly as it's weight, as well as the pellet's, must be taken into account. It doesn't explain the claim of higher pressure though.

jrmichler
Mentor
The spring, the piston mass, the volume of air ahead of the piston, the orifice size, and the pellet mass are all a matched system. Too light a pellet will cause the piston to bang into the end stop. Too heavy a pellet will cause the piston to bounce back. Either case will result in the pellet leaving with less kinetic energy.

A spring piston airgun is a highly dynamic system, where inertial forces are larger than static forces. The inertia of the piston creates the pressure that compresses the air that drives the pellet. The piston peak inertial force (F = ma) is much larger than the peak spring force.

A heavier pellet that will cause the piston to bounce back will not reduce the kinetic energy transferred to the pellet. In fact the heavier pellet will extract the maximum energy (not velocity) from the system.
I did say "spring force". Please excuse my lack of proper terminology. I didn't mean the static force but the culmination of mass times velocity of the piston.
So, is it the piston's peak inertial force that determines the pressure and so the velocity of the pellet or does the resultant heat enhance the final energy to the pellet? I think he's implying extra free energy!

russ_watters
Mentor
"Broadly, there are two types of airguns; springers (including gas rams), and pneumatics. The former compresses the air during the shot, creating heat and pressure, with the heat further increasing the pressure and efficiency." I'm assuming that by efficiency he's implying greater pellet velocity.

That highlighted part of the line is what I have a problem with. jrmichler reminded me of a book I read years ago on line at https://www.scribd.com/doc/124074201/CARDEW-The-Air-Gun-From-Trigger-To-Target. I reread chapter 7-The Air, pages 57 to 60.
There the author explains how the forward moving piston stops and rebounds once the chamber's air pressure is equal to the force it can apply.
So, hypothetically if no heat were produced the piston would simply advance further until that same chamber pressure was reached causeing it to rebound. To me this means the final pressure would be the same either way and the heat doesn't further increasing the pressure on the projectile.
It depends on what you hold constant and what you don't when doing the analysis.

If you pump the air to a certain pressure, then the pressure is the pressure is the pressure.

If you compress (reduce the volume) by a certain ratio, then the rise in pressure is greater than the reduction in volume because of the temperature increase.

I would not assume "efficiency" refers to pellet velocity. I would think pellet velocity is strictly a function of pressure.

"It depends on what you hold constant and what you don't when doing the analysis."

I'm not sure what you mean but the volume is not constant at all.

"If you pump the air to a certain pressure, then the pressure is the pressure is the pressure."

This is my point. I believe the pressure is a factor of the piston's energy alone.

"pressure is greater than the reduction in volume" ?? I don't understand.

"I would not assume "efficiency" refers to pellet velocity. I would think pellet velocity is strictly a function of pressure."

Yes, you're right. Efficiency aside, the statement "with the heat further increasing the pressure" is the true thorne in my foot.

It's not that I don't appreciate the replies it's just that when ever I ask something on this forum I never get a definitive yes, no or we don't know.
Maybe that's how physics is. Of course you guys would say, that all depends. lol
Well thank you anyway, I'll let it go.

russ_watters
jrmichler
Mentor
Here's some hard numbers from a Beeman R9 20 caliber spring piston air rifle that I measured a few years ago. Pellet weights are in grains (7000 grains = 1 pound). The 0.64 grain pellet was a felt cleaning pellet. The pellet kinetic energy is calculated from chronograph velocity measured 5 feet from the muzzle.

Weight Energy - ft-lbs
0.64 0.95
10.82 14.1
11.43 14.3
12.66 14.4
12.69 14.5
12.97 13.9 This pellet was a tight fit
13.40 14.4
14.35 13.8
15.37 13.4

The optimal pellet weight for maximum kinetic energy is about 13 grains plus or minus 0.5 grain or so. There are also other variables such as pellet friction and air sealing.

CWatters
Homework Helper
Gold Member
If the user applies the same energy to both types of air gun then you might think they would both have equal performance. However as I understand it the type that compresses air rather than a spring has lower performance because heat created when the air is compressed has time to dissipate (at least partly) before the gun is fired.

russ_watters
Mentor
"It depends on what you hold constant and what you don't when doing the analysis."

I'm not sure what you mean but the volume is not constant at all.
You can specify a specific compression ratio or pressure, but not both (unless by coincidence they correspond).

E.G., you can say - based on your strength - that you can apply 75 lb to a 0.5 sq in. piston to generate 150 psig.

Or you can say that you have compressed that piston by a factor of 11:1, in which case the heat of compression will result in the pressure being above 150 psig.

The difference, physically, would probably be whether you are constrained by your physical strength (or a pressure limiting valve) or a mechanical stop on the piston.
"pressure is greater than the reduction in volume" ?? I don't understand.
The reduction in volume is the compression ratio. By the math above, if you assume constant temperature (say, by slow compression or a heat exchanger), the 11:1 compression ratio yields a pressure of 150 psig. In reality, a fast compressing piston that heats up the air will yield a higher pressure.
It's not that I don't appreciate the replies it's just that when ever I ask something on this forum I never get a definitive yes, no or we don't know.
Maybe that's how physics is. Of course you guys would say, that all depends. lol
Well thank you anyway, I'll let it go.
The question does have built-in ambiguity. It's partly in the way it is worded, but partly that it really is the physics; there is more than one way to approach this question.

In a spring air gun the increase in pressure and the increase in heat ombine, as it were, into available energy to propel the pellet. The piston starts moving forward which increases the pressure in the air cylinder. This causes the air to heat up further increasing the pressure. At some point the pellet begins to move, the air begins to expand and cool to (roughly) atmospheric pressure as the pellet leaves the muzzle. No air gun I've ever seen uses a pellet heavy enough to retard the piston any measurable amount. In pump guns you actually lose a bit of power if you wait after pumping up to pressure. The air in the air cylinder cools, pressure falls a little.