Maximum velocity and the speed of sound

[Sawney Bean]

So we know that the speed of sound is the upper speed limit of any gas powered gun, but also that the speed of sound will vary depending on the gas being used, the temperature and it's pressure. Under normal conditions however the speed of sound in air is about 1125 fps.

Just sticking with air here, it seems that spring piston rifles can significantly exceed 1125 fps mostly by superheating the air as the piston compresses it. The fastest velocities I have seen claim to be in excess of 1600 fps.

PCP rifles seem to be able to also exceed 1125 fps, but not to the same extent and I haven't found many reputable sources claiming velocities any higher than 1300 fps, This is where things get kind of interesting. AI and most of the physics tutorials regarding the speed of sound will claim that pressure does not play a significant role in the SOS, but it quickly becomes obvious that this is because they are only considering normal atmospheric pressures. When you try and get estimates of the speed of sound at the kinds of pressures we're dealing with there just doesn't seem to be much out there. I've looked at Bernoulis Equation, but trying to find things like the density of air at 5000 psi isn't exactly easy either.

I'm just wondering if any of the engineers or physicists out there have any ballpark ideas on the speed of sound at high pressures. Also, it would seem to me that with the way PCP's operate, the expanding air should be cooling as it expands which would in turn also lower the speed of sound.

 

[Scotchmo]

SOS = speed of sound

SOS is a limiting factor, but it is not the actual velocity limit.

Maximum velocity of air flowing into a tube (barrel) is equal to SOS.

But, besides flow velocity, there is also a simultaneous expansion towards the front. So the front velocity can be faster than SOS.

There will be some variation of the SOS and k values used to determine maximum possible velocity. Temperature (mostly) and pressure (slightly).

The expansion velocity relative to the flowing air can also be near +/- sonic. So a good rough estimate of the maximum possible front velocity, relative to the tube inlet, is about 2x the speed of sound.

Here’s an equation I derived a few years ago from what I could find on the subject. Maximum front velocity from air flowing into, and through a tube:
SOS x sqrt((2/(k-1))+1)

That happens as barrel length approaches infinity and/or projectile mass approaches 0.

I can easily hit 1700+ fps with my high powered airguns with very light projectiles. Some controlled experiments over on the GTA a few years ago were seeing velocities of a little over 2000fps.

There is very little practical value of going supersonic in a PCP airgun.

 

[rcarlisle]

I think you're looking at it inside out. The projectile is not being propelled through ambient pressures of 5000PSI. It may be propelled by 5000 PSI, but in terms of ballistics, the projectile is traveling through normal, breathable atmosphere. Thus those equations would be correct to my thinking.
Edited to add: I think you're probably looking for expansion of HPA and the effects on projectile velocity. I recall an interesting conversation on the GTA:

Theoretical Maximum Velocity in a PCP - Airguns & Guns Forum

Theoretical Maximum Velocity in a PCP, Air guns, Airgun Forum

www.gatewaytoairguns.org

Maybe that will help.

 

[Troy Bakel]

Could one apply the design requirements of a supersonic wind tunnel to an airgun with the result that the air behind the pellet is supersonic as it crosses the crown?!?

Possibly a swing breech design where the swing breech is a convergent-divergent nozzle directly behind the pellet?

Once we have the outlet of the divergent nozzle at supersonic speed .... could we maintain supersonic speed against the resistance of the pellet over the full length of the bore?

That would most likely require a huge differential pressure across the system.

 

[Goldwing]

For fun ​

How does a whip break the sound barrier? (Slow Motion Shockwave formation)​