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Can a propane-air mixture allow projectiles to exceed the internal speed-of-sound limit associated with their combustion?

The following content is generated by AI.

Statement 1: "The upper limit of projectile velocity is determined by the speed of sound."

· Applicable scenario: Steady-state flow (e.g., Laval nozzles, rocket nozzles), or deflagration mode (conventional flame propagation).
· Physical content: In a constant-cross-section duct, choked flow locks the gas flow velocity at the local speed of sound. In deflagration, the flame propagation speed itself is far below the speed of sound, energy release is slow, and the projectile velocity is naturally limited to a relatively low level.
· Conclusion: In this scenario, the speed of sound is indeed a hard ceiling.

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Statement 2: "The projectile velocity can exceed the speed of sound, and the upper limit is far higher than the speed of sound."

· Applicable scenario: Transient expansion (projectile acceleration inside a gun barrel), or detonation mode (supersonic combustion wave).
· Physical content: In transient expansion, the macroscopic directed velocity of gas particles can far exceed the local speed of sound (because the pressure differential is large enough). As long as the gas velocity remains higher than the projectile velocity, the projectile can continue to accelerate. In detonation, the combustion wave itself propagates at supersonic speed, and the driven gas velocity increases correspondingly.
· Conclusion: In this scenario, the speed of sound is not the direct limit on projectile velocity; rather, the macroscopic flow velocity of the gas is the immediate condition that determines whether the projectile can continue to accelerate.

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The ultimate limiting velocity of the projectile is determined by the thermodynamic limit formula:

v_{max} = \sqrt{\frac{2\gamma}{\gamma-1} \cdot R \cdot T_0}

· For propane–air (deflagration, ~2200 K), this limit is approximately 3700 m/s.
· For propane–air (detonation, higher temperature), this limit would be even higher (though extremely difficult to achieve in practice).

However: In a short barrel, the actual velocity the projectile can achieve (200–800 m/s) is far below the thermodynamic limit, because there is insufficient time and space for the gas to fully expand. The speed of sound (~900 m/s) is only one component of this limit, not the direct cause that locks the projectile's velocity.

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Unified conclusion:

"The speed of sound is the 'foundation' that determines the ultimate limiting velocity of the projectile, but it is not the 'wall' that locks the actual muzzle velocity. In transient expansion, the projectile velocity can exceed the local speed of sound, until it approaches the thermodynamic limit determined jointly by the speed of sound and the specific heat ratio."

Potato guns seem to align better with the second explanation. Does this imply that the maximum speed a potato gun can achieve could exceed the upper limit of the internal speed of sound—roughly 950 meters per second? Given a theoretical upper limit of 3,700 meters per second, if sufficient pressure and barrel length are provided, the projectile's final velocity could approach 3,000 meters per second rather than 900 meters per second.

This is confirmed by various extreme tests and records set by enthusiasts: under specialized configurations, PCP airguns can achieve velocities of 1,600 fps (approx. 488 m/s) or even exceed 2,000 fps (approx. 610 m/s). These speeds far surpass the speed of sound in air under atmospheric conditions; therefore, from a purely physical standpoint, PCP airguns are fully capable of accelerating projectiles to supersonic speeds.

This question is answered by John Corner's 1950 book "Theory of the Interior Ballistics of Guns" in section 9.16 titled "The maximum possible muzzle velocity". The equation in the second explanation is one of the equations given by Corner (two different derivations). So yes, the speed of sound itself is not the upper limit.