Projectile Fired by Burning Propellant: Gas Cycle?

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TL;DR
Pressure caused by burning propellant.
In thermodynamics you have ideal gas cycles. A example of this is the Otto cycle where there is adiabatic compression followed by constant volume combustion, followed by adiabatic expansion and then finally heat rejection at constant volume. What I'm wondering is whether there is a similar type gas cycle for a projectile being thrown out of a barrel by a burning propellant. Let's say there is a hypothetical potatoes canon with a small fuel reservoir. The fuel in the reservoir is ignited and the potatoes is launched through the barrel. Is there some sort of ''gas cycle'' for something like that? Please cite sources...
 
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This is the Thermodynamics of Interior Ballistics. I am unable to find anything for a potato gun specifically. Try the graphic on p 16 to start. Plus, I'm not clear on what exactly you need for your definition of a gas cycle? Carnot?

Interior ballistics deals with all the aspects of your question, and a lot more I think.

One important difference is that potato guns, AFAIK, do not use oxygenated propellants, like nitrates in black powder. This creates lower chamber pressures than modern cannons that use black powder. Correct me if I'm wrong.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a590866.pdf
 
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@jim mcnamara let's just say the potato gun is a metaphor for a more generalized type of problem. The problem of throwing something very far, very quickly by burning something else rapidly. Doesn't have to be a gas cycle if the ''industry norm'' isn't gas cycle oriented. Your link is fantastic! Thanks...