I'd say if you're predicting how fast the launcher will shoot by modeling it, you're in pretty deep.

You could calculate acceleration as a function of position in the barrel given the barrel diameter, length, chamber volume, projectile mass, and atmospheric pressure. However, the first real leap comes with getting this into a function of time, not position. You would integrate, (calculus function), "something or another", (my old robotics coach told me all about how to do it, but I've since forgotten), to obtain the correct function with respect to time, and then it would be a simple process of anti derivation to obtain a position function with respect to time, which you could use for muzzle velocity, which can be used for all kinds of things.

Maybe D_Halls over from Spudtech would be able to help you, if you could get a hold of him. He wrote the "Gas Gun Design Tool". It is unknown to me how the program calculates muzzle velocity, but given my computer's inept ability at performing most basic differentiation problems, I would say his program uses some sort of limit process. This would be good, as it means he actually knows the real equations for solving your question.

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