I have the greatest respect for 2-p's scientific approach and unwavering commitment to truth in shotgunning. His theory and math are good. Chamber pressure is not a factor in this question. We are looking at average pressure. "What average pressure will yield the average acceleration to achieve desired velocity within the barrel time (length)?"
Average pressure and acceleration are theoreticals that are not greatly helpful. "So, what do we really need to know?"
What we need is the pressure vs time history/curve. Unfortunately, the equations used to estimate the pressure vs time curve are more than a little complicated. Fortunately, this data is not all that difficult to establish via test firing.
The problem involves a non-linearly increasing volume for the gas, non-linear energy input from the propellant as its gas generation rate (burn rate) is sensitive to pressure, gas cooling due to barrel heat transfer, and payload friction.
Where do we need to go with this discussion now?
DDA
