The primary problem with designing BP artillery on paper is that we don't have any valid pressure measurements (and few velocity measurements) to guide our choices.
An example: a bowling ball has a cross-sectional area of about 58 sq in. If we apply a pressure of 1000 psi to it, the ball will see a force of 58,000 lbs. From F=ma, the acceleration of the ball will be 116,000 ft/sec squared--a whole bunch. But the pressure is inversely related to the volume and as the ball moves along the bore, the pressure will drop. Assume, for easy calculation, the volume of the powder charge is 5.8 cu in; as the ball moves its first inch down the barrel, the volume goes from 5.8 cu in to 5.8 + 58 cu in (63.8 cu in) and the pressure must fall from 1000 psi to only 90 psi. The force on the ball is now 5220 lbs. After the next inch of travel, the pressure is down to 47 psi and the force to 2760 lbs. This goes on until the ball exits the barrel. (You can see why the barrels of mortars didn't have to be very long to be effective.)
The above analysis is extremely simplified (a proper analysis would use calculus and account for other factors) but you should be able to see the basic idea. In theory, one could work backward from velocity measurements and get the pressure but even that would be based on a bunch of simplifying assumptions.
So from a practical viewpoint, building and proof firing guns is the best way. By using the original designs and modern materials, we automatically get an enhanced safety factor. The risk increases when we strike off into new designs or take short cuts trying to use available materials to simplify building. We should keep in mind when building artillery that our pieces are likely to come into the hands of others at some point and they will not necessarily know what we know or use them with the reserve that we use them. So there should be enough safety factor included in the design to prevent accidents in the future.
