The values do not change with granulation. However, the burning rate and ratio of the surface area (So) to volume (Vo) of the black powder do change with the granulation. The burning rate is also effected by the pressure. A simple equation for velocity would look like this:
Velocity = (2*Grains.Burnt*13.56*32.2/Projectile.Weight)^0.5
Grains.Burnt = Powder.Charge * So *Burn.Rate*Time/Vo
Time - is the time from ignition to the projectile leaving the barrel
Burn.Rate = Alpha * Pressure ^ Beta
This equation assumes the temperature of the gases are constant - not correct - the gas temperature changes form 2038 to about 1200 for cannons but are almost constant for mortars.
That Beta is constant for all pressures - it is not - Beta is also a function of pressure - and the relationship is sigmoid. The general sigmoid function shape is shown in the attachment. The sigmoid is very common in science. If you have ever measured the velocity or range of a projectile over a series of powder charges say 30 grains to 120 grains in a golfball mortar you will have noticed the sigmoid effect. At around 80 grains their is a shift in the distance or velocity acheived - what happens - the Beta value changes because pressure changes do to the faster burn.
