Uses flat fire approximations adapted from ARL-TR-3567 and ARL-TR-5574.
CD for each ball size calculated at 0.1Mach intervals from cross plot of CD/Reynolds - this for nominal ball size, so a (very) minor error exists in this form using "high" ball, but the difference is minor. Retardation and exponents calculated to transfer along the range according to method of ARL-TR-5574.
Trajectory assumed rigid at up to -10degree angle of fall, errors increasing with range.
Windage impact obtained from a combination of French and US documents, combined with interior ballistics by Hutton to estimate a 'group' of muzzle velocity from a nominal powder quality. Bore set at +0.5 calibres above the 'cheek' of a carriage given as 4.75 calibres from the gun platform. Platform set at the ground level in accordance with the definition of Point Blank given by Douglas. Guns are originally designed as 20/21 ball/bore, but current graph shows 24/25 using high ball, which was permitted subsequent to the introduction of the new gauges after the Blomfield pattern ordnance was introduced. French windage of Gribeauval system guns was 26/27, although in slightly different calibres, and would show slightly superior performance with it's nominal high ball compared to these curves if this gauge was permitted in the English guns. The original 20/21 ball would penetrate less well at equal velocity (marginally) and would have a substantially lower initial velocity from the same powder and gun, and would also retain velocity over range (marginally) less well.
Penetration from Poncelot with constants 2.306 for material, and 7.45 for shot density.
This is a simplified plot, using only 0, 1, 2, 3, 4, 5 degree angle of initial trajectory, plus supplemental points at half the range for point blank, the range associated with Mach 1, and a 10 degree fall of shot at long direct fire range.
Note that in no case does a smaller bore give higher penetration, and the penetrations collapse towards a single value per calibre at high ranges.