An estimate/calculation of momentum lost during penetration of 21" of Oak, using Short pattern (Frigate main battery) 9lb, 12lb, 18lb and 24lb guns, plus the 32lb gun seen as a pivot gun or the main battery of the heavier rated ships, as well as the longer pattern of carronades in the same calibres.
All three acknowledged charges are displayed as well as the 'top' 5/9 shot from double shot for the lower two (the 'bottom' 4/9 shot isn't displayed. Carronades get their standard 1/12th charge, plus a higher 1/8th and lower 1/16th one.
Note that for a fixed thickness/angle, the same calibre produces the same shaped curve, with the same maximum - only the range of each point is shifted by a fixed amount according to the muzzle velocity of each ordnance and charge ratio.
Different calibres produce different curve shapes, but the forms are related.
Drag curves and residual velocity are computed in a 'flat fire' approximation using NACA sphere drag data.
Penetration is from Bashforth/Didion documents from the period, with their estimate of the Poncelot form penetration coefficients from chronograph measurements.
In imperial measures this penetration is:
An estimate of momentum loss is given by finding:
P(max) from V(impact)
P(residual) by finding the difference between P(max) and thickness(angle adjusted)
If the shot won't perforate, then P(residual)=0
Find the velocity required to obtain P(residual). Velocity loss is then V(impact)-V(residual), and momentum loss is obtained directly.
It can be seen that calibre is a dominant factor in transfer against any single target, but that if the target is much thinner, far less momentum can be transferred (but more remains to dismount carriages/guns and to strike the far side). Overly thick sides result in the maximum momentum transfer (which they *may* be more resistant to, but not in the case of a thin side, highly angled).
Within one calibre, one target and angle, the optimal ordnance or mode of firing is a range based function, and there is a choice between an assured high impluse (slightly below ideal velocity, but a sometimes/often/always failed penetration) and an assured penetration (significantly above ideal velocity) with a lower transfer of impulse, exactly as described for carronade vs gun, but seen in it's full context.
The degree of 'correctness' of any value used is open to question, and there may be some element of non-linearity and inexactitude of this form of assessment. It is however the best approximation I can find to this aspect.
Note that in order to generate splinters a penetration (or a failure by only a very small amount is required), and that for a shot which lodges on exit of the second side will only deliver around 40% of the momentum to the first side and lose the remainder (60%) in just penetrating through the second. A shot which *just* perforates the first side will deliver around 50% more impulse, but less high velocity fragments than the 'fast' shot which is just passing the second.