Concluding Caveat

The foregoing discussion supposes kinetic energy, which increases with the square of velocity, to be the relevant gauge of smashing power. It should be noted that some experts might favor the use of momentum, which varies with simple velocity. Obviously, this would increase the relative importance of the total mass of the cannonballs. In our example comparing equal frontwidths'worth of 3-pounder to 24-pounder guns of like design family, such a substitution of momentum for kinetic energy as the measure of smashing power would result in the 3-pounders delivering not double but quadruple the aggregate smashing power per unit time over their range half-as-long, thus:

Range	24-pounder	3-pounder
Short Range	16	64
Long Range	16	0
Total	32	64

Clearly, this also abolishes the equality (obtained using kinetic energy) among equal frontwidths'-worth of different artillery types in cumulative smashing power delivered upon a steadily approaching enemy over the entirety of its advance. But since their operating costs (denominated in horses required) remain equal, this would make lighter artillery a better buy relative to heavier. The continued inclusion of heavier types among the field batteries would therefore depend upon their long-range capability per se being valued much more highly than otherwise.

On balance, I think the kinetic energy assumption to be the more consistent with the artillery mixes ultimately adopted by the belligerent armies. I view momentum as the better index of cavalry power, but that is another matter.

Sources

Carpenter, Steve. "Russian Artillery in the Seven Years War," Seven Years War Association Journal, Vol. X, No. 2.
Duffy, Christopher. The Army of Frederick the Great.
Duffy, Christopher. Fire and Stone: The Science of Fortress Warfare 1660-1860.
Duffy, Christopher. Instrument of War: The Austrian Army in the Seven Years War.
Duffy, Christopher. Russia's Military Way to the West.
Edmondson, Michael M. "Notes Relevant to the Simulation of Seven Years War Tactical Scenarios," Seven Years War Association Journal, Vol. XII, No. 2.
Esposito, Vincent et al. A Military History and Atlas of the Napoleonic Wars.
Nosworthy, Brent. Anatomy of Victory: Battle Tactics 1689-1763.

Comparative Performance of Seven Years War Artilleries

Introduction
Relative Ranges
Relative Destructive Power within Range
Concluding Caveats and Sources

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