By Nathan Okun
Updated 31 August 1999
Striking velocity V is more important than projectile weight W when attacking face-hardened (usually side) armor, due to the shock-induced failure of the plate occurring prior to the entire projectile "knowing" that it has hit something; only the upper end of the projectile gets involved, which is more or less the same no matter how long the projectile is (increasing length increases weight and the explosive-filled cavity is closer to the base than the nose).
The formula for homogeneous armor penetration is "T = (K)[(0.5)(W/g)V^2]^p", where "T" is the thickness of plate barely penetrated (by whatever definition of "penetration" you want to use), "K" is a constant (a "catch-all" that changes with projectile nose shape, projectile size, projectile damage, definition of "penetration," plate type, and obliquity angle of impact), "W" is the projectile's total weight, "g" is the acceleration of gravity to change weight to mass (inertial resistance) (NOTE: "g" factor is not needed if the weight is in KILOGRAMS, which is already a measure of "mass" and has the "g" division built-in), "V" is the striking velocity, and "p" is a constant--usually between 0.5 and 1.00--that raises the entire projectile total kinetic energy value "KE = (0.5)(W/g)V^2" to a single power as a unit (p does NOT change with projectile properties (other than nose shape), plate type, or obliquity angle, though). Both K and p are good for only a limited range of plate thicknesses, with up to 5 combinations of K and p needed to handle the entire thickness range from paper-thin plate to bank-vault-door thickness for some projectile designs even with no projectile damage. Note that in this formula the two terms W and V^2 are of equal importance, as in any true KE-dependent penetration formula.
The face-hardened formula I use is in its most basic form is: "T = (C)(W^0.2)(V^1.21)", where "C" is similar to "K" (uses quite different values for various parameters that make it up, however), above, "W" and "V" mean the same thing, and there is only this one set of exponents 0.2 and 1.21 for W and V, respectively. Note that the weight's 0.2 power is much smaller than the striking velocity's 1.21 power (the latter gives an equivalent p-value of 0.605, which is halfway between the most widely-used average homogeneous armor p-values of 0.714285 (giving a V-exponent of (2)(0.714285) = 1.42857)--used with the ubiquitous De Marre Nickel-Steel Armor Penetration Formula of 1890--and 0.5 (giving a V-exponent of 1.00), which is the p-value used for an ideal punch cutting out a cylindrical, full-plate-thickness, full-caliber-width plug of steel from the plate at right-angles ("normal") impact obliquity). The small exponent 0.2 for W means that changing W (by lengthening the projectile or making the explosive cavity smaller) has rather little effect on penetration, all else being kept equal, while changing V has a large effect. This definitely is NOT a total-kinetic-energy-dependent formula using the full projectile weight W, since only the weight at the front of the projectile contributes much to the shockwave-induced breaking of the face layer that is the most important part of defeating a face-hardened plate--the base of the projectile doesn't even "know" the projectile has hit the plate face until the punching through of the face layer is all over with! If the face-hardened plate's soft, ductile back layer were not there to act as an "shock energy sink" to keep the hard, brittle face from shattering, the weight exponent would probably be even smaller than 0.2! Much different from the homogeneous armor penetration formula set!
My programs M79APCLC.EXE for homogeneous, ductile steel armor hit by
a medium-point, uncapped AP projectile suffering no damage and FACEHARD.EXE
for all face-hardened armor and projectiles and including projectile damage
(big time!!) are based on the above general concepts, fleshed out with
numbers and formulae for the various parameters mentioned.