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)V2]p
where:
T = the thickness of plate barely penetrated (by whatever definition of "penetration" you want to use)
K = 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 = the projectile's total weight
g = 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 = the striking velocity
p = a constant - usually between 0.5 and 1.00 - that raises the entire projectile total kinetic energy value "KE = (0.5)(W/g)V2" 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 V2 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)(W0.2)(V1.21)
where:
C = similar to "K" (uses quite different values for various parameters that make it up, however), above
W = same as above
V = same as above
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.
