[Kurt505]

Originally Posted by AndrewM

For those that want to skip the read:
Pressure P is a force F per area A
P = F / A.
The change in energy of a system dE is the force exerted on the system (in this case the projectile) times the distance over which the force is exerted dx
dE = -F dx
where the minus sign indicates the force is in the opposite direction of the projectile motion, so that its energy is being reduced. For penetration of a thick target to occur, we need the pressure to equal the cavity strength
P = Yc.
Combining these relations, we find
dE = Yc A dx.
Since this relation is linear, if we know the energy E of the projectile when it initially hits the target, we can easily find the distance penetrated xp
xp = E / (Yc A).
For the purpose of this discussion, we can ignore the potential energy of the projectile, so that its energy is given by its kinetic energy alone
E = ½ m v²
where m is the projectile mass and v is its speed. We now have
xp = m*v²/(A*2*Yc)
SD=m/A
xp=v²*Yc*2*SD
SD and YC are constant. Velocity is not so penetration is not constant. It has a quadratic relationship with velocity.

Wholly shhhhhmokes