The
kinetic energy in a round fired from a gun is well known, 0.5*m*v
2
I was wondering, since the energy goes with the square of the velocity, why doesn't the military just jack up the projectile speed to get the desired kill energy instead of resorting to these exotic, dense materials such as depleted uranium?
Well, I discovered that this is because there is an upper limit of muzzle velocity using the conventional "gun" technique, using explosive chemicals to accelerate projectiles.
From http://www.islandone.org/APC/Catapults/01.html :
"The lowest practical peak acceleration level achievable with these guns is about 10 kgee. Because the final projectile velocity is a function of the speed of sound in the driver gas, the relatively high molecular weight of the combustion gasses (and the finite capability of materials to contain high pressures) used in cannons constrains the upper limit on muzzle velocity for existing guns to about 3 km/s"
There is also another limitation, this being the resistance of the air through which the projectile has to travel. At higher velocities, the projectile may reach such high temperatures due to air friction that it can be destroyed.
So, you quickly reach a limit to the velocity you can impart to your projectile. The only way to deliver any more kill energy to the target is to increase the projectile mass by using something heavier, like tungsten or the famous depleted uranium shell.