Originally Posted by Panzergranate
A gun fires a KE Projectile with a maximum penetration, at range X, of 100mm. of vertical armour.
If the target has 50mm. of vertical armour and is at range X, the shot has a 50% chance of penetration and 50% chance of bouncing off, shattering on impact or becoming embedded in the armour.
This is because muzzle velocity is not a constant but varies according to the burn rate of each individual shell's propellant as it travels along the barrel, the amount residue remaining in the barrel from previous shots (this can vary as each shot can either add more soot or scour the barrel. Fanatical cleaning of AT and tank gun barrels was more out of increasing the chances of survival than routine.
Then there is the blemishes on each individual projectile which varies drag coefficents. Often wondered why tank crews polish AP shells.... now you know.
In flight, air density between the gun and target varies with each shot and so this varies the final velocity of the shot on reaching the target.
All this, generally falling under the "Chaos Theory" banner, when it comes to any hope of consistancy between shots, is why artillery shells fall into an average beaten zone and not land in the same shell hole.
Back to the gun shooting at a target at range X.
Asume that the range of all the test targets is range X, the same gun and projectile are used throughout.
If the target has a horizonal armour thickness of 50mm. but is angled to 30 Degrees, the chances of the shell not penetrating the armour is increased to 68%, so now the shot has only a 22% chance of a penetration.
If the target has a horizontal armour thickness of 50mm. but is angled to 60 Degrees, the chance of the shell not penetrating the armour is increased to 84%, so now the shot has only a 16% chance of penetration.
If the target has a horizontal thickness ranging from 1mm. to anything, but is inclined to any angle from 72 Degrees to 90 Degrees, the chance of the shot not penetrating is now 100% and the chance of the shot pentrating is 0%.
72 Degrees is known as "The Skate Angle" and is what you need to achiece to skip stones across water, be grazed by a bullet, etc.
For a home brew practical experiment, for those with access ti firearms, air or BB guns, try the following to confirm the above.
Take a piece of thick hard wood that you know the gun won't easily penetrate and fire any number of shots at it. Go to the piece of wood and measure the depth of each shot and they'll all be different, even with air and compressed gas weapons.
The difference between a AT weapon's maximum penetration and the average thickness of armour that its intended targets will have is refered to as the "Overkill Margin". This is always desired to give a somewhere between 60% and 70% chance of penetrating the average thickness of armour of known enemy AFVs, even today.
German WW2 AT gun designers went for 80% to 90%, thus ensuring that their enemy's attempts at thickening armour of new AFVs would not be that effective.
Further more, German AFV designers strove to make sure that German tanks would have sufficient frontal armour to give enemy AT weapons only a 30% or less chance of a first shot penetration, bearing in mind that the Germans meticuously tested every gun captured AT weapon and munition at the Rheim-Metal Borstig test facility and ranges.
Upgrade in shell designs maintained this advantage throughout WW2. The Allies struggled to keep up with German AFV designs and upgrades. The Soviets had to be given Allied propellant technology as they were still using Blackpowder, with Celluose Accetate primer, as their propellants in everything from small arms to AT guns, hence the abismal performance of Soviet AT and tank guns during the 1941 invasion.
During the Gulf and Iraq wars, the NATO 120mm. smoothbore tank gun had a better than 75% chance of a first round penetartion of the frontal 100mm. armour of the Iraqi T-54, T-55 and T-62 tanks at 2,000 metres.
By comparison, the 115mm. guns of the Iraqi tanks had a less than 20% chance of penetrating the frontal armour of the US M1 Abrams tank and 0% chance of penetrating the even thicker frontal armour of the British Challenger II tank even at point blank range. The frontal armour of a Challenger II exceeds the point blank maximum penetration, with FSAPDS, of the 115mm. tank gun.
Throw in superior fire control and sighting systems of the Coalition tanks and you have a very in even fight.
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