![]() Let's also assume that the projectile applies force only to the region of the armor directly in its path. ![]() The reason I've chosen a cubic projectile is to have a uniform, time independent stress being applied to the armor. It depends heavily on the rate at which the material is deformed and is typically determined empirically. Toughness is defined as the amount of energy per unit volume a material can absorb before fracturing. ![]() The relevant material property is the toughness. I'm going to assume a uniform slab of armor and a cubic bullet that will not deform at all. The best I can do is give you a method for making a very rough estimate of the stopping power of a material. People spend their whole lives answering this question. How thick would the armor have to be to stop a 40 cm cannonball moving at the same speed? Or what if you doubled the speed? Or what if you doubled the tensile strength of the armor? Etc. Suppose it took 10 cm of iron armor to stop a 20 cm diameter cannonball moving at 300 meters/sec. In case my question isn't clear, what I'm asking is something like the following. (My question is inspired in part from reading about Civil War ironclads, but I also saw the question about chain mail and thought that if that question was legitimate this one should be more so.) I realize that in modern warfare the projectiles are pointed and armor plate isn't a homogeneous slab, but I want to understand the simple case. Is there a simple mathematical expression for the stopping power of a given thickness of armor, given the thickness of armor plate, the radius of a cannon ball, the density of the cannonball and the armor, the tensile strength and/or toughness of the armor, and the speed of the cannonball? For simplicity assume the cannonball is a solid metal sphere and that the armor plate is homogeneous.
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