Kinetic Energy, Density and distance embedded

[MikeyBear]

A projectile hits different surfaces, each time the projectile has varying kinetic energy values, the surfaces also have varying densities. Is there any formula that accommodates for these variables in terms of the distance the projectile embeds into the surface?

 

[mfb]

For large velocities, the distance should be approximately given by the length of the projectile, multiplied by the density ratio of the projectile relative to the surface material (I am too lazy to look for a source). However, the shape and some material constants can be important, too. I don't think there is a universal formula which can cope all relevant effects.

 

[MikeyBear]

Are large velocity impacts classified by a certain velocity or by a percentage of an objects terminal velocity?

 

[mfb]

By something related to material constants. The velocity after the impact (and relative to the target) is 0?

 

[haruspex]

Are large velocity impacts classified by a certain velocity or by a percentage of an objects terminal velocity?

It matters whether the damage is local or widespread. A low speed impact on a strong lightweight material will deform a wide area. That spreads the absorption of energy and limits the peak damage. Impact into a very weak material, like soft earth, will hardly be spread at all. At high speeds into a dense material, the inertia of the surrounding material may prevent spreading, leading to a neat, deep hole.
Dimensional analysis suggests the dimensionless value R.V^{2}/T (R = density, V = impact speed, T = tensile strength) may be critical.