I did mention bullet shape and mass. Assuming the same material density, that would introduce sectional density into the balance, but since that would not be a good assumption it these days, it probably does not. So yes, we do need to mention sectional density. Good catch.
But there's more. I also mentioned bullet shape. You can have two 6.5MM bullets of the same mass, and they will have the same sectional density, by definition. The shape of the bullet will have a lot to do with penetration, just as the shape of an airplane fuselage will have a lot to do with drag, which will determine how far the plane will go when thrust goes to zero. Consider the also the shape of the bow of a boat, and how it will affect performance.
And then there's construction. A bullet with a full metal jacket will penetrate farther than an expanding bullet of the exact same shape, mass, diameter , and velocity. That's because the work required to expand the bullet slows it down; also, the increasing cross sectional diameter adds to the drag, or, if you will, the force acting against the bullet's forward travel.
And there's that pesky term work again. Work is energy--kinetic energy, thermal energy, potential energy, or any combination of the three. In the case of a non-explosive projectile impacting flesh, bone, stone, armor, or the dirt in a backstop and not bouncing off,, the energy starts out in the form of kinetic energy, which is not conserved i that inelastic collision, and is converted into the other forms.
It was work--i.e., energy-- that was required to get the bullet started in the first place, and it is work that determines the force and distance (also calculated as energy) required to stop it.
That's basic physics.
Now, variations in the way a particular bullet expands and in what is required to expand it might well prevent the penetration from being precisely proportional to the sure of the velocity, but it sure won't be directly proportional to the velocity.
It is important to realize that "penetration" is not simply defined by a distance in ballistic gel. One might be concerned with dirt or wall board, with metal prate, and with things that fracture, such as bone.
These days, a lot of munitions research his being directed toward very high kinetic energy non-explosive projectiles. The objective is deep penetration.
Just to broaden the discussion for the sake of illustration: the stopping distance of a car (lets consider one with a very low drag coefficient) is proportional to the square of the velocity (in a conventional car, all of the kinetic energy is converted to heat, but in a hybrid, some of it is turned into electrical energy); the drag on a plane is proportional to the square of the velocity, all other things being equal; and the compression of a spring impacted by a moving object is proportional to the square of the velocity. That means proportional to energy.
I hope that helps.
