One of the ideas getting tossed around here in this thread is that momentum is responsible for penetration, not kinetic energy. Strictly speaking, this isn’t true, BUT IT SEEMS LIKE IT IS. Penetration of bullets into soft targets tends to be proportional to momentum more so than to energy.
What do we mean by Soft target: a material which is not linearly elastic, but which behaves more like a fluid. Examples would be bees wax, soap, animal tissue, ballistic gelatin, modelers clay.
When a bullet impacts a soft target, it arrives with a certain velocity, and the combination of its mass and velocity give it a certain energy. The mass and velocity also give it a certain level of momentum.
Physical laws help predict how deep the bullet will penetrate. One law is the conservation of energy. Another law is the conservation of momentum… Both laws apply all the time, but only one of these laws is useful in predicting how deep the penetration will be, and that is the conservation of energy law.
Lets make a simplifying assumption that the bullet is non-expanding, and it remains undeformed. Let’s also assume that the bullet travels into the target in a straight line and does not yaw.
When the bullet arrives at the target, it has a certain level of energy, and this energy allows it to do work, and that work is penetrating into the target. The more energy the bullet has, the further it can penetrate. But it is not a linear relationship. Twice the energy does not give twice the penetration. In water, twice the energy gives you about 20% more penetration at typical rifle velocities. Other factors are at play here.
One factor is friction: the bullet must use some energy to overcome friction, and in most soft media, friction goes up as velocity goes up. So if the bullet arrives on target with twice the energy, it has (by math) 41% more velocity, and this higher velocity means higher friction forces slowing the bullet down, stealing its precious energy.
Another factor is wave making, or dynamic displacement: The bullet as it moves through the target, is not cutting through like a knife. It is pushing its way through as a blunt object, and it has to shove a large amount of material in front of it, and to the sides of it. This material must be accelerated up to the bullets velocity. In other words, the bullet creates a pressure and velocity wave through the target. This takes energy, and the faster the bullet, the faster and more powerful the pressure/velocity wave. The bullet must use its precious energy to create this wave. The faster the bullet, the more energy is lost in the pressure/velocity wave.
If ALL the energy in the bullet was used purely to cut through the target material, you would expect that twice the energy would give you twice the penetration. But unfortunately, it is not so. You do get more, but not a lot more. There is a lot of wasted energy, and the faster the bullet, the more waste.
In the real world, it is possible that more energy can result in LESS penetration… certainly with expanding bullets this is possible. For instance, fire a handgun HP bullet at rifle velocities, and the bullet will disintegrate rapidly before it achieves a deep penetration. A 125 gr JHP bullet at 3000 ft/sec has an impressive energy of 2500 ft-lb, but it uses all this energy up destroying itself in the first few inches of target material.
Energy is proportional with velocity squared, but observation has shown that penetration into soft media is more proportional to velocity… So doubling the velocity might get you about double the penetration, even though the energy has gone up by a factor of 4…
Now keep in mind that momentum is proportional to velocity, and this has lead people to believe that momentum “causes” penetration. Penetration is proportional to momentum, but only by coincidence. This leads to a lot of arguments, because the people who say this are backed up by empirical evidence… but they got just a little bit confused on the theory.
Bottom line, if I was going to write a simulation code to model a bullet penetrating a soft media, I would model all the energy terms. I would use the law of conservation of energy. The law of conservation of momentum would not be useful to me. Broadly speaking, I do this kind of work… computer simulation using physical laws.
Hope this helps !
Jim
with same energy)
