Interesting article from the Alaskan bowhunting site...Physics or Myth?
Tissue Resistance to Arrow Penetration
Fact: The greater your arrow speed, the greater the resistance to penetration.
Speed in and of itself isn’t bad. Opting for speed at all costs, well, comes at a cost. Here’s one of them. When any object moves through another the object being moved through resists the forward momentum of the other. A good illustration of this is how the wind resists your hand if you put it out the window of a moving vehicle. The faster the vehicle moves, the more the air resists your hand. There is a formula for determining the degree of resistance various substances have to an object attempting to pass through them. It’s officially called the “Force of Drag” but we generally hear it referred to as wind resistance, or water resistance. This force of drag applies to other mediums as well like animal tissue, including hair, hide, flesh and bone.
The actual formula states: is the “force of drag” is the density of the substance being penetrated is the speed of the object relative to the substance being penetrated is the reference area. is the drag coefficient of the moving object. (e.g. 0.25 to 0.45 for a car) That’s a complex formula but here’s what it means to arrow penetration: The faster an arrow is moving the more resistance there is to it. (Even in the air.) Because the velocity is squared in the formula, the resistance increases tremendously as the arrow speed increases. If you double the speed of the arrow, the resistance factor increases by four. (2 x 2 = 4, velocity squared.) Here’s where it gets scary. If the arrow speed increases by a factor of four, then the resistance factor increases by 16 times! (4 x 4 =16, velocity squared) What does that mean to bowhunters? It means an arrow traveling at 150 feet per second is met with four times less resistance to penetration than an arrow traveling at 300 feet per second. Another way to say it is; an arrow traveling at 300 fps has to overcome four times the amount of resistance to penetration than an arrow traveling at 150 fps. The cold hard truth is.... When it comes to penetration, light fast arrows lose the momentum/kinetic energy battle AND when they reach the animal they have to overcome as much as four times the resistance to penetration as slower moving, heavy arrows do.
If you're goal is to gain kinetic energy on paper by shooting lighter arrows faster, science proves it's a lose-lose proposition.
First, you LOSE velocity twice as fast as momentum AND you LOSE penetration potential in what energy you do have left because the medium you're trying to penetrate is resisting that penetration four times more than if you were moving half as fast.