We got into the argument, Sylvan, because you said KE is THE indicator of how much penetration to expect. I don't believe it. It is AN indicator, even one of the prime indicators. But I think it's secondary to momentum.
I guess we will have to agree to disagree. As I read and understand the physics of kinetic energy and momentum, KE dertermines the amount of penetration and momentum determines if penetration will or will not occur. The calculations I have shown you demonstrate that in a homgenious target requiring equal amounts of force to push the arrow through that 2 arrows of equal KE will penetrate an equal amount even though the cary different momentum.
Let me leave you with a couple of quotes from a popular web site regarding the issue. Your welcome to chek it out.
http://homepage.ntlworld.com/joetapley/ here's another that might be more fun...
http://www.batesville.k12.in.us/phys...TMomentum.html
On KE...
The arrow arrives at the target with a given amount of kinetic energy. This energy is lost when the arrow hits the target and the arrow comes to a stop. Most of the energy ends up as heat in the target and some is lost via the flexing of the arrow stuck in the target. If 'x' is the amount the arrow has penetrated into the target at any given moment then there will be a retarding force on the arrow from the pile/shaft behaviour described above at that moment F(x). The definition of Kinetic Energy is that it is the integral over distance of the force F(x). In other words it is the arrow Kinetic Energy that defines how far an arrow will penetrate into the (elastic string) target.
On momentum...
The arrow arrives at the target with a given amount of momentum which the arrow loses as it comes to a halt. The definition of momentum is the integral over time of the force F(x). In other words it is the momentum that defines how long it takes for the arrow to come to a stop. Because the momentum change relates to force x time it is also a measure of the strength of the 'impact' the arrow has on the elastic strings in the target. The arrow momentum is one of the factors which will determine whether the elastic strings will stretch or snap. As how many of the elastic strings are broken affects the value of the frictional force on the arrow F(x) the arrow momentum indirectly affects how far the arrow penetrates into the target. (An extreme example would be shooting at a suit of armour - not enough momentum and the arrow would bounce off i.e. zero penetration irrespective of how much kinetic energy the arrow had).