Strightarrow: Like I said before I agree: "I have said on several occasions that energy as a result of high mass rather than speed is better for maintaing path and "breaking" through bone. "
Here is what I said about why this is true: "If the force holding the molecules together can not be overcome by the force applied by the penetrating object then the penetrating object either breaks apart or bounces off or some of both. This is where momentum comes in to play. By keeping the energy high as a result of mass rather than speed, the point at which the penetrating object bounces off is increased relative to ke. The time it takes for the molecules to stretch out of the way is increased. " When you draw out the time during collision, the force is lowered. Force = mass x accelleration, Newtons 2nd law.

Now it's fine to come up with theoretical examples like "equalizeing" KE between 2 arrows to make a point but of course you must also accept that by chainging arrow weights it is impossible for this to happen for a given archer. Like I've said many times. The archer can't separate ke and momentum. The archer can't equalize KE between 2 arrows and then make momentum go up or down. When he/she puts on a heavier arrow, both ke and momentum go up and of course the reverse. So although what you are saying is absolutely correct it is irrelevant regarding the options the archer has available to him. The archer simply puts on a heavier arrow and gets more penetration. The argument over how you multiply mass and velocity together is irrelevant.

Straightarrow: This is often the reasoning behind why many attribute far greater importance to momentum but this is absolutely false reasoning. Momentum does indeed increase at a faster rate as you increase arrow weight but as has been shown the result is the same. The 17% increase in KE results in precisely the same increase in penetration as the 52% increase in momentum. It would be just as compelling but equally bad logic to argue that because it only takes a small increase in ke to get the same increase in penetration as a much larger increase in momentum then ke is much more important. I would also point out however that if we hold velocity the same between 2 arrows and only increase mass then both momentum and ke increase at exactly the same rate. In this theoretical example if you doulbe the mass you double both ke and momentum. But for the same reason your theoretical example is irrelevant to the archer, so is this. When changin arrow weight the archer can't equalize the velocity between 2 arrows.

Straightarrow: KE and momentum are only mathmatical tools to aid in understanding the phenomenom of mass in motion. The circumstance or event and the question being asked about that circumstance or event is what determines which tool is more usefull in answering the question. IMO the question of which one is of more importance doesn't even make sense. A wrench is not more or less important than a screw driver. Both are dead last on my list of concerns!

P.S. Straightarrow, I just want to thank you for the way you have been disussing this issue. Though it's clear you don't agree with everyting I've said you have kept your comments tehnical and without a sign of rudeness or sarcasm. I hope I have not offended you in any way as well.

One last point...
These definitions are not just for archery. KE = 1/2mv^2. With regard to it "not taking into account what happens when friction increases"...? Again it depends on what the question is. Friction is "force" that resists the movement of the arrow through the material. Clearly as KE is by definition the capacity to apply force, the more of it you have the more friction you can overcome.