I was tinkering around and did a search on this topic... I didn't have a chance to read all posts, but most... Some very interesting thoughts on KE relating to momentum and penetration...

One thing that I think needs to be mentioned when trying to relate KE to Momentum is that we are talking about the speed at impact NOT the speed leaving the bow (which is where everyone is testing on chrono's). The difference in KE to Momentum is greatest at first, but will become closer the further the target is from the point of release. The reason behind this is that a heavier arrow will loose more velocity than a light arrow due to gravity.

That being said, you can't say a heavier arrow will out penetrate a lighter arrow. If KE is the same, a lighter arrow will out penetrate a heavy arrow at a certain point downrange (the velocity difference will eventually even things out and turn momentum in favor of the lighter arrow). This is dependent on how far the target is from the point of release. The heavy arrow will loose velocity quicker, thus the momentum will decrease. The point at which this happens I do not know. I plan to test velocity at various yardages to see the downrange velocity differences with various weight arrows.

For example...

1) 400 grain @ 270 fps (65 ft-lbs. KE) Momentum @ release = 108,000 grains * ft/sec

2) 450 grain @ 255 fps (65 ft-lbs. KE) Momentum @ release = 114,750 grains * ft/sec

In theory Momentum is higher on set-up #2 - largely because we are calculating at the point of release...

@ 20 yrds. if #2 drops to 160 fps and #1 drops only to 180, the momentum on #1 and #2 will be equal at the point of impact. I think KE may actually be a very good gauge for actual momentum and penetration. It depends largely on how much speed difference is seen downrange. I plan to test down-range velocity to see how much greater the speed loss is on heavier arrows. There should be a point downrange, where the increase arrow weight reduces velocity enough to where the lighter arrow will have higher momentum.