A few observations.

Kinetic energy and arrow mass. It has been stated that KE ALWAYS increases with arrow mass (weight). That statement didn’t make sense to me, so I did some math on the idea. A relatively straightforward calculation was to write an inequality that states the KE of a 400-grain arrow is greater than the KE of a 500-grain arrow (KE400 > KE500). Substituting the value of ½ mv2 in for KE one gets ½ mv2400 > ½ mv2500. Then solving the inequality for the velocity of the 400-grain arrow, one obtains v400 >root 5/2v500. Or in other words, if the velocity of the 400-grain arrow isroot 5/2times greater than the velocity of the 500-grain arrow, the 400-grain arrow will have a greater KE than the 500-grain arrow. In more practical terms – if the velocity of a 500-grain arrow were 280 fps and the velocity of a 500-grain arrow were 313.05 fps (280 times root 5/2) the 400-grain arrow would have more KE than the 500-grain arrow. End of story.

A similar argument can be made for momentum. However, the results are considerably different. For a 400-grain arrow to have more momentum than a 500-grain arrow, the 400-grain arrow would have to have a velocity 5/4 times more than that of the 500-grain arrow to have a greater momentum. In other words, the same 500-grain /400-grain arrow comparison – the 500-grain arrow with a velocity of 280 fps would have more momentum than the 400-grain arrow until the velocity of the 400-grain arrow is 350 fps!

Momentum and penetration. The importance of momentum relative to penetration cannot be overstated. From a pure physics standpoint, momentum is penetration. Momentum is, by definition, the resistance to the change on the motion of an object (actually that definition is for inertia – but momentum is inertia in motion). The more momentum an object has, the more difficult it will be to stop. The more difficult the object is to stop, the greater will be its penetration. Again, end of story, at least from a pure physics perspective. To say the momentum is the only argument to consider when developing a hunting rig would be silly. Parameters such as trajectory, broadhead, matching the arrow to the bow, FOC, bow tuning, the list goes on and on (this multitude of variables is one of the things that makes archery so much fun) are all significant considerations.

So, to answer the original question of what arrow will produce the most momentum is, to say the leaset,difficult to answer. Even answering the modified question of which arrow will be the most efficient is going to be difficult to answer, but perhaps easier than the momentum question. It seems the finding that ‘sweet spot’ for the bow, in terms of KE, is as reasonable of an approach as any I have heard.