Sylvan, isn't there a law of deminishing returns that comes into to play somewhere in there
As you go lighter and lighter the transfer of energy to the arrow becomes less and less efficient ultimately to the point where you are dry firing the bow. This of course is the most ineffiecient as all the energy is wasted. The rate of change in efficiency with arrow mass does change but the change in efficiency is always negative when lowering arrow mass and positive when increasing it.
momentum is the key, not how much energy something has stored, but how much energy its going to take to stop something. that's what is important, and i think that's what cougarmag is talking about.
Momentum and KE are both products of mass and velocity therefore both go up and and down together. Not in equal amounts of course but if KE goes up so does momentum and if KE goes down so does momentum. No exceptions. So as you go lighter with the arrow you lower momentum and of course the reverse.
Generally that is true but there are some exceptions. I don't have the #'s on hand anymore, but some bows are so much more efficient with lighter arrows (near the 5 gr/lb range) that the speed increase they achieve generates more KE with the lighter arrows than heavier, when shot from the same bow. Norb Mullaney talked about this phenomena a while back in one of his articles in Bowhunting World, and I've seen the same thing in my own experience.
I do not believe that Norb Mullaney ever said that efficiency goes up when you put on a lighter arrow. If he did he was incorrect. You could put on a lighter arrow and increase KE if you also made some other change to compenstate for the loss in efficiency. For example increase draw weight or lower brace height.