This is all quite interesting, in a macabre sort of way. I have said the following in this thread before, but here it goes again. The statement that KE ALWAYS goes up with increasing arrow mass is, by definition, invalid. The equation from which all else follows in the context of this argument is

F = ma (force = mass x acceleration, elegant in its simplicity eh). Once a modern bow has the draw weight set, the force it can deliver to the arrow (via the string) is, for all intents and purposes, a constant. As such, the only variable in our control is mass (of the arrow). Changing the mass (of the arrow) changes the acceleration (again, of the arrow). Since a = F/m, the instant the mass of the arrow increases from zero the system is on a collision course to acceleration of the arrow becoming zero – there is no escape. Since velocity is a direct result of acceleration [a = (vf – vi)/t], if the acceleration goes down, so does velocity. Now, since KE = ½ mv^2, if velocity goes down, KE goes down (goes down exponentially at that). As such, the statement that KE always increases with increasing arrow mass is, by definition invalid. This is not Los Alamos particle accelerator physics. It is ninth grade, physical science physics. This is not a point of conjecture nor is it a guess. It is physics, as physics is currently understood (although that does tend to be a dynamic argument).

I also did a simple calculation regarding the comparison of Kinetic Energies of arrows. I did the calculation with a 400-grain arrow and a 500-grain arrow as they were so heatedly debated. The math is a simple calculation that comes from stating the KE of a ‘light’ arrow is greater than the KE of a ‘heavy’ arrow, then solving the inequality for the velocity of the light arrow. That inequality is:

V(light arrow) > root m (heavy arrow) divided by root (light arrow) times velocity (heavy arrow). What that inequality states is that if the velocity of the light arrow is the product of the square root of the ratio of the mass of the heavy arrow to the mass of the light arrow times the velocity of the heavy arrow, then the ‘light’ arrow will have more KE than the heavy arrow! In the case of the 500-grain/400-grain arrow comparison, the 400-grain arrow will have more KE than the 500-grain arrow if the velocity of the 400-grain arrow is (root 5)/2 times greater than the velocity of the 500-grain arrow, period, no ifs ands or buts about it!. That statement is not a function of tune of the bow, or spine of the arrow. A ‘light’ arrow with root 5/2 times the velocity of a ‘heavy’ arrow can be flying sideways or turning cartwheels on its merry little path, it will have more KE than the ‘heavy’ arrow (which can also be doing aerial gymnastics as well). The math behind that argument is not integral calculus or Diff. Eq., it is good old friendly ninth grade algebra. If you don’t believe me, then as one of my college professors stated, “Do the math! Do the G.D. math!”