The velocity is multiplied twice which explains why lighter faster arrows calculate a higher KE than heavy slow ones.
Actually this can be true but if we are talking about lighter arrows shot from the same bow it definately is not. Here's why... As was said, in english, kinetic energy equals 1/2 the mass of the arrow times the velocity of the arrow squared or in equation form KE = 1/2mv^2. The reason the equation is what it is, is because energy is by definition the capactity to apply a force over a distance and just as pounds times distance pulled in a force draw curve results in foot pounds of energy stored in the limbs of the bow, 1/2mv^2 is derived to yield equivalent foot pounds of kinetic energy. It's kind of important to understand that in terms of capacity to apply a force, KE and stored energy are equivalent and if a bow were to transfer all of its stored energy to the forward motion of the arrow, the kinetic energy in foot pounds would precisely equal the stored energy in foot pounds. In other words the summation of force times distances pulled in the bows force draw curve would equal KE. But because a bow only transfers part of its energy to the arrow, KE is always lower than stored energy. One other very important thing to understand is that the amount of energy transfered is a function of arrow mass. The higher the mass the more energy is transferred so shot from the same bow the lighter faster arrows always carry less KE not more.
And where do you get the 450, 240?
It's just the result of converting 1/2 the mass of the arrow in the KE equation from weight in grains to mass in slugs. Weight is force not mass and because the equation is 1/2 the mass of the arrow we have to do a converstion. Now beause there are 7000 grains in a pound we first convert grains to pounds by dividing by 7000. Now because the acceleration of gravity is approximately 32.16 ft/sec/sec we divide again by 32.16 and because the equation says 1/2 the mass we divide again by 2. Now 2 times 32.16 times 7000 just happens to be 450,240. So out of convenience and if and only if we have arrow weight in grains, veloctity in ft/sec and we want energy in foot pounds we can simply say that KE = velocity times velocity divided by 450,240. Again the 450,240 is only approximate as 32.16 is only approximately the acceleration of gravity. If you want more accuracy you need to carry more decimal places.
Is everybody bored now? I tried to be as brief I could trying to keep in mind this is a hunting forum not a technical forum. But hey, somebody asked...