KE = (S^2 X W)/450240, where S = speed in feet per second and W = arrow weight in grains.
The 450240 figure is the grains to pounds conversion of 7000 multiplied by the gravitational constant (32.16 fps per second) to convert arrow weight (in pounds) to mass.
There is really no great KE benefit to shooting heavy arrows that will show up shooting thru a chony at 1 yard. It' s true that hefty arrows do absorb a couple more ft lbs from the bow and make the bow shoot quieter with less shock and vibration. But a few ft lbs is the only difference between the heaviest and lightest arrows your bow will shoot with some measure of efficiency. The real benefit to heavier arrows is their capability to carry that energy further downrange than light arrows can.
KE uses speed squared to calculate energy. Wind resistance uses speed of the projectile cubed in it' s calculation. Speed X speed X speed. So, wind resistance increases faster than energy does, the faster the arrow flies. Light arrows flying faster encounter more wind resistance and have to spend much of their energy just cutting thru the air to the target. Heavy arrows flying slower encounter much less wind resistance AND have greater momentum to help them cut the air, so they use less energy getting to the target. The less energy lost in flight, the more energy available to the arrow on impact.
Personally, I like big, momentum-hog arrows ranging between 9-11 grains per pound of draw weight for hunting. A lot of guys like getting down to 5 grains per pound for the speed. I don' t agree with that concept and think they' re pushing the limits beond reason, but I have to admit they can do it because today' s bows crank way more than enough KE into the arrow to get the job done. I guess a smart fella would split the difference and get some of both ends by shooting something around 7-8 grains per pound. Decent speed, moderate momentum, good energy transfer from the bow to the arrow and good retained energy downrange.
Playing around with different arrow weights and speeds on the ballistics program at Jackson' s site is something I' ve spent some time doing. Feed in the particulars about your arrow and it will spit out speed, energy, momentum and arrow drop in 10 yard increments. It' s real easy to compare downrange performance for arrows of various weights and speeds.
www.bowjackson.com