In reality, arrows dont rely on kinetic energy but on cutting power. The same arrow shot at a deer with field tips that sticks half way through will blow right on through and do more damage with a sharp quality broadhead.
There was a very very well written article some time back, i believe it was in an Eastmans EBJ, but could have been in a different bow magazine that went into all the scientific parts that explained it better. However I did retain the part about the misnomers of bullets and arrows having the same flight and impact characteristics and that many instructors teach that and are wrong.
Ok here is an edit, I dug around in my magazine basket till I found it. EBJ 57, article is called "Bowhuntings Biggest Lie" By Darin Cooper.
Great education for those who would take the time to read it.