Dr. Ed Ashby has written gobs on the topic, specifically on hunting arrows and how they penetrate game, hitting or not hitting bone, muscle, broadhead type etc etc etc.
To really (really really) simplify what he has shown through real world testing on game animals (not ballistics gel or soggy phone books) is as follows:
The amount of resistance to penetration increases "exponentially" as speed increases (his "non rocket science" example is hold your hand out the window of a car at 30 mph and compare that to 60 mph - at 60 you don't need to exert twice as much force to keep it in place you have to exert 4 times the force) - so impacting at 400 fps robs way more energy, due to resistance as compared with impacting at 200 fps - so yes, you still have "more power" but you lose more, all else being equal.
(so doubling your speed/KE does not double your penetration, it increases somewhere in the 25% range due to resistance)
Second of his major points is that KE is almost "meaningless" when talking about a hunting arrow impact - it's just a nice neat equation that marketers have grabbed onto and convinced you is of "ultimate importance".
He states that "slug force" is far more important. Slug force has more to do with momentum and weight of the arrow.
(again, layman's terms - it's easier to stop a smart car going down a hill than a tractor-trailer loaded with steel even if the car is travelling at 4 times the speed of the truck - the "weight" keeps moving it forward - I believe that's one of Newton's laws that predate Einstein by a good few years, and is actually proven)
So a slower, heavier arrow will meet less resistance to penetration on impact (so lose less of it's energy) and will take significantly longer to "slow down" after it does - so it will penetrate deeper unless the lighter faster arrow is many, many times faster (like on the order of 8 to 10 times).
He also compares wood to aluminum to carbon shafts (carbon shafts when "lubricated" with blood have way less resistance than wood or aluminum).
Also, 2 blade vs 3 blade vs mechanicals, vs angle of the ferrule - if you can study it, he has probably looked at and collected data.
He is also a great proponent of extreme Front of Center (FOC). He studied and (concluded) that extreme FOC helps "pull" the arrow through the animal compared to less FOC with the same momentum (some cool stuff).
Do a search for "Dr. Ashby arrow" (or the like - there is a great PDF document on file at one of the universities of his paper on the subject) and give yourself a couple of nights to try and digest what he has to say - it's uber technical (but he puts lot's of layman's notes to try and help explain (which you only need a physics degree to understand
)EDIT to ad link - if anyone is interested, below all the pics on this link is the article broken down into a number of parts (and again, it's "heavy" reading)
http://www.alaskabowhunting.com/Dr.-Ed-Ashby-W26.aspx
