I think we can walks. Energy is by definition the capacity to perform work and work is defined as force applied over a distance. So KE for an arrow is a measure of the capacity of that arrow to apply a force over a distance. The more KE you have, the greater the potential force can be applied and/or for a greater distance. Clearly an arrow that carries 50 ft/lbs of ke can apply 50 pounds of force over a distance of 1 foot or 100 pounds for 1/2 foot. When penetrating some medium the force required to "push" the arrow through is a function of many complex factors so an attempt to calculate the force required to push through a deer would be daunting even if you knew the precise path the arrow would follow. In homogeneous mediums where the resistance to penetration is predictable however KE can be used to precisely predict the depth of penetration. In fact given the resistive force of the medium to the penetrating object, KE is the definition of how far it will penetrate. If for example the medium puts up 50 pounds of resistance then an arrow carrying 50 ft/lbs of ke at impact will penetrate precisely 1 foot. Even on a deer though we know without question the more KE you have means more potential penetration.

Just for the sake of expounding a bit. Penetration as a function of KE is not continous. There are at least 2 major disruptions in the function. When an object penetrates a medium at relatively low speed, the molecules of the material are stretched out of the way. The faster this takes place the greater the force of resistance. At some point the force becomes great enough that the molecules begin to break rather than stretch and there is a sudden change in the up to that point continuous funtion. When the molecules break off they are pushed ahead of the penetrating object and the force increases. This is basically the difference between the way bullets penetrate and arrows penetrate. Arrows penetrate because they are sharp and are very good at stretching or cutting the molecules at realatively slow speed leaving a hole that is clean and tends to seal back on itself. Bullets tend to "blast" there way through shearing material and leaving a round realatively ragged hole. If the force holding the molecules together can not be overcome by the force applied by the penetrating object then the penetrating object either breaks apart or bounces off or some of both. This is where momentum comes in to play. By keeping the energy high as a result of mass rather than speed, the point at which the penetrating object bounces off is increased relative to ke. The time it takes for the molecules to stretch out of the way is increased. This is why it is often stated that kinetic energy as the integral of force over distance is a beter predictor of the depth of penetration while momentum as the inegral of force over time is a better predictor of whether or not the object will penetrate at all. These concepts also explain why the arrow wins in the famaous arrow vs bullet shot into a sand bag contest.

This little explination is far from an in depth discussion of the mechanics of penetration but the concepts are simple enough to be usefull. They are not analogous to vortex shedding either. When penetrating a gas the rules change. They are also somewhat differnt when penetrating a liquid.

I'll still go back to my stated position regarding this matter though and that is that the arrows ability to penetrate is a function of its mass and velocity. If you want to multiply these 2 things together in differnt ways and say one way is more important than the other then fine, I'm not going to argue about it. It still comes down to if you want more penetration potential then put on a heavier arrow.