WWAG, of course an arrow's energy is KE. This from Sylvan:
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.
Read that again, carefully. KE is the measure of
CAPACITY to do work. It doesn't do the work itself. In our case, with arrows,
it is momentum that does the work, using KE's capacity to do that work. Think on that definition. KE is capacity and that is all it is. A glass has a certain capacity to hold an amount of beverage. It doesn't drink the beverage itself though. That is similar to the relationship between KE and momentum.
Momentum also regulates how that KE is used in relation to time. Using that same arrow Sylvan used in his example, the one pushing a 50 pound object one foot. Momentum determines how long it will take to move that object. The lower the momentum, the faster it's moved. The higher the momentum, the slower it's moved. Which means, the lower the momentum, the faster the energy is expended. The higher the momentum, the slower energy is expended. With our arrows, We don't want our arrows spending up their energy fast. That's what has happened when you don't get a passthrough... The arrow has simply spent all it's energy too rapidly. In fact, if we want a complete passthrough, it would be ideal if they didn't use up any energy at all during penetration! Anyway, it does take an amount of time for the arrow to hit and go through the animal. So we want our energy conserved over a longer period of time. We want to arrow to spend it's energy slow enough to get through the animal before the energy runs out.
The greater the momentum the longer it takes to drain KE's capacity as the arrow is penetrating a target, animal, or just thin air in flight. So again, like I said many pages ago, if you use a light, low momentum arrow, you've got to be sure to give it enough KE to do it's job. If you cannot give the arrow a lot of KE, it's best to go with a heavier arrow to increase it's momentum, and make it more efficient with what KE you've got available. A heavy, high momentum arrow from a longbow with much less energy can achieve exactly the same amount of penetration as a high energy, low momentum arrow from a compound. A low energy arrow from a light draw weight compound can do the exact same thing, the exact same way.
Tradeoffs. Doesn't matter what aspect of the sport you want to look at, archery is all about tradeoffs. With the same bow, there's hardly any tradeoff with KE due to arrow weight. It's the tradeoff between trajectory and momentum that gets people in trouble. Those that insist on flat trajectory are preoccupied with KE. Since they have to use very light arrows to get their very flat trajectories, then they have traded off momentum to achieve their goal. So, they are absolutely right and correct to be preoccupied with KE. Without much momentum, they've got to have a lot of KE. Problem is, they've either forgotten or never knew WHY they need so much KE. Many of them are so obsessed with KE that they totally disregard momentum and hate to even hear the word mentioned. Sad state of affairs.