Arthur P wrote:
But bows with relatively low KE numbers and heavy arrows can equal the penetration of a bow with high KE and light arrows.
If all things other than KE and mass are equal, that is if the geometry of the arrows are the same and the broad heads are equally sharp such that it takes an equal amount of force to “push” each arrow through the medium, then your statement is absolutely incorrect. All things being equal, arrows carrying equal kinetic energy will penetrate precisely the same amount.
Lets take 2 arrows each carrying 100 ft/lbs of kinetic energy. If there weights are 300 and 600 grains then they will be traveling at 387 and 274 ft/sec respectively. If each “pushes” its way into a medium that for their geometry requires 146 pounds of force you can calculate the penetration for each. I won’t bore everyone with the calculations but the answer is 0.68 feet for both of them. The faster arrow will penetrate to this depth in roughly 3.5 milliseconds and the slower in 5 milliseconds. Just for fun I did the same calculations on an arrow carrying 50 ft/lbs KE that weighed 800 grains. It therefore would be traveling 168 ft/sec and would penetrate this same medium 0.34 feet in a little over 4 milliseconds.