Does Momentum better describe what happens when an arrow strikes a target than Kinetic Energy? I've been researching medieval archery for many years, but I have trouble in visualizing the physical forces involved as relate to penetration.
PLEASE NOTE: All help appreciated but please in words as I've gone over the equations and variables for hours but they don't help visualize the situation; also I've sufficient understanding of arrowhead cross-section, material properties, weight, optimisation for flesh or armour combinations etc.
The following is my summarised lay interpretation - not direct quotes - of two schools of thought:
An expert (and frequently parroted) metallurgist: KE is the determining factor as it represents the energy that transferred on impact (aside from that converted to sound, heat etc) and hence penetration; Momentum describes the mass and position of a body, while energy is what brings about changes in momentum.
A leading bowhunter (ethical) holding doctoral-level scientific qualifications: Momentum, as a vector quantity, indicates energy concentrated behind the head and thus likelihood of penetration; it is not energy itself but describes what is happening, and apparent virtues of KE are actually a function of Momentum. While discussing penetration of flesh, this seems to be born out by the late-medieval period where velocity is sacrificed for mass in order to penetrate the improved armour of the period which is more directly represented by momentum.
An explanation or correction in these terms would particularly help.
Thanks all,
Tim
 A: There is another variable besides kinetic energy (KE) or momentum (p) of the arrow. It is the behaviour of the target material (flesh or different armour materials) with respect to the speed of penetration.
One of the methods to measure metals hardness is through identation, using a sharp diamond tool, mounted with a standard weight. It is a static test, with very low deformation speed. But in the case of a dynamical test, involving the same force but applied suddenly (high deformation speed) the depth of penetration tends to be smaller.
If only the mass of the arrow is increased, both KE and p increase by the same rate, and it is not possible to say which is the relevant factor. As the resistance to deformation is not expected to change, the depth of penetration certainly increases.
If only the speed of the arrow is increased, KE grows with $v^2$ while p grows  with $v$. But we can not say if the depth of penetration increases proportionally to KE or p without knowing the experimental behaviour of the target material. For example, if the resistance of deformation increases with $v^2$, to keep the mass constant, only increasing velocity, doesn't work.
