Dr Ed on Terminal Performance

I posted a short version of the film clip we discussed on TradBow (found it on YouTube). Here’s a copy of what I posted. I definitely think you need to find a way to incorporate this into your presentations; though perhaps not as ‘technically’ or verbose as I tend to write.

“Watch the short film clip below. There is much here that can help one understand the terminal performance of a hunting arrow.

What can be gleaned from this film clip? It tells us a lot about how a projectile applies whatever force it carries. First, a few calculation. The military .30-06 load, circa 1961 was a 172 grain, non-expanding bullet at 2700 fps from the M1 Garand. That indicates 2783.70 ft. lbs of KE (the energy carried by the projectile) and 2.062 slugs (lb-feet/sec.) of momentum (the projectile’s ‘force’). For the arrow we have to do a little assuming. The ‘typical’ arrow, circa 1961, would be about 550 grains at a maximum of 170 fps from a period recurve bow. This indicates 35.29 ft. lbs of KE and 0.4152 slugs of momentum. That means the .30-06 has 78.9 times as much KE as the arrow and 4.97 times as much momentum. Remember that this is a non-expanding bullet of .308 inch diameter – smaller than the typical arrow shaft of 1961, which would likely have been 11/32 inch (0 .34375 inch, or 11.6% greater diameter than the non-expanding bullet from the .30-06).

First, how well did the KE predict the penetration? Not very well at all. While the difference in momentum does not directly predict the penetration either it does come far closer to doing so than does the KE. Why does the arrow’s lower momentum out-penetrate the non-expanding bullet so drastically? Because all momentum is not equal in predicting a projectile’s penetration capability. The arrow derives most of its momentum from the arrow’s mass whereas the .30-06 derives most of its momentum from the bullet’s velocity.

Now, how does this relate to the study’s data? First, it explains why the Heavy Bone Threshold is related to the arrow’s mass rather than the force or velocity the arrow impacts with. The heavier a (structurally intact) projectile is the slower it loses its momentum, which results in a longer TIME OF IMPULSE … it pushes forward for a greater period of time; exactly why the Heavy Bone Threshold is related to the arrow’s mass, rather than the amount of KE or momentum the arrow carries. The heavier arrow ‘pushes’ on the bone longer … long enough to overcome the bone’s mobility and flexion.

A lighter arrow might well “hit harder” (have more KE and/or momentum at the time of impact) but it loses its forward impulse before the bone reaches its limit of mobility and flexion. The arrow can’t even BEGIN to penetrate the bone until the bone’s limit of movement and flex is reached. This is a graphic illustration why the arrow’s mass is the determining factor in the Heavy Bone Threshold; it allows the arrow to apply whatever force (momentum) it does carry to the bone for a longer TIME OF IMPULSE. Whenever that TIME OF IMPULSE is greater than the TIME required for the bone to reach the limit of its movement AND flexion the arrow will begin to penetrate the bone. Whenever the arrow’s retained force, after exceeding the bones movement and flexion, is sufficient the bone will be breached. And that why the mass of your arrow is THE important factor in the arrow’s ability to breach bone, assuming the arrow maintains its structural integrity throughout penetration. It’s also why it is important to design your arrow so that it maximized its potential for conserving as much of the arrow’s force as possible throughout penetration (through maximum utilization of the other arrow-force conserving design features) – the arrow’s remaining force at the time the bone reaches the limit of its mobility and flexion will determine whether the bone is breached or the arrow stops without penetrating the bone.”