cdoc42 said:
Velocity needs to be converted to foot-pounds of energy. You need at least 1000 ftp-Lb for white tails.
Tell that to a bow hunter getting maybe 50-70 ft-lbs out of an arrow at impact, or to anyone who's killed deer with a BP muzzle loader's ball or a .357 Magnum handgun or carbine. There is no simple "at least" available here. Everything depends on the bullet form. The arrow is an extreme example where the shape of the projectile nose is affecting some elements of the lethality mechanism differently from how an expanded bullet shape does. A pointed FMJ would be somewhere in between, though whether it tumbles or not affects how in-between it is.
It is probably worth noting the origin of kinetic energy as a measure of lethality. In the early 1700's, Dutch experimenter Willem s' Gravesande dropped brass balls into soft clay from various heights and found the ball's depth of clay penetration proportional to the height it was dropped from. Since gravity accelerates the ball at about 32 ft/s², he concluded penetration was proportional to the square of velocity. After kinetic energy's definition was settled upon almost a century later, the fact it was also proportional to the square of velocity lead to it being considered a penetration predictor and penetration was associated with lethality.
As you are probably aware, lethality prediction, particularly as it relates to handgun "stopping power", has come to be divided into two mechanism schools, one the penetration school championed by the late Dr. Martin Fackler and Duncan McPherson, and the hydrostatic shock school, exemplified by the oft criticized Strasbourg experiments. I won't resolve any of that grief for anyone. However, it does point out that whatever the equation for stopping ability one comes up with, the optimal range of energies will probably differ with projectile design and with the sectional density and momentum that go along with the energy, as they affect the penetration as well. For example, two similar shape projectiles that have the same impact energy, such as military ball in 9 millimeter and 45 Automatic (both loaded close to 400 ft-lbs in the TM's), the one with the greater momentum (the .45 has about 30% greater in momentum when the ME's match) will tend to penetrate a soft target, like ballistic gelatin, about 30% further. This is because, just as energy increases with the square of velocity, so does fluid drag at subsonic velocities, tending to slow the higher velocity of the two projectiles more rapidly. This is probably the root of the big-slow-projectile school of thought.
My suspicion is, all theories of stopping power aside, there probably is a different optimal velocity range for all bullet designs when achieving their average shot placement position that will maximizes speed of humane kill. Will the KE at impact factor in? Yes, but it won't be the only factor. Will there be a minimum KE? That really depends on shot placement. On another forum we have a moderator who is retired UK police who once investigated the death of a woman killed by a .22 rimfire at about its maximum extreme range. The shot was a miss fired upward at a squirrel in a tree about a mile away. The bullet struck the poor woman in the carotid artery at about 240 ft/s. Approximately 5 ft-lbs of energy at impact. Is that the minimum energy for killing human beings? No. It would likely have been lower if the bullet were pointed. Shape, sectional density, momentum and shot placement all change the energy requirement.