Bullets kill by transferring kinetic energy, delivering shock, and causing damage far outside the actual wound channel. Applying kinetic energy over momentum when it comes to arrows is ridiculous. Arrows kill by creating a cut wound channel...the longer the wound channel, the more there is to bleed...a hole in and another out is better than just one in that's blocked up by an arrow shaft that fails to exit.
Momentum is the tendency for an object to resist a change in direction. This is what keeps an arrow penetrating until resistance stops its forward progress.
Three years back I bought a new bow and went with the "lighter is better" theory to flatten trajectory. I took four deer with the bow, and was dismayed that none of the arrows exited even when they hit no more than a couple ribs. Three of the four were difficult to find because they didn't bleed due to the arrow shaft blocking up the wound channel. The 5th deer I shot that season was the biggest buck I ever put a sight pin on, 12-14 points. He tightened at the snap and dropped a bit, and I hit the shoulder blade. As he ran off it appeared the broadhead never made it through the bone. I tracked him by drops and intuition for a mile but thankfully he dropped the arrow and appeared to survive the incident.
After that I switched to much, much heavier carbon shafts. Every arrow since has exited and left great blood trails. My trajectory is only marginally worse yet the results on penetration with both deer and backstops is extraordinary.
