I was drafting a letter to the Washington State legislators trying to get them to revise the airgun hunting regs and came across this article. I thought it was interesting. Basically, if you put a hole in an animal that is big enough and penetrate certain vital organs they'll go down. It doesn't much matter what size the projectile is beyond that threshold, nor does velocity play a large role in effectiveness. If the produced entry wound is large enough to allow a given volume of blood to flow out of the animal it will go down. This is written about firearms, but the physics and physiology remain the same when talking about air guns I'd think.
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"Once you get to at least a .24 caliber bullet of reasonable sectional density (about .218), construction and sufficient impact velocity to destroy blood-bearing organs and quickly end circulation, the differences in killing power become minor on a light and fragile animal like a whitetail deer. We might like to think that at 150 yards, the maximum range at which an estimated 98% of deer are taken, there is a huge difference between a relatively low energy .30-30 and a more than double the energy .300 Magnum. However, there is actually no significant difference in killing power. Both are more than sufficient to take a whitetail deer quickly, cleanly and efficiently."
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The source study that the above article is based on: http://www.dnr.sc.gov/wildlife/deer/articlegad.html
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"Once you get to at least a .24 caliber bullet of reasonable sectional density (about .218), construction and sufficient impact velocity to destroy blood-bearing organs and quickly end circulation, the differences in killing power become minor on a light and fragile animal like a whitetail deer. We might like to think that at 150 yards, the maximum range at which an estimated 98% of deer are taken, there is a huge difference between a relatively low energy .30-30 and a more than double the energy .300 Magnum. However, there is actually no significant difference in killing power. Both are more than sufficient to take a whitetail deer quickly, cleanly and efficiently."
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The source study that the above article is based on: http://www.dnr.sc.gov/wildlife/deer/articlegad.html