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Technically, it doesn't. Bullets that are stable in air may "tumble" in tissue, or they may not; and "tumbling" itself is generally a mis-statement of what happens. Generally speaking, when a long spitzer bullet hits tissue (long relative to a pistol bullet or a round ball), the center of pressure of the bullet will radically shift forward, to approximately 30% of the length of the ogive behind the point of the bullet; which for most bullets will be very far in front of the center of gravity (and thus the majority of the mass). Because of this, the base of the bullet will tend to rotate around the center of pressure, past the nose once, or at most twice (due to inertia and the initial shock of the wound); and then the bullet will travel base forward (being led by it's mass) until it comes to rest, or exits the body (when it generally WILL completely destabilize and actually tumble). If the bullet travels far enough in tissue (somewhere between 14" and 20" depending on the exact bullet, and the density of the tissue), it will tend to rotate back to point forward, and then to base forward again.

That's not exactly tumbling; and it's certainly not "cutting through flesh like a buzz saw", or anything like it. Source: http://anarchangel.blogspot.com/2007/02/terminal-tumbling.html

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Q: Does the m-16 bullet tumble
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