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The difference between BC and Cd is that if you make a bullet out of aluminum or lightweight plastic instead of lead, you will not change its Cd at all but you will dramatically alter its BC.
The reason a roundball's BC goes up with increasing diameter is that doubling the diameter of a roundball increases its mass eightfold but only quadruples its frontal area and surface area.
This is also why even the best .224 or .308 bullet cannot match the BC of a .50 BMG bullet and why the best .50 BMG bullet cannot match the BC of an artillery round.
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