Hello again!
Posted by mmadsen:
In fact, air resistance is roughly proportional to cross-section and to velocity squared.
Yes, that was pretty much my point. Double the velocity of a bullet, and you'll quadruple the air resistance. Halve the cross-sectional area, and you'll only halve the air resistance. You can see how this would bode ill for energy retention of small, high-velocity bullets.
Cross-sectional area of the sabot bullet we've been discussing here is just slightly over half that of the regular bullet. Velocity is about 1.4 times that of the larger slug, using the figures for the .308 round. (Air resistance for full-diameter slug) x 0.5 x (1.4 squared, or about 2) = pretty much the same resistance for both rounds - that load is right about at the break-even point, the "certain velocity" I mentioned earlier.
The bullets overcome the force of that resistance with the kinetic energy of their movement. And because that energy is equal to the slug's mass times its velocity, you can see that the light slug will lose more velocity than the heavy one when they lose the same amount of energy to overcome the same force of air resistance.
Then, because the smaller bullet is losing velocity faster, it will fairly quickly get into the range where it is facing less resistance than the bigger bullet. At 300 yards, their velocity is pretty even, meaning that the smaller bullet is facing about half the air resistance of the larger. But it still has only a third of the mass, so it is still losing
velocity 50% faster than the larger slug, despite facing less resistance. A glance at the last columns of the table will show how this ends up - the sabot round will be slower despite both its large initial speed edge and its smaller cross-section.
Posted by mmadsen:
But the sabot rounds are smaller in all three dimensions, are they? They have a smaller cross-section, but I thought they were roughly as long as a regular round, giving them the same ratio of mass (and thus momentum for a given velocity) to cross-section as a larger round.
If the sabot rounds were the same length as the standard rounds, then the mass difference would be directly proportional to cross-sectional area difference (edit: assuming same materials for same density, and assuming similar tapering; they're not perfect cylinders) - they'd be half the mass of the .308 slugs. But they're actually a third or less of the mass; the .308 slugs range from about 150 to 180 grains, compared to the 55 of the sabot slug.
The sabot bullets are .224 inches in diameter and 55 grains. M-193 military ball .223 ammo bullets were .223 inches in diameter and 55 grains - virtually identical. That's typical for civilian .223 loads too, though the military's moved to a heavier load in the M-16A2 that requires very fast rifling to stabilize. And .223 bullets I've seen were certainly not as long as .308 slugs.
Again, hope this helps, and hope the other readers are having as much fun with the physics and aero stuff as we are...
