Bullet Sectional Density

In conjunction with the research I have been doing about bullet Sectional Density and the relationship to the required pressure and barrel length, I discovered an interesting fact.... Bullets of equal SD (with similar shapes) have very similar overall lengths.... Here are some bullets of various calibers with an SD of about 0.17....

http://i378.photobucket.com/albums/o...psmaptgb6x.jpg

Some of the bullets were modified slightly to reduce their weight and SD to as close to 0.17 as I could.... You will notice they are all nearly identical in length, at about 5/8" overall.... From left to right:

.224 cal 61 gr (shortened from a 63 gr.) SD = 0.174
.257 cal 74 gr. (Lyman 257420) SD = 0.160
7mm (.284 cal) 96 gr. Bob's Boattail SD = 0.170
.308 cal 118 gr. (Lee 113-RF) SD = 0.178
.357 cal 150 gr. (Lee 150-1R with Meplat) SD = 0.168
.458 cal 260 gr. (shortened Lee 340-F) SD = 0.177

My calculations show that in theory an SD of 0.168 is the heaviest you can drive at 950 fps using 3000 psi of air and a barrel length of 24".... Comparison with real world results has shown that has so far not been reached, to the best of my knowledge.... with the best current results from several custom builders using bore-sized porting, requiring a barrel of about 28" to reach that level of performance at 3000 psi.... If you want to drive a heavier bullet into the mid 900s, you need a longer barrel, more pressure, or a combination of both....

The Ballistics Coefficient is proportional to the SD, but is also influenced by the shape.... Generally, the longer and thinner a bullet is, the less drag, so for a given velocity and SD, it should carry more of that velocity and energy downrange to the target.... It only takes a glance at the above photo to see where the advantage lies, and that is with the smaller caliber.... The difference in BC isn't as great as you might think, however.... At subsonic velocities, the range from best to worst is only about 10%, and at Mach 1, about 25%, in favour of the smaller calibers.... However, there is a catch, and that is the twist rate required to stabilize those long skinny bullets.... For flat base bullets that are 0.625" long, with a 60% Meplat, and an SD of 0.168, the following twist rates are required to produce the recommended Stability Factor of 1.5 at 950 fps.... The BCs shown are subsonic, and at Mach 1.... For a boattail bullet, at least in theory, an even faster twist rate is required.... but the BC will be improved....

.224 cal - 11" Twist - BC = 0.15-0.19
.257 cal - 15" Twist - BC = 0.15-0.18
.284 cal - 19" Twist - BC = 0.15-0.18
.308 cal - 22" Twist - BC = 0.14-0.18
.357 cal - 30" Twist - BC = 0.14-0.17
.458 cal - 49" Twist - BC = 0.14-0.15

In terms of energy, when driven to the same velocity, the advantage of course lies with the larger caliber.... At 950 fps, the FPE is twice the bullet weight in grains, and here is a table of the bullet weights for an SD of 0.168, along with the associated energy....

.224 cal 59 gr. - 118 FPE
.257 cal 78 gr. - 154 FPE
.284 cal 95 gr. - 190 FPE
.308 cal 112 gr. - 224 FPE
.357 cal 150 gr. - 300 FPE
.458 cal 247 gr. - 494 FPE

I thought it might be interesting to present this data in this format.... as it might give a better understanding of what can be used successfully with the typical PCPs of today, and for what purposes they are best suited....

Bob