Sectional density effect on performance on target

[Colorado Redneck]

I understand sectional density. What I don't have a grasp on is the effect of sectional density when evaluating on target performance.

The example chosen to illustrate the question goes like this:

125 gr. .357 XTP with an impact velocity of 1300 fps = 469 ft. lb. of energy. The sectional density is listed by Hornady as 0.140

158 gr. .357 XTP with an impact velocity of 1157 fps = 469 ft. lb. of energy. The sectional density is listed at 0.177

For the sake of clarity, assume the meplat is identical.

So what would be the best selection for penetration and knock down power? And why?

 

[CarbineCaleb]

With expanding bullets, the expansion rate can't be predicted by ballistic factors. So the following approximation is most accurate for FMJ and lead hardcast rounds. The same physics holds for expanding rounds, but they will have a higher drag than predicted from their unspent diameter, due to the increase in cross-sectional area accompanying the expansion.

For handgun bullets, penetration in a ballistic medium can be described well with:
P ∝ S.D. * Vel

i.e. penetration is directly proportional to the product of sectional density with velocity. The constant of proportionality is omitted and is characteristic of the drag/viscosity of the medium, so this doesn't directly yield penetration in inches. What it does tell you is the relative penetration of two rounds.

...and if we plug in your figures above, we get 182 in the lighter bullet case, and 205 in the heavier bullet case. Therefore we'd predict the heavier bullet to penetrate about 10% deeper in tissue.

 

[mete]

For actual performance on game SD has little effect compared to bullet construction.They are all quite low.
For example many are cautious about using the Barnes all copper bullets .The 44 mag is only 225 gr .My old favorite was Speer 1/2 jacket SWHP , also 225 .Both these bullets are very good performers .The only Speer recovered went through almost 30" of deer at less than full load . The Barnes is similar performance.
A premium bullet ,Barnes , Speer Deep Curl, or Swift A-frame ,will do an excellent job regardless of SD. Don't worry about numbers , just practice so you can hit the deer !

 

[Colorado Redneck]

Thank you Caleb

Good explanation. The penetration calculation for 158 gr. compares to 240 gr. 45 caliber like so--

.357 cal - 158 gr. p = 205

.45 cal - 240 gr with S.D. of 0.160 with impact velocity of about 950 fps (the online calculator has quit working for me) and approximately 450 ft. lbs of energy

p = 950 X 0.160 = 152

Is that correct?

 

[Colorado Redneck]

Mete--

I agree with you. Many animals have been taken with low SD rounds. Many people have been killed by .22 long rifles. I am messing around loading some .327 Fed Mag and in the interest of creating a decent load for carry, I am looking at SD, velocity, energy etc. (Mainly because it is interesting to me. The liklihood of having to use a gun in our area is really really low, and we stay in the house after 9:00 pm. )

So it appears to me from Caleb's equation, a .327 caliber 100 gr. XTP at 1300 fps would behave very similarly in penetration to a .357 125 gr. xtp at the same velocity. Of course, the issues of "wound channel" and spent energy are other considerations.

 

[CarbineCaleb]

Hi Colorado, using:
158gr, .357 diameter, I got SD=0.177
240gr, .454 diameter, I got SD=0.166
...using the SD calculator at Beartooth Bullets:
http://www.beartoothbullets.com/rescources/calculators/php/density.htm


So yes, those two are pretty close in SD, with the .357 being a little higher. I didn't see a velocity in your post for the .357, but a standard factory load would push that at about 1250fps.

So it would be
0.177 * 1250 = 221 for the .357, and
0.166 * 960 = 159 for the .45LC
...predicting about 39% greater penetration for the .357 vs the .45LC when loaded like this.

You will find this works pretty well. It's much more predictive than the typical things written in gun magazines.

One thing you may know is that .357, .41 Magnum, and .44 Magnum have very similar penetration potentials - some shooters say "the only thing different is the diameter of the hole!". And if you look, you will find that the 3 rounds, with factory loads, push bullets of about the same sectional density at about the same velocity - so the observation of handgun hunters is bearing out what is predicted by this expression.

An interesting thing to consider, is that S.D. is just mass/area. So
SD * Vel = (mass * velocity) / area = momentum / area. Momentum divided by area is also know as momentum density. So this is the very same thing.

 

[Colorado Redneck]

This makes things understandable

Thanks for your comments, Caleb.

I am more of a small bore enthisiast. Hunting rifles--25-06 and 270 Winchester. Varmint-22-250 and 204 Ruger. Handguns--.327 Fed Mag and 357 mag. (In truth, there is a 44 mag Smith lurking in the safe.) Nothing against larger calbiers, just don't care much for recoil, and like the flat trajectories with smaller bore projectiles in rifles.

Thanks again!

 

[jmr40]

Shortest, most simple answer. The longer the bullet, the better penetration you get. Everything else being equal. A 200 gr 35 caliber bullet at 1000 fps will out penetrate a 200 gr 45 caliber bullet of the same design at 1000 fps. SD is not the only factor to consider. Just remember everything else is almost never equal.

The Barnes and other all copper bullets are playing with a different set of rules. They are longer than other bullets of equal weight. They also will not break up at high speeds. Normally a 100 gr 243 bullet at 3000 fps would blow up at close range and not give the needed penetration to reliably kill the larger game such as elk. But the copper bullets will hold together and likely give complete penetration on an elk at close range because of it's construction.

I know this is the revolver section, but the copper bullets are more effective the faster you shoot them and their gains in performance are not as noticable at handgun speeds