Frontal Area vs. Sectional Density
Question:
>I’m really puzzled by the units in this formula. We end up with:
(energy / area) * (mass / area) or > (momentum**2) / (area**2)
which doesn’t make any physical sense to me at all. The term "penetration >factor" suggests a dimensionless quantity. Could you enlighten us a bit
as to the logic behind this? Like I said this is one of many ways to determine the relative penetrating abilities of different bullets. It is hardly agreed upon as the only one. The numbers are comparative just like Sectional Density numbers. They are only relate to each other not to anything like how deep they will penetrate into an animal. Maybe I should have used the Momentum Value as an example but since this is a better known formula I thought someone else would post it. I think this one is less well known and I do think it does give a close approximation of the relative penetration of different bullets though and is simple enough to use. >Here, we get energy * area which is still counter-intuitive as a measure
of destructive potential. If we hold the energy constant, while >increasing the area that it’s dissipated over, I’d expect the result to
be less destructive. Well I guess we are of different schools of thought on that! I am of the "big hole matters" school. This formula favors that school. I know the "energy is all that counts" school would disagree. I just don’t believe that energy kill critters. Energy is important, but not the only thing that matters. This formula takes in energy but also takes into account frontal area. Of course loads of people will disagree with it. >I can see some sense in taking this approach as a >first order *empirical* model, but it’s generally much better to pick an
empirical model where the units have some physical meaning. I don’t >intend any sort of flame here, just a bit puzzled…
No offense taken! I would like to see other formulas you have. I was hoping that others would offer alternative formulas. I gather them up and put them in my computer for later use! It is nice to see how these work out in the real world on game. Unfortunately I can’t tell you the source of the above two formulas. I didn’t make them up though! I have had them around a while stored in my computer and have forgotten where I got them. I believe they came from an African source so that somewhat explains the weighting of the area over energy. Visit the rec.hunting and rec.hunting.dogs FAQ Home Page at: http://sportsmansweb.com/hunting/ To leave the Hunting listserv list, send a message with SIGNOFF HUNTING
Response:
r.h folks, I would like to add something to this thread that Mike LaGrange wrote in his fine book _Ballistics_in_Perspective_ (ISBN 0-96224807-2-X). This book documents testing Mike did for the Gov’t of Zimbabwe. He shot control for many years, and has taken over 6,000 elephant, and many other animals. Mike is discussing the factory of bullet effectiveness: p.20 "Caliber is compensated to a degree by bullet expansion as suggested. Experience would indicate, however, that its effect is not as marked by using larger diameter bullets. Large diameter bullets are better as they obviously have greater potential to expand than smaller ones and the effect upon the animal is immediate upon penetration. Experience over the years has indicated that there is a significant difference between the effect of calibers below .300 to those above. A 7mm caliber weapon (equivalent to .280 of an inch), seems to have considerably less effect than a .308 Win even it as powerful in terms of energy produced." The importatnce of this quote is the fact that it is base don field observation of many animals shot with a variety of rifles in a variety of conditions….jim dodd Visit the rec.hunting and rec.hunting.dogs FAQ Home Page at: http://sportsmansweb.com/hunting/ To leave the Hunting listserv list, send a message with SIGNOFF HUNTING
Response:
>If I have a 150-grain bullet, and all other things being equal, is it >better to have a fatter bullet with greater frontal area for a wider >wound channel, or a more slender bullet with greater sectional density >for a deeper wound channel? Assuming I can’t have both. Please discuss >the issues involved. Thanks.
John– In short, it depends on how far the bullet needs to penetrate, and what it has to go through. For example, consider a 150 grain bullet of .358" loaded in a .35 Remington and a .308" bullet of the same weight loaded in a .30-30 Winchester. If bullets start out with the same muzzle velocity, the former will lose speed more rapidly due to air resistance, because of its greater cross sectional area compared the latter. When it hits something solid, it’ll give up energy more rapidly for the same reason. If you’re hunting whitetail deer, and limit yourself to broadside shots *behind* the shoulder, either one should do nicely. But if you take a shot where the deer’s quartering away from you, greater penetration becomes more important. Bob Athay Visit the rec.hunting and rec.hunting.dogs FAQ Home Page at: http://sportsmansweb.com/hunting/ To leave the Hunting listserv list, send a message with SIGNOFF HUNTING
Response:
- Hide quoted text — Show quoted text – >Penetration would be one thing to compare. One way to determine relative >penetration is by dividing muzzle energy by frontal area of the bullet then >multiply that by sectional density and then dividing that by 100 to make the >number easier to work with. >So for the 7mm Rem. Mag a 150 grain bullet traveling at 3000 fps we get: >2997/.0633 = 47346 >47346*.266=12594 >12594/100= 126 >126= penetration factor >The 30-06 pushing a 150 grain bullet at 3000 fps we get: >2997/.0745=40228 >40228*.226=9091 >9091/100=91 >91 = penetration factor > <snip>
I’m really puzzled by the units in this formula. We end up with: (energy / area) * (mass / area) or (momentum**2) / (area**2) which doesn’t make any physical sense to me at all. The term "penetration factor" suggests a dimensionless quantity. Could you enlighten us a bit as to the logic behind this? >Determining how that greater area of the .308 bullet effects game is a little >more tricky and I doubt that there will ever be a formula that will satisfy >everyone. One simple way is to multiply the muzzle energy by the area of the >bullet to come out with another number to use as a comparison. >So for the 7mm Remington we get: >2997*.0633=190 >For the 30-06 we get: >2997*.0745=223
Here, we get energy * area which is still counter-intuitive as a measure of destructive potential. If we hold the energy constant, while increasing the area that it’s dissipated over, I’d expect the result to be less destructive. I can see some sense in taking this approach as a first order *empirical* model, but it’s generally much better to pick an empirical model where the units have some physical meaning. I don’t intend any sort of flame here, just a bit puzzled… Bob Athay Visit the rec.hunting and rec.hunting.dogs FAQ Home Page at: http://sportsmansweb.com/hunting/ To leave the Hunting listserv list, send a message with SIGNOFF HUNTING
Response:
>If I have a 150-grain bullet,and all other things being equal, is it >better to have a fatter bullet with greater frontal area for a wider >wound channel, or a more slender bullet with greater sectional density >for a deeper wound channel? Assuming I can’t have both. Please discuss >the issues involved. Thanks.
A trick question! If both bullets penetrate all the way through, fat is better (unless it destroys too much meat, or ruins the trophy). If the fat bullet doesn’t penetrate deep enough, then the one that penetrates farther is better. If "and all other things being equal" means the range, is it near or far? If it means muzzle energy, is it high or low? The answer to your question depends on the range and the power. In general, high sectional density is to be preferred–and by definition that requires a certain minimum mass or ‘heavy-for-caliber’ bullet (in other words, a high SD bullet isn’t small). Assuming you can’t have the benefits of both, "a fatter bullet with greater frontal area for a wider wound channel, or a more slender bullet with greater sectional density for a deeper wound channel", use a fat bullet in close (out to where it no longer penetrates sufficiently) and go for higher sectional density as range increases to the detriment of velocity. At close (point-blank) range all muzzle energy is available to drive the bullet. Farther from the muzzle, the velocity decays and energy is lost. It turns out that efficient long range bullets with a high ballistic coefficient are also of high sectional density. When you say you can’t have the benefits of both types of bullets, you are in effect setting a limit on muzzle energy. If you shoot the 50 BMG, for example, you get both–a fat bullet with a great SD using the 750 gr bullet (and 13,000 ft-lbs ME). If you limit yourself to the amount of energy of a heavy 180 gr 30-06 load (or 175 gr 7mm Mag) of about 3,200 ft-lbs, you can have adequate killing power out to 400 yards with efficient high SD bullets. At the same energy limit and for shots in close, you can use the 45-70 with round-nose 350 gr bullets at 2,000 fps to make big holes in elk, moose, or bears. If you limit yourself by bullet weight as proposed above–the 150 gr bullet–but not energy; then, you can choose between a 270 Wby with about 3,500 ft-lbs of muzzle energy and an efficient bullet to reach way out there, or a 35 Rem with about 1,900 ft-lbs at the muzzle for close work. If you limit energy, recoil stays the same, power stays the same, and bullet shape gives you either a big hole at close targets (using the fat bullet) or a smaller hole with likely equal killing power at long range (using the high SD and high BC bullet). If you limit bullet weight to 150 grs (and I don’t know why you would since you’ll need two different caliber rifles anyway), you need more power for long shots than for short ones. The reason for this is found at the extremes: of caliber (fat); and high SD (very heavy-for-caliber bullets). A fat 150 gr bullet can’t get much wider than .35 caliber without becoming a lead tortilla. But a lead tortilla won’t require much power to get it moving down the barrel. On the other hand it won’t fly too far (unless you use a special ‘frisbee’ twist). To get high SD out of a 150 gr bullet, it necessarily must be of small caliber (about .25 to.277), and so, being heavy-for-caliber, requires a ‘hot’ loading to get at least 2,800 fps for long shooting. In the compromise that is called "the all-round hunting cartridge", limits on caliber (fatness or skinniness), muzzle energy (high or low), and bullet weight, in order to have adequate killing power near and far, without getting killed on the "other end" by recoil or the weight of lugging a heavy weapon, have resulted in the most common modern hunting cartridges. They are medium in caliber and medium in power. Neither too fat nor too skinny, they use bullets that penetrate without disintegrating. They have adequate power, but most shooters can learn to handle them. They use bullets from 140 to 200 grs. These popular cartridges vary to both sides of the 30-06, with the 7mm-08, 308 Win, 270 Win, 280 Rem below and the 7mm Mags, 300 Mags, 8mm Rem, and 338 Win above. The modern tendency is to go with a cartridge that uses a high SD bullet that can be used for long shots–and hope the bullet holds together if it is used for an "up close" shot. In other words, use one that provides an adequately wide and sufficiently deep wound channel. I think the question should have been "Would you rather go up against Wyatt Earp and his long-barreled 45 Colt, or J. Spencer and his longer barreled .243 Win? I’m certain the ‘discussion’ would be more interesting! Visit the rec.hunting and rec.hunting.dogs FAQ Home Page at: http://sportsmansweb.com/hunting/ To leave the Hunting listserv list, send a message with SIGNOFF HUNTING
Response:
comparisons of bullets: >Ignores all expansion characteristics, I.E treating bullets like solids.
These equations allow for nothing wrt to bullet construction and would >only really apply to solids with similar nose configurations. >A 230gn Failsafe from a 340WBY will outpenetrate a .416cal 410gn SN Woodleigh weldcore >(A premium bullet). The failsafe outpenetrates a 350gn Barnes X in the
same caliber. >The 300gn Woodleigh .338cal SD=0.375 gets left well behind the
failsafe. A 210gn Nosler 338cal bullet will almost penetrate as far as >the Woodleigh Weldcores in .416cal (410gn) >My point is that depending on the Expansion Characteristics of the
bullet, whether it is an X a SP, a HP whatever your Effective SD will >change irrespective of the weight. >Really it means very little to compare SD’s of Different Bullets, both
standard and Premium. As when Expansion begins those figures become >irrelevant. >If were talking Solids, that’s another thing.
Of course you are right when you consider comparing two different bullets. It is a mathematical model that gives an idea of penetration and assumes two like bullets. If you put a Failsafe up against a Woodleigh you upset the comparison. Two Woodleighs or two Failsafes would work within the formula. Or at least close enough to give an idea of the relative penetration of both bullets. This is especially so in the two I used for a comparison, 7mm and .308, since the frontal area is close to the same. When you start comparing two bullets of vastly different caliber, you are going to have to factor in other things. The formula is a simple comparison that I believe gives an idea of the relative penetrating qualities of cartridges. It isn’t perfect and like I said it isn’t the only one available. It is fairly simple though and I think good enough for more uses – when you compare like bullets. If you want to talk about Failsafes vs. Woodleighs, that is a whole othe subject. I wrote, in part: – Hide quoted text — Show quoted text -> There are whole bunch of ways to determining the effectiveness of bullets > given your criteria. So I will assume that the choices are between two > popular calibers in the same weight. 7mm Rem Mag and 30-06. > Penetration would be one thing to compare. One way to determine relative > penetration is by dividing muzzle energy by frontal area of the bullet then > multiply that by sectional density and then dividing that by 100 to make the > number easier to work with. > So for the 7mm Rem. Mag a 150 grain bullet traveling at 3000 fps we get: > 2997/.0633 = 47346 > 47346*.266=12594 > 12594/100= 126 > 126= penetration factor > The 30-06 pushing a 150 grain bullet at 3000 fps we get: > 2997/.0745=40228 > 40228*.226=9091 > 9091/100=91 > 91 = penetration factor > So the 7mm Rem Mag with a 150 grain bullet is going to out penetrate the 150 > grain 30-06 bullet when both are traveling at 3000 fps which is obtainable > with both cartridges. No surprise there.
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Response:
- Hide quoted text — Show quoted text – > There are whole bunch of ways to determining the effectiveness of bullets > given your criteria. So I will assume that the choices are between two > popular calibers in the same weight. 7mm Rem Mag and 30-06. > Penetration would be one thing to compare. One way to determine relative > penetration is by dividing muzzle energy by frontal area of the bullet then > multiply that by sectional density and then dividing that by 100 to make the > number easier to work with. > So for the 7mm Rem. Mag a 150 grain bullet traveling at 3000 fps we get: > 2997/.0633 = 47346 > 47346*.266=12594 > 12594/100= 126 > 126= penetration factor > The 30-06 pushing a 150 grain bullet at 3000 fps we get: > 2997/.0745=40228 > 40228*.226=9091 > 9091/100=91 > 91 = penetration factor > So the 7mm Rem Mag with a 150 grain bullet is going to out penetrate the 150 > grain 30-06 bullet when both are traveling at 3000 fps which is obtainable > with both cartridges. No surprise there.
Ignores all expansion characteristics, I.E treating bullets like solids. These equations allow for nothing wrt to bullet construction and would only really apply to solids with similar nose configurations. A 230gn Failsafe from a 340WBY will outpenetrate a .416cal 410gn SN Woodleigh weldcore (A premium bullet). The failsafe outpenetrates a 350gn Barnes X in the same caliber. The 300gn Woodleigh .338cal SD=0.375 gets left well behind the failsafe. A 210gn Nosler 338cal bullet will almost penetrate as far as the Woodleigh Weldcores in .416cal (410gn) My point is that depending on the Expansion Characteristics of the bullet, whether it is an X a SP, a HP whatever your Effective SD will change irrespective of the weight. Really it means very little to compare SD’s of Different Bullets, both standard and Premium. As when Expansion begins those figures become irrelevant. If were talking Solids, that’s another thing. Regards, Mark.. Visit the rec.hunting and rec.hunting.dogs FAQ Home Page at: http://sportsmansweb.com/hunting/ To leave the Hunting listserv list, send a message with SIGNOFF HUNTING
Response:
If I have a 150-grain bullet, and all other things being equal, is it better to have a fatter bullet with greater frontal area for a wider wound channel, or a more slender bullet with greater sectional density for a deeper wound channel? Assuming I can’t have both. Please discuss the issues involved. Thanks. John Hanka Minneapolis MN USA Visit the rec.hunting and rec.hunting.dogs FAQ Home Page at: http://sportsmansweb.com/hunting/ To leave the Hunting listserv list, send a message with SIGNOFF HUNTING
Response:
>If I have a 150-grain bullet, and all other things being equal, is it
better to have a fatter bullet with greater frontal area for a wider >wound channel, or a more slender bullet with greater sectional density
for a deeper wound channel? Assuming I can’t have both. Please discuss >the issues involved. Thanks.
That seems like a strange choice! Usually someone has a rifle with a single caliber the choice is between bullet weights. But I will play along! There are whole bunch of ways to determining the effectiveness of bullets given your criteria. So I will assume that the choices are between two popular calibers in the same weight. 7mm Rem Mag and 30-06. Penetration would be one thing to compare. One way to determine relative penetration is by dividing muzzle energy by frontal area of the bullet then multiply that by sectional density and then dividing that by 100 to make the number easier to work with. So for the 7mm Rem. Mag a 150 grain bullet traveling at 3000 fps we get: 2997/.0633 = 47346 47346*.266=12594 12594/100= 126 126= penetration factor The 30-06 pushing a 150 grain bullet at 3000 fps we get: 2997/.0745=40228 40228*.226=9091 9091/100=91 91 = penetration factor So the 7mm Rem Mag with a 150 grain bullet is going to out penetrate the 150 grain 30-06 bullet when both are traveling at 3000 fps which is obtainable with both cartridges. No surprise there. Determining how that greater area of the .308 bullet effects game is a little more tricky and I doubt that there will ever be a formula that will satisfy everyone. One simple way is to multiply the muzzle energy by the area of the bullet to come out with another number to use as a comparison. So for the 7mm Remington we get: 2997*.0633=190 For the 30-06 we get: 2997*.0745=223 So what do you have? The 7mm Remington will out penetrate the 30-06 in this bullet weight. However the 30-06 is going to more tissue damage for the amount of penetration. So if you are really stuck with this 150 grain bullet weight on say a mule deer hunt and you have your 7mm over one shoulder and the 30-06 over the other and a deer pops up in front of you broadside, the 30-06 would be more effective since reaching the vitals on a broadside shot is not a problem. However if the deer is facing away at an angle better grab the 7mm since penetration is more important then. That is one way to determine the comparative effectiveness of different bullets. There are many more. One is an old one called Momentum Value which I am quite fond of. But I have already taken up enough band width with this method! Visit the rec.hunting and rec.hunting.dogs FAQ Home Page at: http://sportsmansweb.com/hunting/ To leave the Hunting listserv list, send a message with SIGNOFF HUNTING
