# Bullet Penetration

Is kinetic energy or momentum a better indicator of bullet penetration?

Related Classical Physics News on Phys.org
The reason I ask is because of confusion over various dangerous game hunting articles. In one magazine I read not too long ago, the authour discussed hunting elephant in Africa and stated that, to penetrate the elephant, 4,000 pounds of energy is needed and a minimum rifle such as .375 H&H or .416 Rigby. Another article discussed the ability of a .500 Smith and Wesson magnum or a .454 Casull, both which have between 1,500 and 2,800 lb. ft. of energy, to hunt the same kind of dangerous game (elephant, cape buffalo) effectively. How is this possible?

The reason I ask is because of confusion over various dangerous game hunting articles. In one magazine I read not too long ago, the authour discussed hunting elephant in Africa and stated that, to penetrate the elephant, 4,000 pounds of energy is needed and a minimum rifle such as .375 H&H or .416 Rigby. Another article discussed the ability of a .500 Smith and Wesson magnum or a .454 Casull, both which have between 1,500 and 2,800 lb. ft. of energy, to hunt the same kind of dangerous game (elephant, cape buffalo) effectively. How is this possible?
Well firstly neither pounds nor lb. ft. are even a unit of energy. In empirical the units of energy would be lb. ft^2 / s^2. So I woudn't think the physics analysis of whatever you're reading is worth the glossy paper it is written on. Secondly, there are a lot of factors that effect the effectiveness of a bullet other then their muzzle velocity (shape for one).

Well firstly neither pounds nor lb. ft. are even a unit of energy. In empirical the units of energy would be lb. ft^2 / s^2. So I woudn't think the physics analysis of whatever you're reading is worth the glossy paper it is written on. Secondly, there are a lot of factors that effect the effectiveness of a bullet other then their muzzle velocity (shape for one).
I take it these gun articles are probably little more than advertisements.

Seriously though, how can I find out about what determines proper penetration for game?

1. Ft-lbf is a perfectly acceptable unit of energy in the ballistics world. Bear in mind that's pounds force times feet.

2. Let's extrapolate what you need from ballistic standards testing. For standardised vest tests, you find the ballistic limit by finding the bullet velocity at which 50% of the shots will cause penetration. This is found for a specific bullet, meaning it's a combination of mass (hence energy) and geometry (difference between shooting with a spitzer or a ball end round). You could probably penetrate an elephant's skin at the lower bound of the energy ranges stated with a spitzer, but a higher energy for a ball end with the same mass.

Not knowing much about the specific rounds you've mentioned, what's the difference in ogive/ends?

1. Ft-lbf is a perfectly acceptable unit of energy in the ballistics world. Bear in mind that's pounds force times feet.

2. Let's extrapolate what you need from ballistic standards testing. For standardised vest tests, you find the ballistic limit by finding the bullet velocity at which 50% of the shots will cause penetration. This is found for a specific bullet, meaning it's a combination of mass (hence energy) and geometry (difference between shooting with a spitzer or a ball end round). You could probably penetrate an elephant's skin at the lower bound of the energy ranges stated with a spitzer, but a higher energy for a ball end with the same mass.

Not knowing much about the specific rounds you've mentioned, what's the difference in ogive/ends?
Here is the .375 Holland and Holland Magnum cartridge. For whatever reason, it is considered the standard minimum for hunting cape buffalo and elephant:

http://en.wikipedia.org/wiki/.375_H&H_Magnum

This is the .500 Smith and Wesson Magnum revolver cartridge, which has allegedly been used to penetrate deeply into elephant.

http://en.wikipedia.org/wiki/.500_smith_and_wesson_mag

There is a great difference in power between these two cartrdiges, yet both seem to work on elephant. Can a mathematical equation be derived that can show the approximate penetration of a bullet given power and shape?

http://findarticles.com/p/articles/mi_m0BTT/is_167_28/ai_110457317/

Why can a 2500 lb. ft. round from a revolver penetrate an elephant and not a 3,400 lb. ft. shotgun slug? Or can it?

Is kinetic energy or momentum a better indicator of bullet penetration?
Kinetic energy is converted into momentum as the bullet leaves the gun.
The Kinetic energy of the bullet leaving the gun is actually resolved into two components

The forward momentum of the low mass bullet and the reaction force of the gun which is the feedback you get.

Now Kinetic energy is defined by the mixture of gunpowder thats present in the gun, but the momentum is defined by the mass of the bullet, like lets say there is some leakage of gun powder at the time of firing the bullet would actually not travel the distance and be less effective.

Ideally all bullets are designed for penetration . So you possibly need to say what kind of penetration u need

Essentially what you are asking is like is the weight of the hammer or the speed of the blow determining the cracking of the nut. They are quite the same products

Last edited:
Kinetic energy is converted into momentum as the bullet leaves the gun.
The Kinetic energy of the bullet leaving the gun is actually resolved into two components

The forward momentum of the low mass bullet and the reaction force of the gun which is the feedback you get.

Now Kinetic energy is defined by the mixture of gunpowder thats present in the gun, but the momentum is defined by the mass of the bullet, like lets say there is some leakage of gun powder at the time of firing the bullet would actually not travel the distance and be less effective.

Ideally all bullets are designed for penetration . So you possibly need to say what kind of penetration u need

Essentially what you are asking is like is the weight of the hammer or the speed of the blow determining the cracking of the nut. They are quite the same products

Not to be overly blunt or anything, but that's utter crap. KE and momentum are NEVER 'converted to one another' and they are fundamentally different things.

KE = 0.5MV^2

P = MV

Both KE and momentum are defined by velocity and mass.

The penetration could be described by either (but is best described by using both), however it needs more detailed description than just a number. The nature of the impact is the important key to both penetration and damage.

Although you have the hammer analogy kind of correct, the thing that actually cracks the nut is force, not momentum or kinetic energy. As force is the mass times acceleration (which is most conveniently found by differentiating mommentum over impact time).

The reason why large slegehammers are used is because, there is generally a maximum swing speed for a hammer and its very difficult to increase it. Yet its very easy to increase mass.

Not to be overly blunt or anything, but that's utter crap. KE and momentum are NEVER 'converted to one another' and they are fundamentally different things.

KE = 0.5MV^2

P = MV

Both KE and momentum are defined by velocity and mass.
Right converted is possibly the wrong word

But what i was trying to express is that momentum is the motional equivalent, as in KE can be released in the form of heat as well isnt it? Momentum is only a consequence, i dont know if i am getting muddled here

The penetration could be described by either (but is best described by using both), however it needs more detailed description than just a number. The nature of the impact is the important key to both penetration and damage.

Although you have the hammer analogy kind of correct, the thing that actually cracks the nut is force, not momentum or kinetic energy. As force is the mass times acceleration (which is most conveniently found by differentiating mommentum over impact time).

The reason why large slegehammers are used is because, there is generally a maximum swing speed for a hammer and its very difficult to increase it. Yet its very easy to increase mass.
Right but isnt it because of the weight that the impact actually cracks the nut?

I mean what i intuitively figured is that as a hammer is brought down the PE stored in raising it to the hieght becomes intrinsic once it has reached the hieght and then cracks the nut. So I was trying to draw analogy to the KE which is intrinsic to the bullet

Oh i dint intend to write crap btw :tongue2:

There is a great difference in power between these two cartrdiges, yet both seem to work on elephant. Can a mathematical equation be derived that can show the approximate penetration of a bullet given power and shape?
Nope. The closest you'll get is the procedure for finding the ballistic limit for bulletproof vests I mentioned above. There's a big difference between elephants too, so you'd have to find an standardised elephant surrogate for want of a better way of putting it - a thick block of gelatine, covered by a thick leather / aramid skin, backed by a very dense foam.

A list of some variables that could affect this could include:

- bullet mass
- exit velocity
- velocity at target (i.e. taking into account speed loss at impact)
- bullet hardness
- nose geometry (bluff vs. pointed)
- area of elephant impacted
- state of tensing in impact area (difference between hitting a tensed thigh and a loose thigh)
- thickness of skin
- age of skin
etc etc etc

You could simplify to your heart's content and try and model it in a finite element package. But generally speaking I think you'd be better off sticking to field tests. And with a revolver, you'd have to get pretty close, so rather somebody else rather than me.

Kinetic energy cant be realeased as heat (it can be converted to heat though). All kinetic energy is is the energy due to motion, which is merely the potential work it could do if it were brought to rest.

So it'd be more correct to say that KE is the potential of what something can do by decelerating. Momentum more acurately describes what something is doing. (I dont really like this line but I can't think of a better desription atm, expect an edit)

The problem with you using GPE to describe a hammer blow is that it only work if its a gravity drop hammer with not exteral input. If you powered the hammer down you'd find that you could crack the nut with less mass.

We know its the force that does it (so the deceleration of the impact event) becuase using a metal hammer works better for cracking a nut than a rubber mallet does. This is because the impact event for the rubber mallet is longer and the forces are lower.

Back the the bullet: To get a true description of the penetration power, both KE and momentum should be used. Along with the geometry of the bullet and the impact.

Back the the bullet: To get a true description of the penetration power, both KE and momentum should be used. Along with the geometry of the bullet and the impact.
Thanks for all of the replies! This helps me put everything in better perspective. What I'm still having a hard time understanding is the "rules" for dangerous game hunting which require a heavy calibre rifle with + 4,000 lb. ft.^2 of energy to hunt such heavy game while a comparatively low powered revolver cartridge can equally penetrate through heavy bone and muscle. Is it safe to conclude that these hunting requirements are therefore arbitrary and do not reflect real world requirements?

As you can see, the .454 casull, a lower powered round than the .500 magnum, penetrates more deeply into bone than the .500 magnum and almost as well as the .600 nitro express (which has 8,400 lb. ft.^2 of KE). Do you think it's necessary to look at the energy retained by the bullet after it is fired at the time of penetration and not just muzzle energy to explain the disparity?

well not going into two much practical details of ballistics , consider two bullets identical in shape and physical properties execpt mass
b1,b2
considering no loss of energy
E(bullet)=P^2/2m
E(gun)=P^2/2M

Eb + Eg=constant(k)
P^2=(2k /(1/M + 1/m))

M is constant on increasing mass of bullet P increases

but energy of bullet decreases (calculation left)

clearly bullet of higher energy will be able to resist larger force
created by tearing of muscles and hence will penetrate deeper causing larger damage
YES BULLET HAVING SMALLER MOMENTUM STOP QUICKLY BUT OWING TO ITS HIGH VELOCITY TRAVELL DEEPER , MASSIVE BULLET TAKE MORE TIME TO STOP BUT PENETRATE LESS AS ITS VELOCITY IS LESS...

so this is my opinion unless i had made any mistakes in calculation...

Danger
Gold Member
Keep in mind that Elmer Keith developed the .44 Magnum handgun for elephant hunting. It'll do the job, but you'd better make your shots count.
At the other end (when I was still in the gun scene) there was the .475 H&H Magnum rifle. It produced 10,000 ft/lbs of muzzle energy (and a respectable 18 ft/lbs of recoil). You'd probably want to make the first shot count with that as well, because most people wouldn't want to launch a second round without some recuperation time.

Danger
Gold Member
Damn... I still can't edit.
What I was going to add to my last post is a quote from my 'Cartridges of the World' entry about the .475.
'There is absolutely no need for a cartridge of this power to hunt anything on this planet.'

negitron
...the .475 H&H Magnum rifle. It produced 10,000 ft/lbs of muzzle energy....
I don't think that's right. The .454 Casull is currently the reigning champ of handgun carts and it has a max for standard loads of 1923 ft-lbf muzzle energy.

EDIT: and I see now the .500 S&W Magnm beats that, with 3031 ft-lbf.

EDIT again: Oh, rifle. Yeah, I can see that.

Last edited:
turbo
Gold Member
I've got a 50-round box of custom .45-70 hand-loads given to me by a couple that loads for BIG handguns. Some each of 405 and 500 gr solid round nose that tach out at over 1800 fps. Now, I need to get lucky enough to win a moose permit in the yearly lottery. Leona LOVES Tom Selleck, and I helped Bill get her a lever-action Winchester that had belonged to him. Bill knew that I hunted with a single-shot Ruger Model 1, and they surprised me with the hot loads as a thank-you. I have put very strong warnings on the plastic box - those loads would blow up a Marlin or Winchester .45-70 and possibly kill the person pulling the trigger.

Damn... I still can't edit.
What I was going to add to my last post is a quote from my 'Cartridges of the World' entry about the .475.
'There is absolutely no need for a cartridge of this power to hunt anything on this planet.'
I see. The mistake I'm making is starting with the premise that you <i>need</i> over 4,000 ft. lbs. of energy to penetrate an elephant or cape buffalo. Do you think a hard cast shotgun slug would do an adequate job as well. What is the rational basis behind laws that require hunters to use a large caliber rifle on dangerous game in Africa, if you know?

I've got a 50-round box of custom .45-70 hand-loads given to me by a couple that loads for BIG handguns. Some each of 405 and 500 gr solid round nose that tach out at over 1800 fps. Now, I need to get lucky enough to win a moose permit in the yearly lottery. Leona LOVES Tom Selleck, and I helped Bill get her a lever-action Winchester that had belonged to him. Bill knew that I hunted with a single-shot Ruger Model 1, and they surprised me with the hot loads as a thank-you. I have put very strong warnings on the plastic box - those loads would blow up a Marlin or Winchester .45-70 and possibly kill the person pulling the trigger.
You got a Magnum Research BFR?

I am not certain if it has been discussed here, but the material being penetrated and the density and shape of the bullet are often crucial. For instance, I strongly suspect that a 12 gauge shotgun slug has more kinetic energy than a 5.56 fired by an M-16 or a 7.62 fired by an AK-47; however, both those bullets can penetrate body armor that a shotgun slug cannot.

Danger
Gold Member
Frankly, I'm not a hunter. I used to shoot gophers with a .22, but gave it up years ago. The only reason that I shot gophers instead of tin cans is that you don't have to go out and reset gophers. They're also a serious pest around here, and I figured that shooting was a kinder death than poisoning or being ripped to shreds by a hawk. Then the ex-from-hell made me promise not to kill anything that wasn't chasing me down an alley.
As to your question, though, I suspect that the rationale for a large calibre is that the vital organs of something like an elephant are huge. You could probably shoot one through the heart with a .223, but the hole might not be proportionally large enough to cause serious injury. It would be like stabbing a man in the heart with a sewing needle. Also, a large part of gunshot trauma is caused by secondary projectiles, primarily bone fragments. A small calibre might just bounce off of a bone or be stopped by it.
That's just my best guess, though.

turbo
Gold Member
You got a Magnum Research BFR?
Nope, and if I did, I certainly wouldn't want to run those hot loads through it. Ouch! My Model 1 can pummel my shoulder with standard 405 gr .45-70 loads if I put enough rounds through it. It's an accurate rifle for target-shooting, though. My first two rounds ever made an elongated hole in the center of the target at 75 yards, using the open sights. My father was looking through my binoculars and said that I missed the paper. I knew that was not the case, so we had to walk up and verify.

I am not certain if it has been discussed here, but the material being penetrated and the density and shape of the bullet are often crucial. For instance, I strongly suspect that a 12 gauge shotgun slug has more kinetic energy than a 5.56 fired by an M-16 or a 7.62 fired by an AK-47; however, both those bullets can penetrate body armor that a shotgun slug cannot.
I think that has to do with the bullet being made with a steel core. There are steel core shotgun bullets that will penetrate body armour.

I think that has to do with the bullet being made with a steel core. There are steel core shotgun bullets that will penetrate body armour.
It also has to do with the shape of the bullet. Full metal jacketed military rifle rounds are designed to concentrate all of the force into a small point, like a shirk, whereas shotgun buckshot spreads the force over a large area and shotgun slugs are generally very rounded instead of pointed.