Bullet penetration physics questions.

[lbmii]

Let us say we have two bullets that are made of strong non-expanding materials and both of these bullets are the same diameter and have the identical octave or shape in every way possible. Both bullets are shot into a perfectly identical and uniform media and neither bullet yaws or wobbles or expands.

IF:
Bullet #1 has twice the energy (due to either having a different mass and/or a different velocity) of bullet #2. Will bullet number 1 penetrate twice as far as bullet #2?

IF:
Bullet #1 has twice the momentum (due to either having a different mass and/or a different velocity) of bullet #2. Will bullet number 1 penetrate twice as far as bullet #2?

IF:
Bullet #1 has twice the mass but the same velocity of bullet #2. Will bullet number 1 penetrate twice as far as bullet #2?

IF:
Bullet #1 has twice the velocity but the same mass of bullet #2. Will bullet number 1 penetrate twice as far as bullet #2?

I do not know the above answers but would like to know the answers.

 

[EghtySx]

Well, no. Just basic physics. The farther into the mediam the projectile gets the more rapid it's deceleration. Just like when you stop your car. The closer you get to the red light the more quickly you decrease your speed (i.e. it takes you longer to get from 60 to 50 than it does from 30 to 20 and much faster than from 10 to 0). The rate of deceleration increases exponentially. This is in part your increasing effort on the brake pedal and partly due to the physics of an onbect in motion wanting to stay in motion until acted upon by an outside force. Through the first inch of the medium it was going, lets say 2000 fps, it hits the second inch going, lets say 1600 fps. Now, one inch of the identical media is going to have more of an effect on an identical projectile moving 400fps slower than another. Never mind that the slow one is starting to mushroom and tumble. =)

 

[RJ357]

That is probably a difficult question because there are so many factors. One in particular is that the material being impacted is going to pile up in front of the projectile and add to the mass that has to move through the medium.

Decelerating from 60 mph to 50 mph is no different than decellerating from 10 mph to zero mph. Both require the same amount of energy.
The exact same laws hold true for all objects in uniform, nonrotating motion (the principle of relativity).
An object travelling at 60 mph is perfectly justified in claiming it standing still, for example.
There could be a difference in the efficiency of braking system at different speeds, though.

 

[RJ357]

One thing you could do is try to find some penetration tests that were done in ballistic gelatin or water. If you have the bullet weights and velocities, you can estimate the relationship between momentum and penetration (and energy and penetration)

Something that might be relavent also, is the volume of the temporary wound cavity as a function of velocity or momentum.

 

[Molon Labe]

Decelerating from 60 mph to 50 mph is no different than decellerating from 10 mph to zero mph. Both require the same amount of energy.

This is not true. It takes 11 times more energy to decelerate from 60 mph to 50 mph vs. decelerating from 10 mph to 0 mph.

 

[McCall911]

It's rather "geeky" but bullet penetration is addressed in this Italian website:

http://www.earmi.it/balistica/baltermi.htm



(If you right click, you can use the Windows translator into English, but you will get several nonsensical and comical translations probably because of the lack of technical Italian vocabulary. For example, the title is "Terminal Ballistics" but the translation gives "Ballistics finishes them!" LOL )
The formula presented is under the heading Penetration in the soft woven ones of the human body (which should have been "Penetration in soft tissue of the human body.")
How accurate this formula is I do not know, but I think it's interesting nonetheless.

 

[dfaugh]

Actually I think its simple

since you've eliminated variables like bullet expansion, I would think the equations are simple. So my answers swould be:

Yes
Yes
Yes
Not so sure about this one

Now, they probably should be more like

Yes(roughly)
Yes(roughly)
Yes(roughly)
I still don't know

But, in short, with twice the energy (all else being equal) would think you'd get twice the penetration.

Just and opinion, based on my fuzzy recolection of college physics.

 

[TimRB]

Since your projectile needs to do the work of penetration, energy is required. If the force that resists penetration is constant, double the energy would give double the penetration.

E=(1/2)mv^2=f(dot)d

Tim

 

[Aguila Blanca]

Acceleration/deceleration is an exponential function. Eliminating as many external variables as possible, it requires four times as far to decelerate to zero when the speed is doubled. That means double velocity equals four times as much energey.

In this case, the hypothesis is that the ENERGY is double, not the velocity. I believe the amount of penetration would be increased by a factor of the square root of 2.

 

[RyanM]

http://home.snafu.de/l.moeller/Penetration_Calculator_2.html

Here. You can try the experiments yourself.

300 mps, 10 g, 9mm, 3 kg-sec, 450 J = 73.22 cm penetration

600 mps, 10 g, 9mm, 6 kg-sec, 1800 J = 110.66 cm
300 mps, 20 g, 9mm, 6 kg-sec, 900 J = 146.43 cm
424 mps, 10 g, 9mm, 4.24 kg-sec, 899 J = 91.78 cm
300 mps, 10 g, 4.5mm, 3 kg-sec, 450 J = 292.84 cm
300 mps, 10 g, 18mm, 3 kg-sec, 450 J = 18.32 cm

Doubling mass doubled penetration depth, while doubling velocity increased it about 1.511x. Increasing velocity by 1.41x increased penetration by 1.25x.

Looks like the conclusion is what I've been saying all along, on other threads. You need to consider the factors of bullet weight, velocity, expanded diameter, expanded shape, and retained velocity independently.

 

[lbmii]

Interesting calculator, I have come upon it before but never sat down and figured it out.

It looks like all other things being equal, mass has a greater influence on penetration than velocity.

Now I need to get some metric conversions and have at it!

 

[FNFiveSeven]

That calculator program is awesome. The question is very difficult, I wonder where this program came from? I asked several physics professors about the relationship between penetration, momentum, and energy, and noone could give me a straight answer...

 

[RJ357]

"This is not true. It takes 11 times more energy to decelerate from 60 mph to 50 mph vs. decelerating from 10 mph to 0 mph."

Acceleration and deceleration are equivalent.

So:

A gun with a heavy bullet and weak charge fires the bullet. Initially at rest, 0 fps, the bullet accelerates to 10 fps.
Now we put the gun on a railway car travelling at 50 fps. We fire the gun and the bullet, initially at 50 fps accelerates to 60 fps.
Same energy, same acceleration.

 

[rlq9thrk]

right, RJ357

The expression for kinetic energy was given earlier. The actual experimental data beats all mathematical models.

A complete model would be fairly complex: some of the bullet's energy goes into deforming the target material, some is converted into heat, some into deforming the bullet. Higher velocities do more damage to the bullet. You have probably seen those pictures of an armor-piercing round going through a chunk of steel and only a super-heated gas jetting out the other side.

 

[Yooper]

More specifically, the Poncelet equation supports sectional density as a parameter for penetration. It should be independent of caliber.

 

[RJ357]

So does this all show that it really is about energy?

Penetration is proportional to mass.
Energy is proportional to mass.
Penetration is proportional to energy.

Penetration is proportional to velocity squared.
Energy is proportional to velocity squared.
Penetration is proportional to energy.


Penetration is proportional only to the mass component of momentum.
Penetration is not proportional to the velocity component.
Penetration is not necessarily proportional to momentum.

 

[Yooper]

RJ357

I wrote this in response to another thread:

I believe that penetration is the only practical value to be sought, after all, what do we want the bullet to do when it hits the target other than penetrate? I think it may boil down to sectional density and velocity as determinants in projectile potential, regardless of caliber, and penetration is the net result. For a (theoretically) non-expanding bullet there will be an optimum velocity beyond which velocity increases show a diminishing return, but will always increase (though slightly) as velocities increase. Greater sectional densities will yield higher optimum velocities. For expanding bullets, there also will exist an optimum velocity for proper expansion and when velocities increase beyond this point, penetration will actually decrease due to the accelerated expansion. An expanding bullet is effectively changing its sectional density as it expands. All of this is relative to the density and makeup of the medium the bullet is penetrating. We already have the figures for one medium, air, through ballistic tables. As the density increases, the penetration decreases dramatically. Wet newspapers, ballistic gelatin, etc. all have their own characteristics, but none are as diverse as, say, a game animal. An animal has a very elastic skin, muscle tissue, bone, cartilage, internal organs, various fluids. etc. As far as "knock-down" potential or "killing power" are concerned, I don't think they exist. The mass of a bullet is so minute compared with most living targets that it can't "move" the larger mass effectively.

I hope this helps!

 

[RJ357]

lbmii seemed to have discovered a correlation between stopping power and momentum, though, not between stopping power and penetration, which would be more in line with energy.

Knock down power is funny; anything that could do that would also knock the shooter on his butt.

Sectional density and velocity would be important to penetration, no doubt.

What about central nervous system shock? What might correlate better to that?

I guess it also depends on whether you are hunting or defending.

 

[RyanM]

Penetration is proportional to velocity squared.
Energy is proportional to velocity squared.
Penetration is proportional to energy.

Incorrect. If you were paying attention, you'd have noticed a 2x increase in velocity (4x increase in energy) results in a 1.5x increase in penetration. I did some more numbers, with interesting results. There are completely linear correlations between penetration and frontal area, and between penetration and mass. Increased velocity, however, gives diminishing returns. Looks like reducing drag increases the efficiency in using extra velocity.

9mm, 10 g, .57 drag
vel pen. penetration compared to 100 m/s
50, 8.56 0.38
100, 22.48 1.00
200, 52.13 2.32
300, 73.22 3.26
400, 88.63 3.94
500, 100.72 4.48
600, 110.66 4.92
700, 119.09 5.30
800, 126.41 5.62
900, 132.87 5.91
1000,138.66 6.17

 

[FNFiveSeven]

so...

this means that for M193 vs M855, since M855 has greater energy, greater mass, greater momentum, but only slighly lower velocity, that M855 should get better penetration under all circumstances. Especially when you consider that the M855 is steel core and M193 is lead core (softer). If you get diminishing returns on velocity, then the argument that M193 penetrates more simply because it has a slight velocity edge is completely false... but some people claim M193 penetrates better than M855, especially in real world tests... comments?

 

[cracked butt]

An easy everyday nonmathimatical world way of looking at it is if you took a toy balloon and threw it across your living room with a moderate throw, then picked it up again and threw it as hard as you could. Your second throw won't go much farther than the first.

 

[RyanM]

On M16 ammo, M855 is longer and more base-heavy than M193, so it "tumbles" faster on impact with flesh, a wall, etc., at least in theory. In practice, both rounds are all but random in how soon they tumble.

Still trying to generate a reasonably accurate algorithm for penetration. Best I've managed is:

0.00000000093803815542258 X^3 - 0.0000031923097447629 X^2 + .00420116344237 X - .03722554156363

Put X in meters per second in there, and it gives you a penetration factor relative to 300 m/s (if you get 2, then penetration is double the penetration at 300 m/s). That's for bullets with a coefficient of drag of .5, which I think is the equivalent of an FMJ pistol bullet. I think. It's only accurate from 0 to 1250 m/s, though; beyond 1250, the penetration goes up way too fast.

 

[Molon Labe]

RJ357 said:

A gun with a heavy bullet and weak charge fires the bullet. Initially at rest, 0 fps, the bullet accelerates to 10 fps.
Now we put the gun on a railway car travelling at 50 fps. We fire the gun and the bullet, initially at 50 fps accelerates to 60 fps.
Same energy, same acceleration.

No. You are wrong. It takes 11 times more energy to accelerate the bullet from 50 to 60 fps vs. 0 to 10 fps. Even if you fire the bullet from a gun on a train (as long as all energy calculations are refrenced to the earth).

 

[RJ357]

(as long as all energy calculations are refrenced to the earth).

That's what I was referring to. It depends on your frame of reference. Unfortunately I neglected to specify what reference frames I was using.

Now what does a passenger in a decelerating car observe, about the energies involved, since he is not moving relative to the car?

 

[taliv]

this means that for M193 vs M855, since M855 has greater energy, greater mass, greater momentum, but only slighly lower velocity, that M855 should get better penetration under all circumstances. Especially when you consider that the M855 is steel core and M193 is lead core (softer). If you get diminishing returns on velocity, then the argument that M193 penetrates more simply because it has a slight velocity edge is completely false... but some people claim M193 penetrates better than M855, especially in real world tests... comments?

blackrazor, IANAPhysicist, but the higher velocity (= higher rotational rate) and different construction of M193 make it prone to fragmentation quickly (relatively) where M855 stays together longer, and thus, penetrates deeper

just a guess