[McCall911]

McCall's Penetration Predictor
(simplified for desktop calculator)


This is just one portion of the penetration predictor that I worked up some time back from my own independent research (i.e. I ain't read it from no books.) It is intended for use in small arms applications and approximates the results from ballistic gelatin tests, in particular.
What follows is a walkthrough for use on Windows desktop calculator, set to scientific View Mode. All units will be in English measurements.
(My apologies to you calculator wizards for the "baby steps.")

A. Variables (what you need to make it work)
1. Bullet diameter (bd) in inches
2. Bullet weight (w) in grains
3. Impact velocity (v) in feet per second.
4. Bullet shape factor (Cd) unitless
(assume a value of .52 to .55 for most spitzer bullets, .55 to .57 for flatnose to roundnose bullets, .70 for mushroomed, and .83 for
flat cylinder.)

''B. Procedure
1. Find ballistic coefficient
a. Divide bullet diameter by 12, press [=] or [enter]
b. Square [x^2] result of (a)
c. Multilply result (b) by pi and divide by 4
d. Multiply (c) by bullet shape factor, press [=] or [enter]
e. Store this result using [M+] key
f. Clear display using [C]
g. Divide bullet weight by 7000, press [=] or [enter]
h. Divide result of [g] by stored value [MR] and press [=] or [enter] to get ballistic coefficient
i. Clear previously stored value using [MC] and store ballistic coefficient using [M+]
(Note: This ballistic coefficient will look entirely different than the one you may be accustomed to seeing in ballistics tables.)

2. Determine average kinetic energy
(There are two ways to do this, both easy.)
a. Divide impact velocity by 2, press [=] or [enter]
b. Square result (a) by [x^2] multiply by bullet weight, press [=] or [enter]
c. Divide result (b) by 7000, divide again by 32.174, divide once more by 2; press [=] or [enter] to obtain average kinetic energy
(Alternate method:)
a. Square impact velocity with [x^2], multiply by bullet weight, press [=] or [enter]
b. Divide result (a) by 7000, divide again by 32.174, divide once more by 2, divide finally by 4; press [=] or [enter] to find average kinetic energy.
(Explanation: The "average kinetic energy" is important because the bullet stops within the medium. In other words, the velocity
becomes zero.)

3. Obtain unadjusted penetration value
a. Multiply average kinetic energy result from (2c) by stored ballistic coefficient by using [MR]
b. Divide by the constant 52130, press [=] or [enter]
c. Using the result of (b), hit the [x^y] key and enter 0.25; press [=] or [enter]
d. Multiply result of (c) by 12, then hit [=] or [enter] to obtain the unadjusted penetration value (in inches)
e. Clear memory with [MC} and add result (d) back into memory with [M+]
f. Clear display with [C]

4. Obtain estimated penetration (in inches)
a. Estimate bullet surface by dividing bullet diameter by 2 and multiplying by pi; hit [=] or [enter]
b. Use [+/-] key to make result (a) negative
c. Add result of (b) to the memory using the [M+] key; clear display with [C]
d. Review stored value using [MR]
(Note: If this value is zero or a negative number, then stop right here! There is no penetration!)
e. Multiply the value from (d) by 3 for the estimated minimum penetration or by 5 for estimated maximum penetration.
f. Of course, hit [=] or [enter]

I can offer explanations if anyone is interested.

<whew!>

Hit [=] or [enter].

[Andrew Rothman]

It would be pretty easy to make this into a web app, if anyone is interested.

[McCall911]

McCall911's Penetration Predictor

Footnotes:

1-- For expanded bullets, use the expanded diameter as bullet diameter.

2--Assuming less than 100 percent fragmentation, use the recovered bullet weight as the bullet weight. (I do have an estimator for bullet weight retention, but didn't include it here.)

3--For best results, use a bullet shape factor of .70 (mushroomed) with expanded bullets

[McCall911]

It would be pretty easy to make this into a web app, if anyone is interested.

:)
That would be nice, but we'll see.

[McCall911]

McCall911's Penetration Predictor

For those of you who have already looked at it, I think I have tidied up a few loose ends of the baby steps.

Hit [=] or [enter]

;)

[RyanM]

Let's see. For a 9mm 124 gr FMJ at 1120 fps, the calculator returns 17.2" to 28.6". MacPherson's equations say 29.6". Close, but no cigar.

.308 150 gr softpoint, 2600 fps, double expansion, 100% weight retention:
McCall: 21.1"-35.1". MacPherson: 18.0". Kinda close. I guess.

.45 230 gr hardball, 800 fps.
McCall: 17.6"-29.3". MacPherson: 28.6". Closer.

Hypervelocity, spherical magical grain of indestructible sand, .02 cal, .005 grain, DC .355, at 0.1 C (1/10th the speed of light, or 98,357,106 fps). Maybe a diamond micrometeorite or something. And you're in space when you get hit with it.
McCall: 166.4"-277.3". MacPherson, 4.3". Way, way, way off.

I think the main problem, evident by the extreme overpenetration of high-velocity projectiles, is the fact that your equation uses energy. Penetration is not determined by energy. It's actually momentum and drag. Drag increases exponentially as velocity increases, so the relationship between velocity and penetration depth is logarithmic, not exponential.

You can discover this by a very simple experiment. Inflate a balloon. Throw it with moderate force in a room with still air. Note how far the balloon goes. Pick up the balloon, and throw it again, twice as hard. Twice the velocity behind the balloon is four times the energy. Does the balloon go four times as far? Or is it closer to 1.5 to 2 times as far?

[McCall911]

Thank you for the critique, RyanM. (And I'm not being sarcastic in any way.) :)

No, I honestly didn't think I'd found the Mathematical or Scientific Discovery of the Millenium. It was more or less tongue-in-cheek that I threw this "predictor" out there because it was frankly very simplistic. I just wanted to get some input as to whether the "predictor" sank or swam.

So it looks like it swims just a little before it sinks. maybe?

:o

:D

[Biker]

No man, no reason to stop trying. Hell, I enjoyed reading and sure couldn't come up with anything better, or even as good.
A little healthy debate is fun.:)
Biker

[Lucky]

Yea maybe just modify it with momentum density.

[McCall911]

Thanks for the replies, Biker and Lucky.

The explanation for why I didn't use momentum: It just didn't fit it in with what I was working on. That's all.

Why I came up with this: I was looking for something quick and simple that got fairly close when it came to real-world small arms applications (not some hypothetical BS about a single grain of sand traveling at 1/10 the speed of light or a horse's fart or whatever.)

Bud, whiz kids, give me a break already! I've tested it enough to know that it works reasonably well within the narrow range of small arms! I think it's at least marginally satisfying. But, no, it's not perfect. I didn't intend it to be perfect! I knew damn well it wasn't perfect when I came up with it! So go impress someone else with your knowledge, unless you have something better to offer.

And McPherson! Who says McPherson is right in his calculations? Show us the proof, if you have any. Show us something better if you've got anything! And read my sig line, because I mean it: "Put up or shut up!"

[RyanM]

MacPherson's proof is in his books. Pages and pages and pages of scatterplots, showing actual shooting data from actual gelatin, compared to his equation's predictions. And the data follows his equations very closely, with very few discrepencies. The few "flyers" are well explained; for instance, a very small percentage of flat-nosed bullets would penetrate way deeper than his model predicted. This had something to do with stability and yaw and whatnot, and basically it was because those bullets were acting like full wadcutters with the diameter of the meplat, because no gelatin was touching the sides at all. I only had the book on interlibrary loan and I have no scanner, so I can't show you any of the graphs, unforntunately.

Plus there's the fact that he wrote aerodynamic equations for rocket launches, which were in fact used for several successful rocket launches. I believe they were used in all of the Gemini and Mercury launches, as well as a few others. Too bad NASA didn't hire him to help with that Mars lander. Rocket aerodynamics is a lot more complex than bullet penetration, since you've got winds, the atmosphere gets less dense as you go higher, gravity decreases with height, the rocket gets lighter as it burns fuel, etc.

So all told, I think the guy knows what he's doing.

Your model looks good other than using energy instead of velocity vs. drag. That's really the only major flaw. The general rule is that penetration increases proportionally to mass, but not always to velocity. Double the bullet mass, keeping everything else the same, and you double penetration. But velocity is all over the place. Doubling velocity from 100 fps to 200 fps may result in almost 4 times as much penetration, but doubling it from 1000 to 2000 would probably be more like 1.5 times as much.

Shoot some play-dough or throw a balloon or something, and the empirical evidence will bear this out. The higher the velocity is, the less you gain from increasing it more. I only used the grain of sand thing as an example of how the results are way too high, especially with rifles, and with "light and fast" projectiles.

Like here's some actual, calibrated gelatin shooting data.

9mm, 100 grain +P Pow'R'Ball
Actual - 10.9"
MacPherson - 10.6"
Yours - 12.4"-20.7"

.40, 135 gr Pow'R'Ball
Actual - 11.6"
MacPherson - 11.7"
Yours - 13.3"-22.2"

.45, 165 gr +P Pow'R'Ball
Actual - 12.1"
MacPherson - 11.7"
Yours - 13.4"-22.4"

[McCall911]

MacPherson's proof is in his books. Pages and pages and pages of scatterplots, showing actual shooting data from actual gelatin, compared to his equation's predictions. And the data follows his equations very closely, with very few discrepencies. The few "flyers" are well explained; for instance, a very small percentage of flat-nosed bullets would penetrate way deeper than his model predicted. This had something to do with stability and yaw and whatnot, and basically it was because those bullets were acting like full wadcutters with the diameter of the meplat, because no gelatin was touching the sides at all. I only had the book on interlibrary loan and I have no scanner, so I can't show you any of the graphs, unforntunately.

Plus there's the fact that he wrote aerodynamic equations for rocket launches, which were in fact used for several successful rocket launches. I believe they were used in all of the Gemini and Mercury launches, as well as a few others. Too bad NASA didn't hire him to help with that Mars lander. Rocket aerodynamics is a lot more complex than bullet penetration, since you've got winds, the atmosphere gets less dense as you go higher, gravity decreases with height, the rocket gets lighter as it burns fuel, etc.

So all told, I think the guy knows what he's doing.

Your model looks good other than using energy instead of velocity vs. drag. That's really the only major flaw. The general rule is that penetration increases proportionally to mass, but not always to velocity. Double the bullet mass, keeping everything else the same, and you double penetration. But velocity is all over the place. Doubling velocity from 100 fps to 200 fps may result in almost 4 times as much penetration, but doubling it from 1000 to 2000 would probably be more like 1.5 times as much.

Shoot some play-dough or throw a balloon or something, and the empirical evidence will bear this out. The higher the velocity is, the less you gain from increasing it more. I only used the grain of sand thing as an example of how the results are way too high, especially with rifles, and with "light and fast" projectiles.

Like here's some actual, calibrated gelatin shooting data.

9mm, 100 grain +P Pow'R'Ball
Actual - 10.9"
MacPherson - 10.6"
Yours - 12.4"-20.7"

.40, 135 gr Pow'R'Ball
Actual - 11.6"
MacPherson - 11.7"
Yours - 13.3"-22.2"

.45, 165 gr +P Pow'R'Ball
Actual - 12.1"
MacPherson - 11.7"
Yours - 13.4"-22.4"


Seriously: Thanks.

I'm working on getting the kinks out.

Who knows? Maybe it'll be enough to make everybody happy.

:D

[ChickenHawk]

Diameter, length, velocity...

So, length doesn't really matter after all? :D

ChickenHawk

[P95Carry]

Haha - think whatcha like Ken :D :p

[McCall911]

So, length doesn't really matter after all? :D

ChickenHawk

For penetration, No! And I can prove it!

oopssie.....


:eek: :uhoh: :o

[Biker]

Hah hah!

Biker

[McCall911]

McCall's Penetration Predictor
Version 2


Gather round, whiz kids, for my new, improved version of the Penetration Predictor. (Well, I'll say it's "new and improved" at least until I find another gaping hole in it... ) Now if it has to get much deeper than this, then I'm afraid that I'll have to go back to school and redo a lot of the math and physics that I used to sleep through.

As always, you can do this on your Windows desktop calculator (with View mode on Scientific, of course.) I will leave the original posted so that you can compare the differences, if you're so inclined.

A. Variables (what you need to make it work)
1. Bullet diameter (bd) in inches
{Note: If you have an expanding-type bullet, use the final (recovered) diameter in this calculation. I'm working on coming up with a (possible) means of predicting this.)
2. Bullet weight (w) in grains
(Note: For bullets which fragment less than 100 percent, use the recovered bullet weight here. I have an estimator for this (somewhere) but don't have time to dig it out and put it up today.)
3. Impact velocity (v) in feet per second.
4. Drag coefficient/"shape factor" (Cd) is unitless
(Yes, I've added it back in.)
Assume the following values for Cd:
0.52 to 0.55 for most spitzer-type bullets
0.55 to 0.57 for hollowpoints or flat-point bullets
0.57 for roundnose
0.7 for mushroomed
0.83 for flat cylinder
B. Procedure [Note: First make sure your calculator's memory is clear! If not, clear it with [MC].]
(I'll do the "tricky" part first. It's not hard, just has to be done right.)
1. Penetration component #1
a. Multiply Impact Velocity by Bullet weight and divide by 7000; hit [=} or [enter]
b. Square (a) with [x^2] key, divide by 32.174, and again by 52130; hit [=] or [enter]
(Here's the tricky part. Don't hit enter until this step is through, or it'll screw up fo sho.)
c. Using the result from (b), hit [x^y], then 6, then [1/x]; now [=] or [enter]
(End of tricky part)
d. Now store the result of (c) into the memory using [M+] key

2. Penetration component #2
a. Divide Bullet Diameter by 12 and hit [=] or [enter]
b Square [x^2] the result of (a), multiply by [pi], and divide by 4; Multiply again by the drag coefficient/shape factor and then [=] or [enter]
c. "Flip" the result of (b) by using the [1/x] key
d. Multiply (c) by the Bullet Weight and divide by 7000; [=] or [enter]
e. Divide (d) by 62.4; [=] or [enter]

3. The Final Destination (no, not the Grim Reaper just yet!)
a. Multiply the result of (2e) by the stored value using the [MR] key; [=] or [enter]
b. Take the square root of (a) by using the [x^y] key, followed by the value 0.5; [=] or [enter]
c. Multiply the result of (b) by 12; clear the memory with [MC] and add (b) to memory with [M+]
d. Clear the display with [C]
e. Enter the bullet diameter and, with [+/-], make this value negative
f. Add (e) to memory with [M+] and then clear display with [C]
g. Review the stored value with the [MR] key
(Again, if the value is zero or a negative number, then we will assume that there is no penetration.)
h. Clear the display with [C]
i. Obtain the natural logarithm of the impact velocity by entering the impact velocity and pressing the key [ln]
j. Divide the number from (i) by 2 and multiply by [MR}; [=] or [enter]
This is the minimum predicted penetration. (Jot this down or note it.)
k. Clear display with [C] and redo step (i)
l. Divide the number from (k) by 1.25 and multiply by [MR]; [=] or [enter]
This is the maximum predicted penetration.

It won't be perfect, but maybe it'll do until I can (maybe) cook up a Version 3...

Monkey wrenches are dreaded but welcome.

.

[RyanM]

I think one of us did something wrong. Version two says 9mm FMJ penetrates -0.33 * 2-4 inches, and .45 hardball is -0.42 * 2-4

Well, let's see. Didn't round anything, just did that to keep the lines short.

.355
124
1120

1.
a. 1120 * 124 / 7000 = 19.84
b. 19.84^2 / 32.174 / 52130 = 2.347E-4
c. 2.347E-4 ^ (1/6) = 0.2484
d. M = 0.2484

2.
a. .355 * 12 = 4.26
b. 4.26 ^ 2 * pi / 4 = 14.25
c. 1 / 14.25 = 0.07016
d. 0.07016 * 124 / 7000 = 0.001243
e. 0.001243 / 62.4 = 0.00001992

3.
a. .2484 * .00001992 = 4.947E-6
b. sqrt(4.947E-6) = 0.002224
c. 0.002224 * 12 = 0.02669
d. 0.02669 - .355 = -0.32831

Oh, yeah, for the time being, I can only give estimates of penetration of non-deforming solids. On doing some comparisons between MacPherson's equations and expanding round jello data, it looks like his add 2" thing only works for bullets of a certain sectional density (around 0.16-.165), at velocities of 800-1000 fps. With light and slow bullets, 2" is too much, and with heavy and fast bullets, 2" is too little. Still working on a more accurate equation to replace the "add 2" rule. Unfortunately, I don't even know if the major factor here is the sectional density, velocity, or both; or whether the "bonus" penetration should be added or multiplied in (i.e., "add X*Y/Z" vs "multiply by X*Y/Z"). This could take awhile.

[McCall911]

I think one of us did something wrong. Version two says 9mm FMJ penetrates -0.33 * 2-4 inches, and .45 hardball is -0.42 * 2-4

Well, let's see. Didn't round anything, just did that to keep the lines short.

.355
124
1120

1.
a. 1120 * 124 / 7000 = 19.84
b. 19.84^2 / 32.174 / 52130 = 2.347E-4
c. 2.347E-4 ^ (1/6) = 0.2484
d. M = 0.2484

2.
a. .355 * 12 = 4.26
b. 4.26 ^ 2 * pi / 4 = 14.25
c. 1 / 14.25 = 0.07016
d. 0.07016 * 124 / 7000 = 0.001243
e. 0.001243 / 62.4 = 0.00001992

3.
a. .2484 * .00001992 = 4.947E-6
b. sqrt(4.947E-6) = 0.002224
c. 0.002224 * 12 = 0.02669
d. -0.32831

Oh, yeah, for the time being, I can only give estimates of penetration of non-deforming solids. On doing some comparisons between MacPherson's equations and expanding rounds, it looks like his add 2" thing only works for bullets of a certain sectional density (around 0.16-.165), at velocities of 800-1000 fps. With light and slow bullets, 2" is too much, and with heavy and fast bullets, 2" is too little. Still working on a more accurate equation to replace the "add 2" rule.



Doh!

I know what I did wrong, so I'm going back to change it.

Thanks.

[RyanM]

That seems to work much better. Let's see if there are any definite trends in the accuracy...

Looks like FMJ is right around the maximum, hollowpoints are about 80-85% of maximum, and the wadcutter was 70.6% of max. .57 * (1 / 85%) ~ .68, and .57 * (1 / 70.6%) ~ .83, hint hint. I think if you put the coefficient of drag constant back in and use the current maximum as the median, it will be extremely accurate, at least for pistols. Rifles will probably be a bit different.

9mm NATO ball, 124 gr @ 1189 fps
Yours - 14.1-28.2
MacPherson - 30.6
Actual - 27.6 (tumbled twice)

M1911 ball, 230 gr @ 869 fps
Yours - 15.7-31.4
MacPherson - 30.3
Actual - >25.6 (exited block)

6mm steel sphere, 14 gr @ 3382 fps
Yours - 5.5-11.1
MacPherson - 17.5
Actual - 16.9

.69 cal lead sphere, 488 gr @ 540 fps
Yours - 14.7-29.5
MacPherson - 26.2
Actual - 28.7

.38 SPL Safe-Stop plated wadcutter snubby load, 148 gr @ 744 fps
Yours - 14.6-29.3
MacPherson - 20.7
Actual - >20 (exited block)

Then some deforming rounds that are close to .16 SD and 800-1000 fps (still working on those equations)...

.38 +P FBI load, 158 gr @ 880 fps, .59" expanded
Yours - 8.1-16.2
MacPherson - 13.1
Actual - 12.6

9mm Win "supreme" SXT, 147 gr @ 921 fps, .50" expanded
Yours - 9.8-19.7
MacPherson - 16.3
Actual - 17.6 (17.1 corrected)

.40 S&W Win Ranger T, 180 gr @ 905 fps, .70" expanded
Yours - 6.8-13.7
MacPherson - 11.3
Actual - 11.2

[grendelbane]

I am not a mathematiacian, ballistics expert, or a rocket scientist. I have read Duncan McPhershon's book, and he looks like he knows what is going on in terminal ballistics.

Somewhere in the back of my mind is a dusty old formula for predicting penetration. I think I read it in an old American Rifleman column. It is only good for sub-sonic velocities and non-expanding bullets. Perhaps you can add appropriate fudge factors for expanding sub-sonic bullets, but I suspect its accuracy rapidly decreases when you do so. Still, it may be worth the price. Bear with me, as I said, I am not a mathematician.

Take the diameter of your bullet. I will use the .45 ACP as an example. It is .451" in diameter. Add .033 to this and you end up with .484. (This .033 is a constant fudge factor added to any diameter handgun bullet).

Multiply .484 by itself. (.484 x .484, for the mathematically inclined. This comes out to .234256). Divide the weight of the bullet by .234256. This should come out to 981.384, according to my calculator.

Dividing this number by 7000 gives us .1402616! Which is slightly less than the sectional density of a 230 grain .451" bullet, due to the addition of the .033" fudge factor.

Now, most terminal ballistics experts agree that it takes 200 FPS to penetrate skin with a blunt projectile. So, subtract 200 from the muzzle velocity of my Gov't model pistol, which is 840 FPS. 640 x .1402616 = 89.767424. Now, for another fudge factor, and I can not remember if this one is correct for 10% gelatin, or 20% gelatin. A mind is a terrible thing to waste! Anyway, multiply 89.767424 by .233, which is 20.915809".

This is for a round nose bullet. There are fudge factors to account for SWC and WC bullets. Expanding bullets probably require a little real life experimentation. As stated before, there is a fudge factor to account for 10 or 20% gelatin. I have used the 2" rule, plus the expanded diameter of the bullet to predict penetration. My tests used water filled OJ cartons, so they are only accurate at 4" increments. (IOW, not accurate at all, but cheaper and easier than gelatin.

I have compared this model to a chart of shotgun pellet penetration in ballistic gelatin. The correlation was pretty good, the worst discrepancy was about 5%, and most of the time it was within 3% of what the people who prepared the chart reported. I assume that as long as projectiles are round nosed, and travelling between 600 and 1000 FPS, this model is fairly accurate. Probably serves better as a comparison for different loads than anything else. Get trans-sonic, and it ceases to have any value.

I hope this helps. As I said, I am not a mathematician, and I only present it for entertainment value.

[RyanM]

I think you need to go back and read the skin penetration part of Bullet Penetration, Grendelbane. While 200 fps is the threshold velocity for skin penetration, above that, the amount of FPS removed drops off a lot. By the time you hit about 500-600 fps, you're losing less than 10 fps by penetrating the skin. There was a chart somewhere, that estimated what various bullet weights and calibers would lose by going through skin. Wish I had written down those equations...

If you use 835 fps instead of 640, you end up with a more accurate value, of 27.3". Hm. Accuracy isn't too bad within the parameters given, 600-1000 fps and roundnosed.

Also, milk or orange juice cartons are pretty accurate. The bullet will penetrate water-filled cartons about 1.6 times as much as 10% gelatin, so each 4" carton = 2.5" of gelatin.

[grendelbane]

The bullet will penetrate water-filled cartons about 1.6 times as much as 10% gelatin, so each 4" carton = 2.5" of gelatin.

This is pretty close to what I remember. Seems like what I remember is actually .666. This would work out to 2.663. I am not going to get excited over minor differences such as that.

I do believe that as soon as velocities go super-sonic, and the bullet starts expanding, that you might as well forget a simple model predicting what is going to occur. I know that Duncan McPherson shows graphs predicting bullet expansion versus velocity, and velocity versus expansion, and I think he has done wonderful work in this area. Still, there is no simple. (I define simple as something that I can understand when I am sober), calculation to determine penetration of non-expanding solids, let alone expanding solids. Yes, I do believe that Duncan McPherson can come close. I just dont believe that his principles can be reduced to some thing so simple that I can use them.:banghead:

[RyanM]

Actually, according to MacPherson, the biggest change is when a bullet exceeds the cavitation threshold velocity of the target medium. In gelatin, most roundnose bullets have a cavitation threshold of 500 fps. Below that, penetration is linear. Above it, penetration is logarithmic. Speed of sound in air, and speed of sound in water, seem to make no difference at all.


And I think I finally got a workable equation for determining "bonus" penetration for various expanding rounds. I also used a modified version of McCall911's equation, which just takes the maximum penetration and multiplies it by .57/drag coefficient. Looks like the original energy-based one is a little closer for high-powered rifles, for some reason.

.22 LR Aquila super max, 30 gr @ 1266 fps, .38"
McCall - 4.2-8.3
McCall, modified - 7.0
McCall, orig - 7.4-12.4
MacPherson- 5.8+2=7.8
Me - 5.8+1.2=7.0
Way too many Ms - yes
Actual - 7.4

.32 ACP Win Silvertip, 60 gr @ 813 fps, .43"
McCall - 5.7-11.4
McCall, modified - 9.5
McCall, orig - 8-13.4
MacPherson - 7.1+2=9.1
Me - 7.1+0.8=7.9
Actual - 7.1 (7.5 corrected)

.380 Hor XTP, 90 gr @ 1010 fps, .45", 79.8 gr
McCall - 7.1-14.2
McCall, modified - 11.9
McCall, orig - 10.5-17.5
MacPherson - 10.0+2=12.0
Me - 10.0+1.1=11.1
Actual - 11.2 (10.6 corrected)

.380 Win "supreme" SXT, 95 gr @ 865 fps, .59"
McCall - 5.1-10.1
McCall, modified - 8.5
McCall, orig - 9.1-15.1
MacPherson - 6.6+2=8.6
Me - 6.6+1.8=8.4
Actual - 7.6

.38 Fed nyclad, 125 gr @... that site just died. On to the rifle data, then.

.223 Nos partition, 60 gr @ 2685 fps, .41" and 52.5 gr
McCall - 7.0-14.1
McCall, modified - 11.8
McCall, orig - 15.2-25.4
MacPherson - 12.3+2=14.3
Me - 12.3+3.5=15.8
Actual - 18.5

6.8mm SPC Barnes X, 85 gr @ 2865 fps, .53"
McCall - 7.2+14.5
McCall, modified - 12.1
McCall, orig - 17.9-29.8
MacPherson - 12.5+2=14.5
Me - 12.5+3.2=15.8
Actual - 19.3

6.8mm Sierra pro-hunter, 110 gr @ 2500 fps, .64"
McCall - 6.4-12.9
McCall, modified - 10.8
McCall, orig - 17.2-28.7
MacPherson - 10.8+2=12.8
Me - 10.8+5.1=15.9
Actual - 15.6

.308 unknown, 150 gr @ 2923 fps, .768" and 99.9 gr
McCall - 4.1-8.3
McCall, modified - 7.0
McCall, orig - 16.1-26.8
MacPherson - 7.3+2=9.3
Me - 7.3+9.2=16.5
Actual - 16.5

7.62x39 Saspan JHP, 124 gr @ 2297 fps, .63" and 100.5 gr
McCall - 6.0-11.9
McCall, modified - 10.0
McCall, orig - 15.8-26.3
MacPherson - 9.8+2=11.8
Me - 9.8+5.3=15.1
Actual - 15.0

.308 Hor JSP, 110 gr @ 3087 fps, .63" and 56.4 gr
McCall - 3.5-7.1
McCall, modified - 5.9
McCall, orig - 13.5-22.4
MacPherson - 6.1+2=8.1
Me - 6.1+8.4=14.5
Actual - 16.9

.308 Hor AMAX, 168 gr @ 2418, .56" and 144.5 gr
McCall - 10.0-20.1
McCall, modified - 16.8
McCall, orig - 21.1-35.1
MacPherson - 18.0+2=20.2
Me - 18.0+4.8=22.8
Actual - 18.1

[McCall911]

I am not a mathematiacian, ballistics expert, or a rocket scientist. I have read Duncan McPhershon's book, and he looks like he knows what is going on in terminal ballistics.

.


Heck, I'm not any of those either, grendelbane. Plus I can't even balance my blasted checkbook and have the disadvantage of not yet having read Duncan's book.

Anyway, the predictor you posted was very interesting. Thanks.

You mentioned about the velocity loss from penetrating skin, which is a very important matter because skin has a very high tensile strength compared to soft tissue (about 63000 pounds per sq ft versus 835 lb/sq ft.) Neither of my penetration predictors takes this into account, which IMO is one of their many shortcomings.

There have been quite a few penetration calculators from both pros and amateurs (like me) over these many years. From this, it's easy to conclude that trying to predict anything pertaining to terminal ballistics is a very slippery slope! The problem is that none of them appear to be totally right, yet none appear to be totally wrong.

[McCall911]

Actually, according to MacPherson, the biggest change is when a bullet exceeds the cavitation threshold velocity of the target medium. In gelatin, most roundnose bullets have a cavitation threshold of 500 fps. Below that, penetration is linear. Above it, penetration is logarithmic. Speed of sound in air, and speed of sound in water, seem to make no difference at all.


And I think I finally got a workable equation for determining "bonus" penetration for various expanding rounds. I also used a modified version of McCall911's equation, which just takes the maximum penetration and multiplies it by .57/drag coefficient. Looks like the original energy-based one is a little closer for high-powered rifles, for some reason.



RyanM, thanks for helping me in beta-testing this new version. Your ideas are always welcome. If I didn't have to work all this weekend, I'd be doing some beta-testing myself. (It's too cold here in the southeast to go shooting anyway.)


Since I'm off next weekend and since it always rains on my off days, then I'll be in a better position to fine tune some of this stuff. Or work on Version 3!

:what:

:D

[RyanM]

I forgot to mention, if you want to try to incorporate my "bonus penetration" equations, you're welcome to them.

Part 1:
1. If the bullet doesn't expand, if it shrinks, or if expanded diameter is greater than 3x the original diameter assume no "bonus" penetration
2. Calculate: (velocity^.25 * mass^.5 * 0.0525)
3. If the bullet expansion is between 1x and 2.5x the original, multiply the result of step 2 by: (expanded diameter / original diameter - 1)
4. If the bullet expansion is over 2.5x but less than 3x, skip step 3, and multiply the result of step 2 by: (expanded / original * -2 + 6)
5. The number you have there is your unadjusted bonus penetration. Write down the number or use M+ or whatever. Now calculate: (velocity / 900 * 2)
6. Use whichever of these two numbers is smaller, for part 2.

Part 2.
1. If the bullet didn't fragment, you're done. Use your number from part 1.
2. If the bullet did fragment, add your number from part one to: (fragmentation% / 10 * velocity / 2850)
3. Now you're done.

So for the unknown brand .308 softpoint in my last post, it's:

1. .768 / .308 = 2.49X expansion. Has bonus.
2. 2923^.25 * 99.9^.5 * 0.0525 = 3.858
3. .768 / .308 - 1 = 1.494
3.858 * 1.494 = 5.764
4. Skip.
5. 2923 / 900 * 2 = 6.496. 5.764 is smaller, so 5.764" is used for part 2.

1. Skip.
2. (150 gr - 99.9 gr) / 150 gr * 100 = 33.4%
33.4% / 10 * 2923 / 2850 = 3.426
3.426 + 5.764 = 9.19
3. 9.19" is your bonus penetration.

I should probably make fragmentation bonus use the average of the bullet's penetration with and without the fragmentation, but that's probably too hard.

edit. Oh, it's actually not too hard, with a spreadsheet. Still, the procedure above will get you within spitting distance, probably.

[McCall911]

In the ongoing (obsessive) quest for accuracy, I have made a couple of slight modifications to the predictor. Instead of re-posting the whole cotton-pickin thing, I have simply highlighted the new changes in red.

I'm contemplating a couple of more refinements to "PenPred", but for now Version 2 is The One. The refinements will include velocity loss due to skin penetration and bone penetration.

Stay tuned, friends and fellow whiz kids!

:)

As of NOW, I've made all the changes for the time being.

And, as always, feedback makes me nervous but is welcome.

;)

[McCall911]

Velocity loss adjustment for penetration through skin and bone

For whoever is interested, here is the corrected version of the formula I had posted earlier, which is an attempt at estimating the velocity losses after a bullet penetrates skin and bone. This corresponds somewhat with the findings of several ballisticians/scientists, such as Sellier. Mention of his formulas can be found on this Italian
webpage:

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




Instead of doing that walkthrough for the desktop calculator, I'll just explain how it works. I came up with a shortcut for it, but this doesn't really show how/why this application might be valid.

As always, you'll need these four variables:

Bullet Diameter (in inches)
Bullet Weight (in grains)
Impact Velocity (in feet per second)
Drag Coefficient/"Form Factor" (unitless)
Values:
0.52 - 0.55 for spitzer-type bullets
0.55 - 0.57 for flatpoint/hollowpoint bullets
0.57 for roundnose bullets
0.7 for mushroomed bullets
0.83 for flat cylinder

Deceleration through 0.06 inch layer of skin:

Deceleration = 0.5 x V^2 x Density x Tensile strength / Atmospheric pressure (lbs per cubic ft) x area x drag coefficient / Bullet Mass

Where: V= Impact Velocity
Density = 62.4 lb per cubic ft (density of skin)
Tensile strength = 62656 lb per sq ft (tensile strength of skin)
Atmospheric pressure = 2116.8 lb per square ft
Bullet mass = Bullet weight / 7000 = mass in lbs
Area = (Bullet diameter/12) x pi / 4
(Acceleration due to gravity figured in the original equation, but is canceled out in the final version of the formula above.)

Remaining velocity after skin penetration (assuming a 0.06 skin layer)

This is easily solved using textbook physics:

Velocity-resulting = (V^2 - 2 x Deceleration x Depth/12)^.5 [in other words, the square root]

Where Depth = the skin thickness of 0.06 inch

(Note: if the value within the parenthesis is zero or a negative number, then there is no further penetration!)

Deceleration through 0.25 inch bone:

Use the same formulas for Deceleration and Velocity-resulting above, substituting the previously obtained Velocity-resulting as the V value. Also substitute:
Density = 124.8 lb per cubic ft (density of bone)
Tensile strength = 3550.5 lb per sq ft (tensile strength of bone)
Depth = 0.25 inch (estimate of bone thickness)

So, even if it's wrong, this is it! If you like the results, you can substitute these in the original Version 2 formula above.

I've worked a few examples for purposes of illustration:

.380 ACP (90gr)
Initial: 1000 fps
After skin penetration: 847 fps
After bone penetration: 788 fps

9mm NATO (124 gr FMJ)
Initial: 1189 fps
After skin penetration: 1061 fps
After bone penetration: 1008 fps

.45 ACP (230 gr FMJ)
Initial: 850 fps
After skin penetration: 771 fps
After bone penetration: 738 fps

.30 Carbine (110 gr FMJ)
Initial: 1572 fps (@ 100 yards)
After skin penetration: 1429 fps
After bone penetration: 1370 fps

.45-70 USG (405 gr RN)
Initial: 1168 fps
After skin penetration: 1106 fps
After bone penetration: 1078 fps

[roscoe]

You guys need to use Excel - skip this "Memory Clear" stuff.

Have you looked at the Poncelot penetration equation?

[RyanM]

I use MS Works spreadsheet, and OpenOffice spreadsheet. Kind of like Excel, but much crappier. And the Poncelet equation is totally inaccurate. Or it may be based on penetration into seasoned oak, or something. I believe it said a 9mm FMJ will penetrate about 8". The real value is around 30".

Anyway, that skin penetration thing is way off. I think you must have used the values for steel instead of skin, or something. Or maybe 0.06 foot thick skin, like an elephant. I get 663 fps as the remaining velocity of a .45 cal, 230 gr bullet at 850 fps. For humans, velocity loss for that kind of bullet will actually be about 1 to 3 fps. The higher the velocity, the less is lost on going through skin.

[McCall911]

I use MS Works spreadsheet, and OpenOffice spreadsheet. Kind of like Excel, but much crappier. And the Poncelet equation is totally inaccurate. Or it may be based on penetration into seasoned oak, or something. I believe it said a 9mm FMJ will penetrate about 8". The real value is around 30".

Anyway, that skin penetration thing is way off. I think you must have used the values for steel instead of skin, or something. Or maybe 0.06 foot thick skin, like an elephant. I get 663 fps as the remaining velocity of a .45 cal, 230 gr bullet at 850 fps. For humans, velocity loss for that kind of bullet will actually be about 1 to 3 fps. The higher the velocity, the less is lost on going through skin.

Oops!!

Yes, and I just realized too late that there's a hole in the equation big enough to drive a truck through! So don't use it until I correct it.

:o

Here's what I'm looking at with regard to skin penetration: Skin has a density of 1 gm /cm^3, or 62.4 lb/ft^3, and a tensile strength of 3000 kilopascals, or 62656 lb/ft^2. The resisting force on the bullet will increase with half the square of the velocity, multiplied by these two factors, divided by acceleration due to gravity. This result will be in pounds^2 per foot^4. This is in turn divided by atmospheric pressure, or 2116.8 pounds per square foot, conveniently yields a unit of pounds per square foot (just what we need.) Multiply pounds per square foot by the area of the bullet (the area acted on) gives us the resisting force. And what is force? Force = mass x acceleration. (See where I'm heading?) And it's acceleration (or actually deceleration) which is what we need to estimate the velocity loss, per that guy Newton.

(Whew!)

[McCall911]

You guys need to use Excel - skip this "Memory Clear" stuff.

Have you looked at the Poncelot penetration equation?

I write BASIC programs for my personal use, but not everybody else uses this antiquated stuff anymore.

I've played with Poncelet's penetration equation, but it seems to be lacking.

http://home.snafu.de/l.moeller/Poncelet/Poncelet_english.htm

[McCall911]

Corrections/changes made to the previous post. Have fun!

[RyanM]

Finally got time to look at this again. I think the equation is still removing much too much velocity. Are you sure resisting force increases as velocity increases? Drag increases, but that's a force in a fluid medium, while skin is much more solid. It seems like resisting force decrease as velocity increases, since a faster bullet is better able to plow through. At least, the proportional amount of velocity lost decreases very quickly as velocity goes up. Running some numbers through, it seems that for a given bullet weight, shape, and caliber, the equation always takes off a certain proportion of the velocity, no matter what it is.

I can't remember the exact figures, but MacPherson said that for a roundnose, heavy-for-caliber bullet (147 9mm, 180 gr .40, etc), at a velocity of 600 fps, only 7 fps is lost in the skin, 3 fps lost at 800 fps, and 1 fps lost at 1000. Something like that.

According to various sources, the threshold penetration velocity various projectiles are:

skin with no backing:
1/8", 2 grain steel spheres, 170 fps
1/8", 7 grain lead spheres did not penetrate at 161 fps (unknown threshold; same as steel?)
150 gr bullet, unknown caliber, 125-150 fps

cadaver thigh skin:
11.25mm, 131 gr lead sphere, 234 fps
.177, 8.25 gr lead airgun pellet, 330 fps
.22, 16.5 gr lead airgun pellet, 245 fps
.38 cal, 113 gr LRN, 190 fps

According to Wikipedia, human skin averages 2-3mm. That's about .08 to .12 inches. Couldn't find anything on tensile strength, but 3 mPa sounds about right, given that newborn rat skin has a tensile strength of 1.6 mPa. All I could find on human skin is that Young's Modulus is about 65.6 mPa for humans aged 15 to 30. I think I converted it right, anyway. It was given as 6.7 kg/mm^2.

[McCall911]

RyanM, I'm really not sure of anything in this area to be perfectly honest. :D ;) :o

What I was going by concerning velocity loss through skin was what I read from this website (in Italian) several years back:

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

You can translate it into English with the Windows tranlator with some amusing results. ("Ballistics Finishes Them" :D )

[RyanM]

I think I found an accurate set of equations for predicting skin penetration velocity loss.

http://www.dtic.mil/ndia/2005garm/tuesday/hudgins.pdf

First, find P.

P=(2 * m) / (rho * T * A)
m = bullet mass in grams (grains / 7 / 2.205)
rho = density of skin, 1.06 g/cm^3
T = thickness of skin, they say 0.31 cm (.1 to .2 cm may be more accurate)
A = average presented area; with bullets, it's just plain old PI*R^2

Then find the penetration threshold velocity.

V(threshold) = 309.13 * P^-0.38708

This will give you velocity in m/s. Convert to fps by dividing by .3048. Their R-squared value for this equation, using 7 different sources for their data, was .974. That's insanely good.

Then find the velocity remaining after penetration. No tests were done in this article, but they suggest

V(after) = (V(before)^2 - V(threshold)^2)^.5

The results are close enough for me.

Playing around with the remaining velocity equation, using V(before) / V(threshold) instead of 2, and 1 / (V(b) / V(t)) instead of square root seems to give reasonable values, if I'm correctly remembering what MacPherson's test results were. At velocities above about 800 or 1000 fps, velocity loss due to skin was truly insubstantial.