A brief graphical analysis of the 9mm 115 gr. FMJRN and the .45ACP 230 gr. FMJRN

It seems that one of the perennial topics on internet gun forums is the comparison of the 9mm and .45ACP using ball ammunition.

Using the Schwartz terminal ballistic model to analyze the maximum penetration depths and the corresponding mass within the permanent wound cavities of the 9mm 115 gr FMJRN and the .45ACP 230 gr FMJRN across a wide range of velocities (200 fps - 1600 fps), I thought that graphs might be a visually-informative way to illustrate the data for those who might be interested in it.

Since a bullet that lacks the velocity necessary to penetrate skin will fail to penetrate a human body, it was necessary to determine the lower velocity limit to be used in the analysis.

For this task, I used the skin penetration model found in the research paper below-

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

-to determine the minimum velocity at which both the 9mm and .45ACP FMJRNs would successfully penetrate human skin of average thickness (~3mm). Those values are 194.5 fps for the 9mm 115 gr FMJRN and 179.4 fps for the .45ACP FMJRN.

Since either round must have a minimum velocity of less than 200 fps to pass successfully through human skin, 200 fps was used for both rounds as the lower limit for the analysis.



This graph illustrates the maximum penetration depths (in inches) of the 9mm 115 gr FMJRN and the .45ACP FMJRN at impact velocities of 200 fps to 1600 fps-





This graph illustrates the mass (in grams) of permanently crushed soft tissue within the entire volume of the permanent cavity of the 9mm 115 gr FMJRN and the .45ACP FMJRN at impact velocities of 200 fps to 1600 fps-




Using a manufacturer's ballistic table to determine the velocity of the FMJRN at a desired range, the maximum terminal penetration and the amount of permanently crushed soft-tissue within the permanent cavity can be found using the charts above.

One of the most startling implications of this analysis (at least to me) is the amount of penetration that both rounds would produce even at extended ranges where velocities are well below 400 fps.

owen said:

looking at the way those charts work, I'm guessing .357SIG (and Magnum for that matter) will be on exactly the same line as 9mm, and 40 will fall between the two.

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If you want, I'll take a look at those rounds and try to get a chart or two put up- it's kind of tedious work to do it, but I'll do it if you wish.

Just need a bullet weight and a shape (e.g.: FMJRN, FMJFN)...

owen said:

(this is a SWAG)

I think if you were to take these curves, and say do a curve for all of the common bullet weights in a given caliber, and then put a point on each line for the expected impact velocity at a given (short distance), and then connected those points, you's get a nearly straight line, with lighter non-expanding bullets doing slightly better. If you did the same thing out to extended ranges, you'd start to see curves showing the heavier bullets catching up and passing the lighter bullets in terms of penetration.

I think I may just buy that book. I see an opportunity for endless worrying about small theoretical performance differences! We could tie up the forum for months!

Oh, this is going to be so great!

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Oh, joy!

I'll have the next chart ready to go in just a bit- I think that you, wally, and meanmrmustard will be pleased with what I've done- I think that I got all of your requests wrapped up in one chart. I had to make the .45 230 gr. FMJ a flatpoint-truncated cone to keep the projectiles on an even playing field.

OK, guys... these charts take quite a while to produce so this will have to be "it" for the evening- there's always tomorrow.

Here y'all are-



The blue curve is for the 9mm/.357Sig 147 gr. FMJTC, the green curve is for the .40S&W/10mm 180 gr. FMJTC, and the red curve is for the .45ACP 230 gr. FMJTC.

All of these rounds are very close in terms of sectional density and their respective curves are within 2" to 5" of one another across the range of velocities examined.

owen said:

481, what is your graphing software? looks nicer than Excel.

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Thanks.

It is an older version of Excel that I keep around for goofing off like this.

owen said:

oh wow. the kindle version of that book is only $3.99

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That's what I have.

meanmrmustard said:

I'm still calling the Smith and Sig as better penetrators on this one.

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According to the chart (or more precisely, the model), you are correct.

Since I am well aware of 2z1's fondness for his beloved .38 Super pistols (and the very under-estimated cartridge), here is a graph that details the performance of the 130 gr. FMJRN in terms of penetration depth and permanently crushed tissue mass over the velocity range of 200 - 1600 feet per second:





Happy New Year, 2z1!

Shawn Dodson said:

9mm FMJ tends to yaw as it penetrates soft tissues whereas .45 ACP FMJ, in general, does not.

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In general, that may be true, but FMJs in both (and any) calibers are susceptible to, and can, yaw. There is no way to tell when the effect will occur, or to what degree it will occur.

Shawn Dodson said:

A yawing bullet contacts and crushes more tissues than a bullet that penetrates point forward. As a result, if the calculation for "permanently crushed soft tissues" does not account for 9mm FMJ bullet yaw it then will be inaccurate.

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It is impossible to reliably predict if a projectile will yaw during the penetration event (both the 9mm and the .45 are susceptible to this) let alone how much a projectile will yaw, if it actually does so.

Such "accuracy" would require a reliable prediction that 1.) the bullet would yaw in addition to 2.) correctly predicting the angle at which the "test bullet" is going to yaw as well as 3.) at what point along the wound path projectile yaw would occur so that the (correct) increase in tissue damage could be accounted for in the model.

Of the two bullet penetration models that I am aware of, neither the Schwartz bullet penetration model nor the MacPherson bullet penetration model takes this terminal behavior into account- that is, there is no angular expression in either of the two models that allows such a calculation (both models assume a stable, "nose-forward" angle of attack) to be made.

To do so, both bullet penetration models would become enormously complicated and unusable to anyone not having huge computational capacity available to them.

In fact, the second page of the QAS website addresses the issue here-

http://quantitativeammunitionselection.com/endorsements_-_faq/

Q: Under what conditions does the quantitative terminal ballistic model operate?

A: The quantitative model operates under three conditions:

1. All significant plastic deformation of the projectile occurs within periods of 10^ -4 seconds.

2. The projectile behaves as a rigid body after expansion (no further ductile or ablative erosion occurs) and exhibits no significant yaw during any portion of the penetration event.

3. The terminal behavior of the projectile is governed by a material strength variable and the inertial and viscous (or frictional) drag losses that occur during the projectile's penetration through the medium.

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As I continue to work with Excel, I have found that another function that the Schwartz bullet penetration model can be used to explore is the decay of a bullet's velocity (there is an equation for instantaneous residual velocity) and KE (since it is possible to calculate the bullet's mass and instantaneous velocity) over the length of its maximum penetration depth which has been divided into 100 increments in the charts below-

For the 9mm 115 gr. FMJRN @ 1155 fps-





For the .45ACP 230 gr. FMJRN @ 865 fps-