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


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481
December 28, 2012, 06:05 PM
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-

http://i1339.photobucket.com/albums/o710/m831z/9v45MaxPen.gif



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-

http://i1339.photobucket.com/albums/o710/m831z/9v45PCCmax.gif


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.

:)

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meanmrmustard
December 28, 2012, 07:22 PM
Think that's impressive? Add .40 S&W and .357 Sig to this analysis.

Owen
December 28, 2012, 07:28 PM
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.

481
December 28, 2012, 07:41 PM
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.

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)...

wally
December 28, 2012, 08:05 PM
All things being equal, penetration is proportional to the product of velocity and sectional density.

Do the 230gr .45ACP vs. the 147gr 9mm.

meanmrmustard
December 28, 2012, 08:12 PM
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.
I'm betting .40 smashes both, and .357 trumps the Smith offering.

Owen
December 28, 2012, 08:45 PM
look at the charts... impact velocity is the dependent variable (the X-axis) basically its going to come down to bullet weight, and the fudge factor his formula is using for expansion. The .357 SIG with its typical 125 gr bullet, is going to make a line very slightly above the 9mm line, and the .40 is going to split the difference between 9mm and .45 (or shade towards the 9mm line because the typical 155 gr bullet is closer to the 9mm weights than the .45 weights).

Now if you put a specific point on each line depicting the impact velocity at say 10 yards, you'll start to see the differences.

Owen
December 28, 2012, 08:57 PM
(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!

481
December 28, 2012, 09:09 PM
(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!

Oh, joy! :evil:

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.

1SOW
December 28, 2012, 09:15 PM
I see an opportunity for endless worrying about small theoretical performance differences! We could tie up the forum for months!

Now, draw a line or place a dot on the lines at typical max velocities for those calibers--not loaded beyond published max loads.:D:D :D

Bet is, one horizontal line will intersect the dots.

481
December 28, 2012, 09:23 PM
OK, guys... these charts take quite a while to produce so this will have to be "it" for the evening- there's always tomorrow. :cool:

Here y'all are-

http://i1339.photobucket.com/albums/o710/m831z/355v400v451MaxPengif.gif

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
December 28, 2012, 09:27 PM
481, what is your graphing software? looks nicer than Excel.

meanmrmustard
December 28, 2012, 09:29 PM
(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!
I'm still calling the Smith and Sig as better penetrators on this one.

481
December 28, 2012, 09:34 PM
481, what is your graphing software? looks nicer than Excel.

Thanks.

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

Owen
December 28, 2012, 09:35 PM
oh wow. the kindle version of that book is only $3.99

481
December 28, 2012, 09:36 PM
oh wow. the kindle version of that book is only $3.99
That's what I have.

481
December 28, 2012, 09:40 PM
I'm still calling the Smith and Sig as better penetrators on this one.

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

Bobo
December 28, 2012, 09:52 PM
Thanks 481 - saved for future use!

Bobo

meanmrmustard
December 28, 2012, 10:37 PM
According to the chart (or more precisely, the model), you are correct. :)
Sorry, we posted at nearly the same time.

I KNEW they'd penetrate more. Maybe not the 9, but I've seen .45 bounce off of vests at 10 yards. Not a very good penetrator.

2zulu1
December 29, 2012, 01:58 PM
Nice thread, I like the graph idea. Going back a number of decades and we know the introduction of the Super 38 was instigated because 45 ball ammunition failed to give adequate penetration against auto sheet metal and soft body armor of the time. The Super's 356cal, 130gr FMJ/~1300fps changed everything and we can interpolate from the OP's graphs the penetration difference between 38/45 ball ammunition.

In the pic below there is a hole in tin siding caused by a 135gr FMJ @1273fps, after penetrating through a combination of 9" of redwood and fir.

http://i1103.photobucket.com/albums/g474/aztrekker511/38Super135grFMJ1270fps004.jpg

10.5" of redwood yielded the same results. Loading on the left is a 357cal/140gr Sierra JHP.

As the OP has illustrated, the fast nines are capable of producing significant penetration depths through soft tissue. A real world application could be a defensive home invasion scenario in which one needs to shoot through door framing.

The kindle price of the QAS book is great, I have the soft cover version and its price was great too. :)

481
December 29, 2012, 03:39 PM
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:


http://i1339.photobucket.com/albums/o710/m831z/355130grFMJRNPenMassCummAn1gif.gif


Happy New Year, 2z1!

:)

Shawn Dodson
December 29, 2012, 06:21 PM
9mm FMJ tends to yaw as it penetrates soft tissues whereas .45 ACP FMJ, in general, does not. 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.

481
December 29, 2012, 08:22 PM
9mm FMJ tends to yaw as it penetrates soft tissues whereas .45 ACP FMJ, in general, does not.

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.

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.

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.

481
December 29, 2012, 10:29 PM
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-

http://i1339.photobucket.com/albums/o710/m831z/9MM1151155IncDecayVKE.gif



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

http://i1339.photobucket.com/albums/o710/m831z/45230865IncDecayVKEgif.gif

:)

2zulu1
December 30, 2012, 01:07 AM
Are you snowed in? :p

If I'm understanding your velocity decay model correctly, this model could also be applied to JHP designs, but a bit more complicated.

Using a 9mm/127gr JHP @1250fps, let's assume max symmetrical expansion, 1.5xcaliber @2" (0.533"). Calculate total penetration, then calculate/display 1" segments on the deceleration graph.

Will the drag coefficient be the same between 0" to 2" and 2" to 13", or whatever the final depth is? For fun, you could also graph the diminishing crush cavity volume as the bullet slows. I can envision some interesting applications for this type of graph in water testing, including bone as an intermediate barrier. :)

As an aside, JHP performance is only as good as the bullet's weakest petal, FMJs aren't the only bullet design that can tumble.

481
December 30, 2012, 02:04 AM
Are you snowed in? :p

Yep. :D

Using a 9mm/127gr JHP @1250fps, let's assume max symmetrical expansion, 1.5xcaliber @2" (0.533"). Calculate total penetration, then calculate/display 1" segments on the deceleration graph.

You mean like this? (each x-axis increment represents 4.1mm of bullet travel)

http://i1339.photobucket.com/albums/o710/m831z/9mm127VKEDecay1250.gif

Will the drag coefficient be the same between 0" to 2" and 2" to 13", or whatever the final depth is?

From what I've read thus far, the drag coefficient should increase as the bullet decelerates due to viscous drag effects exerting a greater influence than inertial drag effects.

hentown
December 30, 2012, 07:20 AM
I love these threads that feature impressive math, charts, etc., but make comparisons of bullets that nobody uses for s.d. purposes. :cool:

meanmrmustard
December 30, 2012, 08:51 AM
Just for fun. Not everything has to have informational value specifically for defense. It can just be fun to compare....for fun.:)

481
December 30, 2012, 11:15 AM
I love these threads that feature impressive math, charts, etc., but make comparisons of bullets that nobody uses for s.d. purposes. :cool:

Oh, c'mon and enjoy yourself. :) It isn't all about FMJs, although folks some do use them for self-defense. Look at post 26- the chart relates to the behavior of a 9mm 127 gr. JHP at 1250 fps that expanded to 0.533".

I get the distinct impression that 2zulu1 was thinking of the Winchester Ranger 9mm 127 gr +P JHP when he framed his question- it is a highly respected JHP with an admirable track-record.

2zulu1
December 30, 2012, 05:04 PM
Oh, c'mon and enjoy yourself. :) It isn't all about FMJs, although folks some do use them for self-defense. Look at post 26- the chart relates to the behavior of a 9mm 127 gr. JHP at 1250 fps that expanded to 0.533".

I get the distinct impression that 2zulu1 was thinking of the Winchester Ranger 9mm 127 gr +P JHP when he framed his question- it is a highly respected JHP with an admirable track-record.
Yes, I was referring to the RA9TA.

I like the graph aspect as it can also be used to establish exit wound velocity. Also, the graphs illustrate and debunk the energy dump wound trauma incapacitation theory. :)

481
December 30, 2012, 05:46 PM
Yes, I was referring to the RA9TA.

I like the graph aspect as it can also be used to establish exit wound velocity. Also, the graphs illustrate and debunk the energy dump wound trauma incapacitation theory. :)


The QAS model also has a residual velocity equation that can be used to figure that out.

Relying on my trusty Excel spreadsheet to do all of the grunt work for me (I hate punching calculator buttons), a 9mm 127 gr JHP with an impact velocity of 1250 fps that expands to 0.533" would exit a 13" thick target at 232.5 fps.

Probably not fast enough to re-enter another human body according to the model found here-

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

which says that it’d have to be moving at least 257 fps to do so.

2zulu1
December 31, 2012, 02:26 PM
^^^^ This is really good information to know and put into practice given the concerns we have about over penetration. I decided to measure myself, chest front to back is 14". Rotate my body 90 and arm to edge of heart is also 14", my shirt size is 2XT.

While books have been written on the subject, I prefer carrying JHP ammunition that will reliably give 14"-16" of penetration, however, if I know I'll be in crowded environments, I'll drop down to 12" ammunition. These type graphs help visualize data in a way that printed numbers can't IMO.

I remember some time ago seeing a picture of Dr. Fackler pinning pig skin to a block of ballistic gel for the purpose of ascertaining the effects of skin on bullet penetration. Lots of data to digest in the above link.

hentown
December 31, 2012, 03:48 PM
There's just so much meaningless fun a guy can take in a lifetime!! :evil:

481
December 31, 2012, 05:26 PM
In order to use an actual water test of the JHP we've been discussing, I took the liberty of liberating one of your prior water test images and the data for the 9mm Winchester Ranger 127 gr. +P+ JHP (RA9TA) that you shot against no barrier. Forgive me- your photography is far better than mine. :evil:

Winchester Ranger 9mm 127 gr. +P+ JHP vs. water medium:
http://i1339.photobucket.com/albums/o710/m831z/9mm127PWinRanger1250fps1150grs0605004_zps68bcebfd.jpg


Here is the Schwartz bullet penetration model analysis for this test:

9mm Winchester Ranger 127 gr. +P+ JHP (RA9TA) - no barrier, water test medium

Recovered Projectile Data:

Average Recovered Diameter: 0.605 inch
Retained Mass: 115 grains
Impact Velocity: 1250 feet per second

Predicted Terminal Performance:

Penetration Depth (S) = 28.09 cm (11.06 inches)
Permanent Wound Cavity Mass (MPC) = 44.39 grams (1.57 ounces)

Also created a Velocity/KE chart- each chart division is equal to about 2.8mm of bullet travel:

http://i1339.photobucket.com/albums/o710/m831z/Win127VKEDecay_zpsf80e8f44.gif

Not surprisingly, the exit velocity predicted by the Schwartz bullet penetration model is 153.9 fps after passing through 10 inches of soft tissue (between 91st and 92nd divisions of the chart above) - well below the 294.3 fps required for it to break the skin of, and re-enter, another body according to the US Army skin penetration model that I've been using to determine such stuff.

2zulu1
January 1, 2013, 02:38 AM
If I were to do that test now it would be through five layers of clothing. Seems like our Canadian snow bird friends forget to close the door behind them. :)

Here's another 127gr Ranger bullet that didn't have enough remaining velocity, after passing through several one gallon water bottles, to fully penetrate this last plastic barrier.

http://i1103.photobucket.com/albums/g474/aztrekker511/9mmWin127Pcowbonewater006.jpg

Nice carry ammunition if you can find it, it also performs well against bone and the plastic can be analogous to skin.

http://i1103.photobucket.com/albums/g474/aztrekker511/9mmWin127Pcowbonewater001.jpg

Shawn Dodson
January 1, 2013, 04:08 PM
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. 9mm FMJ yaws and .45 ACP doesn't. The reason is because the center of gravity on the 9mm is located toward the base of the bullet - 9mm FMJ RN is much more "pointed" than 45 ACP RN.

481
January 1, 2013, 07:56 PM
9mm FMJ yaws and .45 ACP doesn't. The reason is because the center of gravity on the 9mm is located toward the base of the bullet - 9mm FMJ RN is much more "pointed" than 45 ACP RN.

That is not entirely accurate.

Both 9mm and .45ACP FMJRNs can, and do, yaw.

Even extremely oblate projectile profiles like expanded JHPs, which are far more blunt than the .45 FMJRN and have a CoG even farther forward than the .45 FMJRN, can, and do, yaw. The 9mm is arguably a little bit more prone to do so, but both the 9mm and .45 FMJRNs do indeed yaw and it is not possible to predict if, when, or even to what degree, either one will do so.

Still, the greater point remains- neither the Schwartz bullet penetration model nor the MacPherson bullet penetration model has an expression for the consideration of projectile yaw as doing so would render those models largely unusable/inaccessible to anyone lacking the requisite computational capacity to perform such complex calculations- something that I think both authors would find undesirable.

The proof of these model's accuracy is in their performance and by way of example, I've compared the Schwartz bullet penetration model's prediction against a couple of well-known examples that I am sure most folks here on TFL have seen before:


Example #1:

This .45ACP 230 gr FMJRN @ 869 fps has a total penetration depth of about 65cm or 25.6 inches:
http://i1339.photobucket.com/albums/o710/m831z/45230FMJ-869_zps1414f835.jpg

The Schwartz bullet penetration model predicts a penetration depth of 25.7 inches.

The MacPherson bullet penetration model predicts a penetration depth of 30.3 inches.



Example #2

This "yawing" 9mm 124 gr FMJRN @ 1189 fps has a total penetration depth of about 71-72cm or 28.3 inches if you "straighten out" the upward curve at the end of the bullet's path:
http://i1339.photobucket.com/albums/o710/m831z/9mm124FMJ-1189_zps746b7dc9.jpg

The Schwartz bullet penetration model predicts a penetration depth of 28.7 inches- that's pretty impressive.

The MacPherson bullet penetration model predicts a penetration depth of 30.9 inches.


:)

481
January 2, 2013, 07:49 PM
If I were to do that test now it would be through five layers of clothing. Seems like our Canadian snow bird friends forget to close the door behind them. :)

Wouldn't mind seeing that test. It's a darned good JHP.

481
January 3, 2013, 12:22 AM
Did this for a member of another forum who inquired about comparing the .45 ACP 230 gr FMJRN @ 850 fps against the 9mm M882 @ 1300 fps and thought that my fellow THR members might enjoy it...


Here is the Schwartz bullet penetration model analysis for the 9mm 124 gr FMJRN @ 1300 fps (M882):

Predicted Terminal Performance:
Average Recovered Diameter: 0.355 inch
Retained Mass: 124 grains
Impact Velocity: 1300 feet per second

Penetration Depth (S) = 76.89 cm (30.27 inches)
Permanent Wound Cavity Mass (MPC) = 35.01 grams (1.24 ounces)

http://i1339.photobucket.com/albums/o710/m831z/M882PCMvsPx_zpsb9497fdd.gif


http://i1339.photobucket.com/albums/o710/m831z/M882VKEDecay77mm_zpsa1e9e2ea.gif
Note: Each x-axis graduation (100 elements) = 7.7mm of bullet travel



Here is the Schwartz bullet penetration model analysis for the .45 ACP 230 gr FMJRN @ 850 fps:

Predicted Terminal Performance:
Average Recovered Diameter: 0.452 inch
Retained Mass: 230 grains
Impact Velocity: 850 feet per second

Penetration Depth (S) = 64.47 cm (25.38 inches)
Permanent Wound Cavity Mass (MPC) = 47.67 grams (1.68 ounces)


http://i1339.photobucket.com/albums/o710/m831z/45ACPPCMvsPx_zps53f0c666.gif


http://i1339.photobucket.com/albums/o710/m831z/45ACPVKEDecay64mm_zps99c9ed23.gif
Note: Each x-axis graduation (100 elements) = 6.4mm of bullet travel

:)

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