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More Gun Math Geekery

Not taking away from Caleb’s argument that we spend too much time arguing about stopping power. We do. Shot placement matters a whole lot more. But that aside, I do want to look at one thing Caleb mentions.

When you look at a 9mm, a .40, and a .45 ACP all right next to one another like that, the size difference is almost laughable

You have to look at it from a mathematical point of view, because your instincts when it comes to area and volume are deceptive. For the same reason, a 21″ monitor doesn’t look that much bigger than a 19″, but it is. Area for a circle is A=πr2. In that case, let’s take a look at 9mm vs. .40S&W vs. .45ACP. After all, it’s the area of the bullet that slices through the target, not the diameter.

Round True Radius (D/2) Surface Area (A=πr2)
9mm Luger 4.51mm 63.9mm2
.40S&W 5.08mm 81.1mm2
.45ACP 5.74mm 103.51mm2

So you can see when it comes to diameter, the difference is minimal, but that doesn’t translate when you think about it in terms of surface area cutting through the target. In this view, .40S&W is 27% larger than 9mm, while .45ACP is 62% larger than 9mm and 28% larger than .40S&W. That’s not even considering expanding ammo, which is going to make the numbers even more dramatic.

That also holds when it comes to how much mass you can throw down range, and since stopping power is arguably derived from momentum, sending a 230gr bullet of a .45ACP downrange is going to matter a lot more than the 200gr .40S&W bullet or the 115gr 9mm. Never make the mistake of just thinking about bullets in terms of diameter (caliber). When you start thinking about area and mass, the numbers change more dramatically than instinct would have you believe.

16 Responses to “More Gun Math Geekery”

  1. Noops says:

    That’s all great, but it doesn’t translate to terminal ballistics in reality. Technologies are now at play that effectively level the playing field. A 9mm Speer Gold Dot will smoke an older .45 hydra shock.

    Go read some of Doctor Gary Roberts articles at M4Carbine, Lightfighter, or 10-8.

  2. Flighterdoc says:

    I’ve seen people shot with just about everything, from a .177 pellet to a 12 gauge slug, and survived…the same loads have caused people to die. There is no rhyme or reason to it that I can discern.

    However, I think the advice from the (now 20 year old) FBI report on”Handgun Wounding Factors and Effectiveness”:

    “Given desirable and reliable penetration, the only way to increase bullet effectiveness is to increase the severity of the wound channel by increasing the size of the hole made by the bullet…Of the bullets that penetrate, [b]the edge is always with the bigger bullet”[/b]. (Conclusions, page 16, emphasis added).

  3. Sebastian says:

    I don’t really dispute that, Noops. There’s a lot more to stopping an attacker than the size of the round you’re using. I am just pointing out that small changes in caliber can translate into big changes in surface area and mass.

  4. Flighterdoc says:

    Oh, and comparing a rifle to a pistol, or modern bullet designs against old bullet designs is really comparing apples and elephants. Here’s a factoid for noops: A CB cap in the eye socket is more disabling than a rock tossed at an arm.

  5. Shot placement is very important. I would call it the single most important aspect of ending a gun fight, it’s just not the only important thing. The question of what projectile is making the hit at what velocity is also VERY important.

    A whole lot of folks say what you shoot isn’t important. Do they advocate carrying .32 ACP or .22LR?

    I can hit faster with a .22LR than I can with a .45 ACP or even a 9mm Para. I don’t carry a .22LR because I believe the size of the hole is important along with where the hole is.

  6. martini says:

    in the same vein lets not foget about kinetic energy. As it is the square of velocity times mass you can have dramatic chamges with lighter faster bullets than heavier slower rounds

  7. Sebastian says:

    Yes, but energy and momentum are a bit different. See this paper here. Keep in mind though, this stuff is academic. In the real world, I’m not convinced there’s practically much difference between a .45ACP and a 9mm.

  8. Mark D says:

    We have some very interesting data field data provided by the latest terrorist attack at Fort Hood.

    1. The cops there ain’t using enough gun. 4 hits and that dirtbag should have been DRT ( dead right there)

    2. The dirtbag’s “cop killer” gun isn’t. 13 dead & 30 wounded.

  9. Andrew says:

    As a pipeliner, the one thing that caught my attention early on was the statement the if you want to quadruple your flow through a pipeline, all you had to do was double the diameter.

    An 8″ pipeline carries 4 times the volume as a 4″ pipeline (pressure dependent). Do not discard diameter.

  10. Andrew says:

    Like what Sebastian said.

    I does not take a large increase in diameter to do more damage. And damage is what it is all about when it comes to kill shots.

    Oh, and Tomcatshanger

    Remember, in the heat of the moment, when adrenalin is running high, shot placement is not the thing you think about most. You aim at the largest part of mass, in the dark, usually, so you can’t pick out their right eyeball, and you shoot.

    Placement works fine on the range. Not at 3:00AM, with eye boogers in your eyes, and with your kids in the next room and your wife in the bed behind you. Just don’t shoot to the right or left and behind you. You are just going to blaze away at what is in front of you.

    Unless you have had the experience of shooting homebreakers numerous times. Then I would say “Move”.

  11. I’ve always laughed (quietly, and in private) at people who think that the .45 ACP is a “manstopper” while the 9mm is some wimpy “Europellet” while simultaneously thinking that .223 is wimpy.

    The difference in effectiveness, energy, and momentum between 9mm and .45 ACP is, as Sebastian says, academic at best. The difference between a .45 and .223 is significant and dramatic. It’s simply not possible for a .45 to be an effective manstopper while .223 is not, assuming shot placement is identical.

  12. bombloader says:

    No! You’ve stepped into the .45 vs. 9 debate. Please have mercy and don’t do any AR vs. AK any time soon.

  13. larry weeks says:

    Trick from a Nikon photo class talking about letting in more light (letting out more blood?): multipy diameter times 1.4 to double the area. A 14″ pizza has twice the volume of a 10″ pizza. But, Roy Huntington from American Handgunner and a retired San Diego cop says it’s awfully tough to tell the difference between a 9mm hole and a .45 hole. Not like CSI.

  14. NJSoldier says:

    I just bought a 73″ TV. Can you tell me how much bigger it is than my old 42″? I want to feel good about it.

  15. Clint says:

    The problem I have with these “shot placement” arguments is that shot placement is based on what the shooter does while “stopping power” is based on what the bullet does. In 1986 FBI Agent Jerry Dove made a great shot and hit the bad guy but the bullet didn’t do it’s job. I don’t want to end up in that situation.

    http://en.wikipedia.org/wiki/1986_FBI_Miami_shootout
    http://www.thegunzone.com/11april86.html

    For all the “A 22 in the tear duct is better than…” slogans, I have to say that if you are close enough to hit a tear duct with a pocket 22, you are close enough to shove the barrel in an eyeball. Which is faster and easier.

    And it would be more effective too.

    Reminds me of some people in the hunter community. “You can take elk with a 243, IF you do your part.” So does that me I can slack off and not bother aiming with the 338? Of course not. You have to aim regardless.

    As you good folks can probable tell, False Dichotomy and flippant answers (which I parodied above) tend to disgust me.

    And something I am starting to wonder about; why is it all these arguments, which are basically “My bullet is just as good as anybody else’s bullet” tend to come from people who don’t carry 45’s?

    (and to head off the inevitable response, yes there is a lotta BS on the 45 side. If I have to listen to another chairborne talk about “pinkie shots” I think I’ll puke!)

  16. Clint says:

    To add,

    Something I learned in the Marine Corps;

    If you are planing on “perfect,” you are planing to fail.

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