Some Thoughts On Bang! Flash! Penetration & Cartridge Length

In an earlier posting I made some comments and posted data to support it about the value of small and old and slow cartridges in short barreled guns.

This sent me down a “Dig Here!” rabbit hole looking for what made a cartridge “good enough” with enough penetration. The idea was:

“What would it take to make a cartridge that penetrated ‘enough’ but had the shortest smallest case possible for most ‘case volumes of expansion’?”

Thus a nice quiet low flash round with decent penetration and efficacy for self defense.

I’m quite comfortable with the conclusion that once you are in a 3 inch (or less) barrel gun, short (and thus often older) rounds are about as good as “modern” high pressure high velocity (and especially magnum) loading as most of that added pressure and power ends up as muzzle flash and BANG! not bullet velocity. But what about more modern rounds and longer barrels?

So cutting to the chase of one line of digging: The ideal there would be a .50 caliber round in a case a bit shorter than a .45 ACP. The .50 as that’s the largest diameter allowed by US Law, and the slightly shorter than .45 ACP since it has just a little extra powder room in it, so you could squash that back just a little and make a heavy round going about 700 to 800 fps that would work just dandy. This, in effect, recreates some of the old Webley era rounds, but with a bit more power. OK…

But it is only a very little bit closer to that ideal than the .45 ACP is already, so not really worth the effort. Just get a .45 and put big heavy bullets in it seated a bit deeper over a modest powder charge (reducing the volume raises the pressure so you need to use less power to stay in spec, and work slowly up to max pressure). How much deeper is not very much. And that’s what the rest of this article comes from. Looking for how tall a powder column is needed under how tall a lead column. Turns out that’s pretty much a constant regardless of caliber used, and this has implications for current commercial ammunition performance.

As noted in the other article, at about 6 inches barrel length and higher you are getting most of the power out of any given revolver / pistol type cartridge. (Sera can confirm.. ;-) Just how long seems to vary with the relative length of the cartridge cases. For our purposes here, we’re just looking at “the usual” 6 inch sort of revolver as the exemplar gun. It isn’t very relevant, but it helps avoid the edge cases like the .22 Magnum with horrid falloff of power in shorter barrels.

Sectional Density

The first thing I ran into was that “penetration” is almost entirely a function of sectional density with a minor h/t to bullet shape and material of construction (but even then, the case can be made that a soft lead bullet of 9mm diameter deforming into 18mm diameter is just changing the parameters of its sectional density…) So a hard copper 9mm stays 9mm and the calculation of sectional density uses 9mm while a soft lead turning into an 18 mm (and shorter) uses those values, so penetrates less far.

Metric units

When working with ballistics using SI units, it is common to use either grams per square millimeter or kilograms per square centimeter. Their relationship to the base unit kilograms per square meter is shown in the conversion table above.

Grams per square millimeter
Using grams per square millimeter (g/mm2), the formula then becomes:

SD g/sqmm = Mg/dmm^2

Where:

SDg/mm2 is the sectional density in grams per square millimeters
mg is the weight of the projectile in grams
dmm is the diameter of the projectile in millimeters

For example, a small arms bullet weighing 10.4 grams (160 gr) and having a diameter of 7.2 mm (0.284 in) would have a sectional density of:

10.4/(7.2^2) = 0.200 g/mm2

Basically, it’s grams over area. As diameter varies, the length of the lead lump is all that determines grams per unit area.

You can also change this with different materials (copper or iron vs lead) and you can make the bullet pointy so initial contact area is very small and thus impact sectional density is very high for an instant. But that all comes secondary to just how long your chunk of lead is, in a typical round

The implication here is that if you look at “rounds that work” you ought to find a minimum length of bullet that is effective. In fact, that seems to be the case. For hunting very large heavy animals with thick skins, bullets of 1 or even 2 inches are used. When dealing with self defense ammunition, it looks like the length is about 12 mm. This is based on looking at some various bullets specs in 9mm and .357 and .380 (generally considered to be about the lower bound of ‘works well’ and noticing they are about 1.5 times as long as wide. Then I looked at some .44 / .45 rounds and they were “dumpy” in comparison. Wider but not taller. As a first approximation, 12 mm length is a decent rule of thumb.

Now if you look at the rounds considered “not effective enough”, they often have the same bullet profile as the .38 / 9 mm / 357 rounds, but being less diameter also end up shorter. 1.5 x 6 mm diameter = 9 mm length, not 12mm as desired. So the 20 something caliber (6 mm) gets a reputation of poor penetration. Really what is wrong is the bullet is too short. We see that the .222 Remington and the .223 have much longer bullets. Nobody says they don’t penetrate enough… So to make a decent .25 or .32 caliber round does not need more powder making more bang and flash, so much as it needs a longer pistol bullet to get the sectional density up enough.

Then the question of how much powder to make that bullet move is also pretty easy to find as a rule of thumb. The pressure per unit area of the bullet needs to be the same as those 9mm similar rounds. That takes a similar length of powder charge under each sq. mm of bullet. Again, the cases of the older .25 ACP and .32 ACP are just a little shorter (balanced for their shorter bullets). IF you lengthened the .25 ACP and .32 ACP cases to match the 9mm parabellum, and then put a 12 mm (or so) long bullet on top of that, you would get similar terminal ballistics (though with a narrower hole from the smaller diameter).

It all comes down to performance being a function of absolute length while esthetics had the whole round shrinking in proportion as the diameter shrinks (or historically, getting larger in proportion as newer rounds were invented and things kept getting bigger, until OMG size was reached).

We do find that some of this did happen. The .30 Carbine, for example, is in some ways just a very long .32 ACP and has quite acceptable performance. Certainly much more than the .32 ACP (enough it was used as a battle carbine in W.W.II). In the revolvers, the .32 Short grew to the .32 Long, then the .32 H&R Magnum and now the deceptively named .327 Federal Magnum that’s quite enough round.

Development

Introduced by Federal Cartridge company, the .327 Federal Magnum is an attempt to improve on the .32 H&R Magnum introduced in 1984. Like the .32 H&R, the .327 Federal is a lengthened version of the original .32 S&W cartridge, which dates back to 1878. In 1896, the .32 S&W Long was introduced, which generated slightly higher velocities. The introduction of the .32 H&R increased pressures from 15,000 psi to 21,000 CUP, giving velocities of approximately 1,200 ft/s (370 m/s).[3]

Based on the .32 H&R Magnum, with a 1/8″ longer case, strengthened web at the base of the case, thicker case walls, and different heat-treatment and metallurgy, the .327 Federal can be loaded to much higher pressure levels (45,000 psi (310,000 kPa)) than its predecessor (21,000 CUP). The .327’s actual bullet diameter is .312 in (7.92 mm) and achieves muzzle velocities up to 1,400 ft/s (430 m/s) with 100 gr (6.5 g; 0.23 oz) bullets, and up to 1,300 ft/s (400 m/s) with 115 gr (7.5 g; 0.26 oz) bullets, when fired from the 3 1/16″ (78 mm)-barreled Ruger SP101 revolver.

With its strengthened case and increased pressure ceiling, the .327 Federal reaches the velocity levels of the .357 Magnum, if not the same power. Since the .327 still shares all case dimensions, excluding length, with the .32 S&W,.32 S&W Long, and .32 H&R Magnum, revolvers chambered for the .327 Federal can also safely chamber and fire these shorter cartridges. This makes the .327 Federal unique, as it can fire four different cartridges from the same gun with no modifications.

While felt recoil exceeds that of the .32 H&R, revolvers in .327 Federal are much easier to control than equivalent models chambered in .357 Magnum. Comparing the two calibers, Chuck Hawks says, “There is no doubt that, for most shooters, the .357 Mag. produces uncomfortable recoil and muzzle blast.”

The .327’s recoil energy is 3.08 ft⋅lbf (4.18 J) for an 85 gr (5.5 g; 0.19 oz) jacketed hollowpoint (JHP) load, 5.62 ft⋅lbf (7.62 J) for the 115 gr (7.5 g; 0.26 oz) JHP, and 5.58 ft⋅lbf (7.57 J) for the 100 gr (6.5 g; 0.23 oz) softpoint (SP). For comparison, the figures are 1.46 ft⋅lbf (1.98 J) for an 85 gr (5.5 g; 0.19 oz) .32 H&R Magnum load and 7.22 ft⋅lbf (9.79 J) for a 125 gr (8.1 g; 0.29 oz) .357 Magnum load.

The .32 ACP is loaded with 60 to 73 gr bullets per the wiki, so that 115 gr JHP must be about 115/60 longer as the diameter is the same. Speer has very limited reloading components in .32, but this wad cutter is useful for comparison:

https://www.speer.com/bullets/handgun_bullets/lead_handgun_bullet/19-4600.html

Caliber 	.314
Bullet Weight 	98
Bullet Style 	Lead Wadcutter
Ballistic Coefficient 	.044
Bullet Length In 	0.545in. / 13.84mm
Sectional Density 	0.142
Diameter In 	0.31
Diameter Mm 	7.98

“only” 98 grains but already 13.84 mm long and sectional density of 0.142.

For comparison, their .25 high end Gold Dot protection round:

https://www.speer.com/bullets/handgun_bullets/gold_dot_personal_protection/19-3985.html

Caliber 	.251
Bullet Weight 	35
Bullet Style 	Hollow Point
Type 	Lead
Ballistic Coefficient 	.091
Bullet Length In 	0.355in. / 9.015mm
Sectional Density 	0.079
Diameter In 	0.25
Diameter Mm 	6.38

Only 9 mm long and sectional density down at 0.079

Then the 9mm in the ordinary 115 gr size is:

https://www.speer.com/bullets/handgun_bullets/gold_dot_personal_protection/19-3998.html

Caliber 	.355
Bullet Weight 	124
Bullet Style 	Hollow Point
Type 	Lead
Ballistic Coefficient 	.134
Bullet Length In 	0.560in. / 14.22mm
Sectional Density 	0.141
Diameter In 	0.36
Diameter Mm 	9.02

Where we again see just over 12 mm bullet length at 14.22 mm and a sectional density back up at 0.141.

So at this point I think we’ve got a pretty good demonstration that the “rule of thumb” of a 12 mm bullet length as “enough sectional density” lower bound is probably just about right. You can vary that a little with bullet composition, shape and velocity, but not as effectively as just having the length be right in the first place. Trying to “fix it’ for a too short lead column with ever more powder (so ever more flash / bang and WT?) just is fighting yourself.

Unfortunately, while rifle bullets in .30 – .32 are nice and long, what few pistol bullets there are tend to be short. Especially in the .32 ACP and similar. Then it’s worse in the .25s where lots of long rifle bullets exist but not in pistol loads / guns.

Looking at cases, another surprising things shows up (or maybe not so surprising once thinking in terms of “per mm^2). The case length of the “enough gun” auto loader cartridges tend to a similar lower bound. (I’m skipping the revolver rounds as they were typically designed based on lengthening an old black powder round which was already mostly empty if loaded with modern smokeless powder). I’ve included the .25 ACP and .32 ACP for comparison.

https://en.wikipedia.org/wiki/List_of_handgun_cartridges

Cartridge name Bullet diameter Case length
.25 ACP (.25 Auto Colt Pistol, 6.35mm Browning, .25/6.35mm Auto, 6.35×16mmSR) .251 in (6.4 mm) .620 in (15.7 mm)
.32 ACP (.32 Auto Colt Pistol, 7.65mm Browning, .32/7.65mm Auto, 7.65×17mmSR) .309 in (7.8 mm) .680 in (17.3 mm)
9mm Parabellum (9×19mm Luger, 9mm NATO) .355 in (9.0 mm) .754 in (19.2 mm)
.380 ACP (9×17mm, .380 Auto, 9mm Kurz/Browning Short) .355 in (9.0 mm) .680 in (17.3 mm) .980 in (24.9 mm)
.38 ACP (.38 Auto, 9×23 mmSR) .358 in (9.1 mm) .900 in (22.9 mm)
.38 Super (.38 Super Auto) .356 in (9.0 mm) .900 in (22.9 mm)
.40 S&W (.40 Auto, .40 Short, 10×22mm) .400 in (10.2 mm) .850 in (21.6 mm)
.45 ACP (.45 Automatic/Auto Colt Pistol, 11.43×23 mm) .452 in (11.5 mm) .898 in (22.8 mm)

About 22 mm of case length is all you need, really. The .45 ACP, .40 S&W, .38 Super & Super Auto are all quite competent and about that long. The 9mm is shorter at 19.2 mm, but not by much. Then the “generally agreed minimum” .380 is a bit longer at 25, but not as high pressure.

The “not enough” rounds are 15-17 length. Enough powder for the short bullets, but not enough for a bullet of high enough sectional density.

In Conclusion

So, my conclusion is pretty simple. To make a decent .25 or .32 automatic round, you need a straight case of about 20 mm or up to 22 mm, and then load a bullet of at least 12 mm length (and up to 15 mm if desired). Then adjust the barrel rate of twist for the longer bullet length. (Yes, the amount of twist depends on the length of the bullet to stabilize it).

There are some rounds that address part of this. They do it by making a bottle neck round from a larger one. So the 25 NAA

https://en.wikipedia.org/wiki/.25_NAA

The .25 NAA was introduced by North American Arms company for a smaller and lighter Guardian model. It is based on a .32 ACP case necked down to accept .251″ diameter (.25 ACP) bullets.

The cartridge was originally conceived and prototyped by gunwriter J.B. Wood and called the 25/32 JBW. North American Arms and Cor-Bon Ammunition then further developed the cartridge and the NAA Guardian .25 NAA pistol combination for production in consultation with Ed Sanow. The finalized cartridge and pistol were introduced at the 2004 SHOT Show.

It followed the successful introduction of two other commercial bottleneck handgun cartridges, the .357 SIG in 1994 (which necked a .40 S&W case down to accept .355 cal. bullets); and the .400 Corbon in 1996 (which necked a .45 ACP case down to accept .40 cal. bullets).

So that fixes the case volume needed, but they still have the .25 ACP bullet, so insufficient sectional density. Fine for paper, but more powder in a short barrel works better with a longer heavier bullet and better sectional density. At least on “meat targets”.

Then the .32 NAA does something similar:

https://en.wikipedia.org/wiki/.32_NAA

The .32 NAA is a cartridge/firearm ‘system’ designed and developed by the partnership of North American Arms and Corbon Ammunition. The cartridge is a .380 ACP case necked-down to hold a .32 caliber bullet with the goal of improved ballistic performance over the .32 ACP.

History and Design

Bottleneck handgun cartridge designs experienced early success and have had continuing development since at least the 7.65×25mm Borchardt or earlier, which led to the development of the 7.63×25mm Mauser (also known as the .30 Mauser), followed by the 7.62×25mm Tokarev. The benefits of bottleneck designs include smooth feeding and chambering and simple, robust headspacing.

The .32 NAA uses the .312″ diameter bullet of the .32 S&W, .32 S&W Long, .32 H&R Magnum, and .327 Federal Magnum, and .32 ACP.

The .32 NAA is one of the most recent of a line of commercial bottleneck handgun cartridges. Renewed western interest in bottleneck handgun cartridges began with the .357 SIG in 1994 (necking a .40 S&W case down to a .355 bullet); followed by the .400 Corbon in 1996 (necking a .45 ACP case down to hold a .40 cal. bullet); and then the .25 NAA in 1999 (necking a .32 ACP case down to hold a .25 caliber bullet). 2015 saw the introduction of the 7.5 FK bottleneck cartridge by the Czech company FK BRNO.

So, OK, at least you have a chance of getting a .32 bullet of sufficient length, IF anyone sells that .327 Mag bullet as a component.

Am I going to run right out and try to “Wildcat” a 22 mm case .32 caliber with custom swaged 12 mm bullets? Nope.

I’m satisfied that I can hit what I aim at with the .32 ACP and despite “12 inches of penetration” being the norm for good enough, the typical person is only about 9 inches thick. I’m of the school that says I don’t want a bullet that penetrates the room and exterior wall and then has enough remaining to hurt someone on the street. I LIKE the lower penetration for a pocket gun around the house. That is why the .32 ACP was the gun of choice for police in Europe up until after W.W.II when the caliber escalation began. In W.W.II it was a common officers gun. People’s resistance to being shot has not risen much in one generation…

However, I will be using my two new “rules of thumb” to asses various rounds that I might look at. If, for example, the case is 44 mm long, I’d have to ask “Why?”. Is this some God Awful Magnum with so much flash and bang you can neither see nor hear after shooting it in a semi-dark room? Or if the bullet is only 8 mm long, I’d have to again as “What are you going to shoot at?”. Paper, OK. Hard targets? Uh, no.

22 and 12, easy things to remember.
Allowing a couple of mm each side pretty much covers it.

That same rule of thumb ought to hold for revolver cartridges too, were it not for their history of just being constantly made longer so that new rounds would not fit in old weaker guns. Unfortunately, it looks like just about every possible diameter has been used in revolver rounds, so you can’t just make a new one in an odd caliber and avoid the history problem. (Well you COULD, but there would be no bullets to load into it and it would have to be a really odd caliber, like an 8.5 mm or a 9.5 mm or a .34 caliber…)

So if you want a modern load in a minimum length cartridge in a revolver, you get to buy a revolver that shoots autoloader rounds. I love my Ruger that shoots 9mm. I like the 9mm in it more than either .38 special or .357 magnum. Now I know why too! ;-) It shoots more accurately, with a lot less flash and bang than the .357 loads (those case volumes of expansion) while using less powder (that high efficiency in a small space effect).

At one time I almost bought a Ruger in Stainless in .45 Long Colt / .45 ACP. Unfortunately I didn’t have the $400 ish they wanted for it then, about 30? years ago. Now it’s no longer made in Stainless and prices are much higher. IMHO it would be just about ideal for testing the “enough gun” question of 12 / 22 mm.

Or one could always get a .32 Magnum of some sort and try cutting the brass to 22 mm and then loading some 12 mm+ long bullet into it. A fairly easy “roll your own” wildcat of sorts. That would allow testing the theory that both powder and case volumes of expansion would be about ideal for a “just enough” penetration sized bullet going not-too fast with not-too much flash and bang.

Perhaps someone with more money for toys (and more wildcatting skill) can give it a whirl.

But, for me, I’m going to just accept that a light load 9mm under a 147 grain (subsonic) bullet out of a nice long barrel Ruger Revolver is going to darned near ideal in just about every way. I’ve loaded up something like that myself. Used cast bullets going about 950 fps. It was a good decade ago or so, but I still remember how much I enjoyed shooting them. Now I understand the theory of why…

I’m also going to continue to enjoy the fun shooting qualities of my .22 Short, .25 ACP and .32 ACP “Mouse Guns” even if “penetration” might be lacking in a formal sense. Having a gun at hand matter more than an ideal powerful caliber in that cabinet over there. Shot placement (and skill in aiming) matters more than a lot of flash / bang / and a hole in the neighbors wall. I’m not a cop faced with a half dozen members of a drug gang hopped up on speed and I don’t need “one shot stop” of 99.9%. I need to convince one or two Stupids who thought they could just barge in to instead go away; or buy enough time to reach the 9mm in the drawer. And, knowing “penetration” with a 9mm long bullet will be less, aim for soft spots. I’m OK with that.

And, once the house is sold, IF I really must scratch that itch, the easy path would be to leverage the work of others and just buy the .32 NAA and some reloading dies:

Handguns

The North American Arms Guardian 32 NAA is designed around this cartridge.

Diamondback Firearms offers .32 NAA conversion barrels (2.8″) for their DB380 pistols.

Makarov.com once stocked barrels of two different lengths for converting Makarov pistols to .32 NAA.

Though I’d likely avoid that 2.8 inch barrel. With the added powder volume, you would want about 4 inches to use it well. Might be easier to just get a custom barrel in some other .380 gun. Or just go shoot my Rugar 9mm 8-)

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About E.M.Smith

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
This entry was posted in Emergency Preparation and Risks and tagged , , , . Bookmark the permalink.

4 Responses to Some Thoughts On Bang! Flash! Penetration & Cartridge Length

  1. Steven Fraser says:

    @EM: I have to say, really nice to experience your ‘specs-based’ approach to bullet/gun combinations. Reminds me of discussions years ago about ‘what is the best computer?’ :-)

    Short story: For 4 years, I commuted to Houston weekly for an IT consulting gig. During that period, I took a pistol shooting course, and really liked it. Not too long later, I found a range close to my usual hotel in Houston, and went there every 2 weeks or so. They had an excellent variety of rental pistols from the teeny to the titanic. I tried many of them, and had several favorites.

    One of those favorites was the FN FiveSeveN pistol, 20 rounds in the double stack, with a 28mm cartridge and a 5.7mm (.224 cal,) polymer-tipped round, 40 grain bullet, named the ‘SS197SR Sporting Round’.

    The barrel on the pistol was 4.8″, with muzzle velocity of 1650 fps, and muzzle energy of 242 ft-lbs.

    It was a whale of a lot of fun to shoot, and my hand liked the grip and the stability of the pistol. Rounds were pretty expensive, so did not shoot it often.

  2. Sera says:

    This is a lot of info to process- thank you for doing the research.

  3. E.M.Smith says:

    @Steven Fraser:

    Glad you liked it. Yeah, the high velocity low mass rounds are a lot of fun. Loud though. The 7.62 x 25 Tokarev is like that. But not as efficient nor quiet as the lower velocity stuff.

    @Sera:

    Yeah, I “show my data” and process. But the conclusion is very simple and small.

    To get sufficient penetration and performance for self defence, you need a projectile 12 mm long or longer if lead (or even longer if a lighter material). To make it go fast enough you need a case about 19 to 22 mm long (actual powder height is that, minus head thickness and minus bullet seating depth; but those are similar in middle sized pistol rounds).

    So two “magic numbers”: Bullets 12 mm long or longer. Cases 19 to 22 mm long for optimal comfort and efficiency with enough power. In any caliber!

    Then longer cases (or bottlenose) if you want even faster or more power but at the expense of more noise and flash.

  4. Taz says:

    45ACP is subsonic and easy/cheap to load. It’s projectiles are low tech, and it’s lethality less affected by circumstance or environment. Powders also exist for reduced loads…which are very handy for female shooters. You need to try this powder with your female….her accuracy will surprise.

    http://www.brassfetcher.com/Handguns/45%20ACP/45%20ACP.html

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