# What is the biggest cartridge caliber that can be fired while standing?

I'm designing three guns here: a two-handed rifle, a two-handed shotgun, and a one-handed handgun. All of them are breechloader guns, so they can only shoot once before reloading.

The goals I want to achieve with these gun designs are:

• The guns should have the biggest cartridge caliber that can be fired while standing.
• The guns should be able to shoot accurately. Well, at least it shouldn't be inferior to a musket in accuracy.
• The guns should have the maximum length of a battle rifle. For the handgun perhaps it should have a length similar to a desert eagle. Because the accuracy over long distances doesn't really matter here.
• The guns should be comfortable enough to be carried by a single soldier in "ready-to-fire" position.
• The guns shouldn't have a pistol grip.
• For the shotgun, it's preferable to have a few big pellets, rather than many small pellets.

The biggest cartridges I know are .950 JDJ and .50 BMG, but I doubt if these cartridges are able to be fired while standing. For the shotgun shells, I don't really know much about them.

So, what is the biggest cartridge for each gun that meets the above criteria?

EDIT: My world era is similar to early Cold War era.

EDIT2: Sorry if I'm not clear enough with my detail or if I can't clarify it further with better word, but basically to harm the enemy of my soldier, we need the most powerful guns to penetrate their armor. That's why, I gave a standard breechloader rifle for the frontline soldier. You know, it's like the more powerful version of assault rifle like AK47 or M16 with breechloading mechanism. For close quarter combat, I gave them the shotgun version. For personal defence, I gave them the handgun version. But all of them have to be powerful enough without hindering the soldier from shooting while standing.

• You can fire any calibre you can lift while standing. The trick is in remaining standing after pulling the trigger. – Separatrix Dec 26 '18 at 20:08
• @Seperatrix: after a certain point doesn’t Newton say it’s more a case of ‘you can be fired by any calibre you can lift’?? – Joe Bloggs Dec 26 '18 at 20:11
• Considering we have handheld 40mm grenade launchers and even rocketlaunchers with truly massive projectiles, it would depend on the point where you say it stops being a shotgun/pistol/battle rifle. It would probably depend on the point where you would need to overhaul the design to handle the recoil and how much you want to cut down on the speed of the projectile on launch. – Demigan Dec 26 '18 at 20:16
• The limiting factor is not caliber per se, but muzzle energy. You can have large projectile, but you will not be able to give enough speed to be lethal without getting knocked over. 40mm grenade launcher mentioned by @ Demigan is an excellent example: projectile is large but too slow to do any real damage from impact alone. To make this specific, find muzzle energy for M-16 (can be fired while standing) and Barrett M107 (you have to lay down), then work the math to determine largest projectile that can maintain decent speed. – Bald Bear Dec 26 '18 at 20:20
• (1) Accuracy not inferior to a musket is a very low hurdle. (2) In what historical period? Black powder guns had humongous calibres; 20 mm was not uncommon in the 30 Years War. There is a trade-off between calibre and muzzle velocity. – AlexP Dec 26 '18 at 20:26

## Use Conservation of Momentum

You've asked for the largest round that can be fired while standing. For this answer, I'd assume that bracing the wrist-arm is irrelevant.

In that case, the conservation of momentum governs. Given an average man is 1.5 meters tall, 100 kilograms in mass, assuming a human reaction time (to recover from the blast) is around half a second, and assuming the gun is fired from about waist level, the amount of momentum that would literally knock the firer off their feet is $$100 kg \times ({1 \over 2} 1.5 meters) \times {1 \over 2} second = 32.5 kg * m/s$$

You have four dimensions of the projectile that you can spread that momentum across when designing the weapon: density, diameter, length, and muzzle velocity.

To pierce skin at low speeds the kinetic energy of the projectile needs to be about $$150 MPa \times 0.5 meter = 75 MJoules = 7,500,000 Joules$$

For a solid brass shell ($$density \approx 8,400 kg/m^3$$)

$${1 \over 2} \rho v^2 = 7,500,000 \therefore v = \sqrt{{7,500,000} \over {{1 \over 2} 8,400}} = 42.25 m/s$$

Now that we know velocity and density, we can compute the mass of a specific round of ammunition (instead of a generic one of TBD volume), and from that the volume.

32.5 kg * m/s, the momentum limit we calculated earlier, can be used to calculate the mass of a solid brass round for the density of brass ($$8,400 kg/m^3$$) and the velocity we calculated to pierce an unprotected piece of leather.

$$m v = 32.5 kg * m/s = m (42.25 m/s) \therefore m = {32.5 \over 42.25} = 0.76 kilograms$$

Knowing the mass and density, you can compute the volume. $$m = \rho V = 0.76 kg = 8,400 kg/m^3 V \therefore V = { 0.76 \over 8,400 } = 0.00009157509158 m^3$$

Given those two, you can compute the max caliber of the round. The lower limit on length is $$length = diameter$$ (a round ball round).

The volume of a spherical round is $$Volume = {4 \over 3} \pi radius^3$$

$$\sqrt[3]{0.00009157509158} \over {4 \over 3} \pi = 0.01$$ meters, or 1 centimeter

Which is radius, not diameter. Double to get diameter of 2 centimeters. Converting that to caliber I'm using this unit converter, which says 0.78 cal

The density of lead is higher (11,200 $$kg/m^3$$), so a lead bullet would be smaller. A longer bullet (so that it could be spin-stabilized) will also be smaller.

# Don't just look at caliber!

The two significant factors are the weight of the projectile(s) and the weight and composition of the propellant charge. Ergonomics also matter, and a heavy weapon helps to compensate for the recoil, until it is too heavy to hold.

• The Desert Eagle comes in a version firing the .50 Action Express.
0.5 inch bullet diameter.
Typically a 300-grain (19 g) bullet.
Around 2,000 joules projectile energy.
• The M82 and M107 sniper rifles fire the .50 BMG.
0.5 inch bullet diameter.
Typically 700 to 800-grain (45 to 52 g) bullet.
Around 20,000 joules projectile energy.

Same caliber, but th rifle fires bullets more than twice as heavy with ten times the energy.

Elephant guns used to fire even larger calibers and heavier bullets than the .50, but the propellant produced less energy. (It is a bit pointless to mention grains or grams of propellant because composition and effectiveness changed over time. 30 grains of modern smokeless powder are different from 30 grains of black powder.)

I guess the .50 Desert Eagle reaches the practical maximum for a handgun. There have been more powerful handguns, either built by a hobbyist for the fun of it or for very-close-range defense against tigers or bears. There have been single-shot handguns firing rifle rounds (smaller caliber than .45 or even 9mm, but heavier bullets and more energy). Also look at howdah pistols.

As far as rifles go, look at the elephant guns I linked above.

Sorry if that isn't as specific as you like, but a few grains of propellant more or less can make a huge difference, and that's possible within the same caliber.

• You can get even more specific. A 12 gauge shotgun is equivalent to 0.729 caliber, and those are regularly fired while standing. I suppose they could even be sawed off and fired one-handed, though I've never tried it myself. (There were even larger gauges used in the 19th century - 4 and even 2 gauge, equal to 1.05 and 1.33 caliber - though I think they were fired from mounts - see "punt gun".) – jamesqf Dec 28 '18 at 6:26
• @jamesqf, you are looking at diameters. It is weight and energy which matter, and also the burn characteristics of the propellant. – o.m. Dec 28 '18 at 11:21
• Yes, I am thinking of diameter, because caliber is just another word for diameter, and that's what the OP asked about. But you're of course correct about propellants, and of course bullets of the same caliber could have different masses. Then there's the whole question of penetration, where you can have bullets designed to spread on impact (like hollowpoints), or ones designed to pierce armor. – jamesqf Dec 28 '18 at 18:05

In addition to the above points, also consider the internal design of the weapons recoil system. For example, simply adding an internal spring or even a padded stock to absorb the rearward force can greatly reduce the amount of energy transferred to the user which would possibly allow for a larger caliber projectile. Drilling holes in the barrel or "porting" is another method although that would reduce muzzle velocity along with range and possibly accuracy. Even something as simple as earplugs could make a difference as part of the "jerk" from firing a weapon is simply the normal but involuntary reaction to a large nearby explosion.

In short, if you throw enough recoil reducing systems into the mix you can fire just about anything at least a few times.

At that point size of the projectile would be more limited by the amount of larger sized ammunition one person could reasonably carry along with the risk of critical failure of the weapon itself due to heat, metal fatigue, etc.

Without knowing more about your requirements, it's impossible to say. How great a range do you need? Is that maximum range or maximum effective range (against, let's say, an individual enemy)? What, exactly, are you trying to kill - people or elephants? Do you need to penetrate armor, and if so, how much?

In general, momentum of the projectile is the limiting factor in determining weapon recoil (not energy), and you can always trade off projectile mass and muzzle velocity. Probably a good estimate of the big/slow bullet tradeoff can be found in the American M79 grenade launcher or its current incarnation, the M203 attachment for the M16/M4. This is a 40 mm weapon with a muzzle velocity of 250 fps. Since it is rifled, it is probably more accurate than a flintlock musket at ranges of 100 meters or so, which was the upper limit on musket effectiveness. While the M79 depends on its explosive charge for "ordinary" effect, getting hit with an inert projectile like that would probably be lethal quite often. Certainly, much smaller rubber bullets used by the British killed a few people.

And I'll testify from personal experience that firing a blooper is no big deal.