The most rifle cartridge in the US today is the 22lr a round that first appeared in 1887. It is suitable to small game hunting and while it is less–deadly than larger calibers, data suggests it is effective for personal protection. It is also remarkably low cost. This is because the cartridge in almost entirely empty as shown in the figure at right. It is also incredibly energy efficient, that is to say, it’s incredibly good at transforming heat energy of the powder into mechanical energy in the bullet.
The normal weight of a 22lr is 40 grains, or 2.6 grams; a grain is the weight of a barley grain 1/15.4 gram. Virtually every brand of 22lr will send its bullet at about the speed of sound, 1200 ft/second, with a kinetic energy of about 120 foot pounds, or 162 Joules. This is about twice the energy of a hunting bow, and it will go through a deer. Think of a spike driven by a 120 lb hammer dropped from one foot. That’s the bullet from a typical 22lr.
The Hodgdon power company is the largest reseller of smokeless powder in the US with products from all major manufacturers, with products selling for an average of $30/lb or .43¢ per grain. The CCI Mini-Mag, shown above, uses 0.8 grains of some powder 0.052 grams, or about 1/3¢ worth, assuming that CCI bought from Hodgdon rather than directly from the manufacturer. You will notice that the energies of the powders hardly varies from type to type, from a low of 3545 J/gram to a high of 4060 J/gram. While I don’t know which powder is used, I will assume CCI uses a high-energy propellant, 4000 J/gram. I now calculate that the heat energy available as 0.052*4000 = 208 Joules. To calculate the efficiency, divide the kinetic energy of the bullet by the 208 Joules. The 40 grain CCI MiniMag bullet has been clocked at 1224 feet per second indicating 130 foot pounds of kinetic energy, or 176 J. Divide by the thermal energy and you find a 85% efficiency: 176J/ 208 J = 85%. That’s far better than your car engine. If the powder were weaker, the efficiency would have to be higher.
I will now calculate the pressure of the gas behind a 22lr. I note that the force on the bullet is equal to the pressure times the cross-sectional area of the barrel. Since energy equals force times distance, we can expect that the kinetic energy gained per inch of barrel equals this force times this distance (1 inch). Because of friction this is an under-estimate of the pressure, but based on the high efficiency, 85%, it’s clear that the pressure can be no more than 15% higher than I will calculate. As it happens, the maximum allowable pressure for 22lr cartridges is set by law at 24,000 psi. When I calculate the actual pressure (below) I find it is about half this maximum.
The change in kinetic energy per inch of barrel is calculated as the change in 1/2 mv2, where m is the mass of the bullet and v is the velocity. There is a web-site with bullet velocity information for many brands of ammunition, “ballistics by the inch”. Data is available for many brands of bullet shot from gun barrels that they cut shorter inch by inch; data for several 22lr are shown here. For the 40 grain CCI MiniMag, they find a velocity of 862 ft/second for 2″ barrel, 965 ft/second for a 3″ barrel, 1043 ft/second for a 4″ barrel, etc. The cross-section area of the barrel is 0.0038 square inches.
Based on change in kinetic energy, the average pressure in the first two inches of barrel must be 10,845 psi, 5,485 psi in the next inch, and 4,565 psi in the next inch, etc. If I add a 15% correction for friction, I find that the highest pressure is still only half the maximum pressure allowable. Strain gauge deformation data (here) gives a slightly lower value. It appears to me that, by adding more propellant, one could make a legal, higher-performance version of the 22lr — one with perhaps twice the kinetic energy. Given the 1/3¢ cost of powder relative to the 5 to 20¢ price of ammo, I suspect that making a higher power 22lr would be a success.
Robert Buxbaum, March 18, 2021. About 10% of Michigan hunts dear every year during hunting season. Another 20%, as best I can tell own guns for target shooting or personal protection. Just about every lawyer I know carries a gun. They’re afraid people don’t like them. I’m afraid they’re right.
I get about half the efficiency you do in your calculation. I think the powder measure is optimistic, most 22lr powder charges are 1.5 to 2.1 grains. I just measured a CCI 36 grain HP which is rated at 1260 fps, and I got 1.5 grains of powder on my Dillon Precision scale. That gives me an efficiency of 43% assuming 4000 J/g energy content. That is still good, higher than all necked cartridges I’ve calculated. Most rifles are around 28%, the losses tend to increase with projectile speed. For example, a 125 grain 30-06 is only about 23% efficient, and a 124 grain 9mm Speer is 40%. Apples and oranges comparison, but interesting.
A couple of minor items:
Chamber pressure isn’t set by law. It’s suggested by SAAMI – Sporting Arms and Ammunition Manufacturers’ Institute – https://saami.org/ – but no one with anything to lose is going to ignore the SAAMI tables.
One of the issues the SAAMI specs deals with is older firearms using modern chamberings and the classic example is the .357 Magnum.
In fact, it’s just a .38 Special (not quite *just*, additional thickness was add to case head) that’s been lengthened enough to make it impossible to chamber in a .38 Special revolver some of which date back to the days of black powder and rather poorer quality metals.
As nitro-based propellants (powders) developed it was clear they could produce levels of performance impossible to achieve with black powder but reachable only with higher chamber pressures. Chamber pressures that would disassemble a black powder revolver. The simple solution was to lengthen the case so the rounds couldn’t be loaded into older revolvers.
As a result .38 Special rounds can be used in a .357 revolver with acceptable results but you can’t close the cylinder on a .38 Special revolver into which you’ve tried to load .357 Magnum rounds.
With regard to higher-performance .22 rimfire rounds that happened about 60 years ago with the introduction of the .22 Winchester Magnum Rimfire but it follows the same path as the .357 Magnum – lengthen the case so the round can’t be loaded into a firearm built for the .22 Long Rifle.
More recently there’s been a surge of interest in both small bore rimfires and centerfires with the .17 HMR being perhaps the best known. These are all sporting rounds. For self-defense the .22 WMR is quite well thought of due to its high velocity.
True, SAAMI sets the limit. The point of it was that the actual pressures are only about half the SAAMI limit. There is space in the casing for more powder, and room in the SAAMI pressure limit. It looks like an opportunity, IMHO.