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Looking at Cartridge Efficiency
The .22/243 Win. wildcat is fast and flat. The .358 Winchester is more at home in the deep woods where its heavy bullet is more than a match for deer and black bears. They are both based on the .308 Winchester case. Which is more efficient?
There are a lot of opinions regarding what makes a cartridge efficient, or at least more efficient than others. Arguments on this topic are often based more on the merits of a pet cartridge rather than establishing some type of guideline and looking at the question empirically. The main problem lies in defining efficiency as it relates to cartridges.
This definition comes from Wikipedia and seems to fill the bill nicely: “In general, efficiency is a measurable concept, quantitatively determined by the ratio of output to input.” So, if we take the number of grains of powder as the input in our equation, the output is the bullet’s energy as it leaves the muzzle. Dividing muzzle energy by the number of grains of powder it took to generate that energy should give a useful measurement for comparing cartridges for efficiency. The first step is to calculate the muzzle energy.
Muzzle energy Formula:
Bullet Velocity X Bullet Velocity X Bullet Weight in Grains/450240 = Foot-Pounds of Energy
Using a .45 ACP as an example, its 230 grain bullet at 850 feet-per-second has a muzzle energy of 369 foot-pounds of energy.
850 X 850 = 722,500
722,500 X 230 = 166,175,000
166,175,000 / 450240 = 369.08 ft-lbs
Don’t let the math scare you. This job can easily be done by any of the muzzle energy calculators available online. The math above is just the formula that drives them.
The next step for measuring cartridge efficiency is to look at how many grains of powder were used to achieve that level of energy. The formula here is:
Muzzle Energy of a Given Load / Grains of Powder Used = Energy per Grain of Powder
Using the .45 ACP again as an example, the process begins with its 369 ft-lbs of muzzle energy:
369 / 5.7 (the powder charge weight in grains) = 64.7 foot-pounds per grain of powder
Using a standard based on energy per grain of powder now gives us a place to begin looking at cartridge efficiency. It is not easy to access what are the most efficient cartridges, so we should begin our quest at the other side of the spectrum. Let’s look at a very inefficient cartridge, P.O. Ackley’s .22 Eargesplitten Loudenboomer.
According to Wikipedia, the .22 Eargesplitten Loudenboomer was intended to propel a 50 grain .224 caliber bullet in excess of 5000 feet-per-second. To do this, Ackley necked a .378 Weatherby Magnum case down to .22 caliber and filled it with 105 grains of H570. This monster overbore managed to achieve 4600 f.p.s. Let’s try our efficiency math:
4600 X 4600 X 50 / 450240 = 2349.9 ft-lbs
2349.9 / 105 = 22.38 ft-lbs per grain of powder
Now let’s compare the Loudenboomer to a cartridge that uses a larger bullet at a much lower velocity and using less powder. The .300 AAC Blackout is a pretty good example, with its large bullets and small case capacity. A good load for this cartridge uses 21.4 grains of Accurate 1680 and a 150 grain Matchking Bullet at about 2010 f.p.s. from a 16″ barreled upper.
2010 X 2010 X 150 / 450240 = 1346 ft-lbs
1346 / 21.4 = 62.9 ft-lbs per grain of powder
Using this method, the cartridge that develops the highest energy with the fewest grains of powder is the more efficient. Here are a few popular cartridges measured for efficiency:
.22-.243 Winchester 52 gr. Match 51.5 gr. Magpro 3800 fps 32 ft-lbs per grain
.243 Winchester 100gr BTSP 49.0 gr. Big Game 2980 fps 50 ft-lbs per grain
.308 Winchester 150 gr SST 41.3 gr. A2200 2887 fps 67 ft-lbs per grain
.358 Winchester 250 gr Sierra 48 gr. A2520 2390 fps 66 ft-lbs per grain