Muzzle energy

Pellet exiting muzzle, with formula for energy overlaid.

Muzzle energy is the kinetic energy of a bullet as it is expelled from the muzzle of a firearm. It is often used as a rough indication of the destructive potential of a given firearm or load. The heavier the bullet and especially the faster it moves, the higher its muzzle energy and the more damage it will do.

The general formula for the kinetic energy is

E_{k}={\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}

where

v is the velocity of the bullet

m is the mass of the bullet.

A subsonic variant of ammunition that would otherwise be supersonic has its velocity limited to less than the speed of sound, i.e. v is fixed at around 300 metres per second (980 ft/s). For ammunition with this limitation the muzzle energy is variable only with respect to the bullet mass m.

Calculating muzzle energy

In the SI system the above E_k will be in unit joule if the mass, m, is in kilogram, and the speed, v, is in metre per second.
In United States engineering units, particular care must be taken to ensure that consistent units are used.

Mass, m, is usually given in grains and the speed, v, in feet per second but kinetic energy, E_k, is typically given in foot-pound force (abbreviated ft-lbf). Most sporting arms publications within the United States report muzzle energies in foot-pound force. If m is specified in grains and v in feet per second, the following formula can be used, which gives the energy in foot-pound force:

E_{k}={\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}\times \left({\frac {1{\mbox{ ft}}\cdot {\mbox{lbf}}}{7000{\mbox{ gr}}\times 32.1739{\mbox{ ft}}{\mbox{/s}}^{2}}}\right)

When publishing kinetic energy tables for small arms ammunition, an acceleration due to gravity of 32.163 ft/s² rather than the standard of 32.1739 ft/s² is used. The formula therefore becomes

E_{k}={\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}\times \left({\frac {1{\mbox{ ft}}\cdot {\mbox{lbf}}}{7000{\mbox{ gr}}\times 32.163{\mbox{ ft}}{\mbox{/s}}^{2}}}\right)

The bullet energy, remaining energy, down range energy, and impact energy of a projectile may also be calculated using the above formulas.

The first of the two US formulas can be simplified in conformance with US practice to:

             E = (M x V²) ÷ K
                        
where K = 450,435 and is derived from (2 x 32.1739 x 7000),
            M is the weight of the projectile, in grains,
            V is the velocity in feet per second and
            E is the energy in foot pounds.

Typical muzzle energies of common firearms and cartridges

Example muzzle energy levels of different types of firearms
Firearm (except listed air guns)	Caliber	Muzzle energy
Firearm (except listed air guns)	Caliber	ft-lbs	joules
air gun spring	.177	15	20
air gun mag spring	.22	22	30
air gun PCP	.22	30+	40+
pistol	.22LR	117	159
pistol	9 mm	383	519
pistol	.45 ACP	416	564
pistol	.357 Magnum	640	873
pistol	10mm	775	1,057
rifle	5.56×45 mm	1,325	1,796
rifle	7.62×39 mm	1,527	2,070
rifle	7.62 × 51 mm	2,802	3,799
rifle	.338 Lapua Magnum	4,893	6,634
heavy	.50 BMG	11,091	15,037
heavy	14.5 × 114 mm	23,744	32,000

Average muzzle energies for common pistol cartridges
Cartridge	Muzzle energy
Cartridge	ft-lbf	joules
.380 ACP	199	270
.38 Special	310	420
9 mm Luger	350	470
.45 Colt	370	500
.45 GAP	400	540
.45 ACP	400	540
.40 S&W	425	576
.357 Sig	475	644
.357 Mag	550	750
10mm Auto	650	880
.41 Mag	910	1,230
.44 Mag	1,000	1,400
.50 AE	1,500	2,000
.454 Casull	1,900	2,600
.460 SW	2,400	3,300
.500 SW	2,600	3,500

It must be stressed that muzzle energy is dependent upon the factors previously listed and that even velocity is highly variable depending upon the length of the barrel a projectile is fired from.^[1] Also note that the muzzle energy is only an upper limit for how much energy is transmitted to the target and that the effects of a ballistic trauma depend on several other factors as well. While the above list mentions some averages, there is wide variation in commercial ammunition. A 180 grain bullet fired from .357 magnum handgun can achieve a muzzle energy of 580 foot-pounds. A 110 grain bullet fired from the same gun might only achieve 400 foot-pounds of muzzle energy, depending upon the manufacture of the cartridge. Some .45 Colt ammunition can produce 1,200 foot-pounds of muzzle energy, far in excess of the average listed above.

Legal requirements on muzzle energy

Some jurisdictions stipulate minimum muzzle energies for hunting. For example, in Denmark rifle ammunition used for hunting the largest types of game there such as red deer must 100 m down range have a kinetic energy E₁₀₀ of at least 2700 J and a bullet mass of at least 9 g or alternatively an E₁₀₀ of at least 2000 J and a bullet mass of at least 10 g.^[2] Namibia specifies three levels of minimum muzzle energy for hunting, 1350 J for game such as springbuck, 2700 J for game such as hartebeest and 5400 J for big game, together with a minimum caliber of 7 mm.^[3]

In Germany airsoft guns with a muzzle energy of no more than 0.5 J are exempt from the gun law,^[4] while air guns with a muzzle energy of no more than 7.5 J may be acquired without a firearms license.^[5]

Resources

Edward F. Obert, Thermodynamics, McGraw-Hill Book Co., 1948.
Mc Graw-Hill encyclopedia of Science and Technology, volume ebe-eye and ice-lev, 9th Edition, Mc Graw-Hill, 2002.

References

↑ "BBTI - Ballistics by the Inch - Home". ballisticsbytheinch.com.
↑ "Bekendtgørelse om skydevåben og ammunition, der må anvendes til jagt m.v." [Hunting weapons and ammunition act]. retsinformation.dk (in Danish). Miljøministeriet. 2012-12-17. Ammunition. Retrieved 2015-03-10.
↑ "NAPHA - Namibia Professional Hunting Assiation: Hunting Laws& Rifle Importation". napha-namibia.com. Retrieved 5 July 2015.
↑ "Ab welcher Geschossenergie fallen Soft-Air-Waffen unter das Waffengesetz?" [From which muzzle energy does Airsoft guns fall under the gun law?]. www.bmi.bund.de (in German). Retrieved 2015-09-17.
↑ "Waffengesetz (WaffG)" [gun law]. gesetze-im-internet.de (in German). Retrieved 2015-09-19.

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