Free recoil

Free recoil is a vernacular term or jargon for recoil energy. Free recoil denotes the translational kinetic energy (E_t) imparted to the shooter of a small arm when discharged and is expressed in joule (J) and foot-pound force (ft·lb_f) for non-SI units of measure.

Free recoil should not be confused with recoil. Free recoil is the given name for the translational kinetic energy transmitted from a small arm to a shooter. Recoil is a name given for conservation of momentum as it generally applies to an everyday event.

Free recoil, sometimes called recoil energy, is a byproduct of the propulsive force from the powder charge held within a firearm chamber (metallic cartridge firearm) or breech (black powder firearm). The physical event of free recoil occurs when a powder charge is detonated within a firearm, resulting in the conversion of chemical energy held within the powder charge into thermodynamic energy. This energy is then transferred to the base of the bullet and to the rear of the cartridge or breech, propelling the firearm rearward into the shooter while the projectile is propelled forward down the barrel, with increasing velocity, to the muzzle. The rearward energy of the firearm can be calculated and is called free recoil, the energy of the bullet can be calculated and is called muzzle energy.

The concept of free recoil comes from the tolerability of gross recoil energy. Trying to figure the net recoil energy of a firearm (also known as felt recoil) is a futile endeavor. Even if you can calculate the recoil energy loss due to a: muzzle brake; recoil operated action; gas operated action; mercury recoil suppression tube; recoil reducing butt pad and hand grip; shooting vest and gloves, the human factor is not calculable. Therefore free recoil stands as a scientific measurement of recoil energy, just as the room or outside temperature is measured. The comfort level of a shooter’s ability to tolerate free recoil is a personal perception. Just as it is a person's, personal perception of a comfort level to a specific room or outside temperature.

There are many factors that determine how a shooter will perceive the free recoil of his or her small arm. Some of the factors are but not limited to: body mass; body frame; experience; shooting position; recoil suppression equipment; small arm fit and or environmental stressors.

Calculating free recoil

There are several different ways to calculate free recoil. The substitution method will yield an approximation of the free recoil of a small arm. The momentum short form will yield the exact free recoil of a small arm. The momentum long form will yield the velocity of the recoiling small arm. With the velocity known for the small arm, the free recoil of the small can be calculated using the translational kinetic energy equation. The momentum long form is the most commonly used method for calculating free recoil.

• Substitution method: E_tgu = E_tp • m_p / m_gu • 1000
• Momentum short form: E_tgu = 0.5 • [{(m_p • v_p) + ( m_c • v_c)} / 1000]² / (m_gu)
• Momentum long form: v_gu = {(m_p • v_p) + ( m_c • v_c)} / m_gu • 1000 → E_tgu = 0.5 • m_gu • v_gu²

Where as:

E_tgu is the translational kinetic energy of the small arm as expressed by the joule (J).

E_tp is the translational kinetic energy of the projectile.

m_gu is the weight of the small arm expressed in kilograms (kg).

m_p is the weight of the projectile expressed in grams (g).

m_c is the weight of the powder charge expressed in grams (g).

v_gu is the velocity of the small arm expressed in meters per second (m/s).

v_p is the velocity of the projectile expressed in meters per second (m/s).

v_c is the velocity of the powder charge expressed in meters per second (m/s).

1000 is the conversion factor to set the equation equal to kilograms.

Calculating free Recoil using non-SI units

Fron the momentum long form:

• Momentum long form: v_gu = {(m_p • v_p) + ( m_c • v_c)} / m_gu • 7000 → E_tgu = m_gu • v_gu² / 2 • g_c

Where as:

E_tgu is the translational kinetic energy of the small arm as expressed by the foot-pound force (ft·lb_f).

m_gu is the weight of the small arm expressed in pounds (lb).

m_p is the weight of the projectile expressed in grains (gr).

m_c is the weight of the powder charge expressed in grains (gr).

v_gu is the velocity of the small arm expressed in feet per second (ft/s).

v_p is the velocity of the projectile expressed in feet per second (ft/s).

v_c is the velocity of the powder charge expressed in feet per second (ft/s).

g_c is the dimensional constant and is the numeral coefficient of 32.1739

7000 is the conversion factor to set the equation equal to pounds.

An example of a calculation

Small arm: Mauser 98 chambered in 7 x 57 mm weighing 4.54 kilograms (10 pounds).

Projectile: spitzer type weighing 9.1 grams (140 grains) with a muzzle velocity of 823 meters per second (2700 feet per second).

Powder charge: single base nitrocellulose weighing 2.75 grams (42.5 grains) with a powder charge velocity of 1585 meters per second (5200 feet per second).

The momentum short form:

E_tgu = 0.5 · [{(m_p · v_p) + (m_c · v_c)} / 1000]² / (m_gu)

E_tgu = 0.5 · [{(9.1 g · 823 m/s) + (3.63 g · 1585 m/s)} / 1000]² / 4.54 kg =

E_tgu = 0.5 · [{(7489.3) + ( 5753.55)} / 1000]² / 4.54 kg =

E_tgu = 0.5 · [{13242.85}/1000]²/ 4.54 kg =

E_tgu = 0.5 · [13.243]² / 4.54 kg =

E_tgu = 0.5 · 175.377 / 4.54 kg =

E_tgu = 85.6885 / 4.54 kg =

E_tgu = 19.14 J of free recoil

• For non-SI units of measure of energy see Foot-pound force. The conversion is: 1 J = 0.737 562 ft·lb_f

Calculated free recoil for small arms

• The following free recoil energy table does not take into consideration: recoil suppression devices or loss of energy due to auto loading mechanism.
• English units of measure are enclosed in parentheses.

Pistols and shotguns

Firearm mass-kg (lb)	Cartridge and projectile mass-g (gr)	Velocity-m/s (ft/s)	Powder Charge mass-g (gr)	Free recoil
				J	(ft·lbf)
Glock 17/ 905 g (31 oz)	9 mm Luger/8.0 (124)	374 (1228)	0.39 (6.1)	7.7	5.7
Glock 20/ 1110 g (39 oz)	10 mm Auto/11.7 (180)	338 (1110)	0.5 (7.7)	10.3	7.6
Dan Wesson VH7/ 1390 g (49 oz)	.357 Magnum/9.7 (150)	457 (1500)	1.0 (15.5)	14	10.3
Smith and Wesson M29/ 1390 g (49 oz)	.44 Magnum/15.6 (240)	457 (1500)	1.6 (24)	34	25
Springfield Armory 1911A1/ 1110 g (39 oz)	.45ACP/14.9 (230)	259 (850)	0.47 (7.2)	9.8	7.2
Remington SP10/ 5.0 (11)	10 gauge/64 (2¼ oz)	381 (1250)	3.0 (47)	87	64
Benelli Egale II/ 3.3 (7.2)	12 gauge/32 (1⅛ oz)	366 (1200)	1.3 (19.5)	30	22
AYA No.1/ 3.0 (6.7)	16 gauge/28 (1 oz)	372 (1220)	1.7 (26.5)	33	24
Beretta 686/ 2.9 (6.5)	20 gauge/25 (⅞ oz)	372 (1220)	1.5 (23)	18.4	13.6
Beretta 686/ 2.8 (6.2)	28 gauge/21 (¾ oz)	366 (1200)	1.1 (17.5)	16.7	12.3
Remington 870/ 2.7 (6.0)	.410 gauge/14 (½ oz)	366 (1200)	0.9 (14)	8.0	5.9

Rifles

Firearm mass kg (lb)	Cartridge and Projectile mass g (gr)	Velocity m/s (ft/s)	Powder charge g (gr)	Free recoil
				J	(ft·lbf)
M16 rifle/ 2.9 (6.4)	5.56 x 45 mm NATO/2.6 (55)	985 (3231)	1.6 (25.3)	6.4	4.7
RemingtonM700/ 3.6 (8)	.223 Remington/2.6 (55)	985 (3231)	1.6 (25.3)	5.0	3.7
Mauser/ 4.1 (9)	6.5 x 55 mm Swedish Mauser/9.1 (140)	800 (2626)	3.0 (47)	17.9	13.2
CZ550FS/ 4.1 (9)	7 x 57 mm Mauser/9.1 (140)	792 (2596)	7.8 (42.5)	16.5	12.2
Marlin Model 1894/ 2.9 (6.5)	.30-30 Winchester/11 (170)	617 (2025)	2.0 (31)	17	12.5
M14 rifle/ 4.5 (9.9)	7.62 x 51 mm NATO/10.1 (156)	845 (2771)	3.1 (48)	20	14.9
RemingtonSendero/ 4.5 (10)	.308 Winchester/10.1 (156)	845 (2771)	3.1 (48)	20	14.8
Marlin Model 1894/ 2.9 (6.5)	.32 H&R Magnum/11 (95)	274 (900)	2.0 (8.2)	1.12	0.84
Mauser/ 4.1 (9)	8 x 68 S/14.3 (220)	847 (2780)	4.5 (70)	46	34
RemingtonM700/ 4.5 (10)	9.3 x 62 mm Mauser/18.5 (285)	710 (2330)	1.6 (25.3)	5.0	3.7
Shilo Sharps 1874/ 5.4 (12)	.45-70 Government/25.9 (400)	543 (1783)	3.6 (56)	56	41
Weatherby Mark V/ 4.6 (10.1)	.460 Weatherby Magnum/32.4 (500)	762 (2500)	8.1 (125)	156	115
A-Square Hannibal/ 5.4 (12)	.500 A-Square/38.9 (600)	762 (2500)	7.3 (113)	156	115
M82 Barrett rifle/ 14 (31)	.50BMG/41.9 (647)	902 (2960)	15.2 (235)	127	97
A-Square Hannibal/ 6.8 (15)	.577 Tyrannosaur/48.6 (750)	753 (2470)	10.4 (160)	206	152

Black powder

Firearm mass-kg (lb)	Cartridge and projectile mass-g (gr)	Velocity-m/s (ft/s)	Powder charge mass-g (gr)	Free recoil
				J	(ft·lbf)
Shilo Sharps 1874/5.4 (12)	Government .45-70/27.2 PP (420 PP)	428 (1403)	4.9 (75)	17.9	13.2

See also

• Muzzle energy
• Recoil

See physics of firearms for a more detailed discussion.

Resources

• Arthur B. Alphin, Any Shot You Want, The A-Square Handloading and Rifle Manual, On Target Press, 1996.
• Edward F. Obert, Thermodynamics, McGraw-Hill Book Co., 1948.
• McGraw-Hill Encyclopedia of Science and Technology, volume ice-lev, 9th Edition, Mc Graw-Hill, 2002.