Free recoil
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This article is about the energy produced by small arms when discharged. For other uses, go to Recoil (disambiguation)
Free recoil is a vernacular term or jargon for recoil energy. Free recoil denotes the transitional kinetic energy (Et) imparted to the shooter of a small arm when discharged and is expressed in joule (J) [foot-pound force (ft • lbf) in non-SI units of measure].
Free recoil should not be confused with recoil. Free recoil is the given name for the transitional 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 every day event.
Free recoil sometimes called recoil energy is a by product 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. The result is that the chemical energy held within the powder charge is converted to thermodynamic energy. This energy is then transferred to the base of the bullet and to the rear of the cartridge or breech. Then the firearm is propelled rearward into the shooter and the projectile propelled forward down the barrel; increasing in velocity to the muzzle.
The energy of the rearward 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 to gross recoil energy. Trying to figure the net recoil energy of a firearm is a futile endeavor. Even if you can calculate the recoil energy loss due to a: muzzle break; 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 lever 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.
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[edit] 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 transitional kinetic energy equation. The momentum long form is the most commonly used method for calculating free recoil.
- Substitution method: Etgu = Etp • mp / mgu • 1000
- Momentum short form: Etgu = .5 • [{( mp • vp) + ( mc • vc)} / 1000]2 / (mgu)
- Momentum long form: vgu = mp • vp / mgu • 1000 → Etgu = .5 • mgu • vgu2
Where as:
Etgu is the transitional kinetic energy of the small arm as expressed by the joule (J).
Etp is the transitional kinetic energy of the projectile.
mgu is the weight of the small arm expressed in kilograms (kg).
mp is the weight of the projectile expressed in grams (kg).
mc is the weight of the powder charge expressed in grams (kg).
vgu is the velocity of the small arm expressed in meters per second (m / s).
vp is the velocity of the projectile expressed in meters per second (m / s).
vc 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.
[edit] Calculating Free Recoil using non-SI Units
Fron the momentum long form:
- Momentum long form: vgu = mp • vp / mgu • 7000 → Etgu = mgu • vgu2 / 2 x gc x 7000
Where as:
Etgu is the transitional kinetic energy of the small arm as expressed by the foot-pound force (ft x lbf).
mgu is the weight of the small arm expressed in pounds (lbs).
mp is the weight of the projectile expressed in grains (gr).
mc is the weight of the powder charge expressed in grains (gr).
vgu is the velocity of the small arm expressed in feet per second (ft / s).
vp is the velocity of the projectile expressed in feet per second (ft / s).
vc is the velocity of the powder charge expressed in feet per second (ft / s).
gc is the dimensional constant and is the numeral coefficient of 32.1739
7000 is the conversion factor to set the equation equal to pounds.
[edit] An Example of a Calculation
Small arm: Mauser 98 chambered in 7 x 57 mm weighing 4.54kilograms (10pounds).
Projectile: spitzer type weighing 9.1grams (140grains) with a muzzle velocity of 823 meter per second (2700 feet per second).
Powder charge: single base nitrocellulose weighing 2.75grams (42.5grains) with a powder carge velocity of 1585 meters per second (5200 feet per second).
The momentum short form:
Etgu = .5 • [{( mp • vp) + ( mc • vc)} / 1000]2 / (mgu)
Etgu = .5 • [{( 9.1g • 823m/s) + ( 3.63g • 1585m/s)}/1000]2 / 4.54kg =
Etgu = .5 • [{(7489.3) + ( 5753.55)}/1000]2 / 4.54kg =
Etgu = .5 • [{13242.85} / 1000]2 / 4.54kg =
Etgu = .5 • [13.243]2 / 4.54kg =
Etgu = .5 • 175.377 / 4.54kg =
Etgu = 85.6885 / 4.54kg =
Etgu = 19.14 or
19.14J of Free recoil
- For non-SI units of measure of energy see Foot-pound force. The conversion is: 1J = .737 562 ft • lbf (exactly)
[edit] Calculated Free Recoil for Small Arms
- The following free recoil energy table dose not take into consideration: recoil suppression devices or loss of energy due to auto loading mechanism.
- English units of measure are enclosed in parenthesis. Some of the units of measure are from the cgs system, which is customarily used in place of the larger SI units of measure.
[edit] Pistols and Shotguns
| Firearm mass | Cartridge and Projectile mass | Velocity-m/s (ft/s) | Powder Charge mass | Free recoil | |
|---|---|---|---|---|---|
| J | (ft • lbf) | ||||
| Glock 17/ 905g (31oz) | 9mm Luger/8.0g (124gr) | 374 (1228) | 0.39g (6.1gr) | 7.7 | 5.7 |
| Glock 20/ 1110g (39oz) | 10mm Auto/11.7g (180gr) | 338 (1110) | 0.5g (7.7gr) | 10.3 | 7.6 |
| Dan Wesson VH7/ 1390g (49oz) | .357 Magnum/9.7g (150gr) | 457 (1500) | 1.0g (15.5gr) | 14 | 10.3 |
| Smith and Wesson M29/ 1390g (49oz) | .44 Magnum/15.6g (240gr) | 457 (1500) | 1.6g (24gr) | 34 | 25 |
| Springfield Armory 1911A1/ 1110g (39oz) | .45ACP/14.9g (230gr) | 259 (850) | 0.47g (7.2gr) | 9.8 | 7.2 |
| Remington SP10/ 5.0kg (11lb) | 10 gauge/64g (2¼oz) | 381 (1250) | 3.0g (47gr) | 87 | 64 |
| Benelli Egale II/ 3.3kg (7.2lb) | 12 gauge/32g (1⅛oz) | 366 (1200) | 1.3g (19.5gr) | 30 | 22 |
| AYA No.1/ 3.0kg (6.7lb) | 16 gauge/28g 1oz) | 372 (1220) | 1.7g (26.5gr) | 33 | 24 |
| Beretta 686/ 2.9kg (6.5lb) | 20 gauge/25g (⅞oz) | 372 (1220) | 1.5g (23gr) | 18.4 | 13.6 |
| Beretta 686/ 2.8kg (6.2lb) | 28 gauge/21g (¾oz) | 366 (1200) | 1.51 (17.5gr) | 16.7 | 12.3 |
| Remington 870/ 2.7kg (6.0lb) | .410 gauge/14g (½oz) | 366 (1200) | 0.9g (14gr) | 8.0 | 5.9 |
[edit] Rifles
| Firearm mass | Cartridge and Projectile mass | Velocity-m/s (ft/s) | Powder Charge mass | Free recoil | |
|---|---|---|---|---|---|
| J | (ft • lbf) | ||||
| M16 rifle/ 2.9kg (6.4lb) | 5.56 x 45mm NATO/2.6g (55gr) | 985 (3231) | 1.6g (25.3gr) | 6.4 | 4.7 |
| RemingtonM700/ 3.6kg (8lb) | .223 Remington/2.6g (55gr) | 985 (3231) | 1.6g (25.3gr) | 5.0 | 3.7 |
| Mauser/ 4.1kg (9lb) | 6.5 x 55 mm Swedish Mauser/9.1g (140gr) | 800 (2626) | 3.0g (47gr) | 17.9 | 13.2 |
| CZ550FS/ 4.1kg (9lb) | 7 x 57 mm Mauser/9.1g (140gr) | 792 (2596) | 7.8g (42.5gr) | 16.5 | 12.2 |
| Marlin Model 1894/ 2.9kg (6.5lb) | .30-30 Winchester/11g (170gr) | 617 (2025) | 2.0g (31gr) | 17 | 12.5 |
| M14 rifle/ 4.5kg (9.9lb) | 7.62 x 51 mm NATO/10.1g (156gr) | 845 (2771) | 3.1g (48gr) | 20 | 14.9 |
| RemingtonSendero/ 4.5kg (10lb) | .308 Winchester/10.1g (156gr) | 845 (2771) | 3.1g (48gr) | 20 | 14.8 |
| Marlin Model 1894/ 2.9kg (6.5lb) | .32 H&R Magnum/11g (95gr) | 274 (900) | 2.0g (8.2gr) | 1.12 | 0.84 |
| Mauser/ 4.1kg (9lb) | 8 x 68 mm S/14.3g (220gr) | 847 (2780) | 4.5g (70gr) | 46 | 34 |
| RemingtonM700/ 4.5kg (10lb) | .338 Lapua Magnum/16.2g (250gr) | 891 (2922) | 1.6g (25.3gr) | 71 | 52 |
| RemingtonM700/ 4.5kg (10lb) | 9.3 x 62 mm Mauser/18.5g (285gr) | 710 (2330) | 1.6g (25.3gr) | 5.0 | 3.7 |
| Shilo Sharps 1874/ 5.4kg (12lb) | Government .45-70/25.9g (400gr) | 543 (1783) | 3.6g (56gr) | 56 | 41 |
| Weatherby Mark V/ 4.6kg (10lb) | .460 Weatherby Magnum/32.4g (500gr) | 762 (2500) | 8.1g (125gr) | 156 | 115 |
| A-Square Hannibal/ 5.4kg (12lb) | .500 A-Square/38.9g (600gr) | 762 (2500) | 7.3g (113gr) | 156 | 115 |
| M82 Barrett rifle/ 14kg (31lb) | .50BMG/41.9g (647gr) | 902 (2960) | 15.2g (235gr) | 127 | 94 |
| A-Square Hannibal/ 6.8kg (15lb) | .577 Tyannosaur/48.6g (750gr) | 753 (2470) | 10.4g (160gr) | 206 | 152 |
[edit] Black Powder
| Firearm mass | Cartridge and Projectile mass | Velocity-m/s (ft/s) | Powder Charge mass | Free recoil | |
|---|---|---|---|---|---|
| J | (ft • lbf) | ||||
| Shilo Sharps 1874/5.4kg (12lb) | Government .45-70/27.2g PP (420gr PP) | 428 (1403) | 4.9g (75gr) | 17.9 | 13.2 |
[edit] Also see
See physics of firearms for a more detailed discussion.
[edit] 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.
Mc Graw-Hill encyclopedia of Science and Technology, volume ice-lev, 9th Edition, Mc Graw-Hill, 2002.
