by 1290 » 01 Oct 2014, 11:08 am
OK, here's the behind the numbers part,
Recoil energy
The recoil energy is referred to as the 'free' recoil and is the opposite reaction to the discharge of the firearm, it is not dependent on the shape of the stock, the way you hold it... its the absolute energy you will 'feel' when you discharge the firearm neglecting all other countering actions such as friction... so if the rifle is on roller bearings you would feel the whole of this effect.
The energy is derived from the projectile as well as the burning propellant, which is assigned a fixed velocity of 1585m/s representing the deflagration velocity, which is the velocity of the flame front or shockwave of the burning powder.
E(J) = [ (mp.vp + mc.vc) / 1000 ]2 / 2mr
Mass projectile (g) x Velocity (m/s) + Mass powder (g) x Velocity powder (m/s)
divide answer by 1000 (to convert to kg, SI units!)
Square answer (multiply by itself)
Divide answer by 2
Divide answer by rifle mass (kg)
There you will have it, free recoil energy in Joule (J)!
Example;
Projectile mass: 19.44g (300gr)
Projectile velocity: 914.4m/s (3000fps)
Propellant mass: 6.48g (100gr)
Propellant velocity: 1585m/s (5200fps)
Rifle Mass 4.08kg (9lb)
Do the math;
( 19.44 g x 914.4 m/s ) + ( 6.48 g x 1585 m/s ) = 28047
28047 / 1000 = 28.047
28.047 squared = 786.62
786.62 / 2 = 393.31
393.31/4.08 = 96.4
Free recoil energy = 96.4 J for the above example.
Now, many aficionados will be having conniptions about now due to the lack of feet and pounds, so;
IMPERIAL UNITS (foot-pound-force)
Imperially speaking, the calculation is similar to the above, the only differences are the 5200fps charge velocity and the use of the gravitational constant not required with the metric method; 32.174. The unit is a force.
We (Americanized shooters) prefer to input grain units, so pound conversion has to be considered along with the grav constant as well as the 2 divisor so we can clump those constants together to get the following simplest form;
F(ftlb.f) = ( mp.vp + mc.vc )2 / ( mr x 7000 x 2 x G )
[ Mass projectile (gr) x Velocity (fps) + Mass powder (gr) x Velocity powder (fps) ] squared
All divided by
[Rifle mass (lb) x 7000(grains per pound)squared x 2 x 32.174 (grav const.)]
divisor simplified to;
[Rifle mass (lb) x 7000(squared) x 64.348]
inserting the values from the previous example;
(300x3000 + 100x5200 ) / (9 x 7000x7000x64.348)
= 71.1ftlbf
There you will have it, free recoil force in the old units....!
((I'm sure someone will let me know if there are any errors up there^^))