Recoil velocity of a gun

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Equation / Last modified by AndrewBudd on 2019/07/19 18:22
AndrewBudd.Recoil velocity of a gun

The Recoil velocity of a gun calculator computes the velocity at which a gun will move in the opposite direction in relation to the projectile that it fired.

This recoil is based on Newton's 3rd Law, for every force there is an equal and opposite force.  In this case the force applied to give the bullet it's velocity leaving the muzzle is directly proportional and opposite to the force propelling the rifle backward from the firing direction.

The same force is applied to the small bullet that is applied to the much more massive rifle.  And the velocity is then proportional to the ratio of the mass of the bullet to the mass of the rifle.

INSTRUCTIONS: Choose units and enter the following:

  1. bullet Weight (`"Wt" _"(bullet)"`):  The mass of the projectile. This is commonly measured in grains.
  2. rifle Weight) (`"Wt" _"(rifle)"`): The mass of the weapon.
  3. velocity (v): The initial velocity of the projectile.

Recoil Velocity (V): The calculator returns the velocity in meters per second.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The recoil velocity of a gun is a simple application of the conservation of momentum where the moment of the bullet going away is equal to the momentum of the gun recoil.  The formula for the recoil of a gun is:

     VG = (VB • Bt)/Gn


General Information

When firing a traditional gun that uses expanding gases to propel a projectile out of a barrel there are many forces being exerted. Recoil, commonly referred to as "kick", is the force exerted back towards the shooter. When the gun is fired a bullet is launched forward at high speed and the opposite reaction causes the comparatively much heavier weapon to move in the opposite direction, generally back towards the shooter, though at a proportionately much slower speed.

It is difficult to accurately calculate this value because there are an enormous number of variables that will have an effect on the outcome in the real world. This calculator assumes the simplest possible approximation and will give you a good idea of the velocity of the recoil and thus a notional force of the recoil on the shoulder. 

Other variables that would affect the calculations include muzzle devices that divert gases to lessen recoil, designs that divert gases to cycle the action, atmospheric conditions, and any number of other small and probably insignificant details.

Also keep in mind that the force is not always going to be exerted in a straight line directly opposite the projectile. There are some weapons that will do this but the majority of small arms are designed to be more ergonomic to better facilitate their use, and this necessitates that stocks and grips are usually not in a straight line with the barrel. Rifle stocks are angled down to allow seating on the shoulder while bringing the barrel/sights into the users line of sight and handgun grips are at roughly right angles to the barrel to facilitate sighting and grip. This angling of stocks and grips  on many firearms causes the weapon to rotate about its center of mass (usually seen as muzzle rise or climb) in addition to moving rearwards, thus lessening the force exerted directly rearwards and also the speed at which it moves rearwards.

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