# Physics of Rifle Recoil

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Recoil, commonly referred to as "kick," occurs as a result of Physical properties at work. However, it is often undesirable because it can be uncomfortable for the shooter and can reduce accuracy. The purpose of this webpage is to discuss the physics involved with rifle recoil in order to address various methods of minimizing it.

Rifle recoil is most simply explained by Newton's First and Second Laws of Motion. When a rifle is fired, a force is exerted on the bullet that projects it forward. By Newton's 1st Law, it can be inferred that and opposite force will be imposed on the rifle. From Newton's 2nd Law it can be deduced that this force can cause an acceleration (linear or angular) which results in velocity and therefore kinetic energy. Energy is also transferred into the marksman in the form of work. The total of this energy is called Recoil Energy and can be calculated.

When a gun is being held at rest, there are three forces acting on it. The weight of the gun pushes downward, and the shooter's hands exert a normal force upward on the gun as shown in Figure 2 below. The point P represents the point of contact between the stalk and the marksman's shoulder.

Image - Torque 2
[Figure 2]

When the gun is fired, the bullet is projected forward by a force, and an opposite force (F) pushes backward on the gun. Since the barrel where the force is acting is slightly above the point of contact with the shooter's shoulder, torque is created. The normal forces put on the gun by the shooter's hands momentarily become negligible.* The forces acting on the gun directly after the gun is fired can be simplified as in Figure 3. R is the perpendicular distance between the recoil force and the point P. L is the perpendicular distance between the location of the force due to gravity and the point P. The resulting linear and angular acceleration can be seen in Figure 4.

Image - Torque
[Figure 3]

Image - Torque 3
[Figure 4]

The elevation caused by the angular acceleration can decrease accuracy by altering the trajectory of the bullet, and the horizontal acceleration causes a force to be exerted on the shooter's shoulder which can be painful.

*This suggestion is not completely accurate because the shooter's grip will put a downward force on the gun when the gun is fired.

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However, for the sake of building a model, we shall assume that the shooter is attempting to put minimal strain on his muscles, that is, absorb the least amount of energy possible. Assuming that before the shot the hands are simply acting as a normal force, after the shot is fired that normal force will disappear.

Recoil Energy is the energy that is required to push the gun in the opposite direction of the bullet. When the gun is fired, the mass of the bullet and the gasses move out of the barrel. This causes a force that pushes the gun in the opposite direction.

The Law of Conservation of Momentum can be used to find the theoretical recoil velocity of the gun if the gun were in a closed system (that is, there is no force exerted on the gun by the shooter or gravity). This hypothetical value can be used to calculate Recoil Energy using the formula for calculating kinetic energy:

E=½mv2

A rifle (mass = Mg, Weight = Wg) fires a bullet (mass = mb, Weight = Wb) using gunpowder (mass = mp, Weight = Wp). The bullet has muzzle velocity vb, and the gasses from the exploded powder have escape velocity of vp. Figure 5 shows the calculation for recoil energy.

Note: It can be shown experimentally that vp is about 1.5 times vb.
Image - Recoil Energy Calculation
[Figure 5]

This value is the amount of energy that would be put into the rifle if there were no outside forces. The fact that there are forces acting on the gun does not change the measure of Recoil Energy. However, the energy is not all converted to kinetic energy. Some of the recoil energy is transformed into work.

1. Gas Release

The first method of reducing recoil energy is to release gases through holes drilled in the barrel. Holes drilled with a rearward slant will allow gases to escape in the opposite direction of the motion of the bullet and create an opposing force. The method is most effective if the holes are placed near the tip of the barrel. Figure 6 illustrates this method.

Image - Gas Release
[Figure 6]

There are several problems with the gas release method. One major fallback to this method is that projecting hot gas at a high velocity rearward of the gun can be very dangerous for the marksman. Also, since the gas is being used to propel the bullet, releasing the gas before the bullet has left the barrel can result in decreased muzzle velocity.

2. Spring

The second method is often employed to reduce recoil in assault rifles. The stalk contains a mechanism with a stiff spring that is compressed as recoil occurs. When the gun is fired, the Recoil Force pushes back on the rifle. However, rather than being transferred into to marksman in the form of work, the energy is transformed into the mechanical potential energy of the spring as shown in Figure 7. The major fallback of this method is that it is not practical in most rifle designs and it requires spring with a high spring constant.

Image - AR15 Spring
[Figure 7]

3. Hanging Mass

The third, and most interesting method of recoil reduction is to hang a mass from the rifle. Competition riflemen will sometimes hang a weight from the barrel of their rifle. This reduces recoil because Recoil Energy is inversely related to the mass of the gun. Adding the weight to the rifle will, hence, minimize recoil.

Changing the position of the weight can further alter recoil. Hanging a weight from near the end of the rifle will shift the center of mass to that end and lengthen the radius perpendicular to the Force due to gravity. This will increase the downward torque around the point of rotation. Figure 8 below shows the Torque acting on a rifle of weight W and the Torque on the same rifle with a mass M* hung from the barrel.

Image - Hanging Mass
[Figure 8]

Bibliography
Image - Art 1911
[Image by Joe Patz 2007]

1. Wallack, L. R. (1977). America rifle design and performance. New York, NY: Winchester Press.

2. Nonte, George C. (1978). Handgun competition. New York, NY: Winchester Press.

3. The Ballistician, (2002, April 30). What is recoil and how is it calculated?. Retrieved November 12, 2007, from Loadammo.com Web site: http://www.loadammo.com/Topics/August01.htm

4. The Custodian, (2001, September 25). Recoilless Gun. Retrieved November 12, 2007, from Everything2.com Web site: http://www.everything2.com/index.pl?node_id=1165512

5. Recoil. Retrieved November 12, 2007, from Wikipedia.org Web site: http://en.wikipedia.org/wiki/Recoil

6. Image, http://www.capitanhipower.com/Photos/M1Rifle.jpg