Recoil

Introduction

Recoil, and its management, is one of the central issues concerning ballistic weaponry. Every weapon that has the effect of accelerating a projectile experiences recoil as dictated by the conservation of momentum, one of the fundamental principles of physics and laws of nature. Since this subject is touched upon in many other articles, this page is a "quick and dirty" look at the fundamentals of recoil physics, common recoil management strategies of ballistic weaponry, and speculative notes on the recoil of as-yet-to-be-realized weaponry.

Fundamentals of Recoil Physics

As mentioned previously, recoil is a direct result of conservation of momentum. Momentum is the product of mass and velocity vector of an object. The total change in momentum from an event is called the impulse. The force acting on an object multiplied the time the force is applied gives the impulse and thus the change in momentum (if the force varies over time, the impulse is the integral of the force over time – basically you accumulate small amounts to the impulse over tiny slices of time that are short enough that the force doesn't change much, and add them all up to get the total impulse). For every interaction, if one object exerts a force on another then that other object exerts a force of equal magnitude but opposite direction back on the first. If you push down on a table, the table pushes back up on you. If a magnet pulls on a block of steel, that steel block pulls back on the magnet. Because of this, the impulses the two object impart on each other are also equal in magnitude and opposite in direction. And thus, the net momentum of the system of both objects does not change.

What this means for ballistic weaponry is that for every meter-per-second added to every kilogram of projectile that is thrown down range by the apparatus of kinematic, the apparatus itself (and its bearer) would be propelled in the opposite direction by the same kilogram-meter-per-second, although it is free to choose to pay it in either currency, mass or velocity. This generalized view on recoil is appropriate in so far as it describes the macroscopic consequence of the "power-level" of ballistic weaponry, but it does not aptly describe the process by which this effect is applied, and thus can miss out on important caveats that is of interest to the science fictional author and audiences.

Effects of Recoil

Recoil has a number of drawbacks. If you don’t have experience shooting and you are holding the gun wrong, it can knock you off balance. If you are shooting really big bullets going really fast, the gun recoiling can hurt or even leave bruises, especially if you are a small framed person. Many shooters start to subconsciously anticipate the kick, and flinch as they pull the trigger which will throw off aim. Most seriously, perhaps, is that when you are shooting rapid fire the recoil makes it hard to control the gun. On fully automatic fire, after the first two or three bullets the rapid recoil usually torques the barrel of the gun up into the air so all you are shooting at is the sky. And for really big guns, like cannons, you need to engineer in shock absorbers so the recoil doesn’t damage the cannon’s mount or throw off the aim of subsequent shots.

The total recoil impulse will be the mass of the stuff that is launched out the end of the barrel times the speed of the projectile as it is launched. In math-speak, the recoil impulse will be $-{\vec {p}}$, where ${\vec {p}}=m\,{\vec {v}}$ is the momentum of the projectile with $m$ the projectile mass and ${\vec {v}}$ the projectile velocity. Here, the "projectile" is assumed to be the bullet (or shell or payload or whatever) in addition to any sabot or propellant gases or whatever else is shot out the muzzle of the gun.

The usual expression for the kinetic energy is $K=1/2\,m\,v^{2}$. Using ${\vec {p}}=m\,{\vec {v}}$ for the momentum we can express the kinetic energy as $K=1/2\,{\vec {p}}\cdot {\vec {v}}=p\,v/2$. This shows that for constant kinetic energy, the magnitude of the recoil impulse is $p=2\,K/v$. So the faster the projectile is launched, the less recoil impulse will be produced (however, we must caution that the terminal effects of the projectile depend on more than just kinetic energy and it is a mistake to think that two projectiles with the same $K$ but different $m$ and $v$ will have the same effect on target).

The gun may gain the same recoil impulse as its projectile, but its recoil energy is much less. For a gun of mass $M$ recoiling with impulse $p$, its energy will be $p^{2}/(2M)$. You can see that the heavier the gun, the less energy it will have on recoil. This is one of the reasons that shooting a heavy gun feels like it has less recoil than a light gun with the same cartridge, and why heavy guns are less likely to leave bruises. Holding a gun snugly effectively increases the gun's mass, helping to reduce the felt recoil. The impulse that throws off subsequent shots during rapid fire may be the same, but it will hit your shoulder less hard.

Recoil for Conventional Guns

A conventional gun ignites a flammable substance (usually a granular material called gunpowder) in a rigid metal chamber behind a bullet. The burning of the powder produces hot high pressure gas. The pressure of that gas pushes the bullet down a long tube (the barrel). But the same pressure also pushes out and back on the gun itself from the inside. Because the bullet is pushed down the barrel, the forces on the gun are not balanced and there is a net backward force from the gas pressure pushing back on the back face of the chamber that held the ammunition before firing.

The recoil of a conventional gun is, unfortunately, complicated by the use of a propellant (the powder's combustion gas product) to accelerate the projectile. In addition to the momentum of the projectile itself, the conventional gun has to contend with accelerating both the propellant as they combust and chase the projectile, and after the bullet has left the bore, the further acceleration of the propellant gas itself. So in addition to the impulse from the bullet, the gun also gets recoil from the jet of burned propellant shooting out of the end of the barrel and also the aerodynamic forces of the propellant entraining air to pull along with it. All of this means that guns can have a bit more recoil impulse than just what you get from the bullet, often by about 30%. But those same effects let you design guns with muzzle brakes that re-direct the outgoing jet of propellant gas in order to reduce the recoil and also to re-direct the recoil direction to counter the torque of off-center fire that causes muzzle rise.

Recoilless Guns

So the propellant gases for a gun push the bullet down the barrel and also push back on the back face of the chamber (perhaps the bolt-face) to push the gun back. But what if the back face of the chamber were free to move? What if it wasn't connected to the gun at all? Now the recoil impulse goes to making a plug of something shoot out the back without disturbing the person shooting it (called the countermass).

There are several disadvantages to this. First, it reduces the pressure on the bullet, so it is less efficient and performant. Second, each round needs the mass of stuff it is going to shoot out the back in addition to the mass of the bullet, propellant, case, and primer so each shot is significantly heavier. And third, you have a dangerous plug of countermass shooting out the back. At the very least, you need an over-the-shoulder design for a person-fired gun rather than one with a shoulder stock. If you use bare propellant for the countermass, you get a big blast and fireball that can endanger your squad-mates within a few meters of the back end of the gun and makes it dangerous to use in enclosed spaces where the backblast can bounce off walls and ceilings to affect the gunner. Some designs use an inert material such as plastic flakes or water for the countermass, reducing (but not eliminating) the backblast danger and allowing recoilless guns to be used from inside buildings and bunkers.

However, despite these disadvantages, a recoilless design allows for weapons that can launch significant warheads for taking out bunkers and armored vehicles in a weapon that can be fired by an individual soldier. It also allows for cannons that are lighter than traditional cannons.

Many shoulder-fired "rocket launchers" are actually recoilless guns.

Rockets

When a rocket launches, its high pressure propellant is allowed to vent out the back. The pressure pushes the rocket forward and the escaping propellant is pushed away by that same pressure, carrying away the impulse. As long as the jet of escaping propellant does not impinge on the launcher, the launcher itself will not experience any of the recoil. The jet of hot fast propellant gas does pose a hazard for things behind it, however. One method sometimes used to mitigate this is to pop the rocket out of the launch tube at low speed with a charge of cold compressed gas, and then only when it is a safe distance away does it light up its main motor. The initial low speed of the launch both reduces recoil forces and reduces the backblast danger from the initial launch.

Recoil for Electromagnetic Launchers

An electromagnetic launcher is a device that uses electromagnetic fields and electric currents to push or pull a projectile. For a coilgun, the recoil is straightfoward - the fields of the projectile while it is being accelerated push or pull on the currents in the coils the same amount that the fields from the coils push or pull on the currents in the projectile (for a magnetic projectile, these can be the net currents you get by aligning the spins and angular momenta of the electrons around the atoms in the magnet - they're not the sort of currents that can be measured by a multi-meter, but they still physically exist and make and interact with magnetic fields). So for a coilgun, you directly get the impulse on the projectile being the impulse on the gun in an obvious way.

For railguns, the situation is a bit more complicated. The magnetic forces in the railgun push the rails apart, not backward. So the impulse on the projectile is not countered by the impulse on the rails. Instead, the railgun is pushed back where the circuit is closed at the back end of the rails. Where the current completes the circuit in the driving generators and electronics (and power couplings if the generation is kept distant from the rails) is where the recoil is generated, from the same sort of action of the magnetic field on the current that also propels the bullet down the rails.

There is one additional complication. The operation of an electromagnetic gun will produce electromagnetic radiation (in the form of radio and microwaves). This radiation also has momentum. So you don't always have the force exerted by the gun on the bullet being exactly the same as the force exerted by the bullet on the gun, and the tiny bit of excess impulse flies away as the momentum of the emitted electromagnetic radiation. However, in practice this extra momentum is negligible … if it wasn't, there would be so much power and energy in the emitted radiation that the gun would cook the people around it.

Recoil for Lasers

As mentioned for electromagnetic launchers, electromagnetic waves have a small amount of momentum. A laser weapon works by emitting a very high powered beam of electromagnetic waves. So lasers will produce a small amount of recoil. For most purposes, this recoil is completely negligible. The recoil force is the power of the beam divided by the speed of light. The recoil impulse is the energy of the beam divided by the speed of light. You would only get recoil impulses similar to that of a modern firearm if your laser was emitting as much energy per shot as the detonation of several tons of TNT.

Recoil for Particle Beam Weaponries

Particle beams emitting relativistic particles are going to have recoil forces and impulses similar to that of a laser with the same power and energy per shot. While the particles they shoot do have mass so they will have a bit more recoil than a laser, for highly relativistic beams the recoil will be nearly the same. Even for moderately relativistic beams (with the total particle energy only a bit higher than the rest mass energy) the recoil will be not too much more than for light. It is only for sub-relativistic beams (with particle kinetic energies much less than the particle's mass energy) that recoil will start getting significantly more than that for a laser. And there's not much use for moderately relativistic or sub-relativistic beams as weapons.

Credit

Authors: Phoenix, Tshhmon, and Luke Campbell.