Gun Recoil Simulator

The Gun Recoil Simulator shows Newton’s third law at work in a gunshot. The powder gas pushes the bullet forward and the gun backward; the simulator integrates that shot and then what the gun meets afterwards. It has eight guns (9 mm pistol, .22 rifle, 5.56 mm rifle, .308 rifle, 12-gauge shotgun, .50 BMG rifle, 12-pounder field cannon and 105 mm howitzer), three ways of holding them, and four modes: Simulate, Explore, Practice and Quiz.

Follow the numbers: 1 in Set up the shot, pick a gun from the dropdown (the .308 hunting rifle is the default), choose what holds it and set the bullet, speed, powder and gun mass; 2 press ➤ Fire (or Space on the canvas). The shot plays in slow motion and the canvas says by how much. When it finishes, drag the time slider to go back to any instant. 3 Work through the Try this challenges, which tick themselves.

• Free-recoil sled — the gun is clamped to a carriage on low-friction rails, so nothing resists it. It shows conservation of momentum on its own: the gun leaves the sled’s light gate at V = (m v + β C v)/M, the free recoil velocity. An arrester at the end of the rail catches it afterwards.
• Mechanical shoulder (small arms) — the butt (or, for the pistol, the grip) bears on a padded load cell backed by a spring-mounted body mass, the way recoil test rigs model a shooter. The force graph shows the push on the shoulder; change the pad and its peak changes while its area (the impulse) stays the same. The support hand is a rotational spring, so the gun also rotates: muzzle rise. Rounds 1–5 fire a string at the set interval.
• Recoil system (cannons) — the 12-pounder rolls back on its wheels against friction from the ground you choose; the 105 mm howitzer’s barrel slides back in its cradle against a constant-force hydraulic buffer set by the recoil length, then the recuperator runs it out again.

Detail A (top left, shown while the gas is acting) is a magnified section of the chamber and bore: the gas colour shows the pressure, and the arrows are the third-law pair — the gas pushing the bullet forward and the breech backward. The momentum bars (top right) show bullet, gas, gun and what holds it; they always add to zero. Underneath, the left graph is the shot itself (momentum against time, in milliseconds) and the right graph is the recoil (velocity, shoulder force or recoil distance).

Twenty-four concept cards in six groups: Third law & momentum, Free recoil, Inside the barrel, Felt recoil & muzzle rise, Recoil systems, and Units & standards. Most carry a worked example with the simulator’s own numbers.

Practice draws from fourteen kinds of problem: momentum, recoil velocity with and without the gas, recoil energy, energy sharing, average force from impulse, the steady force of rapid fire, cannon roll-back, buffer force, bullet speed from a recoil sled, muzzle rise, the Lagrange pressure ratio, the gun mass for a recoil limit and the muzzle brake factor. Answers within 2 % are marked correct; Show Solution gives the working. Practice problems are set in SI units. Quiz asks six multiple-choice questions drawn from a pool of twenty-one, with the options shuffled, and scores you with up to three stars.

Momentum: m v + (gas) = M V. For the .308 rifle (9.7 g at 860 m/s, 2.85 g of powder, 4.1 kg): V = (8.342 + 1.75 × 0.00285 × 860) / 4.1 = 3.08 m/s and E = ½ M V² = 19.5 J (14.4 ft·lbf). In the bore the gas moves with the bullet (Lagrange), carrying C v/2; the breech pressure is P_b(1 + C/2m). The pressure curve is a model shape that rises to the cartridge’s rated maximum pressure and falls like an adiabatic expansion, scaled so the bullet leaves the barrel at exactly the published muzzle velocity. After the bullet leaves, the remaining gas momentum C v (β − ½) is delivered as a short exponential pulse. The mechanical-shoulder and body constants are illustrative, so use the force figures to compare, not as a measurement of a real shooter.

The Units switch shows bullets and powder in grams or grains (1 gr = 64.79891 mg), cannon shot in kg or lb, speeds in m/s or ft/s, momentum in N·s or lbf·s, energy in J or ft·lbf, force in N or lbf and pressure in MPa or psi. Your choice is remembered across the site. Example in Imperial: the .308 fires a 150 gr bullet at 2 822 ft/s from a 9.0 lb rifle; free recoil 10.1 ft/s and 14.4 ft·lbf.

Display Controls (top left of the canvas) switch the force arrows, Detail A, momentum bars, labels, smoke and the graphs; turn the graphs off and the scene fills the whole canvas. Your choices are remembered. Right-click (or long-press) the canvas to save an image, copy the readings or fire. PNG also saves the view. The Live equations panel works the numbers of the shot on screen, and Show Calculations (beside Fire) opens the full step-by-step working for the gun and set-up you have chosen: the momentum balance, the free recoil velocity and energy, the force of the gas on the breech, and then how far the gun goes back and the force on whatever stops it (shoulder, wheels on the ground or recoil buffer), each closed-form estimate set beside the simulated value. Add ?gun=howitzer (or pistol, rimfire, carbine, bolt, shotgun, heavy, cannon) to a link to open a particular gun.