How Does a Catapult Work? The Physics Explained

A catapult stores energy slowly and releases it all at once, converting that stored energy into the kinetic energy of a flying projectile. The basic idea is no different from pulling back a rubber band: you do work gradually, the elastic material holds that work as potential energy, and when you let go, the energy transfers almost instantly into speed. What makes catapults interesting, from ancient siege weapons to modern aircraft launchers, is how different designs store and release that energy, and how the physics of levers, torque, and projectile motion determine where the payload ends up.

Energy In, Energy Out

Every catapult, regardless of design, follows the same energy sequence. First, energy goes in. Someone (or something) does physical work to load the device, whether that means cranking a winch, twisting ropes, or hoisting a heavy counterweight into the air. That work doesn’t vanish. It sits in the system as potential energy, waiting to be released. Second, a trigger mechanism holds everything in place until the operator is ready. Third, the trigger releases, and the stored potential energy converts rapidly into kinetic energy, which is the energy of motion. The projectile accelerates along the arm, leaves the device, and follows a curved path through the air governed by gravity and air resistance.

The efficiency of this conversion matters. No catapult turns 100 percent of its stored energy into projectile speed. Some energy goes into moving the arm itself, some into flexing and vibrating the frame, and some into heat from friction at the pivot and trigger. A well-built machine minimizes these losses, but they’re always present. The goal of catapult engineering, ancient or modern, has always been to get as much of the stored energy as possible into the projectile and as little as possible into everything else.

Three Ways to Store the Energy

Historical catapults fall into three broad families, each defined by how they store potential energy before release. Understanding the differences helps explain why some designs threw farther, some threw heavier loads, and some were more practical on a battlefield.

Tension (flexion): The simplest and oldest approach. A flexible arm, like a bow stave or a bent wooden beam, is pulled back against its own springiness. When released, the arm snaps forward. Energy is stored in the elastic deformation of the material itself. This is the principle behind the basic mangonel and the bow-and-arrow.
Torsion: Instead of bending a beam, torsion catapults twist bundles of rope, sinew, or hair into tight skeins. The arm sits inside these twisted bundles. To load the device, the arm is winched backward, twisting the skeins even tighter. The energy stored in the twisted fibers is enormous relative to the device’s size. Roman ballistae and onagers used torsion power, and the design dominated Mediterranean siege warfare for centuries.
Gravity (counterweight): The trebuchet takes an entirely different approach. A massive counterweight, often a box filled with stones or earth, hangs from the short end of a pivoting beam. The long end holds a sling with the projectile. Raising the counterweight stores gravitational potential energy. When released, the counterweight falls, the beam pivots, and the long arm whips the sling upward. Because gravitational potential energy depends on the mass of the counterweight and the height it falls, trebuchets could be scaled up simply by adding more weight.

Each storage method has trade-offs. Torsion devices were compact and could be loaded quickly, making them useful in field battles, but the rope skeins degraded in wet weather and needed regular maintenance. Trebuchets were slow to reload and enormous to transport, but they could hurl stones weighing hundreds of kilograms with remarkable consistency, which made them ideal for breaking down fortification walls during prolonged sieges.

The Lever Arm and Mechanical Advantage

At the heart of most catapult designs is a lever. A rigid beam pivots around a fulcrum, and the ratio of the arm lengths on either side of that fulcrum determines the mechanical advantage. In a trebuchet, the counterweight hangs from the short arm and the projectile sits in a sling at the end of the long arm. When the counterweight drops a short distance, the tip of the long arm sweeps through a much larger arc. The projectile end moves faster than the counterweight end, precisely because it’s farther from the pivot.

This is a direct trade-off: you gain speed at the tip but lose force. The counterweight exerts a large force over a small distance, and the long arm converts that into a smaller force over a larger distance, producing high velocity. The relationship is straightforward. If the long arm is five times the length of the short arm, the tip moves roughly five times as fast as the counterweight’s descent, minus friction and other losses. That speed multiplication is what lets a catapult hurl a projectile much faster than a person could throw it by hand.

In torsion catapults, the lever works differently. The arm is inserted into the twisted rope bundle near the fulcrum, and the entire arm acts as one long lever extending from that bundle. The stored torsion applies a rotational force (torque) at the base, and the tip of the arm, being far from the axis, accelerates to high speed as the arm swings forward. The projectile sits in a cup or sling at the tip, riding along for the acceleration phase and then releasing at the right moment.

What Happens After Release

Once the projectile leaves the catapult, the device no longer matters. From that point on, the physics is pure projectile motion. Two things determine where the projectile lands: its speed at release and its angle of launch. Gravity pulls the projectile downward at a constant rate, while its forward momentum carries it horizontally. The combination produces the familiar arcing trajectory.

In a vacuum with flat ground, the angle that maximizes horizontal range is 45 degrees. At that angle, the upward and forward components of velocity are balanced in a way that keeps the projectile in the air long enough to cover the most ground. But real catapults don’t operate in a vacuum. Air resistance slows the projectile throughout its flight, and the effect is stronger at higher speeds. For dense, compact projectiles like stone balls, air resistance matters less. For lighter or irregularly shaped payloads, it matters a lot, and the optimal angle drops below 45 degrees because getting the projectile moving forward faster (at a flatter angle) compensates for the drag it will encounter.

Height also plays a role. Catapults often sat on elevated ground or atop siege towers, meaning the release point was higher than the target. When you’re launching from above your target, the optimal angle drops further, because gravity has more time to pull the projectile down over a longer horizontal distance even at a shallower launch angle.

The Sling Effect in Trebuchets

Trebuchets have an extra trick that makes them more efficient than a simple pivoting beam: the sling. The projectile doesn’t sit in a rigid cup at the arm’s tip. Instead, it hangs in a fabric pouch attached by ropes to the end of the arm. As the arm swings up, the sling trails behind, then whips forward and releases the projectile at high speed.

The sling effectively extends the lever arm without adding rigid weight. As the arm reaches the top of its arc and begins to slow, the sling continues to accelerate, because it’s still gaining angular velocity through a whipping action. This is the same physics behind a bullwhip crack: energy transfers from a heavier, slower-moving section to a lighter, faster-moving section. The sling can add 50 percent or more to the projectile’s release speed compared to a rigid arm of the same length, which translates to a dramatically longer range, since range scales with the square of speed.

Getting the sling length right was critical. Too short, and you lose the whipping benefit. Too long, and the sling releases at the wrong angle, sending the projectile too high or even backward. Medieval engineers tuned sling length through trial and error, and modern reconstructions have confirmed that small changes in sling proportion produce large changes in accuracy and range. The release angle depends on how one end of the sling slips off a hook or pin at the arm’s tip, and adjusting the angle of that pin was effectively the trebuchet’s aiming mechanism.

Why Catapults Can’t Simply Be Scaled Up Forever

If bigger counterweights throw farther, and longer arms give more speed, you might wonder why medieval armies didn’t just build absurdly massive trebuchets. The answer lies in material strength. Wood, rope, and sinew have limits. Double the length of a wooden beam, and it doesn’t just weigh twice as much. It also bends more under its own weight, because stiffness doesn’t scale linearly with length. Eventually, the arm breaks under the forces involved, or flexes so much during the swing that energy is wasted in deformation rather than transferred to the projectile.

The same scaling problem afflicts torsion machines. Twisted sinew bundles can only store so much energy per unit volume before the fibers snap. Making the bundles larger helps, but the frame holding them must also grow, and the forces on the frame increase faster than the frame’s strength. Historical accounts describe the largest trebuchets throwing stones of around 100 to 150 kilograms over distances of roughly 200 to 300 meters, and those machines pushed the engineering of their era to the edge. The legendary “Warwolf” trebuchet, built by Edward I of England during the siege of Stirling Castle in 1304, was reportedly so large it took weeks to assemble, and contemporary sources suggest it was among the most powerful ever built. But even it had limits dictated by the strength of timber and rope.

Modern materials could theoretically push those limits further, but by the time catapults reached their practical ceiling, gunpowder had arrived and made the whole question moot. Cannons stored energy chemically, in a far more compact package, and didn’t care about beam length or rope quality.

Torque, Angular Velocity, and the Moment of Inertia

When the catapult arm swings, it rotates around the pivot point. How fast it rotates depends on the torque applied and the arm’s resistance to rotation. That resistance is called the moment of inertia, and it depends on both the mass of the arm and how that mass is distributed relative to the pivot. An arm with most of its weight near the pivot is easier to spin than one with the same total mass concentrated at the tip.

This is why catapult arms were tapered, thicker and heavier near the pivot where strength was needed, and thinner toward the tip where speed mattered. A lighter tip accelerates faster for the same applied torque, which means the projectile gets launched at a higher velocity. It’s the same reason a baseball bat is swung from the handle end rather than the barrel end, and the same reason figure skaters pull their arms in to spin faster. Redistributing mass closer to the axis of rotation reduces the moment of inertia and allows faster angular velocity for the same energy input.

In trebuchet design, the counterweight essentially provides the torque. As it falls, gravity acts on it, and the force it exerts on the short arm creates a rotational force around the pivot. The longer the short arm, the more slowly the counterweight falls (because it has farther to swing), but the more torque it produces at the pivot. This is another engineering trade-off: short arms give faster operation but less torque, long arms give more torque but slower cycling. Historical designs converged on short-to-long arm ratios somewhere in the range of 1:3 to 1:6, depending on the intended payload and range.

Catapult Physics in Living Organisms

The principle of storing energy slowly and releasing it fast didn’t originate with human engineers. Biology discovered it hundreds of millions of years earlier. Many animals and even some plants use what biologists call latch-mediated spring actuation: they load energy into elastic structures like tendons, exoskeletons, or specialized tissues, hold it with a latch mechanism, and then release it in a burst to produce movements far faster than their muscles alone could generate.

The mantis shrimp, for example, stores energy in a saddle-shaped spring in its arm and releases it with a latch to strike prey at accelerations exceeding that of a bullet leaving a gun barrel. Trap-jaw ants snap their mandibles shut using a similar latch-and-spring system. Fleas store energy in a pad of resilin, a rubber-like protein, and release it to jump many times their body length. In all these cases, the energy flow follows the same sequence as a catapult: an energy source loads elastic elements in the form of elastic potential energy, opposing forces (the latch) prevent movement during loading, and then as the latch is reduced or removed, elastic potential energy transforms into kinetic energy of the propelled mass.¹ The structures used for storing that elastic energy are often distinct from the mechanisms that actually propel the mass, just as a trebuchet’s counterweight is separate from its sling.

Researchers studying these biological catapults have found that temperature plays a meaningful role in how much energy animals can store and recover. In experiments combining live tissue with computer simulations, an increase in temperature raised the rate at which muscles could develop force, which in turn allowed more energy to be stored in elastic structures during loading. The contribution of direct muscle work after the latch released also increased with temperature.² Cold-blooded animals relying on elastic mechanisms can still strike quickly in cold conditions because the spring release itself is largely temperature-independent, but they store less total energy when cold, reducing the power of each strike.

The framework for studying these systems, known as latch-mediated spring actuation, treats the spring, the latch, and the motor (muscle) as interacting components, much the way an engineer would analyze a catapult’s energy source, trigger, and arm as interconnected parts of a single machine.³ The parallel isn’t just poetic. Biologists have directly borrowed engineering concepts like energy budgets and mechanical advantage to describe how these organisms achieve speeds and accelerations that seem to violate what their muscles should be capable of. They don’t violate anything; they simply decouple the rate of energy input from the rate of energy output, which is exactly what a catapult does.

Modern Descendants of the Catapult

The physics of catapults didn’t become obsolete when gunpowder took over the battlefield. The underlying principle of storing energy and releasing it in a controlled burst shows up throughout modern technology, just with different energy sources. Aircraft carrier launch systems are a striking example. Steam catapults, used on carriers for decades, stored energy as high-pressure steam and released it to accelerate fighter jets from zero to flying speed in about two seconds across a deck roughly 90 meters long. The acceleration involved is punishing, and the energy management challenges are enormous, but the concept is recognizably a catapult: store energy, restrain the load, release it suddenly.

Newer electromagnetic aircraft launch systems replace steam with linear electric motors, storing energy in massive flywheels or capacitor banks and converting it to electromagnetic force along a track.⁴ The energy source is different, the storage medium is different, and the release mechanism is different, but the core physics problem is the same one a Roman engineer faced with a ballista: how do you get the most energy into the projectile in the shortest possible time, with the least wasted on everything else?

Outside the military, catapult physics appears in places you might not expect. Bungee cords and elastic launchers on amusement park rides store elastic potential energy and convert it into kinetic energy for a sudden acceleration. Trap shooting machines use a leaf spring to hurl clay targets along a predictable trajectory. Even the humble mousetrap is a small torsion catapult: a coiled spring stores energy, a latch holds the bar, and the release snaps the bar down with more force and speed than you could generate by pressing it with your finger. The family resemblance across all these devices traces back to the same physics: energy stored, energy held, energy released.