Trebuchet physics
A counterweight falls, an arm swings, a sling whips forward, and a projectile launches on a parabolic arc. The trebuchet is a gravity-powered engine — potential energy converts to kinetic energy through lever mechanics and centripetal acceleration. Adjust the counterweight, arm ratio, and sling length to maximize range.
PE = mgh → KE = ½mv² R = v²sin(2θ) / g
How a trebuchet works
A trebuchet is a gravity-powered siege engine. A heavy counterweight is attached to the short end of a pivoting arm. When released, the counterweight falls and the long end of the arm swings up, accelerating a sling that holds the projectile. The sling adds an extra whip-like acceleration at the end of the swing, effectively extending the arm and increasing the release velocity.
Energy transfer
The counterweight’s gravitational potential energy (PE = mgh) converts to kinetic energy as it falls. The arm acts as a lever, trading force for speed — the long end moves faster than the short end by the arm ratio. The sling further amplifies the tip velocity through centripetal acceleration. In an ideal trebuchet, nearly all the counterweight’s PE converts to the projectile’s KE at release.
The arm ratio
The ratio of the long arm (projectile side) to the short arm (counterweight side) determines the mechanical advantage. A higher ratio means more speed at the tip but requires a heavier counterweight. The optimal ratio depends on the counterweight-to-projectile mass ratio and the sling length. For most configurations, ratios between 3:1 and 5:1 give the best range.
Range equation
Once released, the projectile follows a parabolic trajectory. The range in vacuum is R = v²sin(2θ)/g, maximized at a release angle of 45°. The trebuchet’s challenge is engineering the arm and sling geometry so that the natural release angle is close to this optimum.