# Trebuchet Simulator - Lagrangian Dynamics, Sling Release, Range Optimizer

> Counterweight trebuchet physics: Lagrangian RK4 model of ground slide, sling swing and release, drag flight, range, efficiency, sweeps and onager comparison.

- URL: https://qilingtools.com/en/physics/trebuchet
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

The trebuchet is modelled as what it really is: an arm, a counterweight, a sling and a projectile, coupled through Lagrangian mechanics and integrated with RK4 from the ground slide, through lift-off and the sling swing, to release, followed by a flight with air drag. Switch between a hinged counterweight, a fixed counterweight and a plain lever, change the arms, sling and release angle, and see how range and efficiency respond.

## How to use

1. Pick a preset (giant, medium siege engine, tabletop model) or set arm lengths, counterweight, projectile mass and pivot height
2. Choose the release rule: the projectile velocity angle, or the sling-to-arm angle (a release pin)
3. Press Play to watch the machine in slow motion with trails; range, release speed and efficiency appear below
4. Use the parameter sweep to plot range against sling length, release angle or counterweight and apply the best value
5. Compare the trebuchet with a lever and an onager on the same energy budget

## Features

- Full Lagrangian multibody model (arm, hinged weight, sling, projectile) with energy conserved to better than one part per million
- Ground slide handled as a constraint with a reaction force λ; the projectile lifts off when λ reaches zero
- Slow-motion animation with trails, plus a flight-path chart with and without drag
- Energy efficiency and range efficiency to show where the energy goes
- Parameter sweeps to find the best sling length and release angle
- Comparison with a fixed counterweight, a slingless lever and a torsion onager

## FAQ

### Why does a trebuchet use a sling instead of a cup on the arm?

The sling acts as a second, whip-like segment on the arm. As the arm turns, the sling swings out and the projectile travels most of an extra half turn around the arm tip before release, reaching 1.5 to 2 times the tip speed. It also lets the projectile start on the ground, so the arm can be longer without raising the pivot. In the comparison tab the same arm and weight without a sling typically throw about half as far.

### Why is a hinged counterweight more efficient than a fixed one?

A fixed counterweight swings on an arc and still moves fast sideways near the bottom, so that kinetic energy stays in the machine. A hinged weight hangs from a pivot and falls almost straight down, so by release it is moving slowly and more of its potential energy has gone into the projectile. In the simulation a medium trebuchet usually gains more than ten percentage points of efficiency from the hinge.

### How should I choose the release angle? Why not 45°?

From the ground in a vacuum, 45° gives the longest range. A trebuchet releases its stone from many metres up and the stone feels drag, and both effects push the best angle below 45°. The release angle also changes how long the sling keeps accelerating the stone: too early and it has not reached full speed, too late and the arm is already slowing. The parameter sweep finds the best angle directly, usually between 35° and 45°.

### What is the difference between energy efficiency and range efficiency?

Energy efficiency is the projectile kinetic energy at release divided by the potential energy the counterweight has lost by then, so it measures how well energy is transferred. Range efficiency is the actual range divided by the ideal 2MΔh/m, which assumes all available counterweight energy goes to the projectile, launched at 45° from the ground in vacuum. It combines energy transfer, release height, angle and drag into one figure for comparing designs.

### Is the Warwolf preset historically accurate?

Warwolf was the giant trebuchet Edward I used at the siege of Stirling Castle in 1304. Sources say it was enormous and threw heavy stones, but give no reliable dimensions or counterweight. The preset uses a plausible scale from common reconstructions (an arm over 10 m long, about 10 t of counterweight, a 140 kg stone) to explore the physics of a large machine, not to reproduce historical numbers.

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