Plate VII · Counterpoise engine, fixed weight

Trebuchet Simulator

Round 1

Configure a fixed-counterweight trebuchet, then call the range before anyone fires it. The simulator integrates the beam, sling and shot through the throw and the flight, but it keeps the landing point sealed until you commit. You get the energy budget and the geometry live; the rest is your judgement. Touch any setting after a shot and a new round begins.

Elevation, engine to scale

Your call sealed answer

Range to first impact, from the pivot

Landing point sealed. It is computed only when you commit.

Configuration SI units

Range book stored on this device

Engine	Called	Actual	Error	Score

The model, and what it leaves out

Two degrees of freedom, solved from the Lagrangian with fourth-order Runge–Kutta at 0.2 ms steps: beam angle and absolute sling angle. While the shot lies in the trough, a Lagrange multiplier holds it on the ground; it lifts off the moment that normal force would turn negative.

Rigid uniform beam pivoting on a frictionless axle; the counterweight is a point mass rigidly fixed to the short arm (no hinged bucket).
Massless, inextensible sling; shot is a point mass sliding without friction in the trough.
Idealised release: the shot leaves the instant its velocity reaches your release angle, i.e. a perfectly tuned prong.
Flight over level ground, sea-level air at 1.225 kg/m³, still air. With drag on, the shot is a stone sphere (2,500 kg/m³) with C_d = 0.47.
The arm starts with its tip 0.15 m off the ground. Frame and counterweight are assumed to clear everything; a pit is flagged when the weight would dip below grade.
Range is measured horizontally from the pivot to first contact with the ground.

Efficiency is the shot's kinetic energy at release divided by the potential energy the counterweight has given up by then.