Why does a heavier counterweight or longer projectile arm increase range?

A larger M r_cw − m r_p gives more torque early in the swing, so ω at release is higher. A longer r_p also increases launch speed v = r_p ω, which strongly increases range.

What is missing compared to a real trebuchet?

Real machines have a sling, sliding axle, beam mass distribution, friction, and aerodynamic drag. This model keeps a rigid beam and instant release for clarity.

Trebuchet

A simplified rigid-beam trebuchet: counterweight and projectile lie on one line through the pivot. Gravity creates a torque τ = g cos θ (M r_cw − m r_p); angular acceleration follows τ/I. When the beam reaches the release angle, the projectile detaches with tangential speed v = r_p ω and moves as a free projectile.

Who it's for: Mechanics courses covering torque, rotation, and energy transfer; medieval siege-engine demos.

Key terms

torque
moment of inertia
angular acceleration
tangential velocity
range
lever arm

How it works

A rigid beam pivots on a fixed axle: a heavy counterweight on the short arm and the projectile on the long arm. Gravity produces a torque that accelerates rotation; when the beam reaches the release angle, the projectile leaves with tangential speed v = rω and follows a parabola. Adjust masses, arm lengths, start angle, and release angle to maximize range.

Key equations

τ = g cos θ (M r_cw − m r_p), I = M r_cw² + m r_p² + I_beam, α = τ / I

At release: v = r_p ω (−sin θ, cos θ); then ẍ = 0, ÿ = −g

Frequently asked questions

Why does a heavier counterweight or longer projectile arm increase range?: A larger M r_cw − m r_p gives more torque early in the swing, so ω at release is higher. A longer r_p also increases launch speed v = r_p ω, which strongly increases range.
What is missing compared to a real trebuchet?: Real machines have a sling, sliding axle, beam mass distribution, friction, and aerodynamic drag. This model keeps a rigid beam and instant release for clarity.

Other simulators in this category — or see all 85.

View category →

NewSchool

Chain Sliding Off Table

Uniform chain on a smooth edge: hanging weight pulls, friction on the tabletop resists. Watch when it slips and how acceleration grows with s.

Launch Simulator

NewSchool

Block Stack & Friction

Pull the bottom block in a vertical stack: spring-like links with friction caps show who slips — compare with rigid-stack estimates.

Launch Simulator

NewUniversity / research

Bicycle Stability (2D)

Side view: roll dynamics with fork trail and gyroscopic wheel torques — see speed, trail, and ω = v/R vs lean.

Launch Simulator

NewSchool

Spring Pendulum

2D elastic pendulum: swing and spring stretch together — energy swaps between modes; try chaotic-looking presets.

Launch Simulator

NewSchool

Bridge Resonance (1-D mode)

Damped modal oscillator with harmonic drive: sweep ω near √(k/m) — presets for cadence-like and low-ζ peaks.

Launch Simulator

NewSchool

Rising Bubble (Archimedes)

Ideal-gas bubble expands as it rises (p = p_atm + ρgy); buoyancy vs weight + Stokes drag — depth and velocity graphs.

Launch Simulator

Trebuchet

How it works

Key equations

Frequently asked questions

More from Classical Mechanics

Chain Sliding Off Table

Block Stack & Friction

Bicycle Stability (2D)

Spring Pendulum

Bridge Resonance (1-D mode)

Rising Bubble (Archimedes)

Trebuchet

How it works

Key equations

Frequently asked questions