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

Counterweight-driven beam: torque launches a projectile at a chosen release angle. Explore range vs masses and arm lengths.

About this model

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.

Continue with similar topics in this category — or all 85 in Classical Mechanics.

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Frequently asked questions

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Key equations

Frequently asked questions