Rotary Eddy-Current Disc Brake: Torque vs RPM

Disc Material

Brake Setup

Magnetic flux density B 0.80 T

Air gap 10 mm

Launch spin speed 3000 rpm

Ready — set your parameters and spin up the disc.

Live Readouts

Spin speed

0 rpm

Braking torque

0.00 N·m

Dissipated power

0 W

Revolutions run

0.0 rev

Critical slip speed v_c (peak-stress, at outer pole edge)

— rpm

How it works

This is a rotary eddy-current brake (a Foucault-disc brake, the same principle used in industrial dynamometers and some elevator/exercise-bike brakes) — a genuinely different apparatus from a linear rail brake, not just the same picture spun around. A fixed magnet pole faces one flat side of a spinning conductive disc. Because every point of the disc under the pole moves at a different linear speed (v = ω·r, faster at the outer edge than the inner edge), the local eddy-current braking stress is not a single number — it varies across the pole footprint and has to be integrated.

local stress   τ(r) = 2·τ_max · (v(r)/v_c) / (1 + (v(r)/v_c)²),  v(r) = ω·r

torque         T(ω) = θ_pole · ∫[r0→r1] τ(r)·r² dr   (Simpson's rule, 40 slices)

τ_max ∝ σ·B²/gap³,   v_c ∝ 1/σ   (same conductivity dependence as a linear brake)

Each radial slice of the pole footprint sits at its own local slip speed, so part of the disc can be past its stress peak (falling-off region) while another part is still climbing it — something a single-point force–velocity formula cannot represent.
Braking torque (not force) decelerates the disc: dω/dt = −T(ω)/I, where I = ½MR² is the disc's rotational inertia.
Copper's high conductivity gives it the lowest v_c, so its inner radii peak first as the disc slows; steel needs much higher rim speed to reach its peak.

The heat-mapped arc under the magnet shoe shows the actual computed local stress at each radius, live — brighter where the eddy currents are working hardest right now.

Magnet N-pole (fixed) Magnet S-pole (fixed) Local eddy-current stress