How does an eddy current brake stop motion?

When a conductor such as aluminium or copper moves through a magnet's field, eddy currents are induced in it, and the force between those currents and the field opposes the motion. There's no contact and no wear; kinetic energy becomes Joule heat in the conductor. They're used in roller coasters, rail vehicles, truck retarders and test rigs.

How does braking force vary with speed?

At low speed it's proportional to speed: 75 N at 1 m/s and 132 N at 2 m/s for a 5 mm aluminium fin (0.3 T, 0.01 m² poles). As speed rises, the field from eddy currents pushes out the applied field (magnetic Reynolds number Rm = μ₀σvd exceeding 1), so force peaks at about 180 N near 4.6 m/s and then falls. Force is small just before stopping, so another brake is needed to stop completely.

Does heating change performance?

Yes. Aluminium's conductivity falls as it heats (from about 3.5 to 2.6×10⁷ S/m at 100 °C), cutting low-speed force by about 25%. The peak-force speed rises from 4.6 to 6.1 m/s, so force actually increases at high speed. All kinetic energy becomes heat: stopping a 5 t vehicle from 25 m/s releases 1.56 MJ, heating a 50 kg aluminium fin by about 35 K.

Analysis of Heat Generation in Eddy Current Brakes

Category: Coupled Analysis – Electromagnetic-Thermal | Revised 2026-10-01

Theory: eddy currents brake and become heat

Overview

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Roller coasters slow down with magnetic brakes at the end. Do they brake harder the faster they go?

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Up to a point, yes. A conducting fin moving in a field carries eddy currents whose force with the field opposes motion. At low speed eddy currents grow with speed, so braking force is proportional to speed. At higher speed the eddy currents' own field pushes the applied field out of the fin, so force levels off and then falls; the crossover speed depends on the fin's conductivity and thickness. All kinetic energy removed becomes heat in the fin, and as the fin heats its conductivity drops, changing braking behaviour. Hence electromagnetic and thermal effects are evaluated together.

Speed and braking force

$$ F_{lin} = c_e\,\sigma\,d\,B^2 A\,v,\qquad R_m = \mu_0\sigma v d,\qquad v_c = \frac{1}{\mu_0\sigma d},\qquad F(v) \approx \frac{F_{lin}(v)}{1 + (v/v_c)^2} $$

σ is fin conductivity, d fin thickness (5 mm), B flux density (0.3 T), A pole area (0.01 m²) and c_e a correction for fin edges and current return paths (0.5). The last formula is a simple approximation bridging low-speed proportionality and high-speed decline.

Peak force and temperature rise

$$ F_{max} = \frac{c_e B^2 A}{2\mu_0}\ (\text{independent of }\sigma),\qquad \Delta T = \frac{\tfrac12 m_v v_0^2}{m_f c_p} $$

Coffee Break Trivia

Foucault's eddy currents

The braking of moving conductors by induced currents was found by Arago in 1824, who saw a compass needle dragged by a spinning copper disc; in 1855 Foucault showed that a copper disc spun in a magnetic field heats up, which is why eddy currents are also called Foucault currents. In the 20th century they served as auxiliary brakes on trains and trucks; recently, being wear-free and unaffected by rain, they are widely used on amusement rides and high-speed rail.

Worked examples

Example 1: braking force by speed, material and temperature (per magnet pair)

Fin	Critical speed v_c	1 m/s	2 m/s	5 m/s	10 m/s	25 m/s
Aluminium 20 °C	4.55 m/s	75 N	132 N	178 N	135 N	63 N
Aluminium 100 °C	6.12 m/s	57 N	106 N	175 N	159 N	83 N
Copper 20 °C	2.74 m/s	115 N	170 N	151 N	91 N	39 N

Peak force (about 179 N) in this approximation is independent of conductivity, set by field and area.

Example 2: heat from stopping a vehicle

Item	Value
Vehicle mass and speed	5 t, 25 m/s
Kinetic energy	1.56 MJ
Temperature rise of a 50 kg aluminium fin	about 35 K
Braking power per pair at 25 m/s	1.6 kW

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Copper conducts better, yet aluminium brakes harder at speed.

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Better conductors carry stronger eddy currents whose field expels the applied field more effectively, so force levels off at a lower speed v_c. Copper peaks at 2.7 m/s and aluminium at 4.6 m/s, so above that copper's force falls sooner. For braking from high speed, as on roller coasters, aluminium or thinner fins are better; for strong braking at low speed, copper or thicker fins. Temperature works the same way: hotter aluminium conducts less, reducing low-speed force but increasing high-speed force. Repeated stops heat the fin and change braking, so continuous operation calls for coupled electromagnetic–thermal tracking of temperature and force.

Analysis workflow

Use the magnetic Reynolds number to judge whether field expulsion matters.
Compute eddy currents and force with electromagnetic analysis including moving conductors (moving frame or motion terms).
Pass Joule heat to thermal analysis for fin temperature rise and cooling.
Update conductivity with temperature and track force over repeated stops.
Also check magnet demagnetisation from temperature rise.

Coffee Break Trivia

“Not stopping fully on summer afternoons”

On one ride's eddy-current brake, crowded summer afternoons saw cars fail to stop at the set point, with the auxiliary brake acting more often. Continuous operation heated the aluminium fins, lowering conductivity and reducing force in the latter, low-speed part of the brake zone. Coupled electromagnetic–thermal analysis reproduced the stopping point extending once fins exceeded 70 °C. Thicker fins with more cooling area limited the temperature rise and stabilised stopping.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Assuming force always ∝ speed	High-speed force overestimated	Check Rm
Constant conductivity	Continuous-use drift missed	Update with temperature
Infinite-sheet formula as is	Force overestimated	Analyse edge effects
Expecting it to stop at low speed	Doesn't fully stop	Add another brake
Ignoring magnet temperature	Force loss from demagnetisation	Check magnet temperature

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