Eddy-Current Brake

A brake with nothing to wear out

Every friction brake works the same brutal way: press two surfaces together hard enough that sliding turns motion into heat. The pad and the disc grind against each other, the energy of motion becomes warmth in the rubbing surfaces, and over thousands of stops the pad slowly disappears. Friction brakes fade when they get hot, glaze when they get too hot, and one day the pad runs out.

An eddy-current brake removes the contact entirely. Bring a magnet close to a moving conductor — a spinning copper disc, an aluminium fin, a steel rail sliding past — and the conductor feels a retarding force even though nothing mechanical touches it. The force comes from the same electromagnetic induction that runs every transformer and generator, harnessed in reverse to do braking. Because there is no physical contact, there is nothing to wear, nothing to glaze, and no fade-by-contact: the brake is as fresh on its millionth stop as on its first.

The catch, which we will get to, is that this is a speed-dependent brake. It is strongest when the conductor is moving fast and vanishes completely at standstill. So it is brilliant at bleeding off energy and lousy at holding a parked load — which is exactly why it tends to be paired with a small friction brake for the final stop. Understanding why requires only two pieces of nineteenth-century physics: Faraday's law and Lenz's law.

The mechanism — induction, eddy currents, Lenz's law

Picture a flat conductive disc spinning past the pole of a magnet. Consider a single patch of metal in the disc as it sweeps under the magnet. Before it arrives, that patch sits in almost no field. As it slides under the pole, the magnetic flux threading it rises sharply; as it slides out the far side, the flux falls again. The patch experiences a changing magnetic flux, and Faraday's law of induction says a changing flux drives an electromotive force around any loop enclosing it:

EMF  =  − dΦ / dt          (Faraday's law)

In a solid sheet of metal there are no wires to define the loop, so the induced current closes on itself in swirling whirlpools — the eddy currents that give the brake its name. The crucial part is the minus sign and what Lenz's law makes of it: the induced current always flows in whatever direction makes its own magnetic field oppose the change that created it. The leading edge of the patch, where flux is increasing, generates a field that pushes back against the incoming pole; the trailing edge, where flux is falling, generates a field that tries to pull the pole back. Both effects act in the same sense — they resist the relative motion. The conductor is dragged backward; the magnet, by Newton's third law, is pulled forward. That mutual drag is the brake.

The eddy currents are real currents flowing through a real resistance, so they dissipate power as ohmic heating, exactly like a resistor. This is where the kinetic energy goes. There is no mechanical friction anywhere, yet the moving body slows down, because its energy is being pumped into I²R losses spread through the bulk of the conductor. A heavily used eddy brake disc gets genuinely hot — the energy has to go somewhere, and unlike a regenerative brake, an eddy brake throws all of it away as heat.

How much force? The drag-versus-speed curve

For a thin conductive sheet of thickness t, conductivity σ, moving with velocity v through a region of magnetic flux density B, the retarding force per unit area scales as:

F  ∝  σ · t · B² · v          (low-speed regime)

Three things fall straight out of that expression, and they shape every real design:

• Force grows with the square of field strength (B²). Doubling the magnet's flux density quadruples the braking force. This is why eddy brakes reward strong rare-earth magnets or saturated electromagnets — the payoff is quadratic.
• Force grows with conductivity (σ). A good conductor lets more eddy current flow for the same induced voltage. Copper (σ ≈ 5.96 × 10⁷ S/m) and aluminium (σ ≈ 3.5 × 10⁷ S/m) are the materials of choice; structural steel is roughly six times worse and is used only when its ferromagnetism is worth the conductivity penalty.
• Force grows linearly with speed (v). At low speed, the faster you go, the harder it brakes. This is the famous self-regulating behaviour: an eddy brake naturally resists acceleration and tends to hold a downhill vehicle at a roughly constant terminal speed.

But the linear-with-speed relationship only holds at low speed. At higher speed the eddy currents themselves become strong enough that their own magnetic field distorts and partly expels the applied field — a self-shielding effect related to the skin depth. The drag force rises with speed, reaches a peak at a characteristic critical speed, then actually falls as speed climbs further. The full behaviour follows a curve of the form:

F(v)  =  F_max · 2 · (v/v_c) / (1 + (v/v_c)²)

   v ≪ v_c :  F ≈ 2·F_max·(v/v_c)   (rises linearly)
   v = v_c :  F = F_max              (peak drag)
   v ≫ v_c :  F ≈ 2·F_max·(v_c/v)    (falls as 1/v)

The critical speed v_c depends on the geometry, the conductivity, and the field — for a typical roller-coaster fin brake it sits comfortably above operating speed, so the train stays on the rising part of the curve where more speed means more braking. Designers who ignore this curve get nasty surprises: a brake tuned for peak force at 40 km/h may grow weaker, not stronger, if the train arrives at 70 km/h.

Worked example — a roller-coaster fin brake

Take a representative modern coaster fin brake. Vertical copper fins are fixed to the underside of the train; the track carries opposing rows of neodymium magnets, leaving a gap of a few millimetres on each side. As the train passes, each fin sweeps through the field.

Magnet field in gap:      B ≈ 0.5 T  (NdFeB, narrow air gap)
Fin material:             copper, t = 6 mm, σ = 5.96e7 S/m
Train arrival speed:      v = 25 m/s  (90 km/h)
Effective fin area in field per car:  A ≈ 0.05 m²

Low-speed force estimate (order of magnitude):
   F  ≈  σ · t · B² · v · A
       ≈  5.96e7 · 0.006 · 0.5² · 25 · 0.05
       ≈  1.1e5 N  per car   →  scaled in practice by
       geometry/self-shielding to a usable few kN per fin.

The raw formula over-predicts because it ignores self-shielding and the finite magnet length, but it captures the key levers: the force is set by B², the conductor, the speed, and the swept area. In practice a coaster designer tunes the magnet count and fin overlap so that a fully loaded train decelerates at a comfortable 0.5–1.0 g over the brake run, while an empty train — lighter, so it arrives faster — sees more drag because the brake is on the rising part of the F(v) curve. The brake self-compensates for train weight, which is one of its quietly brilliant safety properties: it cannot be overwhelmed by a fast, light car the way a fixed-force friction brake can.

Because the eddy force dies at low speed, the fins alone bring the train down to a few km/h; a final friction brake or a simple wheel chock parks it in the station. No part of the high-energy braking touches anything, so there is no brake dust, no pad replacement, and no fade on a hot summer afternoon when a friction brake would be cooking.

Permanent magnet versus electromagnet

An eddy brake needs a field, and there are two ways to make one. A permanent-magnet brake uses fixed magnets — usually neodymium — and is controlled mechanically by changing the geometry: move the magnets closer to engage, withdraw them to release, or in the coaster case simply let the fin leave the magnet zone. It is fail-safe (the field is always there) and needs no power, but its strength is fixed by the hardware.

An electromagnet brake generates the field with a coil, so braking is controlled by coil current. Energise the coil and the brake bites; cut the current and it releases; modulate the current and you set the force continuously. This is what truck retarders and most high-speed-train rail brakes use, because the driver or the control computer needs to dial the braking up and down. The cost is electrical: the coil draws current the whole time it is engaged, and on a heavy-duty retarder that can be kilowatts of excitation power, plus the I²R heat in the conductor itself.

Where eddy-current brakes earn their keep

• Roller-coaster brakes. The dominant modern station and trim brake. Copper or aluminium fins on the train pass between permanent-magnet arrays on the track. Intamin and B&M coasters worldwide use them; they replaced the old friction skid brakes precisely because they never fade, never wear, and self-compensate for train weight.
• High-speed-train rail retarders. The German ICE 3 carries linear eddy-current brakes: electromagnet skids are lowered to within a few millimetres of the rail head, inducing eddy currents in the steel rail itself. Used as a wear-free service brake above ~50 km/h and as an emergency brake, it spares the friction discs on long high-speed runs.
• Heavy-truck and bus driveline retarders. A Telma-style retarder mounts an eddy-current unit on the driveshaft. Switched on for long descents, it holds the vehicle at a safe speed and keeps the wheel-mounted friction brakes cool and available for an actual emergency stop — a major safety feature on alpine and mountain routes.
• Exercise machines. Spin bikes, rowing machines, and ellipticals create their resistance with a magnet near a spinning aluminium flywheel. The resistance is silent, infinitely adjustable by moving the magnet, and never wears out — the reason premium gym equipment abandoned friction-pad resistance.
• Instrument and meter damping. Analogue moving-coil meters and the old spinning-disc domestic electricity meters use a small magnet over an aluminium disc to provide velocity-proportional damping, so the needle or disc settles smoothly instead of oscillating.
• Power-tool and machine braking. Some circular saws and industrial spindles use eddy-current braking to stop a coasting blade quickly without a mechanical brake fighting the motor.
• Free-fall ride and zip-line brakes. Drop towers and high-speed zip lines use permanent-magnet eddy brakes as the primary deceleration — fail-safe because the magnets cannot lose their field, and self-limiting because faster arrival means more drag.

Eddy-current brake versus the alternatives

Property	Eddy-current brake	Friction (disc/drum)	Regenerative brake
Contact	None	Pad on disc	None
Wear	Effectively zero	Pads wear, must be replaced	Effectively zero
Energy fate	Heat in conductor (lost)	Heat in pad/disc (lost)	Recovered to battery/line
Force at standstill	Zero — can't hold	Full holding force	Zero — can't hold
Force vs speed	Rises with v, then falls past v_c	Roughly constant	Limited by motor & storage
Fade with heat	None	Significant when hot	None
Hardware needed	Magnet + conductor	Caliper, pads, hydraulics	Machine + power electronics + storage
Typical role	Retarder, high-speed bleed-off	Final stop, parking, emergency	Everyday braking, EV/train

The table makes the division of labour obvious. Regenerative braking is the most efficient because it recovers energy, but it needs a controllable machine and somewhere to dump the power. Friction is the only one of the three that can produce force at zero speed, so it owns the final stop and the parking brake. The eddy-current brake sits in the middle: dead simple, wear-free, fade-free, and self-regulating, but useless below walking pace. The smart system uses all three — regenerative for the bulk of everyday energy, eddy for the high-speed and fail-safe retarding, and friction for the final, locked stop.

Failure modes and trade-offs

• Heat is the real limit. All the braking energy ends up as heat in the conductor. A coaster fin sees brief, intermittent loads and cools between trains, but a truck retarder on a 20-minute descent can dump tens of kilowatts continuously. Discs must be finned, ducted, or liquid-cooled, or the conductor overheats and its conductivity drops — which weakens the very effect you are relying on.
• Conductivity falls with temperature. Copper's resistivity rises about 0.4 % per °C. A hot brake conducts worse, so the eddy currents and the force shrink as the brake heats — a self-limiting effect that protects the hardware but degrades performance exactly when you are working it hardest.
• No holding force. The brake cannot stop a vehicle completely or hold it on a slope. A separate friction or mechanical brake is mandatory for the final stop and for parking. Treating an eddy brake as a complete brake is a design error.
• The force-versus-speed peak. Past the critical speed, more speed means less braking. A brake sized for one arrival speed can underperform badly at higher speed if the designer forgot the falling branch of the F(v) curve.
• Magnet attraction in steel-rail brakes. A linear rail brake also produces a strong static attraction to the steel rail, adding load to the suspension and the rail. The German rail authorities restrict eddy-brake use on certain track because of the thermal and mechanical load it puts into the rail.
• Field-clearance sensitivity. Force scales with B², and B falls steeply with air-gap distance. A few extra millimetres of gap from thermal expansion, wear in the guides, or a bent fin can cut braking force sharply. Gap control is a real maintenance concern on rail and retarder installations.
• Demagnetisation and corrosion. Neodymium magnets lose strength if they exceed their Curie-limited working temperature and corrode without a protective coating. A coaster brake's magnets are nickel-plated and kept well below their thermal limit for exactly this reason.

Design notes that separate a good brake from a bad one

• Maximise B before anything else. Force goes as B², so a stronger magnet and a smaller air gap beat a bigger conductor every time. Halbach magnet arrays, which concentrate flux on one side, are common in high-performance fin brakes.
• Pick the conductor for conductivity, then for heat. Copper brakes harder than aluminium but is heavier and costlier; aluminium is the usual compromise for moving fins where mass matters. Add cooling fins or mass to absorb the heat the brake makes.
• Keep the operating range below v_c. Tune the geometry so the vehicle always works on the rising part of the drag curve; you want faster to mean stronger, not weaker.
• Slot the conductor if you only want damping, not force. Cutting radial slots in a disc breaks up the large eddy loops, which is the wrong move for a brake but the right move for a tachometer cup or a galvanometer where you want gentle velocity damping, not strong drag.
• Always pair it with a holding brake. Design the system, not just the eddy element: a friction brake or pawl for the final stop and the park is not optional.