Linear Induction Motors: A Motor Unrolled Into a Straight Line

Unrolling the motor: from spinning field to traveling wave

A rotary induction motor works by producing a rotating magnetic field. Three-phase windings spaced around the stator are energized 120° apart in time, so the peak of the field appears to sweep around the bore. That sweeping field induces currents in the rotor bars, and the interaction produces torque.

Now imagine cutting the stator along one radial line and unrolling it into a flat strip. The rotating field becomes a traveling field — a magnetic wave that marches straight down the length of the flat winding instead of going in circles. The 'rotor' unrolls too, becoming a flat sheet of conductor: usually an aluminium or copper plate, often backed by iron. This plate is called the reaction plate or secondary. It doesn't need windings, magnets, or power — it just needs to conduct.

The powered, wound part is the primary (the analog of the stator). Crucially, either part can be the mover: in a factory conveyor the primary is fixed and the plate slides; on a train the primary rides the vehicle and the aluminium reaction rail is bolted to the ground between the running rails.

The working principle: slip, eddy currents, and Lenz's law

The field wave travels at the synchronous speed, set purely by geometry and frequency:

vₛ = 2 · τ · f

where τ is the pole pitch (distance between adjacent poles, in metres) and f is the supply frequency in Hz. A pole pitch of τ = 0.25 m at f = 50 Hz gives vₛ = 2 × 0.25 × 50 = 25 m/s ≈ 90 km/h — and notably, that speed is independent of the number of poles, unlike a rotary machine where more poles means slower rotation.

Here is the key: the field must travel faster than the plate. The difference, normalized, is the slip:

s = (vₛ − v) ÷ vₛ

As the field sweeps past the stationary plate, it induces circulating eddy currents in the conductor (the induced current loops the animation shows). By Lenz's law those currents oppose the change that made them, and the interaction of the induced current with the traveling field produces a Lorentz force that drags the plate in the direction of field travel. Thrust scales roughly as F ∝ V² · s at low slip — proportional to the square of the applied voltage and, near synchronism, to slip itself. At s = 0 (plate moving exactly at field speed) there is no relative motion, no induced current, and therefore zero thrust. The motor must run with slip to make force, and that residual slip is where the I²R losses in the plate come from.

Why efficiency is the LIM's Achilles' heel

The single biggest penalty of unrolling the motor is the air gap. A rotary induction motor runs with a mechanical clearance of 0.3–1 mm. A LIM on a vehicle must tolerate track irregularities, thermal expansion, and suspension travel, so its gap is typically 5–25 mm — ten to fifty times larger.

• Big magnetizing current. The reluctance of that gap is huge, so a large fraction of the primary current does nothing but establish flux. This crushes the power factor to roughly 0.3–0.5, versus 0.8–0.9 for a good rotary machine.
• Low efficiency. Full-load efficiency for a single-sided LIM is commonly 30–55%. The reaction plate is a poor secondary (aluminium sheet, no laminations, no cage), so I²R losses are high.
• Normal force. A single-sided LIM produces a large attractive (or, at high slip, repulsive) force pulling the primary toward the plate — often several times the thrust. Designers either fight it in the bearings or exploit it for levitation.

The double-sided LIM — two primaries sandwiching a thin aluminium fin — cancels the normal force and roughly doubles thrust density, at the cost of needing access to both faces of the plate.

The end effect: the flaw that isn't in a rotary motor

A rotary stator is a closed loop — the field wave chases its own tail forever. An unrolled primary has a beginning and an end, and that geometry creates the LIM's signature parasitic phenomenon: the longitudinal end effect.

At the entry edge, the reaction plate is continually meeting fresh magnetic field for the first time. Flux can't build up instantly in the conductor, so induced 'end-effect' currents appear that partially cancel the useful field near the entry and drag as a braking force. The higher the speed, the worse it gets — end-effect losses climb steeply above a few tens of m/s, which is exactly why LIMs struggle to be efficient at high speed.

The strength of the coupling is captured by the goodness factor G (a magnetic Reynolds number): G = 2·µ₀·f·τ² ÷ (π·ρ·g), where ρ is the plate's surface resistivity and g the gap. High G means strong coupling and good thrust — but paradoxically a very high G machine suffers worse dynamic end effects at speed. Real designs trade these off: pole count, plate thickness and pole pitch are all tuned so the machine is 'good enough' to make thrust without letting the end effect run away.

Where LIMs actually earn their keep

LIMs win wherever contactless, low-maintenance, or very high linear speed matters more than raw efficiency:

• Urban transit. The Bombardier Innovia (ART/APM) family — Vancouver's SkyTrain, Toronto's Scarborough line, Kuala Lumpur's Kelana Jaya line — uses a car-mounted primary over a fixed aluminium reaction rail, reaching ~80 km/h. Because propulsion is contactless, wheels don't have to transmit tractive force, so the trains climb steep grades and brake hard in rain and snow without slipping.
• Launch roller coasters. LIM/LSM catapult trains from 0 to 100+ km/h in a few seconds along a strip of fin-magnets or coils — replacing the old chain lift hill.
• Maglev propulsion. Low-speed maglev vehicles (e.g. 160 km/h designs) use single-sided LIMs whose normal force is engineered to assist levitation.
• Industry and defense. Baggage handling and conveyor sortation, sliding doors, curtain movers, and — at extreme scale — electromagnetic aircraft launch and rail-launch systems.

The unifying theme: the load moves in a straight line, the track is long, and eliminating gears, chains, and driven-wheel contact is worth paying an efficiency premium.

A worked spec example

Consider a single-sided LIM for a light people-mover, sized like a transit unit:

• Pole pitch τ = 0.27 m, supply f = 46 Hz → vₛ = 2 × 0.27 × 46 ≈ 24.8 m/s ≈ 89 km/h.
• Operating cruise speed v = 22 m/s → slip s = (24.8 − 22) ÷ 24.8 ≈ 0.11 (11%).
• Active primary length ~2.3 m, width ~0.2 m → ~4,600 cm² active surface. At a thrust density of ~2 N/cm², that's roughly 9 kN of thrust per unit — enough to accelerate a ~10-tonne car at ~0.9 m/s².
• Air gap ~10–12 mm; power factor ≈ 0.45; efficiency ≈ 0.5. To deliver 9 kN at 22 m/s (≈ 200 kW mechanical), the drive must supply about 400 kW real input, and at a power factor of ~0.45 that is roughly 900 kVA of apparent power.

Those last two numbers — half the input lost as heat, and an apparent power draw several times the useful mechanical output — are the price of unrolling the motor. Engineers accept it because the alternative (a geared drive pushing a driven wheel against a rail in the rain) simply can't deliver the same reliability.

Linear induction motor vs. rotary motor + gearbox/rack for producing linear motion

Attribute	Linear Induction Motor (LIM)	Rotary Motor + Rack/Ballscrew
Motion path	Direct linear thrust, no conversion	Rotary torque converted via rack/screw
Contact with load	None — force across an air gap	Meshing teeth or screw threads (wear)
Air gap / tolerance	5–25 mm, very forgiving	Sub-mm mesh, precise alignment
Efficiency (typical)	30–55%, poor power factor (0.3–0.5)	80–95% motor × 90–98% drivetrain
Best domain	High speed, long track, low maintenance	Precise positioning, high static holding