Maglev & Hyperloop: The Physics of Ultra-Fast Ground Transport

Why wheels run out of road

At high speed, two forces dominate a train's power budget: aerodynamic drag F_drag = ½·ρ·C_d·A·v², which grows with the square of speed, and the power needed to overcome it, P = F·v, which therefore grows with the cube of speed. At 350 km/h a train needs roughly 8-12 MW; pushing to 600 km/h on wheels would demand 40-70 MW — impractical. Wheel-rail contact also becomes unstable above roughly 400 km/h, a hunting oscillation that limits how far conventional rail can be pushed even with more power; the TGV's 2007 record of 574.8 km/h required a dedicated track, a shortened train and 25 kV overhead power, and was never remotely practical for commercial service.

Two ways to levitate

Earnshaw's theorem says you cannot stably levitate a magnet with static fields alone — so maglev systems work around it. EMS (electromagnetic suspension) uses electromagnets under the vehicle that attract toward iron rails, with an active control loop adjusting current over 1,000 times per second to hold a roughly 10 mm gap; it can levitate at rest and is used by Transrapid in Shanghai. EDS (electrodynamic suspension) uses superconducting magnets to induce eddy currents in aluminium guideway coils, and Lenz's law turns that into a repulsive force that is stable above roughly 100 km/h — Japan's SCMaglev uses this approach and holds the rail speed record at 603 km/h (2015), needing wheels only at low speed.

Linear motors: the track itself is the engine

Both maglev and Hyperloop use a linear motor — essentially a rotary motor unrolled flat, producing thrust instead of torque. A linear induction motor drives a travelling magnetic wave in the stator that induces currents in a conducting reaction plate, simple and robust and used by Transrapid. A linear synchronous motor, used by SCMaglev, is more efficient at high speed but requires active electromagnets in both vehicle and guideway, with the guideway coils energised sequentially as the train passes — effectively an electric motor hundreds of kilometres long.

Hyperloop: removing the air, not just the friction

Elon Musk's 2013 Alpha Paper proposed passenger pods at 1,200 km/h inside tubes held near vacuum — around 100 Pa, roughly 0.1% of atmospheric pressure — where drag drops by a factor of about 1,000. The catch is the Kantrowitz limit: at transonic speeds, if the pod's cross-section exceeds about 36% of the tube's at Mach 0.9, air piles up ahead of it faster than it can flow around, causing choked flow and a drag spike. Proposed fixes include reducing tube pressure further, adding an axial compressor to the pod's nose, or simply making the tube wide enough. Virgin Hyperloop reached 387 km/h with two passengers over 500 m in 2020, but commercial viability at scale remains unproven — current cost estimates put Hyperloop tube infrastructure at $20-80 million per km, against $30-50 million/km for conventional high-speed rail.

Frequently asked questions

Try it live

Everything above runs in your browser — open Maglev Train, switch between EDS and EMS modes, and watch lift-off speed, the levitation gap, and lift versus drag as the train accelerates from wheels onto a magnetic cushion.