Hyperloop & Maglev: Physics of Ultra-Fast Ground Transport

1. Why Traditional Rail Has Limits

At high speed, two forces dominate:

Additionally, wheel-rail contact becomes unstable above ~400 km/h (hunting oscillation). The TGV speed record is 574.8 km/h (2007) but this required a dedicated track, shortened train, and 25 kV overhead power — entirely impractical for commercial service.

2. Magnetic Levitation Principles

Maglev trains float above the guideway using electromagnetic or electrodynamic forces, eliminating contact friction entirely. The Earnshaw theorem (1842) says you can't levitate a permanent magnet stably with static fields alone — but you can work around it with:

• Active feedback control (EMS): Electromagnets under the vehicle attract toward iron rails. An active control loop adjusts current 1,000+ times per second to maintain a 10 mm gap. Used by Transrapid (Germany/Shanghai).
• Induced currents (EDS): Superconducting magnets on the vehicle induce eddy currents in aluminium guideway coils as they pass. Lenz's law creates a repulsive force. Stable above a minimum speed (~100 km/h). Used by JR Central's SCMaglev (Japan).

3. Linear Motors: Propulsion Without Wheels

Both maglev and Hyperloop use linear motors — essentially a rotary electric motor "unrolled" into a flat strip. Instead of producing torque, it produces linear thrust.

• Linear induction motor (LIM): A travelling magnetic wave in the stator induces currents in a conducting reaction plate. The interaction produces thrust. Used in Transrapid. Simple and robust.
• Linear synchronous motor (LSM): Active electromagnets in both vehicle and guideway. More efficient at high speed. Used in SCMaglev. The guideway coils are powered sequentially as the train passes — the entire track is the motor.

Power delivery is a challenge: in LSM systems, electrical substations must power the guideway coils beneath the vehicle's current position. This is like having an electric motor that's 500 km long.

4. EMS vs EDS: Two Maglev Approaches

5. Hyperloop: Near-Vacuum Tubes

Elon Musk's 2013 Alpha Paper proposed passenger pods travelling at 1,200 km/h inside partially evacuated tubes (100 Pa, ~0.1% of atmospheric pressure). At this pressure, aerodynamic drag drops by a factor of ~1,000.

The physics has two regimes:

Several companies (Virgin Hyperloop, Hyperloop TT, Hardt) built test tracks. Virgin Hyperloop achieved 387 km/h in a 500 m tube (2020) with two passengers. However, the economic and engineering viability remains unproven at scale.

6. Engineering Challenges

• Thermal expansion: A 500 km steel tube expands ~3 m between winter and summer. Expansion joints every 30–50 m are needed, each maintaining vacuum seal.
• Vacuum maintenance: A 500 km tube at 100 Pa has surface area ~800,000 m². Even tiny leaks (O-ring degradation, micro-cracks) require continuous pumping. Estimated pump power: 10–30 MW for the route.
• Safety: Tube breach at 1,000 km/h would be catastrophic — shock waves, deceleration. Vehicles must have emergency braking (eddy-current brakes, 3–4 g limit for passengers) and pressurised cabins like aircraft.
• Cost: Estimated $20–80 million per km (Hyperloop) vs $30–50 million/km (conventional HSR) vs $100–250 million/km (urban maglev). The tube is the dominant cost.
• Passenger comfort: At 1,200 km/h, lateral acceleration in curves must be limited to 0.5 g. Minimum curve radius at this speed: ~23 km. Routes must be essentially straight.

7. Comparison: HSR vs Maglev vs Hyperloop