Railgun Electromagnetic Simulation
Theory: a current loop's urge to expand
Overview
Railguns appear a lot in science fiction. Is the principle actually simple?
The principle is just Fleming's left-hand rule. Put a conducting armature between two parallel rails and pass current: it goes down one rail, across the armature and back along the other. In the field of that loop, the armature current feels a force pushing it forward — you can think of it as a force that tries to enlarge the loop. Actually building one, though, means millions of amperes, millisecond timescales, a high-speed sliding contact, heating and deformation all at once — a very hard coupled problem.
Thrust formula
$L'$ is the inductance gradient — how much circuit inductance increases per metre of armature travel — and $I$ the current. Set by rail shape and spacing, it is typically about 0.4–0.6 μH/m. Thrust scales with current squared, hence the need for enormous currents.
Where the energy goes
At constant current, as the armature advances the magnetic field region between the rails grows, and its stored energy increases by exactly the work done on the armature. So even ideally, at most half the supplied energy becomes kinetic energy — less with resistive losses.
An idea over a century old
The idea of accelerating objects electromagnetically is old; France's Fauchon-Villeplée patented it around 1920. Without power supplies able to deliver huge currents briefly, it stayed unrealised for decades. Research took off after Marshall and colleagues in Australia used energy from a large generator in the 1970s to demonstrate acceleration to several kilometres per second. Power supplies, rail wear and contact damage remain major challenges, and research continues including for launching payloads to space.
Worked example (idealised estimates)
Example 1: current, thrust and velocity
Idealised estimate: L′ = 0.5 μH/m, 1 kg mass, 5 m rails, constant current, no friction or resistive loss:
| Current | Thrust | Acceleration | Exit speed | Kinetic energy | Residual magnetic energy |
|---|---|---|---|---|---|
| 0.5 MA | 62 kN | about 6,400 g | 791 m/s | 0.31 MJ | 0.31 MJ |
| 1.0 MA | 250 kN | about 25,000 g | 1,581 m/s | 1.25 MJ | 1.25 MJ |
| 1.5 MA | 562 kN | about 57,000 g | 2,372 m/s | 2.81 MJ | 2.81 MJ |
The same amount of magnetic energy is left over as the kinetic energy.
Yes — always, at constant current. As the armature leaves the rail ends, this magnetic energy has nowhere to go and tends to release as an arc at the muzzle. Real systems therefore study supply control that ramps current down near the end of launch and circuits that recover the energy. And with accelerations of tens of thousands of g, the strength of the armature and payload is a major issue too.
Example 2: forces pushing the rails apart
Rails carrying opposite currents repel. A crude thin-wire estimate gives about 10 MN per metre at 1 MA and 20 mm spacing, and still about 4 MN at 50 mm, pushing the rails outward. Even slight opening degrades armature contact, causing arcing and damage, so the stiffness of the rail support structure is critical.
How to approach the analysis
Coupled elements
- Transient electromagnetics: time variation and skin effect crowd current to the rails' inner surfaces and the armature's rear; high armature speed adds the velocity skin effect, leaving current behind at the trailing edge.
- Thermal: concentrated Joule heating can melt the contact.
- Structural: rail deformation from repulsion, armature stress from acceleration, vibration.
- Contact: contact pressure, sliding, wear and transition to arcing — the hardest part to model.
“Rails wear out after a few shots”
In railgun experiments, rail surfaces can melt or erode within a few to a few dozen shots, requiring replacement. One cause is the velocity skin effect: the faster the armature, the more current concentrates at its trailing edge, creating local hot spots. Another is rails opening under repulsion, momentarily breaking contact so an arc forms. Neither can be predicted without solving electromagnetics, heat and structure together, and extending rail life remains a research topic in both materials and coupled analysis.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Assuming uniform current | Local heating missed | Transient eddy-current analysis |
| Stationary armature | Velocity skin effect missed | Include motion |
| Efficiency from kinetic energy alone | Residual magnetic energy missed | Check the energy balance |
| Rigid rails | Contact loss not predicted | Solve deformation under repulsion |
| Constant properties | High-temperature resistance change ignored | Use temperature dependence |
I'd like to try electromagnetic force calculations myself.
Try the magnetic force calculator for magnetic force, the magnetic levitation simulator for levitation and the skin depth calculator for skin depth. Related coupled topics are covered in Lorentz force, electromagnetic forming, MHD flow and resistive heating.