Engineering Encyclopedia · Propulsion SystemsPlate 1 — Rev. A

Magnetohydrodynamic
Seawater Thruster Principle · Construction · Parametric Behavior

A direct-current Lorentz-force drive that pushes conductive seawater with no moving parts — and an honest look at why that elegance costs so much power.

Reference Datum — Yamato 1 (Kobe, 1992)
YAMATO 1
World's first full-scale superconducting MHD ship · Mitsubishi Heavy Industries / Ship & Ocean Foundation · first run Kobe harbour, June 1992 · scrapped 2016
Vessel
  • Length 30 m · beam 10.39 m · draft 2.69 m
  • Displacement 185 t · crew 10
  • Cruising speed 8 kn (15 km/h ≈ 4.1 m/s)
  • Hull: anti-magnetic Al alloy; two 2,000 kW generators
Per thruster (one "set")
  • Field at centre 4.0 T [published]
  • Electrode current, normal 2,000 A [published]
  • Thrust 4,000 N/set [MESJ table]
  • Mass 18 t/set · 6 seawater ducts each
  • Conduction type (DC electrodes), not induction
Magnet
  • NbTi superconductor, liquid-He cooled
  • −269 °C (4.2 K), persistent-current mode
  • Six coil units per cryostat, shield-free ring
  • Land-based energizing; onboard re-liquefaction
Two flags worth carrying with the datum. Popular write-ups cite 8 kN per thruster; the primary MESJ particulars table lists 4,000 N/set at 2,000 A — this sheet uses the primary value. Efficiency is often quoted around 15%, but the achieved figure was far lower; loading this datum makes the twin compute drive efficiency from first principles (≈ 1–2% at these numbers), which matches why the programme stalled. The twin is a single-channel F = B·I·d model, so the loaded d, h, L are an effective-channel reconstruction chosen to reproduce the published 4 kN/set — they are not measured duct dimensions.
Sectional View & Live Readout
+ J B F d = 0.100 m h = 0.050 m Acrylic pressure shell Anode (+) Cathode (−) Seawater (σ) SECTION A–A · LOOKING DOWNSTREAM
Fig. 1-1. Transverse section of the duct. Current J crosses the channel from anode to cathode; the magnet supplies field B at right angles; their product drives thrust F out of the section plane. The body force per unit volume is f = J × B.
Operating Readout— DC MODE —
Thrust  F = B·I·d10.0N
Force density  f = J·B2000N/m³
Current density  J0.40A/cm²
Channel resistance  R1.00Ω
Applied voltage  V100.1V
Electrical power in  P10.0kW
Useful power  F·u10.0W
Drive efficiency  η0.10%
Electrode materialPt/Ti
Erosion rate (repr.)mm/yr
Est. electrode lifeyr
Electrode guardWithin limit

Readout recomputes from first principles as you move the controls below. The numbers are not flattering — that is the point of an honest twin.

Parametric Controls — The Modulation Layer
Conventional electromagnet range. Above ~2 T implies a superconducting coil.
Set by the power supply. Drives thrust linearly — and ohmic loss quadratically.
Channel width between electrodes. Widening it raises thrust but also resistance.
Electrode height. Larger area lowers current density and erosion risk.
Active length along flow. Lowers current density and resistance together.
The operating point set by the rest of the vessel. Raises useful power and back-EMF.
Open ocean ≈ 3–5 S/m. The low value is the root cause of poor efficiency.
Set automatically by electrode material below; nudge to override your spec.
Thicker electrodes survive longer before erosion eats through — see life estimate.
Pressure-shell wall. Sets the outer envelope, not the physics.
Un-energised duct run at each end for flow conditioning.
Sets the current-density guard and drives the erosion / life model. Representative data.
Operating View — Flow & Force (CFD-style)
Longitudinal plane · flow left → right u = 1.00 m/s · particles colored by speed
Fig. 1-2. Tracer particles advect through the active channel; the orange vector scales with computed thrust, field markers (⊗) scale with B, and the inter-electrode shading scales with current density. A purely illustrative advection, driven by the live parameters — not a meshed Navier–Stokes solve.
As-Designed Specification — Dual Unit
Table 1-1. Governing quantities, stated in SI and U.S. customary units. Live values track the controls.
SymbolQuantitySI valueU.S. customary
Table 1-2. Representative electrode materials. Order-of-magnitude values for orientation — not certified design data. Selecting a material sets the guard limit and the erosion model above.
MaterialRec. Jmax (A/cm²)Wear (mm/yr per A/cm²)Character
Platinised titanium (Pt/Ti)0.500.02Low wear, high cost — premium anode
MMO-coated Ti (RuO₂/IrO₂)0.400.03Industry-standard “DSA”
Graphite0.100.90Cheap, but consumed
Bare titanium0.050.15Passivates; poor anode
Mild steel0.026.0Corrodes fast — illustrative only
Principle of Operation

The magnetohydrodynamic thruster has no propeller, no piston, and no moving part of any kind. It accelerates a working fluid — here, ordinary seawater — directly, by passing an electric current through it while it sits in a magnetic field. Where the current and the field cross, every cubic metre of fluid feels a body force, and the fluid is pushed along the duct. Reaction to that push is thrust.

f = J × B  (force per unit volume, N/m³)

Because the current crosses a channel of width d while the field is uniform, the total thrust collapses to the same expression as the force on a current-carrying wire. It depends only on the field, the current, and the gap:

F = B · I · d  (N)

This is why thrust rises in proportion to current. The difficulty is that seawater is a poor conductor — a few siemens per metre — so most of the supplied power is spent simply forcing current across the gap as resistive heat, not on propelling the boat. The channel resistance and the electrical bill follow:

R = d / (σ · L · h)   P = I·(I·R + B·u·d)

The only fraction that does useful work is F·u, the thrust times the boat's speed. Dividing the two gives an efficiency that, at sensible field strengths, sits in the low single-digit percent or worse. Strong superconducting magnets improve it because useful power rises with B while resistive loss does not — which is exactly why every serious demonstrator, from the 1992 Yamato 1 onward, reached for the strongest field it could carry.

The instrument panel above is built to show this plainly rather than hide it: push the current up and watch thrust climb a little while power climbs a lot.

Build Order — Why the Couplings Lock the Sequence

You cannot jump a rung: each step needs the result of the one before it. This is the order this plate's own model is solved in.

  1. Solve the field first. B and the channel geometry fix the body force available — nothing downstream can be sized until this is known.
  2. Set the current for target thrust. With B and d fixed, F = B·I·d inverts directly to the current you must supply.
  3. Then size the electrodes. Only now is current known, so electrode area L·h can be chosen to hold J under the erosion guard. Sizing them earlier is guessing.
  4. Check the power and cooling. Resistance and ohmic heat follow from the geometry just locked in.
  5. Apply tolerances last. As-designed dimensions become as-made only after loads and clearances are settled.

This is the single sound idea worth keeping from any "coupling-first" framing: dependency dictates order. The panel enforces it implicitly — change B and every downstream number moves; change a tolerance and nothing upstream does.

Dimensioned Drawing — Sheet MHD-DWG-001
View 1 · Section A–A · looking downstream (+x out of page)
d=100.0 140.0 h=50.0 74.0 SHELL WALL t=12 ELECTRODE t=8 (×2) A B 0.2 A SECTION A–A
View 2 · Section B–B · longitudinal · flow +x →
SEAWATER FLOW L=500.0 700.0 ENTRY/EXIT 100 (×2) ELECTRODE — ANODE / CATHODE SECTION B–B
Notes
  1. All dimensions in millimetres unless noted.
  2. Material — shell: acrylic / GFRP, seawater-sealed. Electrodes: titanium Gr.1, Pt-group clad (representative — set to your spec).
  3. Break all sharp edges 0.5 × 45°.
  4. Electrode faces parallel within ⫽0.2 to datum A. Uneven gap skews current density and erosion.
  5. Linear tolerance ±0.5 unless noted.
  6. Geometry is schematic (NTS). Callout values are the source of truth and track the interactive twin above.
Revisions
RevDescriptionDateBy
AInitial issue — parametrictwin
MHD SEAWATER THRUSTER
SINGLE-CHANNEL DUCT ASSEMBLY
Drawing No.MHD-DWG-001RevA
ScaleNTSUnitsmm
MaterialSEE NOTE 2Sheet1 OF 1
DrawnTWINDate
ProjectionTHIRD ANGLE ⦶

The drawing is parametric: move any control or load the Yamato datum and the dimension callouts (d, h, L, overall width/height/length) update live. Wall thickness (12 mm), electrode thickness (8 mm) and entry/exit length (100 mm) are fixed build constants here — say the word and I'll promote any of them to controlled parameters.

Engineering Encyclopedia · MHD Propulsion · Plate 1 Rev. A Interactive twin — physics computed client-side, no data leaves the page