Phase 0 of the launch-architecture ladder: a desk-scale eddy-current levitation demo. Rev A (Aug 29, 2026): drag-power table fix, alloy-conductivity spec, curvature derating, motor + PSU re-spec, coast-down measurement method, optical gap measurement, full-perimeter guard. Original retained in git history.
A passive magnetic levitation demo: a small cart carrying a Halbach array of permanent magnets floats above a spinning aluminum surface with no power to the cart, no control system, no superconductors. Motion induces eddy currents in the aluminum; the currents repel the array.
Claim scope (rev A): this demo certifies generic conducting-sheet eddy levitation — the flat-drag-power signature (P = mgw, drag force falling as speed rises) that distinguishes EDS from every contact or ∝v³ mechanism over a 3× speed sweep. The flight track is a null-flux ladder (§9); the ladder v2 is the explicit claim-linkage step. This sheet is the physics warm-up and the catalog piece, not the track certification.
Two build variants:
Characteristic speed w = 2/(μ₀σt) depends on the alloy you actually have — the original table silently assumed pure-Al conductivity (3.5×10⁷ S/m); real rims and 6061 tube run 2.5–3.0×10⁷. Both columns below; identify your alloy or treat measured w as the alloy measurement.
| Parameter | Variant A (rim ~1.5 mm eff.) | Variant B (drum 4 mm) |
|---|---|---|
| w — pure Al / 6061-T6 | 30 / 35–42 m/s | 11 / 14–16 m/s |
| Levitation onset (ideal-2D model) | ~100–126 RPM | ~80–95 RPM |
| Hover gap @ 1,000–1,500 RPM | 3–8 mm (curvature-derated, §5a) | 3–8 mm (curvature-derated — NOT the original 8–15 mm) |
| Drag power @ 250 g (flat with speed!) | 74 W (pure Al) – 90–104 W (6061) | 28 W (pure Al) – 34–39 W (6061) |
| Cart mass budget | ≤250 g | ≤250 g |
Model-dependence note (rev A): the onset row is an ideal-2D calculation; expect reality 1.5–2× either way — log the anomaly paragraph, it’s data, not failure. (The original “60 / 54 RPM” figures carried unstated fudge factors.)
Eddy heating (rev A): hover drag dumps 75–100 W into a ~0.5 kg rim ≈ +10 K/min; conductivity falls ~0.4%/K, so w and drag drift ~percent-per-minute. Log run time and keep sweeps short.
| Item | Spec | Source | Est. |
|---|---|---|---|
| Magnets ×10 (8 + 2 spares) | ½” N42 cubes (e.g. K&J B888) | K&J / Applied Magnets | $35 |
| Track | Alloy-rim 700c bike wheel w/ axle (A) — magnet test: doesn’t stick — or 12” OD 6061 tube, 4 mm wall, ≥100 mm long (B) | used bike shop / metal supplier | $15–60 |
| Motor + speed control | ≥200 W (rev A — was ≥50 W: magnetic drag 74–104 W + windage O(100 W) at 1,500 RPM), brushless + ESC, PWM throttle | hobby | $30–45 |
| Bench power supply | sized to the motor (rev A — absent from original BOM) | — | $35–50 |
| Drive | Belt + pulley ratio (rev A — the $5 O-ring friction drive needs ~50 m/s contact under 100+ W and glazes) | hardware | $12 |
| Cart body + magnet jig | PLA, ~100 g — cart underside curved to track radius, or array shortened (§5a) | 3D print | $3 |
| Epoxy | JB Weld or Loctite E-120HP | hardware | $6 |
| Guide rails | 2× smooth rod or aluminum angle + PTFE tape | hardware | $8 |
| Guard | Polycarbonate sheet, full perimeter incl. apex window (rev A — was lower-half plywood) | hardware | $15 |
| Frame | 2×4 lumber or 2020 extrusion, bearing blocks | on hand | — |
| Instruments | macro camera + mm-grid card (gap — optical), digital scale 0.1 g, phone tachometer app, multimeter — |
— | $12 |
Eight cubes, magnetization rotating 90° per cube, two full wavelengths (λ = 50.8 mm). Arrows show the direction each cube’s north pole points. TRACK SIDE IS DOWN.
cube #: 1 2 3 4 5 6 7 8
N points: ↓ → ↑ ← ↓ → ↑ ←
(↓ = toward track, → = direction of track surface motion)
STRONG side (field concentrated): BOTTOM (track side)
WEAK side (field canceled): TOP (cart side)
Verify before gluing: hold the assembled clamped array over a steel washer — the strong face snaps it hard, the weak face barely holds. Mark cube tops with paint dots (red = N-out, blue = S-out) before assembly. Pacemaker wearers keep distance from the strong face.
Halbach neighbors repel and twist. Never assemble by hand-holding. Print the open-top channel jig (12.9 mm inner width, 110 mm, M4 clamp boss + pusher block); insert-orient-epoxy one cube at a time, clamp until full cure. Work over a towel, one cube out of the shipping stack at a time, stack a meter from the jig — two ½” N42 cubes blood-blister fingertips and shatter each other on impact.
A flat 101.6 mm array over a curved track loses its ends to sagitta: 4.1 mm extra end-gap on a 700c rim, 8.6 mm on the 30 cm drum — against a field decay length of 8.1 mm. On the drum as originally drawn, the end cubes contribute a lift factor of ~0.12: the original Variant B “more lift” column is unreproducible. Fix (pick one): print the cart underside curved to your track radius (preferred — keeps all 8 cubes working), or shorten the array and accept the lift loss. This is why Variant B’s rev A gap column matches A instead of beating it.
Why the method changed: motor-watts-difference does not isolate magnetic drag — brushed-motor I²R loss grows with load (~30 W systematic on a 775-class), varying with RPM, inside the gate’s ±30% band. Feeler gauges are deleted: at 1,500 RPM the rim surface moves at 49 m/s (176 km/h) carrying ~0.9–1.6 kJ; a steel gauge between an N42 array that snatches it and that surface is a projectile generator.
| Symptom | Cause | Fix |
|---|---|---|
| No lift at any RPM | Array glued weak-side-down | Rebuild (spares exist for a reason) |
| Lift far below table | Flat cart on curved track — end cubes lost to sagitta | Curved underside per §5a |
| Cart slams sideways | No lateral constraint — Inductrack gives lift+drag only | Rails per §6; or V-groove the drum (B) |
| Cart creeps in spin direction and jams | That’s the drag force working | Angle rails 2–3° or soft end-stop — behind the apex window, not exposed |
| Violent buzz at high RPM | Rim runout / imbalance | True the wheel; stay ≤1,500 RPM |
| Drag drifts during a long sweep | Eddy heating dropping σ | Shorter sweeps; log run time |
| One magnet pops out | Under-epoxied joint | Re-glue; clamp harder |
Hard limit: 1,500 RPM. Fully expressive by 1,200; above that the rim’s kilojoule buys risk, not physics.
Companion documents: Space Transportation Architecture (Beam Line, §Demonstration Ladder Phase 0; Appendix C carries this sheet’s Variant B numbers and updates with it — consistency register C-5). Provenance: phase0_revA_rederive.py.