Phase 0 of the launch-architecture ladder. Rev A (Aug 29, 2026): continuum-recoil correction — the original thrust table assumed free-molecular recoil in a continuum regime and overstated thrust by 10²–10⁴×. This revision re-derives the physics at 1 atm, adds a null-control ladder, and re-bands Gate 002 as a differential-vs-null measurement. Original retained in git history.
A ~2 mm dyed-water droplet floats in an acoustic levitation trap (TinyLev, the open-source cousin of Bristol’s MATD). A laser fired horizontally at the droplet heats its lit side. The trap doubles as the instrument: it’s a spring, so the droplet’s displacement from the trap node reads out whatever force acts on it. A micro-force balance on a desk.
What rev A corrects: at 1 atm, sub-boiling evaporation is Stefan-flow limited — escaping vapor drifts at ~cm/s and exchanges its thermal momentum isotropically with the surrounding air, which returns it as pressure. Continuum recoil pressure is p ≈ J²/ρᵥ, and at these fluxes that is 10²–10⁴× smaller than the free-molecular numbers in the original sheet (which implied a 226 m/s effective exhaust velocity — a vacuum figure). The honest expectation at gate power is a null differential against a non-evaporating control droplet — and that null, published with the artifact menu it excludes, is the experiment’s real product: it is exactly what Phase 1 needs to know before any high-power laser spend (recoil validation requires reduced pressure or pulsed regimes).
What the flight comparison honestly is: at gate power the flux gap to the flight panel is ~30,000× (48 MW/m² of nozzle-expanded flow vs diffusive evaporation into counterpressure). The bench measures photothermal forces on a beam-riding droplet — a real and useful control-physics testbed — not flight-mechanism thrust. Same molecules, different regime.
2 mm droplet: 4.19 mg, weight 41 μN, lit cross-section 3.14 mm². Table is absorbed power; india-ink water absorbs ~50–80% of incident. Evap column is the generous all-evaporation bound; at 5 mW, convection (h ≈ 26 W/m²K, 0.33 mW/K) takes most of the power at ΔT ≈ 15 K, so true recoil is smaller still.
| Absorbed | ΔT (all-convective) | Evap bound | Continuum recoil | Displacement @ k = 1–10 μN/mm | v0 sheet claimed |
|---|---|---|---|---|---|
| 5 mW | ~15 K | 2.2 μg/s | ≤ 7×10⁻⁵ μN | ≤ 0.07 μm — sub-optical | 0.5 μN (~10⁴× high) |
| 50 mW | boil transient | 22 μg/s | ~3×10⁻³ μN | ≤ 3 μm | 5.0 μN (~10³× high) |
| 100 mW | boil transient | 44 μg/s | ~8×10⁻³ μN | ≤ 8 μm | 10 μN (~10³× high) |
| 500 mW | atomization | 221 μg/s | ~0.08 μN (0.02–0.3 band) | ≤ 0.08 mm | 50 μN, “T/W 1.2” (~10²–10³× high) |
Bounding physics: a trapped 2 mm droplet passively evaporates at ~3 μg/s (lifetime ~10–25 min, humidity-dependent) with no laser at all — passive loss, not laser heating, dominates every “droplet life” row at gate power. “Hover on its own steam” is not achievable at 1 atm at any listed power.
The artifact menu (all mimic thrust and pass the horizontal + snap-back controls):
| Artifact | Scale | Signature |
|---|---|---|
| Thermal-acoustic node shift | ~15 μm per 2 K of beam-path air heating | beam-aligned, ms–s reversible — the perfect mimic |
| Marangoni coupling | ~0.75 μN at ΔT ≈ 5 K | 4 orders above honest recoil |
| Beam-dump convection cell | 0.15 m/s of air fakes ~0.05 μN | grows with enclosure heating |
| Laser-perturbed acoustic streaming | run-dependent | check vs drive amplitude |
Genuinely negligible and correctly ignored: photophoresis (Kn ≈ 3×10⁻⁵, deep continuum) and radiation pressure (~nN).
Gate 002 (rev A re-band): PASS = the water − glycerol differential is consistent with zero within measurement error at ≤5 mW, with common-mode displacements identified against the artifact menu. Any apparent thrust at 10⁻¹ μN scale is an artifact until proven otherwise — the original pass band (“implied absorption 0.1–1.0”) was calibrated to the wrong physics and could only be passed by measuring an artifact.
| Item | Spec | Est. |
|---|---|---|
| TinyLev acoustic levitator | 72× 16 mm 40 kHz transducers, Arduino Nano, L298N driver, 3D-printed frame — kit or self-build | $70 |
| Laser module | ≤5 mW, 650 nm red, Class 3R — the ONLY laser this sheet needs | $10 |
| Null-control ladder (rev A) | black solid beads (1–2 mm) · glycerol + india ink (Marangoni control, zero evaporation) · water + india ink | $10 |
| Laser power meter | required (rev A — was optional): absorbed-power calibration now; goggle-verification instrument for any future Class 3B work | $25 |
| OD filter/window, camera port (rev A) | blocks the specular fan that exits both enclosure holes | $10 |
| Digital scale | 0.1 g — droplet-mass bookkeeping | $12 |
| Enclosure | cardboard/foamcore, matte-black interior; black felt beam dump | $10 |
| Droplet handling | 1 mL syringe + blunt 25 ga needle | $5 |
| Camera | phone macro/slow-mo on tripod, mm-grid card behind trap | on hand |
| Photodiode (optional) | photodiode + resistor into multimeter — backscatter channel | $2 |
Deferred entirely (rev A): the 100–500 mW 445–450 nm module and OD4+ goggles. They are post-gate purchases — the honest expectation at any 1 atm power is a null differential, so the 3B laser buys risk, not data, until a reduced-pressure or pulsed-regime path is designed (Phase 1 decision).
Laser: at ≤5 mW Class 3R the residual rules still apply — beam path inside the enclosure, terminated in the dump, horizontal at desk height, never at face height. If Class 3B is ever revisited: rated goggles verified by power-meter-through-lens before first use ($30 imports routinely fail their rating); OD window on every optical port; key/switch control.
Ultrasound (rev A — upgraded from a pets note): TinyLev’s focal region runs ~155 dB at 40 kHz. Loading puts fingers and face in the near field — reduce drive amplitude while loading, keep exposure to seconds, not minutes, and keep animals out of the room (cats hear well past 40 kHz).
Magnets (rev A): this bench sits near Build 001’s Halbach array — pacemaker wearers keep distance; the array’s strong face is a genuine implant hazard.
| Symptom | Cause | Fix |
|---|---|---|
| Nothing happens | Underdyed liquid — beam passes through | More ink (match both ladder liquids) |
| Droplet atomizes on laser-on | Boiling onset / drive too hot | Lower power; smaller droplet; reduce drive |
| Droplet drifts without laser | Room air currents | Seal enclosure; settle 60 s |
| Large “thrust” on BOTH water and glycerol | Common-mode artifact (node shift / streaming / convection) | That’s the control ladder working — report it, don’t claim it |
| Displacement vertical not horizontal | Convection or beam above/below node | Re-align through node center |
Companion documents: Build Sheet 001 (Inductrack, Phase 0); Space Transportation Architecture (§Demonstration Ladder, §Technology Risk Register — heat exchanger); Phase 0 checklist (Gate 002 rev A criterion). Provenance: phase0_revA_rederive.py; continuum-recoil finding independently verified before adoption.