EPG design session v3: reasoning

Base-grid sweep, 20,736 candidates, scoring on a blend of net output and efficiency. I was varying bore, loop length, coil count and turn-count, spiral pitch, and holding the medium fixed at 25% magnetite slurry, 65% remanence (M 61.8 kA/m, ~583 G in the 80mm bore). Flow parked at 1 m/s laminar throughout.

Winner (#1): 80mm bore, 4×1800-turn AWG18 coils, 39.77Ω. It puts 114 V into a 100Ω load at 12.5 Hz, 66.8 W net. Read the budget honestly. The electrical gross is 93.3 W; coil I²R eats 26.6 W of that before anything reaches the load — 28% of gross gone to copper heat. On the mechanical side, the mover is the Lenz reaction, not the pump: hydraulic input is only 3.55 W and eddy loss in the tube wall is negligible (3.4e-7 W). The 96.9 W mechanical input is overwhelmingly the reaction torque against the induced current. So η=68.9% is output-per-mechanical-input, and mechanical input is being supplied by whatever accelerates the slurry. This is a transducer, not a source — it consumes ~97 W of shaft/pump work to deliver 66.8 W. It does not overproduce.

Modulation depth 0.974 is why it wins at all. Coil-length/pitch is 0.13 — the coil is short against the 80mm magnetic pitch, so the pickup sees nearly full field swing as the polarized column passes. A uniform, unmodulated column induces nothing (dΦ/dt→0); the whole output rides on that spatial contrast. Compare #4, where 25mm coils drop depth to 0.847 and net falls despite identical copper.

What's still wrong: coil I²R is the dominant loss and I'm not pricing it against turns properly — #2 doubles coils for 2× net but craters η to 55%. Also everything sits at Re 1829 laminar; I never tested whether flow speed buys modulation bandwidth. And matched load (39.77Ω) is ignored — I'm driving 100Ω.

Next session: sweep flow velocity (0.5–3 m/s) to separate hydraulic cost from induced EMF; sweep spiral pitch against coil length to push modulation depth past 0.97 at lower copper; and evaluate at the matched 39.77Ω load, not 100Ω, to see real deliverable power. Add a copper-mass penalty term to the score so #2-style brute-force stops ranking equal to #1.