EPG design session v4: reasoning

This session split the two costs that were tangled together last time. I swept flow velocity to separate the hydraulic pumping penalty from the induced EMF, pushed modulation depth by trading spiral pitch against coil length, and — the important change — I stopped scoring at a fictitious 100Ω and started reading each candidate at its own matched load. 3600 candidates, slurry medium at φ=25%, 65% remanence throughout.

The winner (#1) is a 5×2400-turn AWG18 array, 66.28Ω, riding a 60mm-pitch spiral in an 80mm bore. Physically it says this: at 1.00 m/s the column moves slowly, Re 1829, dead laminar, and the hydraulic input is trivial — 3.55 W to push the slurry. That is the whole point of the velocity sweep: pumping is NOT what this costs. The cost is Lenz reaction. Gross electrical is 384.67 W, and of the 388.22 W mechanical input, essentially all of it above the 3.55 W hydraulic and the negligible 0.6 µW eddy is the back-reaction against the magnetized column being decelerated as it induces current. Then coil I²R eats 153.33 W of the gross before it ever reaches the load, leaving 231.34 W net. η = 59.6%. That is a loss. This device consumes 388 W mechanical to deliver 231 W electrical; it is a generator with a mediocre efficiency, not an overunity anything, and I will not pretend otherwise.

Modulation depth 0.971 is what makes it work at all — a uniform magnetized column has dΦ/dt = 0 and induces exactly nothing. The 60mm pitch against the 8mm coil (ratio 0.13) chops the field into a spatial ripple the coils can see at 16.7 Hz.

What is still wrong: I²R is 40% of gross — that copper mass is strangling the thing. 66Ω is too much wire for the current. And the flow is so laminar the mixing/refresh of polarization is questionable at 1 m/s.

Next session: sweep AWG heavier (16, 14) to break the I²R wall at fixed turns; sweep velocity upward past laminar to test whether induced EMF scales faster than the hydraulic penalty grows; and push modulation depth below 0.10 coil/pitch to find where diminishing ripple sets in.