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The science
Magnus force on a spinning cylinder
A cylinder spinning in a stream drags a layer of air round with it, so the flow is faster on the side where the surface moves with the wind and slower on the other: a pressure difference, and a force sideways to the flow. Ideal-flow theory gives a circulation Γ = 2 π R2 ω and the Kutta-Joukowski lift per metre L' = ρ V Γ, i.e. a lift coefficient CL = 2 π SR with the spin ratio SR = ω R / Va. Real rotors fall short of that: the model uses CL = kAR x / (1 + (x/7.5)1.6)1/1.6 with x = 0.8 · 2 π SR, which saturates near 6 to 7, and end plates make the effective aspect ratio AR = 1.6 H/D.
Drag and the apparent wind
CD = 0.45 + 0.35 e-SR + CL2/(π AR) (profile plus induced drag). The rotors feel the apparent wind, the true wind minus the ship's velocity: Va = Vw - Vs. Lift acts at right angles to Va (the spin direction is chosen so the forward component is positive) and drag along it; per rotor F = ½ ρa Va2 D H (CL, CD). Because the apparent wind swings ahead as the ship speeds up, the best true wind angles are near the beam.
Hull, propeller and the speed balance
Hull resistance is ½ ρw S V2 [(1+k) Cf + Cw] with the ITTC-1957 line Cf = 0.075/(log10 Re - 2)2, form factor 0.25, a Froude-number wave term and a 1.8 factor for roughness and appendages. The propeller thrust is T = ηp P / V. Speed follows m dV/dt = T - Rhull + Fx,rotors + Fx,windage; with a speed governor the engine power falls until the target speed is just held. Fuel saving compares engine power with the same speed and no rotors, charging the rotor motors at 0.6 of their electrical power (spin power ≈ Cf ½ ρ (ωR)3 2 π R H / 0.85).
Honest simplifications
Steady coefficients fitted to the shape of published spinning-cylinder data rather than a specific rotor; no leeway, rudder trim, heel or wave added resistance (the 3D ship heels only for show); wind at deck height only, no boundary-layer gradient; constants are plausible orders for a 130 m cargo ship, not a design. Independent educational model, not affiliated with any rotor manufacturer.