The science
P ≈ ½ ρ A Cᵈ v³ η [W]. Rotor angular speed follows dω/dt = (ωtarget − ω)/τ [rad/s²]. Battery energy: E(t+Δt) = clamp(E(t) + (Pgen − Pload − Pbrake)Δt/3600, 0, Emax) [Wh].
Assumptions: uniform air density, deterministic gusts, idealized electrical storage, simplified rotor lag. The power extraction model is approximate; Cd is an illustrative effective coefficient, not a validated turbine power coefficient. The analytic graph reference assumes steady wind and instant rotor response.