This 2D companion replaces the 3D version's arbitrary "kick force" slider with the actual aerodynamics that govern a real wind rotor: the power coefficient Cp(λ,β) as a function of tip-speed ratio λ and blade pitch β (Heier's generic wind-turbine model, the standard textbook/Simulink Cp curve), and Betz momentum theory linking Cp to the axial induction factor a and thrust coefficient Ct.
λ = ωR / v (tip-speed ratio)
λi = 1 / (1/(λ+0.08β) − 0.035/(β³+1))
Cp = 0.5176·(116/λi − 0.4β − 5)·e^(−21/λi) + 0.0068λ
Cq = Cp / λ (torque coefficient)
τ_aero = ½ρAv²R·Cq
4a(1−a)² = Cp → solve for a (Betz induction factor)
Ct = 4a(1−a) (thrust coefficient)
T = ½ρAv²·Ct (rotor thrust)
I·dω/dt = τ_aero − k_load·ω² − c_f·ω
- Wind speed and blade pitch jointly set λ and Cp; pitching the sails toward feather (high β) collapses Cp toward zero — the same mechanism real turbines use to shed power in high wind.
- Generator load is the quadratic electromagnetic/brake torque the rotor must overcome; raising it slows the equilibrium RPM for the same wind.
- The rotor settles at the ω where aerodynamic torque balances load and friction torque — nudge any slider and watch the RPM readout relax to a new equilibrium rather than jump instantly.
- Tower base moment = thrust force × hub height. Sustained moment above the rotor's safe threshold accumulates structural fatigue; a Gust (a real transient wind spike, not a decorative click) tests how the tower responds to a sudden overload instead of a scripted collapse animation.