🌬️ Wind Turbine Farm: Power Curve (2D)

This 2D companion trades the 3D scene's orbiting camera for the physics that actually decides how much power a wind farm makes: each rotor's mechanical output follows P = C_p(λ)·½ρAv³, where the power coefficient C_p is read off the standard tip-speed-ratio curve rather than assumed constant. Below the 12 m/s rated wind speed the simulated controller tracks the optimal tip-speed ratio to hold C_p near its peak — maximum power-point tracking, the strategy real turbine controllers use — so power climbs with the cube of wind speed. Above rated wind speed, blade pitch is modeled as trimming C_p down so power plateaus instead of overloading the drivetrain, and outside the 3.5–25 m/s operating window the rotor sits parked or shuts down entirely. Four sliders — wind speed, rotor diameter, turbine count and air density — feed straight into that formula, and a live readout panel tracks tip-speed ratio, power coefficient, rotor RPM, blade-tip speed and total farm output in real time.