This simulation models the aerodynamic power capture of a horizontal-axis wind turbine using the standard rotor equation P = ½ρAV³Cp, where air density ρ is 1.225 kg/m³ and A is the swept area. The power coefficient Cp is derived from a tip-speed-ratio curve and is hard-capped at the theoretical Betz limit of 16/27 ≈ 0.593. As you change the wind, pitch and rotor size, it shows in real time how much of the available wind power a turbine can actually extract.
A 2D animated turbine plus live telemetry. The script computes the Cp(λ, pitch) curve, finds the optimal tip-speed ratio λ for the current pitch, applies a small blade-count correction, then evaluates power P = Cp·½ρAV³. A side graph plots the Cp–λ curve with the Betz line and the current operating point.
Four sliders drive everything: Wind Speed (1–25 m/s), Blade Pitch (0–45°), Rotor Diameter (10–200 m) and Number of Blades (1–6). The telemetry panel reports rotor RPM, tip-speed ratio λ, Cp, efficiency relative to Betz and power output, while the bar shows how close you are to the limit.
No turbine can ever convert more than 59.3% of the wind's kinetic energy into mechanical power. Albert Betz proved this limit in 1919: slowing the air too much makes it pile up and divert around the rotor, so an optimum trade-off exists at 16/27 of the incoming power.
It calculates the aerodynamic power a turbine extracts from the wind using P = ½ρAV³Cp. Here ρ is air density (1.225 kg/m³), A is the rotor's swept area from the diameter slider, V is wind speed, and Cp is the power coefficient. It also reports rotor RPM, tip-speed ratio and efficiency relative to the Betz limit.
The Betz limit is the maximum fraction of wind kinetic energy a turbine can capture, equal to 16/27 or about 0.593. If a rotor slowed the air completely the air would stop flowing through it; if it barely slowed it, little energy would be taken. The optimum between these extremes caps the power coefficient at 59.3%, and the simulation never lets Cp exceed it.
Tip-speed ratio λ is the speed of the blade tips divided by the wind speed, λ = ωR/V. The simulation sweeps λ to find the value that maximises Cp for the current pitch, then derives rotor speed from it. Increasing blade pitch shifts and lowers the Cp curve, while changing the number of blades applies a small efficiency correction around the three-blade optimum.
It is a faithful educational approximation. The core power equation and the Betz cap are exact, and the Cp(λ, pitch) curve uses a widely cited empirical formula for variable-pitch turbines. It assumes ideal maximum-power-point tracking and steady, uniform wind, so it omits turbulence, wake losses, generator and gearbox inefficiency, and structural limits that a real turbine must handle.
Because available wind power scales with the cube of wind speed (V³). Doubling the wind speed produces roughly eight times the power, which is why a modest increase in wind has such a dramatic effect on output. This cubic relationship also explains why real turbines must shut down in very high winds to avoid structural overload.