A turbine's power output is P = ½·ρ·A·V³·Cp(λ,β), where A = πR² is the swept area, V is wind speed and Cp is the power coefficient — the fraction of the wind's kinetic energy the rotor actually extracts. Cp depends on the tip-speed ratio λ = ωR/V (how fast the blade tips move relative to the wind) and on the blade pitch angle β (how the blades are twisted relative to the wind). This lab uses the standard empirical Heier approximation for Cp:
1/λi = 1/(λ+0.08β) − 0.035/(β³+1)
Cp(λ,β) = 0.5176·(116/λi − 0.4β − 5)·e^(−21/λi) + 0.0068λ
Cp is capped at the Betz limit of 0.593 — the theoretical maximum fraction of kinetic energy any rotor can extract from a free wind stream. Feathering the blades (increasing β) spills lift and sheds power in high wind — exactly what real turbine pitch-control systems do to protect the drivetrain above rated wind speed. "Set optimal pitch" searches β for the value that maximizes Cp at the current λ.