Horizontal and vertical axis wind turbines

Tip speed ratio is $\lambda = \dfrac{\omega R}{v}$, where $\omega R$ is the blade tip speed. The curve of $C_p$ against $\lambda$ shows how a rotor type behaves.

HAWT versus VAWT

Types of VAWT

• Savonius: two or three half-cylinder cups; a drag device; high starting torque, low speed, $\lambda \approx 1$, $C_p \approx 0.15$–0.2; used for water pumping and ventilation.
• Darrieus: curved or straight blades (H-rotor) with aerofoil section; lift device; $\lambda \approx 4$–6, $C_p \approx 0.35$–0.40; needs starting help.

$C_p$-$\lambda$ characteristics

 Cp
 0.5|          ___ 3-blade HAWT
    |        /     \
 0.4|      /  _.-Darrieus
    |     / /      \
 0.2|  Savonius       \
    | _/_.-'''-.       
    +---------------------- lambda
     1   2   4   6   8

• Multi-bladed American windmill: peak at $\lambda \approx 1$, high torque, low $C_p$ (about 0.3) and good for pumping.
• Three-blade HAWT: peak $C_p$ at $\lambda \approx 6$–8, high speed, suitable for electricity.
• Each rotor has one optimum $\lambda$; away from it $C_p$ drops, so variable-speed operation keeps $\lambda$ near the optimum.