Windenergie 3 - Rotor Aerodynamics

29 April 2026, Po Wen Cheng

Blade Design According to Betz and Schmitz (Repetition)

Diagram on Slide 6

To extract the maximum amount of Energy from the Wind, the Velocity infront of the rotor has to be 2/3 and 1/3 far behind the rotor. Tangential velocity $\Omega_r$ is much bigger than the wind velocity.
Tip Speed Ratio is the ratio between these two velocities, can be as high as 10 on modern wind turbines - Tangential speed is ten times higher than wind speed
Together, these two velocity form the inflow velocity $C$

Schmitz: $\frac{\alpha_3}{\alpha_1} = \frac{1}{3}$
Betz: $\frac{v_3}{v_1} = \frac{1}{3}$

\ Skizze 1, also see Slide 8

At the outer part of the rotor, you dont need to consider the tangential induction, because Dominating velocity component at the tips is $\Omega_r$

Blade Element Momentum Method (BEM)

Iteration Steps

  1. Initial guess: $a_0 = \frac{1}{3}$
  2. $\alpha_2 = arctan(\frac{a-\alpha_i}{\frac{r}{R}\lambda_A})$
  3. Angle of attack: $\alpha_{AoA} = \alpha_2-\alpha_{Bau}$
  4. Airfoil coefficients from polars: $c_{L_{(\alpha_{AoA})}}$ und $c_{D_{(\alpha_{AoA})}}$
  5. $\alpha_{i+1}$ calculate:

$$ \alpha_{i+1} = \frac{(1-a_i)^2+(\lambda \cdot \frac{r}{R})^2}{2 \cdot \pi \cdot r \cdot 4 \cdot (1- a_i)} \cdot t \cdot z \cdot [c_A \cdot cos(\alpha_2) + c_W \cdot sin(\alpha_2)] $$

Extensions and Correction Models