Wind Turbine Blade Design Lab
Adjust blade count, blade length, and pitch angle to discover how turbine design affects power output. See how closely you can approach the theoretical Betz limit of 59.3% efficiency.
Guided Experiment: Pitch Angle Optimisation
Which blade pitch angle do you predict will produce the highest power output and why?
Write your hypothesis in the Lab Report panel, then click Next.
Turbine View
Controls
Power Output
Power vs Wind Speed
Data Table
(0 rows)| # | Trial | Blade Count | Blade Length(m) | Pitch(deg) | Wind Speed(m/s) | Power(W) | Efficiency(%) |
|---|
Reference Guide
Betz Limit
No wind turbine can convert more than 59.3% of the kinetic energy in the wind into mechanical energy. This upper bound was derived by Albert Betz in 1919.
The limit arises because a turbine must leave some kinetic energy in the air downstream, otherwise flow would stall and the turbine would not turn at all.
Real turbines typically achieve 35-45% efficiency, well below the theoretical ceiling, due to blade drag, tip losses, and mechanical friction.
Blade Pitch Angle
Pitch angle is the angle between the blade chord line and the plane of rotation. A well-chosen pitch maximises lift and minimises drag.
At too low an angle the blade stalls, producing turbulent flow and little lift. At too high an angle drag dominates and power drops. The optimum is typically near 10-15 degrees for most wind speeds.
Modern turbines use variable-pitch blades that rotate to maintain the optimal angle as wind speed changes.
Tip Speed Ratio
Tip speed ratio (TSR) is the speed of the blade tip divided by the wind speed. There is an optimal TSR for each blade count configuration.
Three-bladed turbines perform best at a TSR of around 6-8, making them the standard for utility-scale wind power. Increasing blade count lowers the optimal TSR and reduces overall efficiency at typical operating speeds.
Two-bladed designs have a higher optimal TSR (around 9-10) and produce more noise and mechanical stress, which is why three blades became the industry standard.
Wind Power Equation
The power available in the wind passing through a swept area A is given by:
P = 0.5 x rho x A x v^3
Where rho is air density (1.225 kg/m^3 at sea level), A is the swept area (pi x r^2), and v is wind speed in m/s. The cubic relationship means doubling wind speed increases available power eightfold.
The swept area depends on blade length squared, so longer blades capture dramatically more power from the same wind resource.
