Meaning and mechanism
The mass flow rate of air passing through the rotor is ρAv, and the kinetic energy of the air per unit mass is v²/2. Multiplying these two factors yields the available wind energy.
If we extract energy from the air, the airflow at the rear decreases. If we completely stop the air, it becomes impossible to maintain continuous flow, which limits the recovery rate.
Relationships and conditions
P = ½ρAv³Cp, and the area of the circular rotor is πr². The theoretical limit of the Betz factor for an ideal actuator disc is Cp≤16/27.
Actual turbines exhibit startup, rated, and wind cutoff characteristics, as well as power losses. Therefore, actual power output does not continuously increase as a cube of wind speed in all conditions.
What to observe in the simulation
At fixed radius and power coefficient, doubling wind speed multiplies power by eight.
This rotor model assumes steady uniform wind. Cut-in, rated-power limits, shutdown and generator losses are omitted. Real turbine curves differ.
Key relationships and symbols
P = ½ρπr²v³Cp · Cp ≤ 16/27
| Symbol | Meaning | Unit |
|---|---|---|
| Cp | Power coefficient for extracting wind energy | Dimensionless |
| A | Rotor swept area | m² |
| v | Upstream wind speed | m/s |
Worked example
At fixed wind speed, doubling blade radius multiplies power by what factor?
4 · At fixed radius and power coefficient, doubling wind speed multiplies power by eight.
Common misconceptions
- The limit of wind power is not the limit of wind speed, but the limit of the ratio of wind energy that can be recovered under ideal conditions.