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Energy From Wind

Swept area, blade length and turbine mass

  • 3 things to know
  • AS 1

Overview

Swept area and its calculation, how power grows with blade length, why doubling blade length multiplies mass by about eight, glass and carbon fibre blades, stiffness and fatigue, and siting limits on blade size.

What you need to know

Answer each one before you reveal it.

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Key term

What is the swept area of a wind turbine rotor?

Key term

How does power output depend on swept area?

Numbers

Calculate the swept area of a rotor 100 m in diameter.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is the swept area of a wind turbine rotor?

    Model answer

    The swept area is the circular area traced out by the blade tips as the rotor turns. Swept area is calculated as A = πr², where r is the rotor radius.

  2. 2

    How does power output depend on swept area?

    Model answer

    Power output is directly proportional to swept area, because a larger area intercepts more moving air each second. A rotor with twice the swept area captures twice the power.

  3. 3

    Calculate the swept area of a rotor 100 m in diameter.

    Model answer

    The swept area is about 7,850 m². The working is π × 50² = 7,854 m².

  4. 4

    Calculate the swept area of a small turbine with a rotor diameter of 3 m.

    Model answer

    The swept area is about 7.1 m². The radius is 1.5 m, and π × 1.5² = 7.07 m².

  5. 5

    Calculate the power available to a 3 m diameter rotor in an 8 m/s wind, taking air density as 1.2 kg/m³.

    Model answer

    About 2.2 kW of power is available in the wind. The working is ½ × 1.2 × 7.07 × 8³ = 2,170 W.

  6. 6

    Demonstrate the effect of blade diameter on power output by comparing rotors of 2 m and 4 m diameter in the same wind.

    Model answer

    The 4 m rotor sweeps 12.6 m², four times the 3.14 m² of the 2 m rotor. The larger rotor therefore captures about four times the power.

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