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Turning the generator is the job of the turbine blades. This page shows that it is quite easy to calculate the available power using simple physics equations.

## Calculating Energy and Power

Imagine a cylindrical volume of air approaching a wind turbine. If we can work out how much kinetic energy it has, then we can calculate how much energy is available. The amount of energy available per second gives us the power.

The density of air is 1.2 kg m

If the length of the cylinder is 15 metres and the wind speed is 15 ms

Kinetic energy = 1/2 mv

If all that kinetic energy is transferred to the turbine in 1 second, what is the power of the turbine?

Do you think that all the energy will be transferred? See

If all the energy was extracted from the wind, the air would stop behind the turbine. It turns out that you can never convert more than 59% of the wind energy into rotational energy in the turbine.

Will altitude make any difference to available power?

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**Figure 3: **This Siemens 6 MW turbine has a 77 m radius. The swept area is 18,629 m^{2} and a maximum rotation speed of 11 revolutions per minute. (Courtesy of Siemens.)

- What is the mathematical relationship between wind speed and power output?

- What is the mathematical relationship between blade length and power output?

- For the turbine in Figure 3, what is the maximum speed of the blade tips in km per hour?

- The equation for calculating electrical power is Power (in watts) = Voltage x Current (P=VI).
If the generator is developing a voltage of 690 V and the power output is 6 MW, what is the current in amps running down the copper cables to the grid connection at the base of the tower?

- The tidal flow turbine uses the energy of flowing water. Find out the density of water and compare it to the density of air. How many times more kinetic energy is in flowing water compared to wind blowing at the same speed?

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How does a wind turbine work? (Courtesy of Alstom.)

The copper content per installed wind turbine is 2.5–6.4 tonnes per megawatt, as follows:

Generator: 0.7–4.0 tonnes of copper
Cabling: 0.7–1.0 tonnes of copper
Transformers: 0.7–1.4 tonnes of copper.

**Figure 2:** Diagram showing why 100% energy capture by the wind turbine is not possible. (Wikimedia)