In the previous article we have discussed about how wind energy and wind power is calculated when wind hit the wind turbine. However, we don’t yet discuss about what is the energy that could be collected by the wind turbines as well as their limitation and efficiency. Readers who might missed the article, is advisable to read the first article, What is Wind Energy? An Introduction. This is important because in this article we are going to go on some theory and calculation, which is closely related to the previous article.

Vestas V164 is the world’s largest ocean wind turbine

In 1919 a German physicist Albert Betz had concluded that no wind turbine can convert more than 59.3% of the kinetic energy of the wind into mechanical energy turning a rotor. Today this is known as Betz Limit or Betz Law.

However, the same maximum result was obtained earlier by a British scientist Lanchester in 1915 and also obtained by a Russian aerodynamic scholar Zhukowsky in 1920. Al Jazari, the father of robotic engineering even a number of centuries earlier had explained about the utilization of wind energy in his book, the Book of Ingenious Devices (Arabic: Kitab al-Hiyal).

Wind Energy: Kinetic Energy of Wind Turbine

Betz limit is actually has nothing to do with the efficiency of the wind turbine rather than the maximum limit of any wind turbine could collect wind energy. The simple explanation for this limit could be described by the diagram below.

The incoming wind energy to the wind turbine is at 100%, say E_input = 100. Wind energy is a kinetic energy and is given by equation ½ mv². The equation describe that the kinetic energy is relatively dependent on the speed (or velocity) of the wind, v.

For example, if the wind turbine could collect or gain wind’s kinetic energy 100% from the incoming wind E_input. The wind energy at the exit of the wind turbine would be zero. The velocity or speed of the wind also would be zero.

If the wind stops moving at the exit of the wind turbine, then no more fresh or new wind could get in, because it’s being blocked. This explains why that the wind turbine could not gain 100% of kinetic energy from wind rather than maximum of 59.3% from the total wind’s kinetic energy.

For a wind turbine to rotate and collect wind’s kinetic energy there has to be some wind movement to the turbine, some of the wind energy collected and some is left and flow out.

Wind Energy: Turbine Efficiency

Based on the first article that we have discussed previously about wind power and wind energy, all those numbers could be multiply with 0.593. This is the theoretical maximum power of any design of wind turbines.

Equation from the previous article for power of wind hitting the turbine:

Power_wind = 1/2 x Swept Area x Air Density x Velocity³

Theoretical maximum power of wind turbine:

Power_max-turbine = 0.593 x (1/2 x Swept Area x Air Density x Velocity³)

In real world limit below “Betz limit” such as 0.35 to 0.45 is a common even among the world’s best designed wind turbines. So if somebody comes to convince you saying that their product could collect 80% from wind energy you already know the answer. On the other hand if somebody comes and telling you the truth that their design could collect only 25% of wind energy, you have to shake his hand immediately for his honesty.

Further, there other inefficiencies in the whole system that could not be avoided such as generator, bearings, power transmission etc. Thus approximately 10 to 30% of the power of the wind is actually could be converted to electricity.

This is the link for some models of smaller wind turbines for home usage if readers might be interested to see, Wind Energy for Home. In their website you could find as well some DIY models which are easy for installation. Hopefully, we are going to discuss more on other topics of wind energy in the next coming articles. Thanks for reading.

Next & Previous articles in series:

• What is Wind Energy? An Introduction
• Horizontal and Vertical Axis Wind Turbine – An Introduction