Wind Turbine Power: Calculating Max Output

In summary, the conversation discusses the calculation of the maximum power that can be obtained by a wind turbine. It is derived from the equation Power = \frac{1}{2}\rho A v^3, where A represents the area of the turbine and can be calculated using the formula A = \pi r^2. However, in a real-life situation, the blades of the turbine are attached to a center, so the question arises whether the entire circle or just the "doughnut-like" shape should be used in the calculation. The latter can be calculated using the formula A = \pi (r_{total}^2 - r_{center}^2). The conversation also mentions the finite efficiency of turbines and the Betz
  • #1
Donald.
1
0
Hello everyone, I've found these forums extremely helpful in the past and I've decided to create an account in order to answer a question that has been going in my mind and I can't seem to find the answer.

The power a wind turbine can generate can be derived from the equation:
[itex]Power = \frac{1}{2}\rho A v^3[/itex] and the area ([itex]A[/itex]) of the turbine can be calculated using the area of a circle equation: [itex]A = \pi r^2[/itex].

This equation would give you the theoretical maximum power obtained by the turbine, however all turbine have a center from which the blades are attached. In a 'real life' situation would one use the whole circle or the 'doughnut like' shape area to calculate the maximum power that can be obtained?

The doughnut area could be calculated using the formula:
[itex]A = \pi r_{total}^2 - \pi r_{center}^2[/itex]


Thank you,
Donald.
[itex]A = \pi (r_{total}^2 - r_{center}^2)[/itex]
 
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  • #2
Your formula is giving the total Kinetic Energy in the volume of air that passes each second. You could never get that much out at one location because that would imply that the wind has to have zero speed afterwards - and how do you get rid of it all?

Any turbine (air / gas / water) can only get a certain amount of the power out (finite efficiency) and I think the efficiency is, in fact, so low that the small adjustments you suggest, although correct, are not really relevant in the overall scheme of things.


This link suggests that you can't do better than 60% in any case. The Betz Limit, apparently. God that man was such a pessimist.
 

1. How is the maximum output of a wind turbine calculated?

The maximum output of a wind turbine is calculated by multiplying the rated power of the turbine (in kilowatts) by its capacity factor (a percentage representing the average power output of the turbine over time).

2. What factors influence the maximum output of a wind turbine?

The maximum output of a wind turbine is influenced by several factors, including the turbine's size and design, wind speed, air density, and temperature. The location and terrain also play a role in determining the maximum output.

3. How do wind speed and air density affect the maximum output?

Wind speed and air density have a direct impact on the maximum output of a wind turbine. Higher wind speeds and lower air density result in a higher maximum output, while lower wind speeds and higher air density result in a lower maximum output.

4. Can the maximum output of a wind turbine be accurately predicted?

While the maximum output of a wind turbine can be estimated based on factors such as wind speed and turbine design, it is difficult to accurately predict due to the constantly changing nature of wind. Additionally, external factors such as maintenance and changes in technology can also affect the maximum output.

5. How can the maximum output of a wind turbine be optimized?

The maximum output of a wind turbine can be optimized by carefully selecting the location and design of the turbine, regularly maintaining and monitoring its performance, and utilizing advanced technology such as wind forecasting to predict and adjust for changes in wind speed and direction.

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