# Is the main goal for wind turbines to take maximum energy for a given diameter?

If you increase the number of blades, that will increase torque, for the same RPM you get more power,...simple logic

So why only three blades, is main goal for wind turbine take maximum energy for given diameter?

• Multi-blade, almost full disc machines do exist -check out how they work and what they are used for. They are still sold: aermotorwindmill.com Dec 31, 2021 at 10:21
• Also check out the Betz limit. Dec 31, 2021 at 10:22
• More blades linearly increase your cost, mass and drag. But only add a tiny faction to captured wind. 3 blades already capture about 85% of the available energy in the swept area. Dec 31, 2021 at 16:27
• @JurgenM sigh. intro to turbine efficiency: Betz limit says maximum energy that can ever be extracted from a given volume of wind is 59.3% of the kinetic energy of the wind. This is max "available" energy. Actual large 3-blade offshore turbines hit 49.5%. That is 83.5% of the available energy. Not too bad. Even dinky 2-storey turbines manage 35.5% total, which is 60% of available energy. Adding more blades will up the capture percentage, but also up the drag, both aero and mechanical. not worth it, when there is so little remaining improvement available. Dec 31, 2021 at 16:45
• The goal is to extract the maximum energy for the minimum cost. Cost to build the turbine components, cost transport them and erect the turbine, cost to acquire the land the turbine sits on, etc. Dec 31, 2021 at 22:33

The function of the wind turbine is to extract as much as possible energy from the moving mass of air. The energy of a mass $$m$$ of air is $$KE = \frac{1}{2}m v^2$$

and the power is (because the mass rate is $$\dot{m} = \rho A v)$$

$$P = \frac{1}{2}\dot{m} v^2=\frac{1}{2} \rho A v^3$$

So, the energy in the air is a function of the velocity. As energy is extracted from the air, its velocity drops.

However, due to the preservation of mass, the mass rate before and after needs to be the same so:

$$\rho A_0 v_0 = \rho A_f v_f$$

where:

• $$\rho$$ is the air density which should remain the same for incompressible flows
• $$A_0, A_f$$ are the initial and final cross-sections
• $$v_0, v_f$$ are the initial and final (average) velocities

So for decreasing $$v_f$$ the cross-section will increase. See image below.

Figure: Betz tube (source wikipedia)

it is not possible to extract all energy from the moving air. If you could then the air would have no velocity, and therefore it would get stuck. Betz in 1919 calculated the theoretical limit that power can be extracted from air. That limit is 59.3%. This is the absolute maximum for any configuration.

It is true that adding more blades has the result of the air interacting more with the generator, however in that case the overa efficiency is harmed the faster the turbine operates. The following diagram shows the overall efficiency for different wind turbines.

Figure: Betz limit for various types of wind turbines (source:Van Kuik)

The horizontal axis on the graph is the wind tip ratio (which has a limit around 7 in order to avoid hypersonic flows). This is also worth looking at to understand a bit more.

• So video at 1;30 - 1;52 is wrong?youtube.com/… Dec 31, 2021 at 14:36
• @JurgenM seen that diagram in many books etc about wind energy so I’ll vote for the answer not youtube this time. Dec 31, 2021 at 16:26

Aside from the efficiency, the blades of wind turbines are basically a wing, aerofoil, the actual upwash and downwash zone are much greater than the wing's cross-section.

If the blades are too close they can interfere with each other flow stream and actually create debilitating turbulence.

The wind turbines are designed to work in a wide range of winds.

The two or three-blade format with the profile of the blades is the optimal configuration.

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to get more power out of the available wind, it is better practice to increase the diameter of the blade disc instead of adding more blades, which greatly increases the size & complexity of the main hub to which the blades are affixed.