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Why Only One Set Of Blades On A Wind Turbine?

We’re all familiar with the iconic three-bladed wind turbine, whether against a backdrop of blooming tulips in the Netherlands, spinning slowly over waving grain fields in the prairies, or sprayed with the salt water of the North Sea. But why do they have one set of blades, and why are the blades in front of the mast?

Let’s deal with these one at a time.

First, let’s look at the stacked model. The image on the left is a standard three-blade horizontal-axis wind turbine with an 80 meter mast and 50 meter blades. The grey circle represents the swept area. The image on the right is a stacked model with the same height of mast and non-overlapping 20 meter blades. The small grey circles are the swept area while the large circle is exactly the same size as the one in the image on the left.

Screen Shot 2016-05-30 at 3.24.45 PM

Putting two sets of blades on the same height mast has one very obvious problem that should be visible from the diagram alone, and one less obvious problem.

The amount of energy from the wind is a function of two things: swept area and wind velocity. The swept area is calculated by pi*r^2. Energy from the wind is a maximum of Betz’ Limit of 59.3% of available energy, and available energy is calculated from the cube of wind velocity (P=1⁄2*ρ*A*v^3 where ρ = density, A = Area, and v = velocity).

The swept area of the left turbine with its 50 meter blades is about 7,850 square meters. Assuming 20 meter blades on the turbine on the right to give a little spacing between blade tips, and pushing the lower set of blades a little lower, we see a swept area of about 2,510 square meters, or about 32% the first swept area.

So, just stacking two sets of blades that don’t overlap on a wind turbine would result in about a 68% loss of potential harvested energy. If we overlapped 30 meter blades, we’d only see a swept area of about 75% of the simpler turbine without some additional problems that will be discussed later.

Screen Shot 2016-05-27 at 5.31.25 PMThe less obvious factor is related to the energy being a factor of the cube of wind velocity, as wind velocity increases further from the ground due to laminar flow drag from the ground, trees, etc. This simple visual gives a sense of it, but the formula is called the wind power profile law and is calculated as:

Screen Shot 2016-05-30 at 3.19.32 PM

Turning this into a table provides rough estimates of wind velocity at various altitudes.

We can see that the wind power speed increases relatively slowly with height, but the power density increases rapidly, as it is increasing by the cube of velocity.

Back to the diagram of the turbines, we can easily see that a lot more of the swept area of the single turbine model is going to be in stronger air and we can calculate roughly what that will mean. With the velocity variance, we see that we would get about 29% of the energy from the stacked turbine as from the standard turbine, or about 10% less than just the difference in swept area would suggest.

As for the rotors being in front of the mast and not having an extra pair behind the mast, that’s a different problem, but there is a relationship.

The first part of the relationship is that they would be so close together that they would effectively still be limited to Betz’ Law, so they could only achieve a 59.3% maximum efficiency, not double as would seem to be intuitive.

The second is that wake effects prevail very strongly in that situation. The downwind blades are flying in much more turbulent air due to eddies from the turbine blades that are upwind. As turbine blades are airfoils which get a significant vector of energy from aerodynamics, not simply the pressure of wind on the blades, this seriously impacts the downwind blades’ aerodynamic efficiencies. Typically, cavitation and stalling of the airfoil are regular occurrences in this situation, which leads to substantially reduced generation but also to very substantially increased stress and strain on the device. This, in turn, leads to greater engineering for strength and increased maintenance in some combination, which makes it uneconomical fairly rapidly.

Downwind blades also increase wind turbine noise substantially, specifically low-frequency thumping from the stalling of the blade. An attempt was made to build self-stabilizing turbines with rotors downwind from the mast to avoid having to yaw the turbine into the wind using auxiliary power. The rotor passing behind the mast caused regular stalling and very low low-frequency thumping that propagated a long way, causing significant irritation to nearby residents.

This combination of turbulent air reducing efficiency, increasing maintenance concerns, and increasing noise is another reason why putting two sets of blades one above the other with an overlap is not a good idea. It just increases the problems without increasing generation, and the interaction would likely reduce the 30 meter example’s actual generation even further.

Modern, utility-scale wind turbines are actually marvels of concinnity and compromise. They have an apparently simple design which is highly effective at achieving its goals. They have no unnecessary parts. And they work very well and inexpensively.

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