Wind turbine, conceptual question

[mikelepore]

For years I have been wondering why wind turbines are designed with very skinny blades (photo http://en.wikipedia.org/wiki/File:Turbine_aalborg.jpg ). Most of the available wind passes right through the circular "reach" of the device without touching the blades. Wouldn't it be more efficient if the blades were shaped something like those of a typical electric fan (photo http://en.wikipedia.org/wiki/File:Electric_Fan_720x1070.jpg ), or a pinwheel toy (photo http://en.wikipedia.org/wiki/File:Green_pinwheel.jpg ) ? I would have assumed that the objective would be to maximize the surface area to capture as much wind as possible. I note that the sail of a sailboat is given a shape to produce a lot of surface area. I note that expressions for flux (light, electric, magnetic) are proportional to intensity multiplied by surface area. Can anyone please explain this design shape to me?

 

[cesiumfrog]

There is a trade-off: you also want to maximise the mass of air going through the turbine. Too much obstruction and the through-flow slows down (more air bypasses around instead) and less energy can be extracted. Also consider how fast the skinny blades can move across the wind.

 

[Topher925]

Like Cesiumfrog stated, there is a trade off. Its really an optimization problem to reduce the velocity of the out flowing air as much as possible while maintaining a maximum mass flow rate. This can not be done with wide blades. This phenomenon can be described with Betz limit.

http://en.wikipedia.org/wiki/Betz'_law

 

[rcgldr]

Part of the overhead with an airfoil is the change in kinetic energy of a wind. By diverting more air at a slower speed, you get the same force (momentum related) but with less work done on the air (less kinetic energy change). It turns out that using long, "skinny" (high aspect ratio) wings is more efficient, than fat short ones. If the goal is to only divert a large amount of air a small amount, then a "fat" wing doesn't help since it's just wasted surface area because of the small amount of diversion.

One exception is for small wings at slow speeds, the wind speed times chord length called Reynolds Number becomes an issue and lower aspect ratio ("fatter") wings are used on small, slow speed model gliders for maximum efficiency. For contest models, the wing spans are limited by rules (1.5 meter, 2 meter, unlimite (usually 3 to 4 meters)), and the 1.5 meter models have low aspect ratios compared to the 3 meter and larger models.

Unlike a wing, the goal of a wind turbine is to generate power, not force, efficiently. However power = force x speed, and long thin blades increase the average "speed" of the blades because of the larger radius.