If we look at wind turbines used for power generation, they typically have 3 blades, and the blades are very slender compared to the blades of a house fan. I don't understand how such a slender blade can capture a significant amount of the wind's energy. The energy available in the wind is proportional to the swept area under the blades. But it seems to me that only a small fraction of the circular area is actually occupied by a blade, so most of the air will just pass through the circle without hitting a blade. So, how are these turbines able to extract a significant fraction of the available energy in the wind?