Wind turbines are generally designed so that over the range of wind speeds at which they operate, the blade tips rotate at a speed 5-7X the wind speed.

a) If the ratio of the blade-tip speed to the wind speed is 6, sketch the direction of the wind as seen by an observer riding on the rotating blade at three points: near the hub, halfway out, and near the tip. Also show the direction of the wind as seen by a stationary observer.

b) Consider a blade that momentarily runs straight up from the hub. Imagine cutting a cross section through that blade in the horizontal plane. That cross section has the shape of an airfoil, but its orientation changes with distance from the hub. On the sketch you made in part a), draw which way it's oriented for each of the three locations. Explain why you chose the orientations you drew.

c) If the blade is 10m long and the wind speed is 10m/s, at what rate does the blade rotate? What is the ratio of that frequency to 60 Hz, the line frequency in the US electrical system?

d) To spin the magnet in the generator, a variable-ratio gear box converts the rotation frequency to something closer to 60 Hz. If the magnet rotates at exactly 60 Hz, what must be done in addition to ensure that the voltage matches the standard 110 V rms?