A 100 m diameter, three-bladed wind turbine produces 4375 kW at a wind speed (hub height) of 12 m/s. The air density is 1.225 kg/m3. 

Find 

a) The rotational speed (rpm) of the rotor at a tip-speed ratio of 6.0. 

b) What is the tip speed (m/s)? 

c) If the generator turns at 900 rpm, what gear ratio (step-up) is needed to match the rotor speed to the generator speed? 

d) What is the efficiency of the drive train (including gearbox, shafts, and generator) under these conditions, assuming that the rotor has the maximum theoretical power coefficient?