Chapter 10, Problem 71P

You’re asked to check the specifications for a wind turbine. The turbine produces a peak electric power of 1.50 MW while turning at its normal operating speed of 17.0 rpm. The rotational inertia of its rotating structure—three blades, shaft, gears, and electric generator—is 2.65 × 10⁷ kg·m². Under peak conditions, the wind exerts a torque of 896 kN·m on the turbine blades. Starting from rest, the turbine is supposed to take less than 1 min to spin up to its 17-rpm operating speed. The generator is supposed to be 96% efficient at converting the mechanical energy imparted by the wind into electrical energy. During spin-up, the electric generator isn’t producing power, and the only torque is due to the wind. Once the turbine reaches operating speed, the generator connects to the electric grid and produces a torque that cancels the wind’s torque, so the turbine turns with constant angular speed. Does the turbine meet its specifications?