Squaw Valley ski area in California claims that its lifts can move 47800 people per hour. If the average lift?

Question

Squaw Valley ski area in California claims that its lifts can move 47800 people per hour. If the average lift carries people about 205 m (vertically) higher, estimate the maximum total power needed. (Assume an average mass per person of 70 kg.)

Answer 1

Energy = Force * distance = mass * acceleration * distance

mass = 47800 * 70 kg

acceleration (of gravity) = 9.8 m/s^2

distance = 205 m

therefore; Energy = 81.977 MJoules

Power = Energy/time

Power = 81.977 MJoules / 3600 seconds = 22.77 kW = 30.5 HP

Note: that's just for the people -- it ignores a lot of friction.  The power to lift the seats and the cable will be regained by the empty seats and cable going back downhill, so that's a 'wash'.

This sounds about right -- the tramway in Albuqurque has about a 1000 m vertical lift; doesn't carry nearly as many people, and it uses a 50 HP motor.

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