Science Puzzle
How Much More Power Is in Twice the Wind?
A wind turbine makes electricity from moving air. On a breezy day, with the wind at 5 metres a second, there's a certain amount of power in the wind passing through its blades. The next day the wind blows at 10 metres a second, exactly twice as fast.
How much more power is there in the wind passing through the blades?
The Answer
8 times as much. The power in the wind rises with the cube of its speed: 2 × 2 × 2 = 8.
Two things change at once. First, each kilogram of air is moving twice as fast, and the energy of anything moving goes up with the square of its speed, so each kilogram carries 4 times the energy. Second, faster wind delivers more air: twice as many kilograms sweep through the blades every second. Four times the energy in each kilogram, arriving twice as quickly, gives 8 times the power.
That's why wind farms are put on hilltops and out at sea, where the wind is a little stronger. A site where the wind blows just 10 per cent faster on average has about a third more power in its wind. It's also why turbines have to protect themselves in a gale: at around 25 metres a second they turn their blades edge-on to the wind and stop.
No turbine can catch all of that power, though. If it stopped the air dead, the air would pile up and no more could flow through. The most any turbine can take, in theory, is about 59 per cent; real ones manage a good deal less.
The principle: Wind power rises with the cube of wind speed. Doubling the speed doubles the air arriving each second and quadruples the energy each kilogram carries, so the power goes up eightfold.