To estimate the energy in wind, let’s imagine holding up a hoop with area
A, facing the wind whose speed is v. Consider the mass of air that passes
through that hoop in one second. Here’s a picture of that mass of air just
before it passes through the hoop:
And here’s a picture of the same mass of air one second later:
The mass of this piece of air is the product of its density ρ, its area A, and
its length, which is v times t, where t is one second.
The kinetic energy of this piece of air is
So the power of the wind, for an area A – that is, the kinetic energy passing
across that area per unit time – is
This formula may look familiar – we derived an identical expression on
p255 when we were discussing the power requirement of a moving car.
What’s a typical wind speed? On a windy day, a cyclist really notices
the wind direction; if the wind is behind you, you can go much faster than
miles/ hour |
km/h | m/s | Beaufort scale |
---|---|---|---|
2.2 | 3.6 | 1 | force 1 |
7 | 11 | 3 | force 2 |
11 | 18 | 5 | force 3 |
13 | 21 | 6 | force 4 |
16 | 25 | 7 | |
22 | 36 | 10 | force 5 |
29 | 47 | 13 | force 6 |
36 | 58 | 16 | force 7 |
42 | 68 | 19 | force 8 |
49 | 79 | 22 | force 9 |
60 | 97 | 27 | force 10 |
69 | 112 | 31 | force 11 |
78 | 126 | 35 | force 12 |