# B   Wind II

## The physics of wind power

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 (B.1)

So the power of the wind, for an area A – that is, the kinetic energy passing
across that area per unit time – is (B.2)

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 I’m using this formula again:

mass = density × volume
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
Figure B.1. Speeds. Buy the book on paper