normal; the speed of such a wind is therefore comparable to the typical
speed of the cyclist, which is, let’s say, 21 km per hour (13 miles per hour,
or 6 metres per second). In Cambridge, the wind is only occasionally this
big. Nevertheless, let’s use this as a typical British figure (and bear in mind
that we may need to revise our estimates).

The density of air is about 1.3 kg per m3. (I usually round this to 1 kg
per m3, which is easier to remember, although I haven’t done so here.)
Then the typical power of the wind per square metre of hoop is

(B.3)

Not all of this energy can be extracted by a windmill. The windmill slows
the air down quite a lot, but it has to leave the air with some kinetic energy,
otherwise that slowed-down air would get in the way. Figure B.2 is a
cartoon of the actual flow past a windmill. The maximum fraction of the
incoming energy that can be extracted by a disc-like windmill was worked
out by a German physicist called Albert Betz in 1919. If the departing wind
speed is one third of the arriving wind speed, the power extracted is 16/27
of the total power in the wind. 16/27 is 0.59. In practice let’s guess that a
windmill might be 50% efficient. In fact, real windmills are designed with
particular wind speeds in mind; if the wind speed is significantly greater
than the turbine’s ideal speed, it has to be switched off.

As an example, let’s assume a diameter of d = 25m, and a hub height
of 32 m, which is roughly the size of the lone windmill above the city of
Wellington, New Zealand (figure B.3). The power of a single windmill is

(B.4)
(B.5)
(B.6)

Indeed, when I visited this windmill on a very breezy day, its meter
showed it was generating 60 kW.

To estimate how much power we can get from wind, we need to decide
how big our windmills are going to be, and how close together we can
pack them.

Figure B.2. Flow of air past a windmill. The air is slowed down and splayed out by the windmill.
Figure B.3. The Brooklyn windmill above Wellington, New Zealand, with people providing a scale at the base. On a breezy day, this windmill was producing 60 kW, (1400 kWh per day). Photo by Philip Banks.