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 m^{3}. (I usually round this to 1 kg

per m^{3}, 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.