times more power by putting 99 more turbines downstream from the first.
The oomph gets extracted by the first one, and there isn’t any more oomph
left for the others. The “you can have only one row” assumption is the right
assumption for estimating the extractable power in a place where water
flows through a narrow channel from approximately stationary water at
one height into another body of water at a lower height. (This case is
analysed by Garrett and Cummins (2005, 2007).)

I’m now going to nail my colours to a mast. I think that in many
places round the British Isles, the “tide is like wind” assumption is a good
approximation. Perhaps some spots have some of the character of a narrow
channel. In those spots, my estimates may be over-estimates.

Let’s assume that the rules for laying out a sensible tide farm will be
similar to those for wind farms, and that the efficiency of the tidemills will
be like that of the best windmills, about 1/2. We can then steal the formula
for the power of a wind farm (per unit land area) from p265. The power
per unit sea-floor area is

 power per tidemill = π 1 ρU3 E area per tidemill 200 2

Using this formula, table G.6 shows this tide farm power for a few tidal
currents.

Now, what are typical tidal currents? Tidal charts usually give the
currents associated with the tides with the largest range (called spring
tides) and the tides with the smallest range (called neap tides). Spring
tides occur shortly after each full moon and each new moon. Neap tides
occur shortly after the first and third quarters of the moon. The power
of a tide farm would vary throughout the day in a completely predictable
manner. Figure G.5 illustrates the variation of power density of a tide farm
with a maximum current of 1.5 m/s. The average power density of this tide
farm would be 6.4 W/m2. There are many places around the British Isles
where the power per unit area of tide farm would be 6 W/m2 or more. This
power density is similar to our estimates of the power densities of wind
farms (2–3 W/m2) and of photovoltaic solar farms (5–10 W/m2).

We’ll now use this “tide farms are like wind farms” theory to estimate
the extractable power from tidal streams in promising regions around the
British Isles. As a sanity check, we’ll also work out the total tidal power
crossing each of these regions, using the “power of tidal waves” theory,
to check our tide farm’s estimated power isn’t bigger than the total power
available. The main locations around the British Isles where tidal currents
are large are shown in figure G.7.

I estimated the typical peak currents at six locations with large currents
by looking at tidal charts in Reed’s Nautical Almanac. (These estimates could
easily be off by 30%.) Have I over-estimated or under-estimated the area
of each region? I haven’t surveyed the sea floor so I don’t know if some
regions might be unsuitable in some way – too deep, or too shallow, or too

U tide farm
(m/s) (knots) power
(W/m2)
0.5 1 1
1 2 8
2 4 60
3 6 200
4 8 500
5 10 1000
Table G.6. Tide farm power density (in watts per square metre of sea-floor) as a function of flow speed U. (1 knot = 1 nautical mile per hour = 0.514 m/s.) The power density is computed using (π/200)12ρU3 (equation (G.10)).