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 | ρU^{3} |
^{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/m^{2}. There are many places around the British Isles

where the power per unit area of tide farm would be 6 W/m^{2} or more. This

power density is similar to our estimates of the power densities of wind

farms (2–3 W/m^{2}) and of photovoltaic solar farms (5–10 W/m^{2}).

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/m^{2}) |
||

0.5 | 1 | 1 |

1 | 2 | 8 |

2 | 4 | 60 |

3 | 6 | 200 |

4 | 8 | 500 |

5 | 10 | 1000 |