tidal amplitude (half-range) h(m) |
optimal boost height b(m) |
power with pumping (W/m ^{2}) |
power without pumping (W/m ^{2}) |
---|---|---|---|

1.0 | 6.5 | 3.5 | 0.8 |

2.0 | 13 | 14 | 3.3 |

3.0 | 20 | 31 | 7.4 |

4.0 | 26 | 56 | 13 |

that generation has an efficiency of *ε*_{g} = 0.9 and that pumping has an

efficiency of *ε*_{p} = 0.85. Let the tidal range be 2*h*. I’ll assume for simplicity

that the prices of buying and selling electricity are the same at all times, so

that the optimal height boost *b* to which the pool is pumped above high

water is given by (marginal cost of extra pumping = marginal return of

extra water):

Defining the round-trip efficiency *ε* = *ε*_{g}*ε*_{p}, we have

For example, with a tidal range of 2*h* = 4 m, and a round-trip efficiency of

*ε* = 76%, the optimal boost is *b* = 13 m. This is the maximum height to

which pumping can be justified if the price of electricity is constant.

Let’s assume the complementary trick is used at low tide. (This requires

the basin to have a vertical range of 30 m!) The delivered power per unit

area is then

where *T* is the time from high tide to low tide. We can express this as the

maximum possible power density without pumping, *ε*_{g}2*ρgh*^{2}/*T*, scaled up

by a boost factor

which is roughly a factor of 4. Table G.10 shows the theoretical power

density that pumping could deliver. Unfortunately, this pumping trick

will rarely be exploited to the full because of the economics of basin con-

struction: full exploitation of pumping requires the total height of the pool

to be roughly 4 times the tidal range, and increases the delivered power

four-fold. But the amount of material in a sea-wall of height *H* scales as

*H*^{2}, so the cost of constructing a wall four times as high will be more than

four times as big. Extra cash would probably be better spent on enlarging

a tidal pool horizontally rather than vertically.

The pumping trick can nevertheless be used for free on any day when

the range of natural tides is smaller than the maximum range: the water