G   Tide II

Power density of tidal pools

To estimate the power of an artificial tide-pool, imagine that it’s filled
rapidly at high tide, and emptied rapidly at low tide. Power is generated
in both directions, on the ebb and on the flood. (This is called two-way
generation or double-effect generation.) The change in potential energy
of the water, each six hours, is mgh, where h is the change in height of
the centre of mass of the water, which is half the range. (The range is the
difference in height between low and high tide; figure G.1.) The mass per
unit area covered by tide-pool is ρ × (2h), where ρ is the density of water
(1000 kg/m3). So the power per unit area generated by a tide-pool is

2ρhgh ,
6 hours

assuming perfectly efficient generators. Plugging in h = 2 m (i.e., range
4 m), we find the power per unit area of tide-pool is 3.6 W/m2. Allowing
for an efficiency of 90% for conversion of this power to electricity, we get

power per unit area of tide-pool    3 W/m2.

So to generate 1 GW of power (on average), we need a tide-pool with an
area of about 300 km2. A circular pool with diameter 20 km would do the
trick. (For comparison, the area of the Severn estuary behind the proposed
barrage is about 550 km2, and the area of the Wash is more than 400 km2.

If a tide-pool produces electricity in one direction only, the power per
unit area is halved. The average power density of the tidal barrage at
La Rance, where the mean tidal range is 10.9 m, has been 2.7 W/m2 for
decades (p87).

The raw tidal resource

The tides around Britain are genuine tidal waves. (Tsunamis, which are
called “tidal waves,” have nothing to do with tides: they are caused by
underwater landslides and earthquakes.) The location of the high tide (the
crest of the tidal wave) moves much faster than the tidal flow – 100 miles
per hour, say, while the water itself moves at just 1 mile per hour.

The energy we can extract from tides, using tidal pools or tide farms,
can never be more than the energy of these tidal waves from the Atlantic.
We can estimate the total power of these great Atlantic tidal waves in the
same way that we estimate the power of ordinary wind-generated waves.
The next section describes a standard model for the power arriving in

Figure G.1. A tide-pool in cross section. The pool was filled at high tide, and now it’s low tide. We let the water out through the electricity generator to turn the water’s potential energy into electricity.