Energy and Human Ambitions on a Finite Planet, 2021a

16 Small Players 280
not expect geothermal to assume a large role in the energy l<strong>and</strong>scape of
tomorrow.
16.2 Tidal Capture
Table 10.2 (p. 168) indicates that the earth currently receives 3 TW of
power in the form of tidal energy. Gravity from the moon (<strong>and</strong> the sun 16 )
tug on the earth, pulling slightly harder on the nearest side, <strong>and</strong> less
enthusiastically on the far side. This deforms the otherwise spherical
Earth 17 into a prolate ellipsoid, which is a fancy way to say oval—somewhat
like an egg. The bulges that form on either side (near <strong>and</strong> far; see Figure
16.1) as a consequence are more pronounced in the ocean than the l<strong>and</strong>,
but both indeed deform.
16: The tidal influence from the sun is subdominant,
at 45% the strength of lunar tides,
so for simplicity we will describe just lunar
tides from here on.
17: Actually, an even larger (21 km) effect is
the spinning motion of the earth flattening
it into an oblate ellipsoid.
bulge
Moon
(10× farther)
Figure 16.1: The moon (pictured closer here
to fit on page) raises bulges on the near <strong>and</strong>
far side of the earth, while the earth rotates
underneath, causing two high tides <strong>and</strong> two
low tides each day.
The earth rotates “under” these bulges, since the bulges point along the
Earth–Moon axis <strong>and</strong> take a month to make a complete revolution in
space, while the earth rotates once per day. At a fixed position on Earth,
then, the experience is two high tides <strong>and</strong> two low tides each day. 18 As
the tide comes in <strong>and</strong> flows out, friction between l<strong>and</strong> <strong>and</strong> water results
in energy dissipation, to the tune of 3 TW. 19
The idea for capturing this natural flow of energy is to allow the tide to
enter a bay or inlet—raising the water level by perhaps several meters—
then closing the exit, trapping the water behind a wall. At this point, the
situation is very much like a hydroelectric dam (Sec. 11.2; p. 175), but at a
much lower water height than is typical for hydroelectric dams. All the
same, exiting water can be forced through turbines turning generators to
create electricity. Draining through turbines over a 6-hour period allows
the process to begin again at low tide, opening the gates to refill the inlet
as the tide comes back in.
18: The sun also contributes, sometimes
adding to the peaks <strong>and</strong> troughs (near new
<strong>and</strong> full moon, when Earth, Moon, <strong>and</strong> Sun
are arranged along a line), <strong>and</strong> sometimes
moderating the tides by filing in the gaps a
bit (at quarter moon phases).
19: An aggressive global-scale tidal capture
enterprise could actually increase the total
tidal energy budget, which would have the
side effect of pushing the moon further
away, slowly, as is described in Sec. D.4
(p. 402).
The amount of energy depends on the area of the captured body of
water <strong>and</strong> the height of water trapped behind the wall. We use the
familiar gravitational potential energy: E mgh to calculate the energy
involved (Sec. 11.1; p. 173). If the height of water trapped behind the wall
at high tide is called h, the height of water behind the wall smoothly
transitions from h → 0 as the water drains out, so that the average height
of water behind the wall is h/2, <strong>and</strong> the gravitational potential energy
available really looks like mgh/2. The mass is density (ρ 1,000 kg/m 3 )
times volume, <strong>and</strong> volume is the area of the captured water surface,
A, in square meters, times the initial water height, h.Togetpower,we
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.