%\section{How to make lunar energy}
%{ Tidal resources}
The moon and earth are in a whirling, pirouetting dance around the
sun. Together they tour the sun once every year, at the same time
whirling around each other once every 28 days. The moon also turns around
once every 28 days so that she always shows the same face
to her dancing partner, the earth. The prima donna earth doesn't
return the compliment; she pirouettes once every day.
This dance is held together by the force of gravity:
every bit of the earth, moon, and sun is pulled towards every other
bit of earth, moon, and sun.
The sum of all these forces is {\em{almost}\/} exactly what's required to
keep the whirling dance on course. But there are very
slight imbalances between
the gravitational forces and the forces required to maintain the
dance. It is these imbalances that give rise to the tides.
The imbalances associated with the whirling of the moon and earth
around each other are about three times as big as the imbalances
associated with the earth's slower dance around the sun, so
the size of the tides varies with the phase of the moon,
as the moon and sun pass in and out of alignment.
At full moon and new moon (when the moon and sun
are in line with each other) the imbalances reinforce each other,
and the resulting big tides are called \index{spring tide}{\dem{spring tides}}.
(Spring tides are {\em{not}\/} ``tides that occur at spring-time;''
spring tides happen every two weeks like clockwork.)
At the intervening half moons, the imbalances partly cancel and the tides
are smaller; these smaller tides are called \index{neap tide}{\dem{neap tides}}.
Spring tides have roughly twice the amplitude of neap tides:
% 3+1/(3-1)
the spring high tides are twice as high above mean sea level
as neap high tides,
the spring low tides are
twice as low as neap low tides, and the tidal currents are twice
as big at springs as at neaps.
%
\marginfig{
\begin{center}
\mbox{\epsfbox{metapost/earth.155}}
\end{center}
%}{
\caption[a]{An \ind{ocean} covering a
billiard-ball earth. We're looking down on the
North pole, and the moon is 60\,cm off the page to the right.
% 60 earth radii radius should be 1cm if earth.mp right
The earth spins
% pirouettes
once per day inside
a \uk{rugby-ball-shaped}{football-shaped} shell of water.
The oceans are stretched towards and away from the moon
because the gravitational forces supplied by the moon
don't perfectly match the required
centripetal force to keep the earth and moon whirling around their
common centre of gravity.\par
Someone standing on the equator (rotating as indicated by the arrow)
will experience two high waters and
two low waters per day.
}\label{fig.oceanearth}
}
Why are there\index{tide!explanation},
%% addition Sat 28/9/13
in many places in the world,
two high tides and two low tides per day?
Well, if the \ind{earth} were a perfect sphere, a smooth \ind{billiard ball} covered by
% correction added Sat 28/9/13
extremely deep
oceans, the tidal effect of the earth-moon whirling would be to deform the
water slightly towards and away from the \ind{moon}, making the water slightly
\uk{rugby-ball }{football-}shaped (\figref{fig.oceanearth}).
Someone living on the equator of
this billiard-ball earth, spinning round once per day within the
water cocoon, would notice the water level going up and down twice
per day: up once as he passed under the nose of the
\uk{rugby-ball}{football}, and up a second time as he passed
under its tail. This cartoon explanation is some way from
reality. In reality, the earth is not smooth, and it is not
uniformly covered by water (as you may have noticed).
Two humps of water cannot whoosh round the earth once per day
because
%% correction Sat 28/9/13
the oceans are too shallow and
the continents get in the way. The true behaviour of the tides
is thus more complicated. In a large body of water
such as the Atlantic Ocean,\index{Atlantic Ocean!tides}
tidal crests and troughs form but, unable\index{tide!in oceans}
to whoosh round the earth, they do the next best thing:
they whoosh around the perimeter of the Ocean. In the North Atlantic there
are two crests and two troughs, all circling
the Atlantic in an anticlockwise direction once a day.
Here in Britain we don't directly see these Atlantic crests
and troughs -- we are
set back from the Atlantic proper,
separated from it by a few hundred miles
of \ind{paddling pool} called the \ind{continental shelf}.
Each time one of the crests whooshes by in the Atlantic proper,
it sends a crest up our paddling pool. Similarly each Atlantic trough
sends a trough up the paddling pool.
Consecutive crests and troughs are separated by six hours.
Or to be more precise, by six and a quarter hours, since the time between
moon-rises is about 25,
not 24 hours.
% lunar day is 29.53 days
% Both the rotation of the Moon and its revolution around Earth
% takes 27 days, 7 hours, and 43 minutes.
\marginfig{
\begin{center}
\begin{tabular}{@{}c}
%{\mbox{\epsfxsize=45mm\epsfbox{../../images/WoodbridgeTidemill175px.jpg.eps}} }\\
%\mbox{\mbox{\epsfxsize=53mm\epsfbox{../../images/Ted36c.JPG.eps}}%
\mbox{\mbox{\epsfxsize=49mm%
\lowres{%
\epsfbox{../../images/Ted03cS.eps}%
}{\epsfbox{../../images/Ted03c.eps}%
}}%
\raisebox{35mm}{\makebox[3mm][r]{\epsfxsize=32mm\epsfbox{../../images/TideMillc.jpg.eps}}}%
}%
\\
\end{tabular}
\end{center}
% }{
\caption[a]{\ind{Woodbridge} {\tidepool} and {\tidemill}.\index{River Deben}
Photos kindly provided by Ted Evans.
}
\label{fig.DEBEN}
}%
The speed at which the crests and troughs travel varies with the
depth of the \ind{paddling pool}.\index{wave speed}\index{tide speed}
The shallower the paddling pool gets, the slower the crests and troughs
travel and the larger they get.
Out in the ocean, the tides are just a foot or two in height.
Arriving in European estuaries, the tidal range is often as big as four
metres.\label{tidepoolcalc}
% Tidal crests and troughs move up the English channel at roughly 70\,km/h.
% round the north of Scotland at about 150\,km/h, and down the North Sea at about 100\,km/h.
In the northern hemisphere, the \ind{Coriolis force}
(a force, associated with the rotation of the earth,
that acts only on moving objects)
makes all tidal crests
and troughs tend to hug the right-hand bank as they go. For example, the
tides in the English channel are bigger on the French side.
% (That is, the vertical amplitude is bigger.)
Similarly, the crests and troughs entering the North
Sea around the \ind{Orkney}s
hug the British side, travelling down to the \ind{Thames Estuary} then
turning left at the Netherlands to pay their respects to Denmark.
Tidal energy is sometimes called \ind{lunar energy}\index{tide},
since it's mainly
thanks to the \ind{moon} that the water sloshes around so.
Much of the tidal energy, however, is really coming from the
rotational energy of the spinning earth. The earth is very gradually
slowing down.
So, how can we put tidal energy to use, and how much power could we extract?
\section{Rough estimates of tidal power}%{\Tidepool}s}
When
\marginfig{
\begin{center}
\begin{tabular}{c}
%{\mbox{\epsfysize=1.2in\epsfbox{../tide/tidepoolR.eps}}} \\
\mbox{\epsfbox{metapost/tide.4}} \\
\end{tabular}
\end{center}
\caption[a]{An artificial \tidepool.
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.
% the change in potential energy of the water
% is $mgh$, where $h$ is the change in height of the centre of
% mass of the water, which is half the range.
}
\label{tidepool}
}%
you think of \ind{tidal power}, you might think of an artificial
pool next to the sea, with a water-wheel that is turned as the \ind{pool}
fills or empties (figures \ref{fig.DEBEN} and \ref{tidepool}).
% We'll start by estimating the
\Chref{ch.tide2} shows how to estimate the
power available from such {\tidepool}s.
% is
% easy to estimate,
% and it's
% not very impressive by modern standards, as we will now
% estimate.
% \subsection{Power from an artificial {\tidepool}}
% Every twelve-and-a-bit hours, there's a high tide (in most European ports,
% at least). Six hours later, there's a low tide.
% What range between high and low tide shall we assume
% for our artificial {\tidepool}?
% The range between high and low tide depends on the phase of the moon
% and on your location.
% Mid-ocean tides are just a foot or two in height.
% In European estuaries, the range is often as big as 12
% feet.\label{tidepoolcalc}
% Let's assume
Assuming a range of 4\,m, a typical range in
many European estuaries,
% in a few special spots -- the Severn estuary, Blackpool, and The Wash --
% the range is sometimes 7\,m or more.)
\margintab{
\begin{center}\small
\begin{tabular}{cc} \toprule
tidal & power \\
range & density \\ \midrule
2\,\m & 1\,\Wmm \\%0.82
{\bf{4\,\m}} & {\bf{3\,\Wmm}} \\%3.27
6\,\m & 7\,\Wmm \\
8\,\m & 13\,\Wmm \\
% Amplitude & Power per \\
% of tide & unit area \\ \midrule
% 1\,\m & 1\,\Wmm \\
% 2\,\m & 4\,\Wmm \\
% 3\,\m & 8\,\Wmm \\
% 4\,\m & 15\,\Wmm \\
\bottomrule
\end{tabular}
\end{center}
\caption[a]{Power density (power per unit area) of {\tidepool}s,
assuming generation from both the rising and the falling tide.
% The amplitude is half the tidal range.
% This chapter's end-notes explain
% where these numbers come from.
}\label{tab.tidepoolP}%
}%
the maximum power of an artificial {\tidepool} that's filled
rapidly at high tide and emptied rapidly at low tide,
generating power from both flow directions, is about
$\pdcol{3\,\Wmm}$.
This is the same as the power per unit area of an offshore
{\windfarm}.
And we already know how big offshore {\windfarm}s need to be to make a difference.
{\em They need to be country-sized.}
So similarly,
to make \index{tide-pool}{\tidepool}s capable
of producing power comparable to Britain's total consumption,
we'd need the total area of the {\tidepool}s to be
similar to the area of Britain.%
%% and to make 1GW (average) you'd need 250\,km$^2$ or 16km x 16km
%
\begin{figure}
\figuredangle{
\begin{center}
\begin{tabular}{cc}
\raisebox{0.6in}{\mbox{\epsfbox{metapost/tide.5}}} &
%\mbox{\epsfysize=1.2in\epsfbox{../tide/tidepool2.eps}}} &
{\mbox{%\epsfysize=3in
\epsfbox{../../images/PUBLICDOMAIN/maps/northsea.eps}}}\\
%\lowres%
%{\mbox{\epsfysize=3in\epsfbox{../../images/PUBLICDOMAIN/NorthSea.jpg.eps}}}%
%{\mbox{\epsfysize=3in\epsfbox{../../images/PUBLICDOMAIN/NorthSea.eps}}}
\\
\end{tabular}
\end{center}
}{
\caption[a]{%
% A natural {\tidepool}.
The \ind{British Isles} are in a fortunate position:
the \ind{North Sea} forms a natural {\tidepool},
in and out of which great sloshes of water
pour twice a day.
}
\label{tidepool2NS}
}
\end{figure}
% \subsection{Natural tidepools}
Amazingly, Britain is already supplied with
a
% {\em natural\/}
{natural} {\tidepool} of just the required dimensions.\nlabel{pTideNS}
This \index{tide-pool}{\tidepool} is known as the \ind{North Sea}
(\figref{tidepool2NS}).
If we simply insert generators in appropriate
spots, significant power can be extracted.
The generators might look like
\ind{underwater windmill}s.\index{windmill!underwater}
Because the density of water is roughly 1000 times that of
air, the power of water flow is 1000 times
greater than the power of wind at the same speed.
%
We'll come back to {\tidefarm}s in a moment, but first let's discuss
how much raw tidal energy rolls around Britain every day.
\subsection{Raw incoming tidal power}
% \section{Tides as tidal waves}
The tides around Britain are genuine \ind{tidal wave}s --
unlike \ind{tsunami}s, which are called ``tidal waves,''
but are nothing to do with tides.
Follow a high tide as it rolls in from the Atlantic.
The time of high tide becomes progressively later as we move east up the
English channel from the \ind{Isles of Scilly} to Portsmouth and on to Dover.
% falmouth to eastbourne: 244 mi, 392 km, in 5.9 hours
% 66.4 km/h eg 13.31 low -> 1930 low.
The crest of the tidal wave progresses up the channel at about
70\,km/h. (The crest of the wave moves much faster than
the water itself, just as ordinary waves on the sea move faster than the water.)
Similarly, a high tide moves clockwise round \ind{Scotland}, rolling
down the North Sea from Wick to Berwick and on to Hull at a speed of
about 100\,km/h.
These two high tides converge on the \ind{Thames Estuary}.
By coincidence, the
Scottish crest arrives about 12 hours later than the crest that came via
Dover, so it arrives in near-synchrony with the next high tide via Dover,
and London receives the normal two high tides per day.
% \subsection{Sanity-check using total arriving power}
The power we can extract from tides can never
be more than the total power of these tidal waves
from the Atlantic.
% Chapter \ref{ch.tide2} shows how to
% estimate the total power
% of these great Atlantic tidal waves.
% in the same
% was as we estimate the power of their smaller cousins,
% ordinary waves. [Need to reorder chapters if refering to waves!]
% \Appref{app.tide2}
% estimates that
% At locations A, B, and C in \figref{fig.TideLine}
% the incoming power from the Atlantic
% is about 900--1500\,kW per metre of wavecrest
% at spring tides, and 240--440\,kW$\!$/m at neaps.
% Multiplying by 1200\,km of exposed Atlantic,
% the total incoming tidal power is about 1000\,GW (or 400\,kWh/d per person)
% at springs and 270\,GW (100\,kWh/d per person) at neaps.
The total power crossing the lines in \figref{fig.TideLine}
has been measured; on average it amounts to 100\,kWh per day per person.\label{ptide100}
If we imagine extracting 10\% of this incident energy,
and if the conversion and transmission processes are 50\%
efficient, the average power delivered would be
\marginfig{
\begin{center}
% THIS IS A BIG FILE I THINK
%{\mbox{\epsfxsize=50mm\epsfbox{../../images/PUBLICDOMAIN/NorthSeaLCSmall.png.eps}}}\\
{\mbox{\epsfxsize=50mm\epsfbox{../../images/PUBLICDOMAIN/maps/northseaT.eps}}}\\
\end{center}
\caption[a]{% Three lines near the edge of the continental shelf.
The average incoming power of lunar tidal waves crossing these two
lines has been measured to be 250\,GW\@. This raw power,
shared between 60 million people, is
100\,kWh per day per person.\index{power per unit length!tide}
% :, of which 76\,kWh/d/p comes over
% the France--to--Ireland line, and
% the other 24\,kWh/d comes over lines B and C.
}
\label{fig.TideLine}
}%
\OliveGreen{5\,kWh per day per person}.
This is a tentative first guess, made without specifying any technical details.
Now let's estimate the power that could be delivered by three
specific solutions:
{\tidefarm}s, barrages, and offshore tidal lagoons.
%\end{figure}
% So, on average,
% perfect extraction of all tidal energy could deliver no more than
% \section{Estimating the extractable lunar energy}
\section{Tidal stream farms}% al stream}
One way to extract tidal energy would be to build
{\tidefarm}s, just like {\windfarm}s.
The first such underwater windmill, or ``tidal-stream'' generator, to be
connected to the grid
was a ``300\,kW'' turbine,
% weight 200 tons!!
installed in 2003 near
the northerly city of \ind{Hammerfest}, \ind{Norway}.
% Currents there reach 2.5\,m/s. It was expected to generate 80\,kW on average.
% http://www.e-tidevannsenergi.com/
% 400m wide, mean velocity 1.8m/s, maxdepth 50m
% weight 107 tons?
% 20m diamter
% 700,000 kWh per year, sufficient for 35 homes in Norway. The 1,088 residents of Kvalsund Kommune consume 21 GWh per year.
Detailed power production results have not been published, and no-one has
yet built a {\tidefarm} with more than one turbine,
so we're going to have to rely on physics and guesswork
to predict how much power {\tidefarm}s could produce.
Assuming that
the rules for laying out a sensible {\tidefarm} are similar to
those for {\windfarm}s, and that the efficiency of the tide turbines
will be like that of the best wind turbines,
table \ref{tidetable1} shows the power of a {\tidefarm}
for a few tidal \ind{current}s.%
\margintab{\small
\begin{center}
% 1 knot = 0.514444444444444444 m/s
\begin{tabular}{c@{\,\,\,\,}c@{}c} \toprule
\multicolumn{2}{c}{speed} & power density \\
{\small (m/s)} & {\small (\ind{knot}s)} & (\Wmm) \\ \midrule
0.5 & 1 & 1 \\
1 & 2 & 8 \\
2 & 4 & 60 \\ % 62.8
3 & 6 & 200 \\ % 212
4 & 8 & 500 \\ % 502
5 & 10 % 9.72
& 1000 \\ % 981.7
\bottomrule
\end{tabular}
\end{center}
%}{
\caption[a]{{\Tidefarm} power density (in watts per square metre
of sea-floor) as a function of \ind{flow} speed.\index{current}
(1 knot = 1 nautical mile per hour = 0.514\,m/s.)
}
\label{tidetable1}
}
Given that tidal currents of 2 to 3 knots are common,
there are many places around the British Isles where the power per unit
area of {\tidefarm} would be
% sea-floor is
$6\,\Wmm$ or more.
This power per unit area can be compared to
% is a bit bigger than
% lies between
our estimates for {\windfarm}s (2--3\,\Wmm)
and for photovoltaic solar farms (5--10\,\Wmm).
% And about the same as our estimate of the power density of
% an off-shore wind farm ($3\,\Wmm$).
Tide power is not to be sneezed at!
How would it add up, if we assume that there are no economic
obstacles to the exploitation of tidal power at all the
hot spots around the UK?
%
% Assuming that we can add up power contributions of adjacent pieces
% of sea floor, {\tidefarm}s could deliver something like
% [Finish this bit off by stealing from \pref{pSteal1}.]
% Answer:
\Chref{ch.tide2} lists the flow speeds in the best areas around the UK,
and estimates that \OliveGreen{9\,kWh/d per person} could be extracted.
\begin{figure}
%\figuremarginb{
\figuredangle{
\begin{center}
\hspace*{1.62cm}\begin{tabular}{l}%p{\textwidth}}
\raisebox{3.9cm}{\makebox[0in][l]{% made by larance10.sh
\epsfig{file=../../images/PUBLICDOMAIN/maps/strangford10.eps}}}%
\hspace{9mm}\mbox{\epsfig{file=../../images/PUBLICDOMAIN/maps/larance10.a.eps}}
\hfill\raisebox{3.9cm}{{%
\epsfig{file=../../images/PUBLICDOMAIN/maps/strangford10.c.eps}}}%
\\[-3cm]
\hspace*{10.9cm}\mbox{\epsfig{file=../../images/PUBLICDOMAIN/maps/larance10.b.eps}}\\
\end{tabular}
\end{center}
}{
\caption[a]{The
\ind{Severn barrage} proposals (bottom left), and \ind{Strangford Lough}, \ind{Northern Ireland} (top left),
shown on the same scale as the
% existing
% 750\,m--long
barrage at \ind{La Rance}\index{Rance} (bottom right).\index{Saint-Malo}
% , just south of Saint-Malo.
The map shows two proposed locations for a Severn barrage. A barrage at
Weston-super-Mare would deliver an average power of 2\,GW (0.8\,kWh/d per person).
The outer
alternative would deliver twice as much.
There is a big tidal resource in Northern Ireland at Strangford Lough.
Strangford Lough's area is 150\,km$^2$; the tidal range
in the Irish Sea outside is 4.5\,m at springs and 1.5\,m at neaps --
sadly not as big as the range at La Rance or the Severn.
The raw power of the natural {\tidepool} at Strangford Lough is
roughly 150\,MW, which, shared between the 1.7\,million people
of Northern Ireland, comes to 2\,kWh/d per person.
{Strangford Lough} is the location of the first grid-connected
tidal stream generator in the UK\@.
% the turbine they put in there is 1.2MW peak?
% 89W
%% 1685000 N.I.
% 150 * 1 MW
}
\label{pBarrage3}
\label{pBarrageSL}
}
\end{figure}
\section{Barrages}
Tidal barrages are a proven technology.\nlabel{larance}
The famous barrage at \ind{La Rance} in France, where the tidal
range is a whopping 8 metres on average, has
produced an average power of 60\,MW since 1966.
The tidal range in the \ind{Severn Estuary}\index{Bristol channel}
is also unusually large.
At \ind{Cardiff} the range is 11.3\,m at \ind{spring tide}s, and 5.8\,m at \index{neap tide}neaps.
If a barrage were put across the mouth of the
Severn Estuary (from Weston-super-Mare to Cardiff),
it would make a 500\,km$^2$ {\tidepool} (\figref{pBarrage3}).
Notice how much bigger this pool is than the estuary at \ind{La Rance}.
What power could this {\tidepool} deliver, if we let the water
in and out at the ideal times, generating on both the flood and the ebb?
% , according to our calculation
% on \pref{pagetidepool}?
% The
% amplitude $h$
% (the half-range) varies between 5.6\,m and 2.9\,m.
% When the amplitude is $5.6\,\m$, the average power
% contributed by the barrage (at $30\,\Wmm$) would be at most $14.5\,\GW$,
% or {\bf{5.8\,kWh/day each}}.
% When the amplitude is $2.9\,\m$, the average power
% contributed by the barrage (at $8\,\Wmm$) would be at most $3.9\,\GW$,
% or {\bf{1.6\,kWh/day each}}.
% range varies between 11.3\,m and 5.8\,m.
According to the theoretical numbers from \tabref{tab.tidepoolP},
when the range is $11.3\,\m$, the average power
contributed by the barrage (at $30\,\Wmm$) would be at most $14.5\,\GW$,
or {\bf{5.8\,kWh/d per person}}.
When the range is $5.8\,\m$, the average power
contributed by the barrage (at $8\,\Wmm$) would be at most $3.9\,\GW$,
or {\bf{1.6\,kWh/d per person}}.
These numbers assume that the water is
let in in a single pulse at the peak of high tide,
and let out in a single pulse at low tide.
In practice, the in-flow and out-flow would be spread
over a few hours, which
would reduce the power delivered a little.
The current proposals for the barrage will generate power in one direction
only. This reduces the power delivered by another 50\%.
% and the turbines would not extract all the potential energy perfectly: a 10 or 20\% loss is likely.
% [On the other hand, a sneaky trick might be used to boost the
% power: when the tide is high,
% pumps could shove a little {\em{extra}\/} water
% behind the barrage; the energy required to create this
% small head is recovered, with interest, when the water is let out
% at low tide. This trick, and the complementary trick at
% low tide, could be used to significantly
% boost the power delivered at neap tides. I'll discuss this
% \ind{pumping} trick later.]
%% notes are on paper in Nokia book. In principle a 3-fold boost seems
%% plausible if it were permitted to raise the high tide by 3H where
%% H is the range.
The engineers' reports on the proposed Severn barrage
say that, generating on
the ebb alone, it would contribute
{\OliveGreen{0.8\,kWh/d per person}}
on average.\label{severn}
% and cost 60 pounds per MWh cf selling price of about 27.
% so at a carbon price of 33 pounds per ton, it becomes better than coal
% plus it helps avoid flooding, which they value at 20 pounds per MWh
% DTI-PIU said
% 50\,TWh/year, which is {\bf{2.3\,kWh/day each}}.
%% Ask Roger Hull of McAlpine (friend of Deep Throat)
% [I have a problem with this figure: it corresponds to
% 5.7\,GW, and I thought the peak power was 8\,GW and the
% average was 2\,GW, which means 0.8\,kWh/d.
% The Friends of the Earth document
% says the barrage would deliver
% 18\,TWh/y, 2\,GW average.
%
%]
The barrage would also provide protection from flooding
valued at about \pounds120M per year.
%% Check tidal range here (Cardiff) and in Dundee.
\section{Tidal lagoons}
% Tidal lagoons are like artificial estuaries.
Tidal lagoons are created by building walls in the sea; they
can then be used like artificial estuaries. The
required conditions for building lagoons are that the water must be
shallow and the tidal range must be large. Economies of scale apply:
big tidal lagoons make cheaper electricity than small ones.
The two main locations for large tidal lagoons in Britain are the Wash on the
east coast, and the waters off Blackpool on the west coast (\figref{fig.lagoons}).
Smaller facilities could be built in north Wales, Lincolnshire,
southwest Wales, and east Sussex.
% Mention the pumping trick.
%
%% morgan horne material SECRET - removed to horne.tex
% Insert estimates of tidal lagoons here:
% 64\,TWh/y available in six sea locations:
% Lancashire, North Wales,
% Lincolnshire,
% Southwest Wales, East Sussex,
% and The Wash.
% 64\,TWh/y is 7.3\,GW, or
% \OliveGreen{3\,kWh/d per person}.
If two lagoons are built in one location, a neat trick can be used to
boost the power delivered and to enable the lagoons to
deliver power on demand at any time,
independent of the state of the tide.
One lagoon can be designated the ``high'' lagoon,
and the other the ``low'' lagoon. At low tide, some power generated
by the emptying high lagoon can be used to
pump water {\em{out}\/} of the low lagoon, making its level
even lower than low water. The energy required to
pump down the level of the low lagoon is then repaid with
interest at high tide, when power is generated by letting water
into the low lagoon.
\marginfig{
\begin{center}
{\mbox{\epsfbox{../../images/PUBLICDOMAIN/maps/lagoon.eps}}}\\
\end{center}
\caption[a]{%
% The two main location for tidal lagoons in British waters.
Two tidal lagoons, each with an area of 400\,km$^2$,
one off Blackpool,
and one in the Wash.
The Severn estuary is also highlighted for comparison.
}
\label{fig.lagoons}
}%
Similarly, extra water can be pumped into the high lagoon
at high tide, using energy generated by the low lagoon.
Whatever state the tide is in, one lagoon or the other would be able
to generate power.
Such a pair of tidal lagoons could also work as a \ind{pumped storage} facility,
storing excess energy from the electricity grid.
The average power per unit area
of \ind{tidal lagoon}s in British waters
could be \pdcol{4.5\,\Wmm},\nlabel{pdTidalLag}
so if tidal lagoons with a total area of 800\,km$^2$ were created (as
indicated in \figref{fig.lagoons}), the power generated would be
% 800e6 / 60e6 * 4.5
% 60W
\OliveGreen{1.5\,kWh/d per person}.
\section{Beauties of tide}
Totting everything up, the barrage, the lagoons, and the
tidal stream farms could deliver something like \OliveGreen{11\,kWh/d per person}
(\figref{fig.tide}).
% 0.8 + 1.5 (2.3)
% Stream... 9 Total 11.3
Tide power has never been used on an industrial scale in Britain,
so it's hard to know what economic and technical challenges
will be raised as we build and maintain tide-turbines
-- corrosion,
silt accumulation, entanglement with flotsam? But
here are seven reasons for being excited about tidal
power in the British Isles.
\begin{inparaenum}
\item
Tidal power is completely predictable; unlike wind and sun,
\ind{tidal power} is a renewable on which one could depend;
it works day and night all year round;
using tidal lagoons, energy can be stored so that power can
be delivered on demand.
\item
Successive high and low tides
% roll in from the Atlantic and
take about 12 hours to progress around
% the coast of
the British Isles, so the strongest currents off Anglesey,
Islay, Orkney and Dover occur at different times
from each other;
thus, together, a collection of {\tidefarm}s could produce a
more constant contribution to the electrical grid
than one {\tidefarm}, albeit a contribution that wanders up and down
with the phase of the moon.
\item
Tidal power will last for millions of years.
\item
It doesn't require high-cost hardware, in contrast to solar
photovoltaic power.
\item
Moreover, because the power density of a typical tidal flow is
greater than the power density of a typical wind,
a 1\,MW tide turbine is smaller
in size than a 1\,MW wind
turbine; perhaps tide turbines could therefore be cheaper than wind turbines.\index{wind!compared with tide}\index{tide!compared with wind}
\item
Life below the waves is peaceful; there is no such thing as a freak tidal storm;
% , in which tidal currents are ten times bigger than normal.
so, unlike wind turbines, which
require costly engineering to withstand rare windstorms,
underwater tide turbines
will not require big safety factors in their design.
\item
Humans mostly live on the land, and they
can't see under the sea, so objections to the visual
impact of tide turbines should be less strong than the
objections to wind turbines.
\end{inparaenum}%\een
\pagebreak[4]
\subsection{Mythconceptions}
\pagebreak[0]
\beforeqa
\qa{Tidal power, while clean and green, should not be called renewable. Extracting power from the tides slows down the earth's rotation. We definitely can't use tidal power long-term.}{
{\em False.}
%
The natural tides already slow down the earth's rotation.
The natural rotational energy loss is roughly 3\,TW
\citep{Shepherd03}.
% MOVE to p91 ***
Thanks to natural tidal friction,
each century, the day gets longer by 2.3\,milliseconds.
% Tidal energy is a renewable that will be available for millions of years.
%
% Natural slowing rate of the earth's rotation
% owing to tidal friction is
% 2.3\,ms/day per century.
%
Many tidal energy extraction systems are just extracting energy
that would have been lost anyway in friction.
\marginfig{
% \begin{figure}
\begin{center}
\begin{tabular}{@{}cc}
% {\small\sc Consumption}& {\small\sc Production}\\
\multicolumn{2}{@{}c}{\mbox{\epsfbox{metapost/stacks.285}}}\\%31}} }\\
\end{tabular}
\end{center}
% }{
\caption[a]{Tide.}\label{fig.tide}
}%
But even if we {\em{doubled}\/} the power extracted from the
earth--moon system, tidal energy would still last more than a billion years.
% how long would tidal energy last?
% 3.7 billion years
%
% The answer is: more than a billion years.
% In two
% 2.6
% million years, the length of a day would be
% longer by two minutes instead of one minute.
}
\small
\section{Notes and further reading}
\beforenotelist
\begin{notelist}
\item[page no.]
\item[\npageref{tidepoolcalc}]
{\nqs{The power of an artificial {\tidepool}}.}
The power per unit area of a \tidepool\ is derived in
\chref{ch.tide2},
\pref{pTidePool}.
\item[\npageref{pTideNS}]
{\nqs{
Britain is already supplied with a
{natural} {\tidepool} \ldots\ known as the North Sea}.}
I should not give the impression that the North Sea fills
and empties just like a {\tidepool} on the English coast.
The flows in the North Sea
are more complex because the time taken for a bump
in water level to propagate across the Sea is similar to
the time between tides. Nevertheless, there are
whopping tidal currents in and out of the North Sea,
and within it too.
% , with a power way beyond the power of
\item[\npageref{fig.TideLine}]
{\nqs{The total incoming power of lunar tidal waves crossing these
lines has been measured to be
100\,kWh per day per person}.}
Source: \citet{Cartwright1980}.
% Near the Orkneys the incoming powers
% are 14\,GW and 12\,GW.
For readers who like back-of-envelope models, \appref{app.tide2} shows how
to estimate this power from first principles.
\item[\npageref{larance}] {\nqs{La Rance}}
%%
generated 16\,TWh over 30 years.
%% 1966-1996
That's an average power of 60\,MW\@. (Its peak power is 240\,MW.)
%% at 18.5 centimes per kWh
%% Kaplan turbines
% total capacity 240MW (10MW per bulb,
% each bulb weighing 470t)
% 470kg/10kW = 47 kg per kW
The tidal range is up to 13.5\,m;\label{pRanceFacts}
the impounded area is 22\,km$^2$; the
barrage 750\,m long. Average power per unit area:
\pdcol{2.7\,\Wmm}.
% 600 GWh per year
%
Source: \tinyurl{6xrm5q}{http://www.edf.fr/html/en/decouvertes/voyage/usine/retour-usine.html}.
\item[\npageref{severn}]
{\nqs{ The engineers' reports on the
% proposed
Severn barrage\ldots
say 17\,TWh/year.}}
% , which is {0.8\,kWh/d per person}. }}
\citep{DTISevern}.
% file15363.pdf
This (2\,GW) corresponds to 5\% of current UK total electricity consumption, on average.
% \item[]
% \ind{Cardiff Bay barrage},\index{barrage} completed in 1999,
% cost \pounds220 million, and is
% 1.1\,km long.
\item[\npageref{pdTidalLag}]
{\nqs{Power per unit area of tidal lagoons could be 4.5\,\nWmm.}}
\cite{MacKayLagoons}.
\end{notelist}
\normalsize