%%%% NOT USED
I'll assume that we put the ground loops in a layer
$h=5$\,m deep -- much shallower,
and the ground temperature would fluctuate more during the year, reducing
the pump's efficiency; much deeper, and
the resulting temperature drop induced by our heat pump would reduce efficiency
too. (Redo this, showing what the optimal depth actually is?)
%% cambridge population = 109,000; but need population density by street.
\margintab{\small
\begin{center}
\begin{tabular}{p{30mm}r} \toprule
\multicolumn{2}{r}{people per km$^2$} \\ \midrule
Bangalore & 26\,719\\%/km$^2$\\
Manhattan & 25\,849\\%/km$^2$\\
Paris & 24\,775\\%/km$^2$\\
% Royal Borough of
% Kensington and
Chelsea & 15\,177\\%/km$^2$\\
Tokyo & 13\,800\\%/km$^2$\\
Moscow & 10\,275\\%/km$^2$\\
Taipei & 9626\\%/km$^2$\\
The Hague & 6600\\%/km$^2$\\
San Francisco & 6423\\%/km$^2$\\
Singapore & 6411\\%/km$^2$\\
Cambridge MA & 6086\\%/km$^2$\\
Sydney & 5736\\%/km$^2$\\
Portsmouth & 4689\\%/km$^2$\\
\bottomrule
\end{tabular}
\end{center}
\caption[a]{Some urban population densities.}% of cities}
}%
Let's pick 6200/km$^2$ as our representative density of a residential area;
that's 160\,m$^2$
per person. This is the population density of a typical English suburb:
rows of semi-detached houses with about 400\,m$^2$ per
house (including pavements and streets).
%% cf if you take my house and street and just a little bit of back garden,
%% and all of front garden:
%% 3760 m**2/16 dwellings = 235 per dwelling = 94 m**2 per person (at 2.5)
% with no back garden at all, 2857 /16/2.5 = 71.4
% with full back gardens 6279.0 /16/2.5 = 157
% with full back gardens 6590.0 /16/2.5 = 164
% And let's assume that three quarters of that area is exposed
% to the elements. (The other quarter, being covered by buildings
Then the maximum power per person deliverable by ground source
heat pumps, if everyone
in a neighbourhood has them,
is 320\,W, which is 8\,kWh/d per person.
Add in the electrical contribution, assuming a COP of 3: 12\,kWh/d per person.
If I'd said $\mbox{depth} = 1.25\,$m then the flux could be
8\,\Wmm, and the maximum power delivered could be 48\,kWh/d per person.
But bear in mind I assumed that the ground is granite all the way through.
The conductivity of dry soil is about ten times smaller
than that of granite.
%\subsection{Ground source heat pumps -- details}
% WARNING: this section is intended for an undergraduate science
% audience.
%
% Let's work out a cartoon theory for
% below-ground temperatures, and for what
% happens when we lay down tubes and suck out heat.
I'm going to assume the ground is made of \ind{granite}.
%% 2.255