BIFURCATION POINT AGAIN
OK, plugging in our English population density: 380 people per
square kilometre, or 2600 square metres per person, we find that
wind power could plausibly generate
\beq
2.2 \,\W/\m^2 \times 2600 \,\m^2/\person \simeq 6\,\kW \,\per\,\person,
\eeq
if windmills were packed at the maximum possible density
across the whole country.
Converting to our favourite power units,
that's
\beqa
\lefteqn{ \mbox{Maximum conceivable wind power (assuming 6\,\m/s)} \hspace{2in} }\\
& =& 140\,\kWh\,\mbox{per person per day}.
\eeqa
This calculation depended sensitively on our estimate of
the windspeed.
Is 6\,\m\ per second plausible as a long-term typical windspeed?
The mean windspeed in St.\ Magwan, on the coast
of South-west England, the windiest
part of England, ranges from
10\,knots (5\,\m/\s) to 14\,knots (7.2\,\m/\s).
In Bedford, a typical town in the middle of England,
the mean windspeed ranges from
8\,knots (4\,\m/\s) to 11\,knots (5.6\,\m/\s).
%% http://www.metoffice.com/climate/uk/location/southwestengland/wind.html
%%% http://www.metoffice.com/climate/uk/averages/19712000/sites/bedford.html
(These are the figures at the standard weather-man's height of
10\,\m.)
%% \,per\,second
If we replace 6\,m/s by Bedford's
4\,m/s as our estimated
windspeed, we must revise our estimate down by a factor of $(4/6)^3 \simeq 0.3$.
[Remember, wind power scales as wind-speed cubed.]
%\beq
% \mbox{Maximum conceivable wind power (assuming 4\,\m/s)}
% = 40\,\kWh\,\mbox{per person per day}.
%\eeq
% On the other hand, to estimate the typical power, we shouldn't take the
% mean wind speed and cube it; rather, we should find the mean cube of the windspeed.
% The mean cube
%
Let's be realistic. Can we really imagine completely covering
the country with windmills? What fraction of the country can
we really imagine filling densely with these windmills?
Maybe 10\%? Taking 10\% of the maximum
conceivable wind power (assuming 6\,\m/s),
we obtain
\beq
\mbox{Maximum conceivable wind power (assuming 6\,\m/s and 10\% filling)}
= 14\,\kWh\, \mbox{per person per day}.
\eeq
Incidentally, the number of windmills of the Wellington size
if this plan were implemented
%% square of size 125m, i.e. 8x8 is 64 per sq km
%% total area 130 000 sq km, with
%% 5% filling ->
would be 400,000.
Now, this whole calculation has been very Anglocentric: the country
to which our calculation applies is England, and any other country
with the same population density and wind speed; I felt it would
be impertinent to lump England together with Scotland. For the benefit of
a reader who is
happy to propose turning 10\% of the wilds of Scotland
into wind farms for the benefit of Sassenachs, we
can easily redo the calculation.
\begin{table}[htbp]
\figuremargin{
{\small
\begin{tabular}{lrrrr} \toprule
Region & Population & Area & Density & Area each \\
& & (km$^2$) & (per km$^2$) & (m$^2$) \\ \midrule
World & {\bf{6\,440\,000\,000}} & {\bf{148\,000\,000}} & {{ 43}} & {{ 23\,100}} \\
Scotland & 5\,050\,000 & 78\,700 & {{ 64}} & {{ 15\,500}} \\
European Union & {\bf{456\,000\,000}} & 3\,970\,000 & {{ 114}} & {{ 8\,710}} \\
Wales & 2\,910\,000 & 20\,700 & {{ 140}} & {{ 7\,110}} \\
{\em\textbf{United Kingdom}}& {\bf{59\,500\,000}} & 244\,000 & {{\em 243}} & {\em{ 4\,110}} \\
{\em England} & {\em 49\,600\,000} & {\em 130\,000} & {\em 380} & {\em 2\,630} \\
\bottomrule \end{tabular}
}
}{
\caption[a]{Some regions with population density greater than
or equal to the world average.
Populations above 50 million and areas greater than 5 million\,\km$^2$
are highlighted.
}
}
\end{table}
The area per person in the United Kingdom is 4\,000\,m$^2$,
which is about 50\% bigger than England's 2\,600\,m$^2$.
So assuming the same wind speed as before, which perhaps
underestimates the contribution from windier Scotland, we find
Wind can offer the U.K.\ 22\,kWh\,per\,person.
Conclusion: if we covered the most productive
10\% of the country with
windmills, we might be able to generate {\bf\em one fifth}
of the energy used by driving an invalid carriage 100\,\km\,per\,day.
% \begin{center}
%{\mbox{\epsfbox{crosspad/wind6.ps}}}
% \end{center}
\amarginfig{t}{
% \begin{figure}
\begin{center}
\begin{tabular}{cc}
{\sc Consumption}& {\sc Production}\\
\multicolumn{2}{c}{\mbox{\epsfbox{metapost/stacks.22}} }\\
\end{tabular}
\end{center}
% }{
\caption[a]{Chapter \protect\ref{ch.wind}'s conclusion:
the maximum plausible production from on-shore windmills
in England is 14\,units\,per\,day\,per\,person.
Should I give the U.K.\ figure instead?
22\,kWh/d.
}
}
% \end{figure}