%% http://www.polmontweather.co.uk/windspd.htm
% The UK has the best and most geographically diverse wind resources in Europe,
\myquote{%
The UK has the best wind resources in Europe.
}{Sustainable Development Commission}
% page 12 of their wind document.
\myquote{%
Wind farms will devastate the countryside pointlessly.
}{{James Lovelock}}
% Monday Jan 27th, 2006.
%\end{quote}
% \noindent
How much \ind{wind} power could we plausibly generate?
%
\amarginfignocaption{b}{
\begin{center}
\begin{tabular}{@{}c@{}}
\lowres{\mbox{\epsfxsize=53mm\epsfbox{../../images/AngleOnWindS.jpg.eps}}}%
{\mbox{\epsfxsize=53mm\epsfbox{../../images/AngleOnWind.jpg.eps}}} \\
\end{tabular}
\par\vspace{0pt}
\end{center}
% \caption[a]{}
\label{germanWindmill}
}
We can make an estimate of the
potential of {\em{on-shore}\/} (land-based)
wind in the United Kingdom by multiplying the average power per unit land-area of a
{\windfarm} by the \ind{area per person} in the \UK:
\[%beq
\mbox{power per person}
=
\mbox{\OliveGreen{wind power per unit area}}
\times \mbox{area per person} .
\]%eeq
% Appendix
Chapter \ref{ch.wind2} (\pref{ch.wind2})
explains how to estimate the power per unit area of a \ind{\windfarm} in
the \UK.\index{power density!wind farm}
If the typical windspeed
is 6\,m/s (13\,miles per hour, or 22\,km/h),
%% 13.4 mph
%% 21.6 kph
the power per unit area of \windfarm\ is about \OliveGreen{2\,\Wmm}.\par
\begin{figure}[hbtp]
\figuremargin{
\begin{center}
\mbox{\epsfxsize=\textwidth%
\mono{\epsfbox{../data/cambridge/mono/Cam2006.eps}}%
{\epsfbox{../data/cambridge/Cam2006.eps}}%
%%% made by load 'gnu'
}
\end{center}
}{
\caption[a]{Cambridge\index{data!wind!Cambridge} mean wind speed in metres per second, daily (red line),\index{wind!data}
and half-hourly (blue line) during 2006. See also \figref{fig.windhisto}.
% Thanks to Digital Technology Group, Computer Laboratory, Cambridge.
\medskip
\par
\mbox{\epsfig{file=../../images/PUBLICDOMAIN/maps/wind0.eps,angle=270}}% cairngorm and cambridge
}
\label{fig.camb.wind}
}
\end{figure}
\noindent
This figure of 6\,m/s is probably an over-estimate for
many locations in Britain.
For example,
%\marginpar{
%\begin{center}
%\end{center}
%\label{pwind0}
%}
\figref{fig.camb.wind}
shows daily \ind{average windspeeds}\index{windspeed!Cambridge} in Cambridge
during 2006.
%
The daily average speed reached 6\,m/s on only about 30 days
of the year -- see \figref{fig.camb.wind2} for a histogram.
But some spots do have windspeeds above 6\,m/s -- for example, the summit
of Cairngorm in Scotland (\figref{fig.cairngorm}).
Plugging in the British population density: 250 people per
square kilometre, or 4000 square metres per person, we find that
wind power could%
\begin{figure}[hbtp]
\figuremarginb{
\begin{center}
\mbox{\epsfxsize=\textwidth%
\mono%
{\epsfbox{../data/cairngorm/mono/CairngormWind2006.eps}}%
{\epsfbox{../data/cairngorm/CairngormWind2006.eps}}%
}%
\end{center}
}{
\caption[a]{Cairngorm\index{data!wind!Cairngorm} mean wind speed in metres per second,\index{wind!data}
% daily (heavy line),
% and half-hourly (light line),
during six months of 2006.
\index{windspeed!Cairngorm}
}
\label{fig.cairngorm}
\label{pwind0}
}
\end{figure}
generate
\[
% 2.2 \,\W/\m^2 \times 4000 \,\m^2/\person \:\simeq\:
% 9\,\kW \,\per\,\person,
2 \,\Wmm \times 4000 \,\m^2/\person \: = \:
8000\,\W \:\per\:\person,
\]
if wind turbines were packed
% at the maximum possible density
across the {\em{whole}\/} country, and assuming 2\,\Wmm\ is the correct power
per unit area.
Converting to our favourite power units,
that's 200\,{kWh/{d} per person}.
%\beqa
% \mbox{maximum conceivable wind power}
%% \lefteqn{ \mbox{Maximum conceivable wind power (assuming 6\,\m/s)} \hspace{2in} }\\
%& \simeq & 200\,\mbox{kWh/{d} per person}.
%% was 210 , then 192...
%\eeqa
Let's be realistic.
% Can we really imagine completely covering the country with windmills?
What fraction of the country can
we really imagine covering with windmills?
% filling densely
Maybe 10\%?
% Taking 10\% of the maximum
% conceivable wind power,
%% (still assuming 6\,\m/s),
% we obtain%
%\beqa
%\lefteqn{ \mbox{maximum conceivable wind power (assuming 2\,\Wmm} }
%\\
% \mbox{in 10\% of the UK)}
% & = \:\: \OliveGreen{20\,\kWh/\d\ \mbox{per person}}.&
%% used to be 21.
%\eeqa
% 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 244 000 sq km
% would be 300\,000.
%% pr 60e6 * 21.0 / 1400 / 3.0
%% 300000.0
%% pr 64 * 244000.0 * 0.1
%% 1561600.0
%
\amarginfig{c}{
% \begin{figure}
\begin{center}
\begin{tabular}{@{}cc}
{\small\sc Consumption}& {\small\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 the United Kingdom is 20\,kWh per day per person.
}
}%
% \end{figure}
Then we conclude: if we covered the windiest
%% most productive
10\% of the country with
windmills (delivering 2\,\Wmm), we would be able to generate
\OliveGreen{20\,kWh/d per person}, which is
{\bf\em half\/}
of the power used by driving an average fossil-fuel car
50\,\km\ per day.
Britain's onshore wind energy resource may be ``huge,'' but it's evidently not
as huge as our huge consumption.
We'll come to offshore wind later.
% AMMO ***
%\section{How audacious an assumption I'm making}
I should emphasize how generous
% audacious
an assumption I'm making.
Let's compare this estimate of
British wind potential with current installed wind power
worldwide.\label{pWorldWind}
The windmills that would be
required to provide the UK with 20\,kWh/d per person
amount to 50 times the entire wind hardware of \ind{Denmark};
7 times all the {\windfarm}s of \ind{Germany};
and double the entire fleet of all wind turbines in the world.
% 50 times the Danish fleet;
% and seven times the German fleet.
%%% wwindea.org
%%% world capacity = 74GW at end of 2006. Germany has 20.6GW, Spain and USA both 11.6. Denmark 3.1
%%% capacity required to get 20 kWh/d is 50GW average ie 150 GW peak
%%% 150 is 7 times germany and 50 times Denmark
% http://www.energinet.dk/en/menu/Frontpage.htm#
% cool danish site has live export display
% [ 50kWh/d is 375 GW peak ]
%
% \begin{center}
%{\mbox{\epsfbox{crosspad/wind6.ps}}}
% \end{center}
Please don't misunderstand me. Am
I saying that we shouldn't bother building {\windfarm}s? Not at all.
I'm simply trying to convey a helpful fact, namely that if we want
wind power to truly make a difference, the {\windfarm}s must cover
a very large area.
%\section{Calculate it again}
This conclusion%
\margintab{\small
% \begin{figure}
\begin{center}
\begin{tabular}{cc} \toprule
\multicolumn{2}{l}{\sc\OliveGreen{Power per unit area}}\\ \midrule
\windfarm & \OliveGreen{2\,\Wmm}\\
(speed 6\,m/s) \\
\bottomrule
\end{tabular}
\end{center}
% }{
\caption[a]{Facts worth remembering: {\windfarm}s.
%% , number 1
}
}
% Mean wind speeds in Dundee (\figref{fig.dundee}) never passed 3\,m/s.
-- that the
maximum contribution of onshore wind,
% most that onshore wind could add up to,
albeit ``huge,'' is much less
than our consumption -- is important, so let's
check the key figure, the assumed
power per unit area of {\windfarm} (2\,W$\!$/m$^2$),
against a real UK {\windfarm}.
% estimate what wind could
% offer in a second way.
% Let's go a to a real
%% state-of-the-art
% windfarm and find out what it generates.
% Let's go back to cars and try to understand them better.
% Whitelee windfarm on Eaglesham moor near Glasgow
The \ind{Whitelee \windfarm}\index{wind farm!Whitelee} being built
near \ind{Glasgow} in Scotland
% (a windier place than average in the UK) to come on stream mid 2009
has 140 turbines with a combined
{\em peak\/} \ind{capacity} of 322\,MW in an area of 55\,km$^2$.
That's 6\,\Wmm,
% 5.85\,\Wmm,
{\em peak}. The average power produced is smaller
because the turbines don't run at peak output all the time.
The ratio of the average power to the peak power is called
the ``\ind{load factor}''
or ``\ind{capacity factor},'' and it
varies from site to site, and with the choice of hardware
plopped on the site; a typical
factor for a {{good}\/} site with modern turbines
is $30\%$.\nlabel{pCapFacNotREFd}
% this label is not refd but the same fact is refd in wind2.tex ***
If we assume Whitelee has a \ind{load factor} of 33\%
% --40 (since winds are stronger in Scotland)
then the average power production per unit land area is
\OliveGreen{2\,\Wmm} --
%% --2.3
exactly the same as the power per unit area we
assumed above.
% *** these tables are not referred to
%% BIFURCATION POINT old version is in __wind.tex
\amargintab{b}{\small
% \begin{figure}
\begin{center}
\begin{tabular}{c@{\,$\leftrightarrow$\,}c} \toprule
\multicolumn{2}{c}{\sc Population density }\\
\multicolumn{2}{c}{\sc of Britain }\\ \midrule
250 per km$^2$ & 4000\,\m$^2$ per person \\
\bottomrule
\end{tabular}
\end{center}
% }{
\caption[a]{Facts worth remembering: \ind{population density}.
See page \pageref{pDensities}
% and \pageref{countriesD}
for more population densities.\index{population density}
%% , number 1
}
}
% estimated assuming a typical wind speed of 6\,m/s.
\vfill
\pagebreak[4]%%newpageone
%% see _wind.tex for further notes
\section{Queries}
\qa{Wind turbines are getting bigger all the time.
Do bigger \ind{wind turbine}s change this chapter's answer?
}{
% Appendix
Chapter \ref{ch.wind2} explains.
Bigger wind turbines deliver financial \ind{economies of scale}\index{economics!of wind},
% -- a good idea,
% financially
but they don't greatly increase the total power per unit land area,
because bigger windmills have to be spaced further apart.
A \windfarm\ that's twice as tall will deliver roughly
30\% more power.
% pr 2.0**(3.0/7.0)
% 1.34590019263236
% 2**(1.0/7) = 1.1041
}
\qa{Wind power fluctuates all the time.
Surely that makes wind less useful?
}{
Maybe. We'll come back to this issue
in \chref{ch.storage}, where we'll look
at wind's intermittency and discuss
several possible solutions to this problem, including energy storage
and demand management.
}
\begin{figure}[tbp]
\figuremargin{
\begin{center}
\begin{tabular}{c@{ \ \ \ \ }c}
\mono%
{\epsfxsize=2.05in\epsfbox{../data/cambridge/mono/DailyHist.eps}}%
{\epsfxsize=2.05in\epsfbox{../data/cambridge/DailyHist.eps}}%
&
\mono%
{\epsfxsize=2.05in\epsfbox{../data/cambridge/mono/HalfHourlyHist.eps}}%
{\epsfxsize=2.05in\epsfbox{../data/cambridge/HalfHourlyHist.eps}}%
\\[14pt]
{\footnotesize speed (m/s)}&
{\footnotesize speed (m/s)}\\
\end{tabular}
\end{center}
}{
\caption[a]{Histogram of Cambridge\index{data!wind!Cambridge} average\index{windspeed!Cambridge}
wind speed in metres per second: daily averages (left),
and half-hourly averages (right).\index{wind!data}
%% Mean wind speed was 2.7 m/s
% DO I NEED TO SAY WHAT VERTICAL AXIS IS?
}
\label{fig.camb.wind2}\label{fig.windhisto}
}
\end{figure}
\beginfullpagewidth\small
\section{Notes and further reading}
\nopagebreak
\beforenotelist
\begin{notelist}
\item[page no.]
\item[\npageref{fig.camb.wind}]
{\nqs{\Figref{fig.camb.wind} and \figref{fig.camb.wind2}}}.
Cambridge wind data
are from
the Digital Technology Group, Computer Laboratory, Cambridge
\protect\tinyurl{vxhhj}{http://www.cl.cam.ac.uk/research/dtg/weather/}.
The weather station is on the
roof of the Gates building, roughly 10\,m high.
Wind speeds at a height of 50\,m are usually about 25\% bigger.
Cairngorm data ({\nqs{\figref{fig.cairngorm}}})
are from\index{wind!data}
Heriot--Watt University Physics Department
\tinyurl{tdvml}{http://www.phy.hw.ac.uk/resrev/aws/awsarc.htm}.
\item[\npageref{pWorldWind}]
{\nqs{The windmills required to
provide the UK with 20\,kWh/d per person
are 50 times the entire wind power of \ind{Denmark}}}.
Assuming a load factor of 33\%, an average power of
20\,kWh/d per person requires an installed capacity of 150\,GW\@.
At the end of 2006, Denmark had an installed capacity of 3.1\,GW;
% new numbers at end of 2007 3.125
\ind{Germany} had 20.6\,GW\@.
% 22.247
The world total was 74\,GW
% 93.849
(\myurl{wwindea.org}).
Incidentally, the load factor of the Danish wind fleet was 22\% in 2006,
and the average power it delivered was 3\,kWh/d per person.
% 5,468,120 denmark population
% 3.1GW ~=
% http://www.windpower.org/composite-1463.htm
%% In 2006, the turbines in Denmark produced 6,108 GWh.
% that is 0.697 GW That is 22.49% load factor
% [16.8 percentage of the electricity consumption in Denmark]
% per person, it's 6108e6 / 365 / 5468120
% 3.0603 kWh/d/p
\end{notelist}
\ENDfullpagewidth
\normalsize
%% http://news.bbc.co.uk/1/hi/uk/6969865.stm
%% Costing the Earth