\subsection{Oxen power}
In `coal substitution', we imagined growing plants and feeding them
to a power station, which set fire to them and generated electricity
and heat.
Another way of using plants to make electricity is to feed the plants
to oxen and have the oxen drive an electricity mill.
% An ox can work for 8h per day at a speed of 1.5 feet per second
% while pulling 130lb * g , which is 1/3 of a hp.
% 1.5 feet per second * 130 lb * 9.81 m/s/s in W is 264W instantaneous
% and thus 88W on average.
% The book indicates that in other machines scuh as whins or carts
% the ox does better but hardly ever reaches 0.5 hp.
The power of an ox is 300\,W, and it can work for 8 hours per day,
so its average delivered power is 100\,W (2.5\,kWh/d).
% http://books.google.co.uk/books?id=M5c0AAAAMAAJ&pg=PA294&lpg=PA294&dq=power+of+an+ox&source=web&ots=JXWrMo7gSN&sig=tA26ZUW2Yxh-ebzm7JaUSBoVVH8&hl=en
% Mechanics for the Millwright, Machinist, Engineer, Civil Engineer,
% A horse consumes 11lb of Carbon per 24h (+ 1lb of Hydrogen)
% By Frederick Overman
% Published 1851
%% http://www.ieer.org/reports/energy/3-power.html
To supply 15\,kWh/d per person, each person needs a team of six oxen.
What's the land area required to feed an oxen-powered power station?
(It's possible that in some countries such as India, this
question is irrelevant: perhaps farming already produces sufficient
byproducts to feed the oxen without any additional cost in land area.
But let's explore the assumption that the oxen's feed
has to be grown on extra land.)
Oxen are about 10\% efficient at turning chemical energy
into work.\index{draught animal}\index{animal!draught}\index{ox}\index{bullock}\index{steer}\index{cow}
A life-cycle analysis of oxen takes into
account the upstream requirements:
each ox must first gestate inside an energy-consuming mother, then
grow up for three energy-consuming years, before it can take up
employment, which might last ten years.
This bumps the net efficiency down to 7\%.
If we could feed oxen on plants with a power density of 0.5\,\Wmm (an optimistic
figure)
then the net power density of the oxen-powered power station would be
0.035\,\Wmm. This means that to deliver 15\,kWh/d per person, an area
of roughly 2 hectares per person would be required.
If we assume plants with a more realistic power density of 0.1\,\Wmm
the area required rises to roughly 10 hectares per person.
``A thousand hours of work per year (6 hours per day for about 175 days)
and 250 watts of average output, is about the maximum that
a South Asian bullock will provide in energy output per year.
(But surely it {\em{could}\/} provide more.)
Under these assumptions, the annual output of energy amounts to 250 kilowatt hours or 0.9 gigajoules. This is a practical upper limit for the annual energy output of an average bullock.''
``we take the input to be 20 gigajoules per animal per year, the lower limit of our estimates for energy intake''
[which went from 20 to 40].
About 25\% of the input energy can be collected as dung and used as fuel, so that the net energy input is about 15 gigajoules.
For an output of 0.9 gigajoules, we get an estimate of the efficiency of draft animals of 6\%. If we ignore dung recovery, then the efficiency would be 4.5\%. This is about the upper limit of a range of efficiencies which one might calculate for draft animal use in agriculture.
(On a daily basis Rao estimates the efficiency of an adequately fed bullock as 8.6\% (Rao; p. 542). Lawrence and Smith estimated the efficiency of draft animals on a daily basis as 10\%, which gives an annual efficiency estimate of about 5\%.)
% 1000 hours per year at 250\,W.
This annual output corresponds to average power of 30\,W.
% 28.5W
The input, in chemical energy in food, is 600\,W (some of which can be
recovered by using dung as fuel).
% 634\,W
% (20\,GJ per year)
But a more accurate accounting takes account of the
upstream costs:
A 3-year old bullock will have consumed 54,666 MJ of feed and its caretaker 1788 MJ of food for a total input of 56,454 MJ before it can begin to provide work output.
It might have a ten-year working life.
Spreading this embodied energy of 50\,GJ over 10 years means the average
total energy input per year of work is 25--45\,GJ.
Feed's calorific value is 13\,GJ per ton.
% ((25e9 (J per year)) / (13e9 (J per ton))) / (2 ((ton / ha) / year)) = 0.961538462 hectares
% 1.73 ha
% This land productivity incidentally corresponds to
% (13e9 J per ton) * (2 ton/ha/year ) in W per sq metre
% (13e9 (J per ton)) * (2 ((ton / ha) / year)) = 0.0823907881 W per (sq meter)
% roughly 0.1 W/mm
If the feed is produced from land at a rate of 2\,ton/ha/y
then a single bullock consuming 25--45\,GJ requires
1--1.7\,ha.
% 28.5W
Delivering 30\,W from this area, we deduce the power density
achieved by the plant--bullock--electric generator chain is
0.0016--0.003\,\Wmm.
%% 0.002964 W / (sq meter)
%% http://66.102.9.104/search?q=cache:8vX-CjkjTlMJ:cigr-ejournal.tamu.edu/submissions/volume1/CIGREE98_0001/Energy.pdf+land+area+required+to+feed+an+ox&hl=en&ct=clnk&cd=7&gl=uk&client=firefox
%% second opinion:
%% Energy use in agriculture \cite{EnInAg}
%% http://cigr-ejournal.tamu.edu/submissions/volume1/CIGREE98_0001/Energy.pdf
% The feed needed to supply the ox for about 200 hours of work is 150 kg of
%concentrate (maize) and 300 kg of forage (Morrison, 1956). The concentrate consumed
%by the ox is derived from the 1,944 kg of maize produced per hectare and reduces the net
%yield. In addition, the ox consumes forage from 2 hectares of pasture on marginal land.
% Can I extrapolate and say For 1000 hrs of work need 750kg of maize?
% And thus 0.5ha?
% takes 50 hours to plough 1 ha with a double ox plough.
%% http://www.ieer.org/reports/energy/2-ovrvw.html
Energy input
\begin{tabular}{lrrr} \toprule
\multicolumn{4}{c}{South Asian Rice Production, 1988}\\ \midrule
Country
&Cultivated
Area
&Yield
&Production
\\
&
($10^6$ ha)
&
(kg/ha)
&
($10^6$ tons)\\ \midrule
Bangladesh &10 &2190 &21.9\\
India & 41 &2487 &102\\
Nepal & 0.63 &2649 &1.7\\
Pakistan &1.4 &1991& 2.8\\
\bottomrule
\end{tabular}
Wheat:
yield is 1750 kg/ha.
Coarse grain: 1000 kg/ha.
% From
%% Energy use in agriculture
%% http://cigr-ejournal.tamu.edu/submissions/volume1/CIGREE98_0001/Energy.pdf
Slash and burn agriculture with a 20-year cycle
required 2\,ha per person.
%% About 1,144 hours of manpower is
% required to produce about 1,944 kg/ha of maize in this system
% The only other input is for 10.4 kg/ha of maize seed. The 1,144 hours of
%labor represent approximately 60% of the total labor output for one adult per year. The
%farmer is assumed to consume about 3,000 kcal/day of food and requires about 6,000
%kcal/day of fuelwood for cooking and preparing food
%
%Using cattle-power and crop rotation, get the
%area required down to 0.8\,ha per person.
%
%Yields of 2000\,kg per hectare can be
%raised to 8000\,kg/ha by other
%farming methods -- possibly
%requiring fossil fuels?