by Prof J Hugill, Abingdon, U.K. <jan@hugill.force9.co.uk>

Introduction
When planning a new source of energy, it is conventional, as for any other project, to calculate the capital cost and the likely return on capital over its lifetime. A useful concept is the payback time, TPB$ in which the capital cost (and the interest on the capital) is covered by income, after which the project starts to make a profit. Most projects will also have a lifetime, TLT after which the costs of maintenance outweigh the income and the project is terminated. Obviously no one would consider a project unless TLT was greater than TPB, hopefully much greater. One can define a figure of merit by M = (TLT TPB) / TLT ; clearly 0 < M < 1 and the closer its value to 1 the better.
For systems designed to provide energy, the same kind of analysis is possible in principle with regard to the energy invested in the system during its construction and operation compared with the net energy output during operation. If the energy invested is Einv and the net average power output is Pout , the energy payback time is TPBE = Einv / Pout . There is no a priori reason why TPB$ and TPBE should be equal and, as we will see below, they are generally not.
For systems that are built with low grade energy, such as is obtained from burning fossil fuels, but output high grade and more valuable power, such as electricity, TPB$ will tend to be less than TPBE and an attempt will be made to quantify this difference below. A typical example of such a system would be a wind farm. The larger value of TPBE may be a disadvantage for such systems and it would be if the electricity produced were used as a substitute for low grade energy instead of tasks such as lighting, electric motors or perhaps in the future the production of hydrogen by electrolysis of water.
The approximately four times higher cost of electrical energy compared with fossil energy is obviously related to the thermodynamic efficiency of the conversion of heat into mechanical work, about which little can be done at present, and the losses associated with the transmission of power from the point of  production to the point of use. Except in the case of combined heat and power schemes, the heat energy that
cannot be converted to electricity, amounting to typically 70% is simply lost to the environment at as low a temperature as practicable.
Energy auditing
The amount of energy used in the construction of a project is a difficult thing to calculate. The suppliers of raw materials such as steel, concrete and other building materials can probably make a reasonable estimate of the energy invested in their products. For these producers energy costs are likely to be a substantial fraction of the total cost of production. The same applies to transport costs to the construction site.
However, in a modern economy, raw material costs are likely to be a small fraction of the total construction cost. This will usually be dominated by the cost of wages.
There is also an implicit energy cost in wages. This is because wages, or a part of them, will be spent on energy and this is energy that would not be used if the project did not proceed. Clearly it would be an almost impossible task to track down the usage of energy by every individual working on a project. At this point it is necessary to make some drastic assumptions. Let us assume a ‘standard employee’ who will spend most of his wages on goods and services. For each of these expenditures a greater or smaller fraction will be direct expenditure on energy. For items such as household heating and lighting, running a car, flying on holidays and similar items, this fraction will be relatively large. For others, such as eating out, local
entertainment, paying for services provided by the government through taxes etc., it will be relatively small. Let us suppose that we can determine the fraction of direct expenditure on energy for each of these goods and services and find that the average employee spends a fraction f of his income directly on energy and the rest 1 – f on payments to others – they are essentially his employees.
But this is not the end of the matter. His employees will also spend a similar (assume the same) fraction of their income from him on energy, i.e. a fraction f (1 – f) of his salary. This is also energy that would not be expended if the project did not proceed that must be included in the energy audit. His employees will also spend the rest of their income on yet others, and so on down the economic chain. If we sum up all the
subsequent expenditure on energy, we get a series of the form:
f [1 + (1 - f) + (1 - f) 2 + (1 - f) 3 + . . .]
that sums to unity. The interpretation of this result is that, sooner or later, the greater part the original employee’s wages will be spent on energy, whatever the value of f. The conclusion that money circulating in the economy is eventually spent of energy should not be too much of a surprise. The rapid growth in the wealth of the socalled developed nations since the industrial revolution is based on the replacement of the
work of men and animals and renewable resources, such as provided by windmills, waterwheels and wood burning, mainly by energy from fossil fuels, with much smaller contributions from renewables and hydroelectric power. The consequence has been a massive increase in the energy available to each individual and a consequent increase in what is loosely described as the standard of living. One only has to compare the standard of living in developed countries with that in countries in a preindustrial state to realise how much the former have come to depend on cheap supplies of energy. President Bush has recently remarked on the fact.
Now that the competition for energy is intensifying due to the rapid industrialisation of developing countries and the continuing growth in world population, the cost of energy is likely to rise. This is bound to impact on the standard of living that developed countries have come to enjoy, at least as measured by each individual’s energy consumption. Hence the need to develop alternative energy sources, not just to compensate for the finite reserves of fossil energy but also to try to alleviate the worst effects on the earth’s climate by its combustion.

The relation between the expenditure of money and energy
The argument above suggests that a large fraction of the money spent by individuals, businesses,  organisations and governments is, directly or indirectly, eventually spent to purchase energy. The next question is how much energy can be bought for a given expenditure. Here it is useful to employ an economic argument: that no-one is going to spend more on goods and services than necessary, or if he/she is forced to by lack of competition or taxes, the excess profit or tax will just be spent by someone else, with the same result so far as energy consumption is concerned. This leads to the conclusion that the best way to calculate the energy consumed per dollar spent is to look at the price of energy in the wholesale market. Clearly this is highly variable, so the data given below is only a snapshot. The table below is for different types of fossil
fuel and electricity used by manufacturing industries in the UK. Prices for domestic consumers are about a factor of two higher. The fossil fuels account for about 85% of the world’s energy consumption [1].

Table I Fuel prices for manufacturers in the UK, 2004 [2]. Data are given in p/kWh and have been converted to MJ/$ using a $/£ exchange rate of 1.74.
Type of fuel p/kWh MJ/$
Electricity 3.2 65
Heavy fuel oil 1.2 172
Natural gas 0.8 259
Coal 0.5 414
The figures in this table will be taken as representative of developed economies in the calculations given below.
Financial and energy payback times for wind power An example of an alternative energy system is the proposed Capewind wind farm [3]. This project is estimated to cost $800 million and to provide an average net output of 170 MW. Assuming that the power is sold on the wholesale electricity market at the price given in table I, the capital cost will be repaid in a time TPB$ = 9.7 years. This time will be halved if the electricity can be sold directly to domestic customers at a price twice that of the wholesale market. To calculate the energy payback time, assume that the project uses normal manufacturing methods and road transport and that the basic fuels involved are oil and natural gas. The relationship between the project cost and the amount of energy consumed can be estimated from the figures in the last column of table I. Taking a
rough average of the figures for oil and gas at 200MJ/$ and the cost of the project given above indicates an energy consumption for construction of 1.6×10 11 MJ. The time to pay back this energy from the 170MW mean power output, TPBE = 29.8 years.
As noted above, the much smaller value of TPB$ compared with TPBE in this simplified analysis simply reflects the fact that a project of this type is constructed by consuming a large amount of low grade energy from fossil fuels but produces more valuable high grade energy in the form of electricity. However, it is apparent that, if wind power is to make any substantial contribution to overall energy requirements, the energy investment in construction will produce a negative effect on fossil fuel consumption in the short ( approx 30 years) term. It is also clear that the lifetime of such projects will have to be much longer than this to make a net positive contribution to energy generation.
Conclusion
When considering alternatives to the use of fossil fuels for energy supply, it is useful to look at the energy consumed in their construction as well as the financial cost. For systems producing electrical power, the energy payback time can be several times longer than is apparent from financial considerations. During this time, which could be as much as 30 years if the analysis given here is correct, such systems will have a
negative impact on energy consumption. In the case of wind power in particular, the other problems associated with it, such as lack of responsiveness to demand, will restrict it to a minor role in overall energy supply.
Acknowledgements
I am indebted to Gioietta Kuo Petravic for bringing the problems associated with wind power to my attention and stimulating this contribution to discussion and to Phil Edmonds for conversations about the relation between development and energy usage.
References
[1] International Statistics www.scaruffi.com/politics/stats.html (2006)
[2] Department of Trade and Industry, UK www.dti.gov.uk/energy/inform/energy_prices/index.shtml (2006)
[3] Cape Wind www.capewind.org (2006)