ECONOMICS

If we have cost data and efficiency/ performance data on WEC-load systems then we can calculate whether the use of WEC's is economic for the location in question. This obviously depends also greatly on interest rates, current and projected energy costings, and profit and loss and cash flow projections. If we have an existing WEC on the site then we can evaluate whether it is extracting a suitable amount of energy according to the formulae as above. If not, and if the WEC is an impulse type WEC, then we can examine whether the cut-in speed setting is a factor causing the lack of energy yield (or whether it is something else).

10. It should be mentioned also here that the variation of windspeed and wind energy with height is calculable by the formula v/v2 = log(h/r)/log(2/r), where r is roughness parameter, typically 0.02 metres for short grass; values for speed and for energy (v^3) variations with height are tabulated below, using a r = 0.02:

Height Windspeed Wind Energy

2 1.00 1.00

6 1.23 1.90

10 1.35 2.46

16 1.45 3.06

100 1.85 6.33

11. For converting the energy values to watts, kilowatts etc, then the formula E = 0.5 pAv^3 should be used,

where p is air density - this is 1.23 kg/metre^3 at sea level, and 1.18 kg/m3 at 1000 metres altitude, 1.12 kg/m3 at 2000 metres altitude, and 1.07 kg/m3 at 3000 metres altitude; A is WEC cross sectional or swept area in metres^2; v^3 is the Energy integral in metre^3/second^3, as in items (4a) and (4b) above.

12a. The following approximate peak efficiencies apply to WEC types (exact peak efficiency depends on precise design and on production quality) :

Fast Propeller 42%

Darrieus Rotor 42%

Multiblade impulse 20%

Savonius Rotor 15%

Note that the 20% and 15% values are applicable with the energy yields as in (4b) for impulse type WEC's.

12b. Note that if calculations are to be done with water pumping, then a piston pump can be reckoned on average to be 60% efficient (due to valve losses and piston friction losses, and that power required can be calculated by the formula:

P = d.g.h.(v/t) / e

where d = density of water (1 kg/litre)

g = gravitational constant 9.81 metre/sec^2

h = head in metres

v/t = volume per time - flowrate in litres/second

e = efficiency (take as 0.6 as above)

13a. Note that 1995 energy costs are typically (as per the Economist newspaper, 7-13 October 1995) :

US$ per kiloWatt-Hour of electrical energy

Fossil fuel power stations 0.05 - 0.08

Hydro Electric 0.05 - 0.10

Nuclear Power 0.10 - 0.20

Wind Power 0.10 - 0.20

Biomass/ ethanol 0.20 +

Solar power stations 0.20 +

Solar photovoltaic 0.30 +

Wave Power 0.30

13b. WEC Costings are quite variable, but can be said to be approximately:

Conventional windpump (without pump) US$ 250/m^2

Wind Electric Generator (large) US$ 120/m^2

Low Cost Impulse Type WEC's (e.g. cretan sail) US$ 50/m^2