WORKED EXAMPLES

14a. Worked example nr 1:

A windsite has an average cca indicated windspeed of 3.0 metres per second. It is proposed to install a 6 metre diameter multiblade windmill at a mean height of 6 metres above ground level, over short grass (2 cm roughness factor). Air density is 1.23 kg/m3 (sea level value); the peak efficiency of the windmill is estimated at 20% (normal). Calculate energy yield per year and also monetary value generated if the resultant mechanical energy is costed at US$ 0.10 per kilowatt hour. Calculate also the optimal cut-in windspeed for the WEC-load to achieve these figures.

Use our formula Emax = 20.1 * (vcca^1.50) to give 104.44 m3/s3 of maximum useable energy by a impulse type WEC at 2 metres above ground level. WEC cross sectional area is (6 * 6 * PI / 4) = 28.27 m2; thus with density of 1.23 then maximum useable power flux is

(104.44 * 28.27 * 1.23 * 0.5) = 1816 watts

With 20% peak efficiency, then average generated power = 1816 * 0.2 = 363 watts mechanical energy.

Converting the above figures for 2 metres above ground level to 6 metres above ground level, we have 363 * 1.90 = 690 watts average mechanical power output. Over 8760 hours per year this gives 690 * 8760 / 1000 = 6044 kiloWatt-Hour of mechanical energy per year.

With a costed value of US$ 0.10 per kWatt-hour we have value added per year = 6044 * 0.10 = US$ 604-40.

Rate of return and interest rate calculations can be taken from there on.... obviously capital cost and durability/longevity are also major considerations here.

Using the formula as in (5) above, vciopt = 2.2 + ( 0.78 * 3.0) = 4.54 metre/second at 2 metres above ground level; this is equivalent to (4.54 * 1.23)

= 5.58 metre/second at 6 metres above ground level.

4b. Worked example nr 2: with 5 locations of the 59 Tanzanian having greater than 85 m3/s3 wind value average and also 5 having greater than 60 m3/s3 wind value on a worst-month basis, and using low-cost WEC's of US$ 50-00/m2, and using WEC peak efficiencies of 20%, with air density of 1.23 kg/m3 and a WEC mean height of 6 metres, and with energy costing of US$ 0-10/kWh, then calculate value added/year for unit capital investment....

The above produces returns of US$ 17.40 per annum per investment of US$ 50-00 for an average annual basis, and US$ 12.28 p.a. per investment of US$ 50-00 for a worst-month basis.

These correspond to approximately 3 years and 4 years payback periods respectively, which could be classified as moderately yielding investments; note that the investments are expected to last 20 years without major repairs or maintenance.

However, note that these figures are for the best 10% of locations only; also that they depend on having VERY low-cost WEC's - typically one fifth the unit cost of conventional commercial multivane windpump WEC's; it is not sure that durable machines of this type can be produced for that kind of price.