PDF《WINDPUMPING》

2 Technical The power in the wind The wind systems that exist over the earth'

s surface are a result of variations in air pressure. These are in turn due to the variations in solar heating. Warm air rises and cooler air rushes in to take its place. Wind is merely the movement of air from one place to another. There are global wind patterns related to large scale solar heating of different regions of the earth'

s surface and seasonal variations in solar incidence. There are also localised wind patterns due the effects of temperature differences between land and seas, or mountains and valleys. Windspeed data can be obtained from wind maps or from the meteorology office. Unfortunately the general availability and reliability of windspeed data is extremely poor in many regions of the world. However, significant areas of the world have mean windspeeds of above 3m/s which make the use of windpumps an economically attractive option. It is important to obtain accurate windspeed data for the site in mind before any decision can be made as to its suitability. Methods for assessing the mean windspeed are found in the relevant texts (see the '

References and resources'

section at the end of this fact sheet). The power in the wind is proportional to: ? the area of windmill being swept by the wind ? the cube of the wind speed ? the air density - which varies with altitude The formula used for calculating the power in the wind is shown below: PW = ? ρ A V3 where, PW is power in watts available in the wind (W) ρ is the air density in kilograms per cubic metre (kg/m3 ) A is the swept rotor area in square metres (m2 ) V is the wind speed in metres per second (m/s) The fact that the power is proportional to the cube of the wind speed is very significant. This can be demonstrated by pointing out that if the wind speed doubles then the power in the wind increases by a factor of eight! It is therefore worthwhile finding a site which has a relatively high mean wind speed. Wind into watts Although the power equation above gives us the power in the wind, the actual power that we can extract from the wind is significantly less than this figure suggests. The actual power will depend on several factors, such as the type of machine and rotor used, the sophistication of blade design, friction losses, the losses in the pump or other equipment connected to the wind machine, and there are also physical limits to the amount of power which can be extracted realistically from the wind. It can been shown theoretically that any windmill can only possibly extract a maximum of 59.3% of the power from the wind (this is known as the Betz limit). In reality, for a windpump, this figure is usually around 30% to 40% and for a large electricity producing turbine around 45% maximum (see the section on coefficient of performance below) So, modifying the formula for '

Power in the wind'

we can say that the power that is produced by the wind machine can be given by: PM = ?.Cp ρ A V3 where, PM is power (in watts) available from the machine Cp is the coefficient of performance of the wind machine Windpumping Practical Action

3 It is also worth bearing in mind that a wind machine will only operate at maximum efficiency for a fraction of the time it is running, due to variations in wind speed. A rough estimate of the output from a windpump can be obtained using the following equation;

PA = 0.1 A V3 where, PA is the average power output in watts over the year V is the mean annual windspeed in m/s Principles of wind energy conversion There are two primary physical principles by which energy can be extracted from the wind;