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< prev - next > Energy Mechanical Power KnO 100432_Windpumping (Printable PDF)
Practical Action
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 = ½.Cp ρ A V3
where, PM is power (in watts) available from the machine
Cp is the coefficient of performance of the wind machine
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;
these are through the creation of either lift or drag force (or through a combination of the two).
The difference between drag and lift is illustrated by the difference between using a spinnaker
sail, which fills like a parachute and pulls a sailing boat with the wind, and a Bermuda rig, the
familiar triangular sail which deflects with wind and allows a sailing boat to travel across the
wind or slightly into the wind.
Drag forces provide the most obvious means of propulsion, these being the forces felt by a
person (or object) exposed to the wind. Lift forces are the most efficient means of propulsion
but being more subtle than drag forces are not so well understood.
The basic features that characterise lift and drag are:
drag is in the direction of air flow
lift is perpendicular to the direction of air flow
generation of lift always causes a certain amount of drag to be developed
with a good aerofoil, the lift produced can be more than thirty times greater
than the drag
lift devices are generally more efficient than drag devices
Types and characteristics of rotors
There are two main families of wind machines: vertical axis machines and horizontal axis
machines. These can in turn use either lift or drag forces to harness the wind. The horizontal
axis lift device is the type most commonly used. In fact other than a few experimental
machines virtually all windmills come under this category.
There are several technical parameters that are used to characterise windmill rotors. The tip-
speed ratio is defined as the ratio of the speed of the extremities of a windmill rotor to the
speed of the free wind. Drag devices always have tip-speed ratios less than one and hence turn
slowly, whereas lift devices can have high tip-speed ratios (up to 13:1) and hence turn quickly
relative to the wind.
The proportion of the power in the wind that the rotor can extract is termed the coefficient of
performance (or power coefficient or efficiency; symbol Cp) and its variation as a function of
tip-speed ratio is commonly used to characterise different types of rotor. As mentioned earlier
there is an upper limit of Cp = 59.3%, although in practice real wind rotors have maximum Cp
values in the range of 25%-45%.
Solidity is usually defined as the percentage of the area of the rotor, which contains material
rather than air (see Figures 1 & 2 below). High-solidity machines carry a lot of material and
have coarse blade angles. They generate much higher starting torque (torque is the twisting or