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Wind turbines is the generic term, for machines gaining shaft power from the wind. Each wind turbine utilizes a rotor turning on an axis for electricity generation or, less commonly, for direct mechanical power. The generation of electricity by wind turbines, also called aerogenerators, wind energy conversion systems, (WECS), and wind turbine generators, is a modern development for international commerce (see reports in Wind Power Monthly). From 1980 to 1995 about 15,000 modern grid connected machines were installed worldwide with a total electricity capacity of more than 3,000 MW. Capital costs are about $US 1,000 per rated kilowatt. Capacity installed each year grows at about 10%/y as costs decrease and the value of electricity generation without chemical pollution increases. Direct use of the mechanical power occurs for water pumping at sites remote from an electricity grid, although historically milling and sawing were of significant economic importance. Direct "Joule heating" by dissipating mechanical power in friction has not been accepted.

The overwhelming proportion of wind turbines for electricity have a rotor of blades turning on a horizontal axis, with machinery in a nacelle on a tall tower. Vertical axis machines are now very uncommon. A typical commercial wind turbine for utility power has: a tower of 30 to 50 m height, 2 or 3 blades on a rotor of 30 m diameter connected to a horizontal drive shaft, a gear box connected to a 400 kW electricity generator which itself is connected to a local electricity grid to export the power, 2 independent means of braking (usually a disc, brake before or after the gearbox, and blade tips or whole blades that can be turned to stall). However, a full range of machines is available, from battery chargers of 50 W capacity (diameter 1 m) to very large developmental turbines of multi-megawatt capacity (diameter to 100 m).

The basic theory of wind turbines is established [see Golding (1976), Twidell and Weir (1986), Freris (1990)]. The power in unperturbed wind of speed u across an area A is the kinetic energy of a cylinder of air, density ρ, passing per unit time:


A fraction Cp, the power coefficient, is captured by the turbine, so the useful power produced is:


Since the wind is in extended flow, air must continue with some kinetic energy beyond the rotor. The linear momentum theory of Betz is accepted to define the maximum fraction of power abstracted by a turbine rotor of any dimension:


In practice, commercial wind turbines have Cp,max ≈ 40%. The cubic power dependence with wind speed means that negligible power is produced at u < ≈ 4 m/s, so machines are braked to "cut-in" at higher wind speeds. As u increases above cut-in speed, power increases rapidly to the rated generator capacity, corresponding to the rated wind speed ur. Above ur, power stays constant by either adjusting the pitch angle of the whole blades or the blade tips, or having "self-stalling" blade profiles. Maximum power production over a year usually occurs if ur is between 1.5 to twice the average wind speed.

Optimum power capture depends on the speed of rotation (the frequency) of the rotor; too slow, and wind passes unperturbed through the blades; too fast, and streamlined flow is disrupted as with a solid object. The nondimensional characteristic to determine the optimum speed of rotation is the tip speed ratio λ:


where R is the blade length (rotor radius) and ω is the rotational radian frequency. The optimum value of λ, λopt, for maximum Cp depends primarily on the number of blades per rotor and on the blade profile. λopt varies between about 4 for a 10 bladed wind pump, 7 for a 3-bladed rotor to about 10 for a 2-bladed or single bladed rotor. Thus the fewer the number of blades, the faster is the optimum speed, and the more suitable for electricity generation. It also follows that the longer the blade length, the slower is the optimum rotational speed.

The torque on the rotor increases with the solidity (i.e., the fraction of activator disc area filled by the stationary blades). Thus the high torque and low speed required for wind water-pumps is produced by high solidity rotors with many blades. The low torque/high speed needed for efficient electricity generation is given by low solidity rotors with few blades, of which the least is a single, counter balanced, blade. However, because a steady rate of turning is appreciated and because some acoustic noise increases with rotor speed, the most common number of blades on commercial turbines for electricity generation is 3, and often 2.

Acoustic noise is one aspect of environmental impact that is central to obtaining planning permission to install wind turbines. Noise, which may be reduced by well established methods, arises mainly from the nacelle machinery, vortex shedding of air off the blades (of which blade protrusions should not occur), perturbation from blades passing the tower, and other aerodynamic causes. In practice acoustic noise decreases to equal ambient, background, noise of about 30 dBa at a distance of about 300 m, although all such criteria depend on wind speed and many other factors. The other dominant impact is visual impact which is particularly severe for wind turbines because they have to be sited in open areas, preferably with unperturbed fetch for the wind in high open countryside or across extended water. In practice of less concern generally are potential impacts on telecommunications, radar, birds and aircraft. Loss of land is trivial, since on a wind farm of many machines the ground sterilized by the tower base and access is only about 1 % of the total land area. The turbines should be placed at least 7 tower heights apart to allow the wind to reform from machine to machine, so allowing agriculture, natural flora and fauna, or leisure pursuits to continue unaffected in the area between the turbines.

Knowledge of the wind strength and variation is crucial to successful wind turbine economics. In general wind is caused by synoptic weather conditions having a wind speed distribution following a Weibull Distribution, where the probability of wind speed u > u is:


with k the shape factor (commonly k = 2 for a Raleigh Distribution) and c the scale factor (c = 2ü/√π, for a Raleigh Distribution with ü the mean wind speed).

From the equation for a Weibull Distribution, integration gives:


With a Raleigh Distribution for wind speed variation, which is very common, and knowing the power wind speed relationship of Eq. (5) and (6), the average annual power production is given approximately by:



Freris, L. L., Ed. (1990) Wind Energy Conversion Systems, Prentice Hall International, UK.

Golding, E. W. (1976) The Generation of Electricity by Wind Power, reprinted with additional material, E. and F. N. Spon, London.

Twidell, J. W. and Weir, A. D. (1986) Renewable Energy Resources, E. and F. N. Spon, London.

Wind Power Monthly, News Magazine, Vinners Hoved, 8420 Knebel, Denmark.


  1. Freris, L. L., Ed. (1990) Wind Energy Conversion Systems, Prentice Hall International, UK.
  2. Golding, E. W. (1976) The Generation of Electricity by Wind Power, reprinted with additional material, E. and F. N. Spon, London.
  3. Twidell, J. W. and Weir, A. D. (1986) Renewable Energy Resources, E. and F. N. Spon, London.
  4. Wind Power Monthly, News Magazine, Vinners Hoved, 8420 Knebel, Denmark.
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