# Variation of wind speed with height

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Taller windmills see higher wind speeds. The way that wind speed increases with height is complicated and depends on the roughness of the surrounding terrain and on the time of day. As a ballpark figure, doubling the height typically increases wind-speed by 10% and thus increases the power of the wind by 30%.

Some standard formulae for speed v as a function of height z are:

1. According to the wind shear formula from NREL [ydt7uk], the speed varies as a power of the height:

10 m where v10 is the speed at 10 m, and a typical value of the exponent a is 0.143 or 1/7. The one-seventh law (v(z) is proportional to z1/7) is used by Elliott et al. (1991), for example.

2. The wind shear formula from the Danish Wind Industry Association [yaoonz] is log(z/z0)

where z0 is a parameter called the roughness length, and vref is the speed at a reference height zref such as 10 m. The roughness length for typical countryside (agricultural land with some houses and sheltering hedgerows with some 500-m intervals - "roughness class 2") is z0 = 0.1 m.

In practice, these two wind shear formulae give similar numerical answers.

That's not to say that they are accurate at all times however. Van den Berg

(2004) suggests that different wind profiles often hold at night.

12 11 10

10 100 height (m)

Power density of wind v. height 400

Wind speed versus height

DWIA —

1

JR

-iE

iL

Power density of wind v. height 400

 DWIA 1 JR -it L / y - Figure B.7. Top: Two models of wind speed and wind power as a function of height. DWIA = Danish Wind Industry Association; NREL = National Renewable Energy Laboratory. For each model the speed at 10 m has been fixed to 6 m/s. For the Danish Wind model, the roughness length is set to Zo = 0.1 m. Bottom: The power density (the power per unit of upright area) according to each of these models. E 350 J 250 w S 150 I 100 10 100 height (m) Figure B.7. Top: Two models of wind speed and wind power as a function of height. DWIA = Danish Wind Industry Association; NREL = National Renewable Energy Laboratory. For each model the speed at 10 m has been fixed to 6 m/s. For the Danish Wind model, the roughness length is set to Zo = 0.1 m. Bottom: The power density (the power per unit of upright area) according to each of these models. Figure B.8. The qr5 from quietrevolution.co.uk. Nota typical windmill.