# Vertical Wind Profile - Logarithmic Law

## Description

Wind speed extrapolation

In wind energy studies, two mathematical models or 'laws’ have generally been used to model the vertical profile of wind speed over regions of homogenous, flat terrain. The first approach, the log law, has its origins in boundary layer flow in fluid mechanics and in atmospheric research. It is based on a combination of theoretical and empirical research. The second approach is the power law. According to the log law, the increase of wind speed, with height in the lowest 100m, can be described by a logarithmic expression that calculates the wind speed v2 at a certain height h2 in relation to an original height h1 and speed v1, assuming a logarithmic vertical profile of wind speed function of the roughness length z0

Related formulas## Variables

v2 | mean wind speed at height z_2 (m/s) |

v1 | mean wind speed at height z_1 (m/s) |

z2 | height (m) |

d | zero plane displacement (m) |

z0 | surface roughness (m) |

z1 | height (m) |