windpowerlib.wind_speed.hellman(wind_speed, wind_speed_height, hub_height, roughness_length=None, hellman_exponent=None)[source]

Calculates the wind speed at hub height using the hellman equation.

It is assumed that the wind profile follows a power law. This function is carried out when the parameter wind_speed_model of an instance of the ModelChain class is ‘hellman’.

  • wind_speed (pandas.Series or numpy.array) – Wind speed time series.
  • wind_speed_height (float) – Height for which the parameter wind_speed applies.
  • hub_height (float) – Hub height of wind turbine.
  • roughness_length (pandas.Series or numpy.array or float) – Roughness length. If given and hellman_exponent is None: hellman_exponent = 1 / ln(hub_height/roughness_length), otherwise hellman_exponent = 1/7. Default: None.
  • hellman_exponent (None or float) – The Hellman exponent, which combines the increase in wind speed due to stability of atmospheric conditions and surface roughness into one constant. If None and roughness length is given hellman_exponent = 1 / ln(hub_height/roughness_length), otherwise hellman_exponent = 1/7. Default: None.

Wind speed at hub height. Data type depends on type of wind_speed.

Return type:

pandas.Series or numpy.array


The following equation is used [1] [2] [3]:

v_{wind,hub}=v_{wind,data}\cdot \left(\frac{h_{hub}}{h_{data}}

v: wind speed, h: height, \alpha: Hellman exponent

h_{data} is the height in which the wind speed v_{wind,data} is measured and v_{wind,hub} is the wind speed at hub height h_{hub} of the wind turbine.

For the Hellman exponent \alpha many studies use a value of 1/7 for onshore and a value of 1/9 for offshore. The Hellman exponent can also be calulated by the following equation [2] [3]:

\alpha = \frac{1}{\ln\left(\frac{h_{hub}}{z_0} \right)}

z_{0}: roughness length

Parameters wind_speed_height, roughness_length, hub_height and obstacle_height have to be of the same unit.


[1]Sharp, E.: “Spatiotemporal disaggregation of GB scenarios depicting increased wind capacity and electrified heat demand in dwellings”. UCL, Energy Institute, 2015, p. 83
[2](1, 2) Hau, E.: “Windkraftanlagen - Grundlagen, Technik, Einsatz, Wirtschaftlichkeit”. 4. Auflage, Springer-Verlag, 2008, p. 517
[3](1, 2) Quaschning V.: “Regenerative Energiesysteme”. München, Hanser Verlag, 2011, p. 279