# windpowerlib.wind_speed.hellman¶

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’.

Parameters: 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. pandas.Series or numpy.array

Notes

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

with:
v: wind speed, h: height, : Hellman exponent

is the height in which the wind speed is measured and is the wind speed at hub height of the wind turbine.

For the Hellman exponent 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]:

with:
: roughness length

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

References

 [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