Cup Anemometer Overspeeding

Statistical considerations are applied to a general equation of motion for cup anemometers in a turbulent wind. It is shown that the relative overspeeding ΔS/S can be expressed as ΔS/S = Ih2 · Js(l0/Λs) + cIw2, where Is and Iw are the horizontal and the vertical turbulence intensifies, respectively. The function Js depends on the shape of the spectrum of horizontal turbulent energy, l0 is the distance constant for the anemometer, and Λs is a characteristic length scale of the horizontal turbulence. The constant c is of order unity.
If Λs is suitably chosen as the scale of the energy-containing eddies, then Js is satisfactorily approximated by Js = (1 + Λs/l0)−1 in most atmospheric applications.