Errors in wind-speed measurements by rotation anemometers

A perturbation theory approach of non-linear mechanics is applied to the solution of a non-linear rotation anemometer dynamic equation in a gusty wind. The first two terms of the perturbation series give a simplified equation for the wind-speed overestimation by a rotation anemometer (u-error) in terms of a wind velocity spectrum (or a correlation function). The equation agrees satisfactorily with all the known analytical or numerical solutions of rotation anemometer equations. It agrees, in particular, with recent theoretical estimations of the u-error magnitude by Kondo et al. (1971) and Hyson (1972), but disagrees significantly with the experimental findings of Izumi and Barad (1970) and Högström (1974). The same approach is also used for the estimation of the influence of the vertical wind fluctuations on the rotation anemometer readings (w-error). It is shown that w-error is usually of the same sign as u-error and that the sum of these both types of errors may be in some cases of the same order as an experimental wind-speed overestimation observed by Izumi and Barad and by Högström. However, it seems probable that some additional types of errors contribute also to the real overspeeding of rotation anemometers in a gusty wind.