The responses of rising or falling spherical wind sensors to atmospheric wind perturbations.

Analysis of the responses of rising or falling spherical wind sensors to atmospheric wind perturbations on the wind profile in the vertical, using Fourier transform techniques. The linearized equations of motion of a sensor that is subject to drag and gravitational body forces are developed by perturbing a sensor about an equilibrium uniform motion with wind fluctuations which have vertical variations. The wind environment and sensor velocities are decomposed with stochastic Fourier-Stieltjes integrals, and the linearized equations of motion are used to derive the response functions and phase angles of the sensor motions. The results of the analysis are used to analyze the response properties of the Jimsphere balloon wind sensor. It is shown that, in general, the transfer functions associated with the horizontal sensor motions are smaller than the transfer functions associated with the vertical sensor motions in the omega times T product range from zero to infinity, omega being the wind perturbation frequency and T a time constant of the system. Thus, the sensor is more responsive to vertical than to horizontal air motions.