## Abstract

A first-order theory of the fluctuating lift and drag coefficients associated with the aerodynamically induced motions of rising and falling spherical wind sensors is developed. The equations of motion of a sensor are perturbed about an equilibrium state in which the buoyancy force balances the mean vertical drag force. It is shown that, to within first order in perturbation quantities, the aerodynamic lift force is confined to the horizontal, and the fluctuating drag force associated with fluctuations in the drag coefficient acts along the vertical. The perturbation equations are transformed with Fourier-Stieltjes integrals and the resulting equations lead to relationships between the power spectra of the aerodynamically induced velocity components and the spectra of the fluctuating lift and drag coefficients.

Experimental evidence shows that the aerodynamically induced motions of the Jimsphere balloon occur predominantly in the horizontal plane. This implies that the root-mean-square (rms) horizontal lift coefficient is much larger than the rms vertical drag coefficient. The aerodynamically induced motion of the Jimsphere is found to be sinusoidal in nature. The dimenionless frequency (Strouhal number) and nondimensional variance of the induced zonal and meridional velocity components are given as functions of the Reynolds number. The experimental range of the Reynolds number is 1.4 × 10^{5} to 6.6 × 10^{5} The ratio between the rms lift coefficient and the mean, or zero-order, drag coefficient is found to be approximately 0.36.

The theory shows that the Fourier components of the first-order fluctuating horizontal lift coefficient vector lead those of the induced horizontal velocity vector, and that the fluctuating part of the drag coefficient lags the induced vertical velocity for rising balloons and leads the induced vertical velocity in the case of falling balloons. The phase angles of the induced lift and drag associated with the characteristic frequency of oscillation of the Jimsphere are given as functions of the Reynolds number.

The rms lift coefficient of smooth 2 m ROSE balloons operating at supercritical Reynolds numbers is found to be approximately twice the value obtained from wind tunnel data. This result suggests that caution should be exercised when wind tunnel data of constrained bodies are applied to free balloons.