The error in the magnitude of the horizontal wind field as computed for balloons with linear and quadratic rise rates ascending through a light, moderate, or severe wind field is derived. The rise rate function of the Jimsphere is analyzed as a special case. Figures are presented of wind error versus altitude for each rise rate and wind field, assuming linear smoothing. The ultimate capability of rising balloon systems for measuring wind from the surface to 18 kilometers can be determined from the data and the wind accuracy can be computed by knowing only the rise rate behavior versus altitude. The radii of smooth and roughened spheres needed to achieve the desired rise rate at various altitudes are derived. The radii for smooth and roughened balloons for tow-meter-per-second to 20-meter-per-second rise rates at 10 and 14 km altitudes, and the wind-following capability for each are tabulated.

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