The drag coefficient of a sphere: An approximation using Shanks transform

An accurate model for the drag coefficient (CD) of a falling sphere is presented in terms of a non-linear rational fractional transform of the series of Goldstein (Proc. Roy. Soc. London A, 123, 225-235, 1929) to Oseen's equation. The coefficients of the six polynomial terms are improved through a direct fit to the experimental data of Roos and Willmarth (AIAA J., 9:285-290, 1971). The model predicts CD up to Reynolds number 100,000 with a standard deviation of 0.04. Results are compared with eight different formulations of other authors.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► The drag coefficient of a falling sphere is presented in terms of a non-linear rational fraction. ► The model predicts CD in the range 0.1 < Rp < 100,000 with a standard deviation of 0.04. ► Results are compared with eight different formulations of other authors.