Fall velocity of multi-shaped clasts

Accurate settling velocity predictions of differently shaped micro- or macroclasts are required in many branches of science and engineering. Here, a single, dimensionally correct equation is presented that yields a significant improvement on previous settling formulas for a wide range of clast shapes. For smooth or irregular clasts with known axial dimensions, a partially polynomial equation based on the logarithmic values of dimensionless sizes and settling velocities is presented, in which the values of only one coefficient and one exponent need to be adapted for different shapes, irrespective of the Reynolds number. For irregular, natural clasts with unknown axial dimensions, a polynomial equation of the same form is applied, but with different coefficients. Comparison of the predicted and measured settling velocities of 8 different shape classes as well as natural grains with unknown axial dimensions in liquids, representing a total of 390 experimental data points, shows a mean percentage error of −0.83% and a combined R2 value of 0.998. The settling data of 169 differently shaped particles of pumice, glass and feldspar falling in air were also analyzed, which demonstrates that the proposed equation is also valid for these conditions. Two additional shape classes were identified in the latter data set, although the resultant equations are less accurate than for liquids. An Excel spreadsheet is provided to facilitate the calculation of fall velocities for grains settling individually and in groups, or alternatively to determine the equivalent sieve size from the settling velocity, which can be used to calibrate settling tubes.