Dynamics of falling raindrops

A standard undergraduate mechanics problem involves a raindrop which grows in size as it falls through a mist of suspended water, droplets. Ignoring air drag, the asymptotic drop acceleration is g/7, independent of the mist density and the drop radius. Here we show that air drag overwhelms mist drag, producing drop accelerations of order 10(-3) g. Analytical solutions are facilitated by a new empirical form of the air drag coefficient C = 12R(-1/2), which agrees with experimental data on liquid drops in the Reynolds-number range 10 < R < 1000 relevant to precipitating spherical drops. Solutions including air drag are within reach of students of intermediate mechanics and nonlinear dynamics.