Abstract: The article adopts the spherical raindrop model and uses the strict expression of the air resistance coefficient CD, namely the Wallis formula, to calculate the v~t image of a raindrop with a diameter of 5 mm when it freely falls from rest in still air at 20 ℃. The article also solves the analytical and universal v(t) function under the approximation of CD being uniformly taken as 0.44, and produces the corresponding v~t image. The results show that these two v~t curves almost completely coincide, indicating that the approximate treatment is completely appropriate. The article explains the reason for this and points out the reason for the limit rate measured in the experiment is 2.00 m/s lower than the theoretical value under the spherical raindrop model is the actual raindrop shape presents a Hamburg shape, and its actual air resistance coefficient is calculated to be about 0.52. We believe that the spherical raindrop model is generally practical.

Key words: spherical raindrop model, still air, free falling motion, air resistance coefficient, approximate treatment