### Re: terminal velocity of rain

Date: Sun Jul 2 18:36:10 2000
Posted By: Carl Morgan, Forecaster, Meteorology, National Weather Service
Area of science: Physics
ID: 961909601.Ph
Message:

Ryan,

You are correct...2-9 cm/s is way too slow, and I'm sure the source meant to say 2-9 m/s, which is about right.

Terminal velocity of raindrops is dependent upon the size of the drop, among other things. Obviously the larger the drop, the faster it will fall.

The following table contains fall speeds based on observations by Gunn and Kinzer (1949). These data were collected under sea-level conditions (1013 millibars and 20 degrees C).

```Diameter (mm)    Fall speed (m/s)         Diameter (mm)    Fall speed (m/s)
0.1               0.27                       2.6              7.57
0.2               0.72                       2.8              7.82
0.3               1.17                       3.0              8.06
0.4               1.62                       3.2              8.26
0.5               2.06                       3.4              8.44
0.6               2.47                       3.6              8.60
0.7               2.87                       3.8              8.72
0.8               3.27                       4.0              8.83
0.9               3.67                       4.2              8.92
1.0               4.03                       4.4              8.98
1.2               4.64                       4.6              9.03
1.4               5.17                       4.8              9.07
1.6               5.65                       5.0              9.09
1.8               6.09                       5.2              9.12
2.0               6.49                       5.4              9.14
2.2               6.90                       5.6              9.16
2.4               7.27                       5.8              9.17
```

Unfortunately, no single formula will work well for the entire range of drops. A scientist by the name of K.V. Beard (1976) developed complicated formulas to represent this data, that apply to three different ranges of drop diameter. Below is the one that works for the range of diameter 1.2 mm to 4 mm.

u = (k)(r**0.5)

where u = Terminal fall speed and k = 2.01 X 10**3 cm**0.5 s**-1

Note that the table lists drop diameter, but drop radius is used in the equation.

The constant "k" is composed of several values to account for the density and dynamic viscosity of the air, gravity, and the drag coefficient.

This may be a complicated formula, but not nearly as complicated as it will be for you to use this information to figure out how fast you have to drive your pickup to keep your gear from getting wet.

Your biggest challenges will be determining the diameter of the drops that are falling at the time, and avoiding red stoplights.

My personal advice is to invest in a waterproof tarp.

References:

Beard, K.V. (1976) Terminal velocity and shape of clouds and precipitation drops aloft. Journal of Atmospheric Science. 33, 851-864.

Gunn, R. and Kinzer, G.D. (1949) The terminal velocity of fall for water drops in stagnant air. Journal of Meteorology. 6, 243-248.

[note added by MadSci Admin: there is at least one previous answer in our archives that talks about the subject of running (or walking) through rain, which might provide some insight into your question of how fast to drive your truck to keep your gear dry.]

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