MadSci Network: Earth Sciences

Re: How does gravity affect the speed of a raindrop?

Date: Wed May 23 09:53:08 2001
Posted By: Nezette Rydell, forecaster,National Weather Service
Area of science: Earth Sciences
ID: 989630895.Es

Two forces act on a falling raindrop.  The Earth's gravitational force is a
downward acting force and the force exerted by the air (frictional 
resistance) is an upward acting force.  

Earth's gravity pulls objects downward at a constant rate, 9.8 meters per 
second each second ( 9.8 meters per second squared).  The raindrop's fall 
will accelerate (or speed up) until the gravitational force is equal
to the force of the air pushing up against it.  The net force on the
raindrop is then zero and according to Newton's second law, the drop 
stops accelerating and continues to fall at a constant speed.  This speed 
is called the terminal velocity.  

The terminal velocity depends on the size of the raindrop.  Smaller 
droplets have lower terminal velocities.  (The smallest drops, cloud 
droplets, are suspended in the atmosphere and do not fall.)  The upward 
force exerted on the raindrop is proportional (directly related) to the 
cross-sectional area of the raindrop.  If the raindrop is round, 
then its area is given by the area of a sphere, ( (pi) times (the radius of 
the raindrop squared) ).  The downward force is proprotional to the 
volume of the sphere, ( (4/3 pi) times (radius of the raindrop 
cubed) ).  For larger drops, the downward force changes more, at a cubic 
rate, while the upward force changes less, at a squared rate.  The downward 
force on the raindrop is greater with larger raindrops.  

In reality, raindrops are not round.  The smallest cloud droplets are 
indeed spheres.  Larger drops are distorted by the upward force and are 
essentially squashed as they fall, becoming flat on the bottom.  A 
great little book about raindrops and other stuff is 
From Raindrops to Volcanoes:  Adventures in Sea Surface Meteorology by 
Duncan Blanchard.  It is out of print but can be found in libraries and 
used book stores.  

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