Terminal Velocity of Hail
Date: 3/24/2004, up-dated Winter 2010-11
I needed to find the terminal velocity of a hail stone and the impact
force. And was wondering if there was any way you could show me step
by step how to solve this.
The equation for terminal velocity applies for a perfect
sphere, which a hailstone isn't necessarily, but it is the
best that we can do.
Vt = [(0.667*g*d*Dh)/(Cd*Da)]**0.5
where * stands for multiplication, ** stands for exponent (we are taking
the square root in this case), / stands for division, g is the acceleration
of gravity (980.6 cm/s**2), Dh is the density of the hail (0.917
g/cm**3 for ice),
Da is the density of air (approximately 0.0012923 g/cm**3), d is the diameter
of the hailstone in cm, and Cd is the drag coefficient (approximately 0.83
and it is unitless).
For a hailstone 1 inch in diameter (2.54 cm),
Vt = 1191.5 cm/s
or translating to some other units, (using 1 cm/s = 0.03281 ft/s), 39.1 ft/s
or (using 1 cm/s = 0.02237 mph), 26.7 mph.
Our calculation of terminal velocity does not take into consideration that
the hailstone usually is hindered from falling by being in a thunderstorm
updraft during most of its formation and fall to the ground, and by
collisions with other hailstones or water droplets as well, thereby slowing
its fall, not to speak of it normally not being round or smooth.
The terminal velocity of pea size hail, say 0.3 cm in diameter is
409.5 cm/s, or 13.4 ft/s, or 9.2 mph.
Hailstone speeds (combined with their large size and impact force) can be
damaging, as I received sizable dents in my car and in the
aluminum siding on my house after a hailstorm of 1.25 inch diameter hail in 1985.
David R. Cook
Climate Research Section
Environmental Science Division
Argonne National Laboratory
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