In this issue of Math in the News we dissect the forces involves in tornadoes and discover why they can cause so much damage. Conservation of angular momentum and centripetal forces are key to understanding the power of tornadoes.

1. 5/9/11

2. Tornado Damage
Data Analysis
• The Fujita Scale is used Category Wind Speed (mph)
to determine the F5 261-318
severity of a tornado. F4 207-260
F3 158-206
• The kinds of tornadoes
F2 113-157
that can level whole
F1 73-112
buildings are in the F4
F0 < 73
and F5 range.

3. Tornado Damage
Angular Momentum
• One of the reasons
that tornadoes have
such high winds is due
to the conservation of
angular momentum.

4. Tornado Damage
Angular Momentum
• The best example of
this is when a figure
skater brings her arms
in and increases her
rate of spin.
• This video gives a clear
example of this:
http://youtu.be/AQLtcEAG9v0

5. Tornado Damage
Angular Momentum
• The funnel shape of
the tornado causes the
narrower part of the
tornado to have a
faster wind speed.

6. Tornado Damage
Angular Momentum
• A simple model of
a tornado is a
cylinder. Both
tornadoes shown
have the same
angular
momentum (L)
but different radii
and angular
speeds.

7. Tornado Damage
Angular Momentum
• The tornado on
the right has four
times the angular
speed of the
tornado on the
left, even though
it has half the
radius of the first
tornado.

8. Tornado Damage
Centripetal Force
• But how do swirling
winds create such
damage to buildings?
• The swirling winds of a
tornado create a
strong centripetal
force.

9. Tornado Damage
Centripetal Force
• In this diagram, the
force shown is from
the swirling wind. The
speed (v) is the speed
of the wind. The value
of r is the radius of the
circular swirl. And m is
the mass of the wind
against the building.

10. Tornado Damage
Centripetal Force
• Calculate the
mass (m) by
multiplying the
air density by
the volume of
air.
• Think of the
column of air in
the tornado as a
hollow cylinder.

11. Tornado Damage
Centripetal Force
• In this diagram, the
force shown is from
the swirling wind. The
speed (v) is the speed
of the wind. The value
of r is the radius of the
circular swirl. And m is
the mass of the wind
against the building.

12. Tornado Damage
Centripetal Force
• Use the following data Variable Value
to calculate the force 1.2 kg/m3
on a building from an h 10 m
F4 tornado. r1 8m
r2 10 m
v 112 m/s
r 9m

13. Tornado Damage
Centripetal Force
• This massive force is
equivalent to nearly
half a million pounds
of weight!