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Mathematics Goes to the Movies

by Burkard Polster and Marty Ross

**The Dam Busters (1955)**

Story of the skipping bomb that was used by the British in WWII to destroy German
dams. This special kind of bomb is dropped at low level from an aircraft and
ricocees several times off the surface of the lake behind the dam and over any
possible torpedo nets before it hits the wall of the dam at water level. It
then sinks down the wall of the dam to a certain level before it explodes.

39:25

Inventor to guy in charge of the military operation Dr B.N. Wallis.

INVENTOR: I’ve got an idea for a special type of bomb, only it would have
to be dropped at very low level.

Air force guy (Wing Commander Guy Gibson): Oh, they told us about low flying.

INVENTOR: Oh they have, that is something. Well, I do not know whether you are
scientifically minded, in any case it would not be necessary for you or any
of your crews to understand the theory and mathematics of the weapon.

AIR FORCE GUY: I’d like to try and understand it if I can.

After they watch a movie of the bomb in action….

Each aircraft will only be able to carry one bomb and it must be dropped from
exactly 150 feet at a speed of 240 miles an hour. Above and below that height
and speed and it just doesn’t work…. Yes, I’m sorry we are
tied so closely but as you see its all a question of gravity and mathematics.

Since the altimeter of the planes are no good at this height they come up with
a neat trick based on triangles: two spotlights are fixed to the bottom of a
plane at angles such that the plane is flying at the desired height exactly
if the two spots created by the lights are side-by-side (picture at 49:57).

Another little gadget with a mathematical foundation is used to determine when
exactly the bomb has to be released: It comes in the form of an isosceles triangle
with an eye hole at the distinguished vertex and two parallel rods at the other
two vertices. The bomb gets released when the two towers on the dam wall overlap
the rods when viewed through the eye hole (the distance between the towers is
known, picture at 59:11)