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)