The Dam Busters

1
The Dam Busters

• Trigonometry

2
The Dam Busters
Photo shows a Lancaster Bomber testing a
prototype bomb.
During World War II (1943), British scientist
Barnes Wallis invented the spinning cylindrical
bomb -- a bomb in a barrel -- to blow up German
dams. The German dams provided hydroelectric
power, water supply, a control of canal levels
thus a blow to the dams would be devastating to
the Germans. A regular bomb would do no harm to
the dams the water would just cushion the
impact unless the bomb was right up next to the
dam. Torpedoes would not work because the
Germans had set up nets around the dam to
prevent such an attack. But if a bomb could be
dropped from an airplane and then skip/bounce
along the water right up to the dam, it could
work. So Wallis performed many experiments to
determine if it could work at all, the size of
the bomb, and how far from the dam it needed to
be dropped. He determined that the barrel bomb
had to be dropped at a speed of 230 mph and a
height of 60 ft -- dangerously low. A special
squadron of British pilots was gathered by Wing
Commander Guy P. Gibson to do the job, the 617
Squadron (also called the Dam Busters and the Dam
Raiders). Their targets were the Mohne, Eder,
and Sorpe Dams on the Ruhr in Germany. They
successfully breached the Mohne and Eder Dams,
devastating Germany, but lost fifty-three men in
the process.
3
As the bombs had to be dropped at a height of
exactly 60 feet above the water surface, it was
important that the pilots knew that they were
exactly at this height. To enable them to know
this, two large searchlights were fitted 56 feet
apart on the underside of the plane at points A
and B respectively. The angles of depression of
the beams of light from A and B were 60 and 71
as shown in the diagram. When the beams from
these lights met exactly on the water surface,
the pilot knew that his aero plane was flying
horizontally and 60 feet above the ground.
4
Using trigonometry, perform calculations to
verify that, with the above arrangement of
lights, the height of the Lancaster Bomber above
the surface of the water would be exactly 60
feet.