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most diving U-boats did not reach that depth before the depth charge exploded, so
they escaped serious damage. A shallow depth of 25 feet was optimal for aircraft
depth charge settings.
When World War II started, 20,000 antiaircraft shells were needed to shoot
down one airplane. By the middle of the war, based on analog fire-control com-
puters and operations research applied to antiaircraft loading and aiming opera-
tions, the number of shells needed per destroyed aircraft was down to 4,000.
Note
The huge ratio of shots to hits explains why surface-to-air missiles
(SAMs) with computer guidance systems would replace antiair-
craft guns as the best method of air defense in later decades. To
be effective, SAMs required compact onboard radar, small analog
computers for guidance, and other sophisticated electronics such as
heat sensors. These would not come together during the war but ar-
rived in 1947 and became very sophisticated in later decades.
These real-world military problems combine a need for empirical data and stat-
istical analysis with complex calculations performed at high speeds. These are the
very problems that digital computers and software would eventually tackle with
great success in future decades.
After the war, operations research and digital computers would apply these
concepts to a huge variety of complex civilian problems, including queuing theory,
telephone network optimization, supply chain management, “just-in-time” manu-
facturing, freight delivery-route optimization, railroad and airline traffic analysis,
and game theory, among many others.
At the level of individual projects, critical path analysis and PERT diagrams
were offshoots from operations research. At a higher corporate level, organization
dynamics, business process reengineering, and market analysis would also be de-
rived from World War II operations research.
Digital computers and software would eventually be the best tools in history for
solving complex logical problems at high speeds, but many more years and many
more inventions would be needed before digital computers and software became
truly effective tools for complex real-world problems.
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