Why were Los Alamos scientists so confident “Little Boy” would work?

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The 1945 Trinity test was run to prove the complicated “Fat Man” design would even work. But why were scientists so confident of the “Little Boy” design that the didn’t feel the need to do a full test of the design? The design was simpler, but still, no one had ever done it before. Was it purely for time? Lack of materials? Or was the design and principles so sound, it couldn’t fail?

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A gun type design (Little Boy) was a more simple theory and design that they were very confident would create the necessary critical mass to function in a gravity weapon and not just a static test.

The implosion type device (Fat Man)was a more complicated theory and design with much more exacting specifications that needed proving before being placed in a gravity weapon and dropped.

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