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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The actual fission reaction of Little Boy was guaranteed to happen, so long as the steps leading up worked.
So as long as the conventional explosives detonated, and as long as the slug didn’t get stuck in the barrel, once it reached the other end, you were guaranteed a runaway fission chain reaction, so all of the ways in which the bomb could fail had nothing to do with the actual nuclear explosion, and so those things could be tested and verified without actually needing a live nuclear payload.
The design of fat man was different, it relied on increasing the pressure of the fissile material enough to make it critical, so even *if* the conventional explosives did detonate, you still weren’t guaranteed a fission reaction, because it was impossible to predict exactly how the explosive pressure wave would propagate. Furthermore, the fat man design used a neutron source, a small ball of material embedded in the fissile core, that was theoretically supposed to emmit a flood of neutrons when the bomb went off, and therefore trigger a lot of fission reactions at once, to kick start the bomb. Both of these mechanisms could have failed to go off, even if the convnetial driving explosives detonated, and so the scientists needed to verify that the force from those driving explosives was actually large enough to trigger fission like they wanted, and that required an actual live fissile test.
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