Thats not quite true. The
groves memorandum clearly states that at oak ridges rate of production, they would have a gun type bomb available in august (which they did), and another ready in september.
I suggest you consult the Hull-Seaman memorandum of AUG1945 for a later and more realistic estimate of the production rate: one MK1 for the initial round of bombings (e.g. 'Little Boy') and a second before the end of the year, specifically too late for the initial round of
Downfall landings, scheduled for the first half of NOV1945.
Thats an interval of two months, not four. Your claim doesn't correspond with the rate of uranium enrichment that would have been taking place at oak ridge. In my scenario, they would have a bomb available in march of 1945, and another ready in may.
Except that doesn't correspond with historical data, unless you're taking figures from someone like Peter Vogel. A the memorandum states
Remember the MK1 was a terribly inefficient design, using 64kg of HEU80 to produce a 63TJ explosion while the M
K1 design used one-tenth as much plutonium to produce an 88TJ explosion. Hence Oppenheimer's proposal to scrap the MK1 in favour of composite pit implosion bombs.
While its true that oak ridge was more expensive than hanford, one should realize than uranium has certain advantages over plutonium. Reactors consume far more uranium feed than a gaseous diffusion plant or calutron will. Moreover, plutonium can only be utilised by the implosion method, a staggeringly difficult undertaking that required major advances in hydrodynamics and computation. The implosion method wasn't an option in early 1945 because the science still hadn't been worked out.
If the entire Manhattan Project had started earlier, i.e. without the faffing around, it's quite reasonable to assume the implosion design would be developed in a similar amount of time and hence plutonium implosion bombs would have been available after a similar working period.
This is especially true if the resources used at Oak Ridge were ploughed into the plutonium path.
Actually, the groves memorandum reveals that they were thinking about applying the implosion method towards uranium. After the trinity test validated the concept, it wouldn't take much additional effort to make this happen. I'm not sure what the yield of a uranium implosion bomb would be, though.
After the Trinity test (19JUL1945) Oppenheimer suggested that the MK1 be dropped, pointing out that the uranium wasted in the inefficient gun-barrel design could be recast into five HEU pits. Each would be rather more powerful than the MK1, in the range of 80-80TJ, comparable with the MK3. He also suggested that composite pits would be even more efficient.
Before it was terminated the Manhattan Project was working on a composite pit design, as well as core levitation (which would have dramatically increased yield, potentially 2-3 times). If
Downfall had proceeded the production rate in 1946 would have been perhaps 6-8 bombs per month.
Fair enough, but they would still need to work through the problems with xenon poisoning. Also, was work on the implosion method far enough along that they could even attempt a test like trinity in december of 1944? There were still alot of unknowns at that time, IIRC.
If you're going to start the project early then it's reasonable to assume the elements proceed as they did historically unless there's a specific reason to assume otherwise.
Historically the implosion design was chosen after the first samples of reactor bred plutonium demonstrated the presence of sufficient Pu
240 to make a gun-barrel design unfeasible (no super-grade plutonium in 1944). The implosion design was validated through the RaLa tests which historically began in JUL1944. These tests proceeded relatively leisurely but by FEB1945 the implosion design was fully validated.
