Projects plural! I had no idea about these! They got the U-238 from Germany via submarine and had figured out thermal diffusion of uranium hexaflouride by the time we dropped ours on them!
I believe it was Sin-Itiro Tomonaga who told Feynman "What took you so long?" he was expecting the A-bomb to be dropped on Japan at least one year earlier. Understood everything about it. Indeed, the people at Los Alamos were in fact just screwing around, trying to get things perfect, when 70% of perfect would have worked just fine. Groves finally had a fit and told them to quit horsing around and get a bomb out to Tinian right away. We were losing 200 men a day at that stage of the war.
Of course to be fair, the plutonium (Nagasaki) bomb was far more complicated, and instantly made the uranium (Hiroshima) bomb obsolete. Little Boy was so crude that we never even tested it. We never built another one, although we had already cast the casings for it.
That the Japanese had exploded a uranium bomb left me absolutely gobsmacked. We built an entire city just to filter UF-6. Where would the Japanese get the uranium? Central Africa (The Belgian Congo?) Hardly. Colorado? * Don't think so. And how on earth could they separate the light isotope? Well, Germany was the answer to #1, and they were using thermal diffusion for #2...no city necessary. The U.S. Navy had a thermal program but it didn't go anywhere. It was working, but we already had the Oak Ridge filters up and running, not to say Hanford, Washington for the Plutonium. Interesting that the Iranians are investing in centrifuges, another method we did not use.
Everybody knows E = mc^2, but that has absolutely nothing to do with how atomic bombs work. The first lecture everyone got when they arrived at Los Alamos was the fact that electrical potential, not relativity, is the driving concept. Stop me if you've heard this.
Let's make a uranium nucleus. Get a proton and hold it in one place. Now take another proton at infinity, and bring it in to the first at a distance R. The work you have just done is integral (infinity to R) of k qXq/x^2 dx. Now take another proton and bring it into the first two. The work is integral (infinity to R) of k qX2q/x^2 dx. Then integral (infinity to R) k qX3q/x^2 dx, k being Coulomb's constant. Keep adding until you bring the 91st proton in. That is the work you have done in assembling a uranium 92 nucleus.
Now add the 55 integrals for barium 56 and the 37 integrals for strontium 38. You will see that the uranium work FAR exceeds the work done in assembling the other two. That's the secret of the atomic bomb. (Lecture #1, The Los Alamos Primer, by Robert Serber.)
Keeping it really simple, let the first integral have a value of 1. Then uranium is 1 + 2 + 3 +...+91 = 91X92/2 = 4186 units of work.
Barium clocks in at 1 + 2 + 3 + ... 55 = 55X56/2 = 1540 and strontium is 37X38/2 = 703. So barium and strontium add up to 1540 + 703 = 2243.
So each reaction unleashes 4186 - 2243 = 1943 units of work (energy). Of course, all three radii are slightly different, but this is only a first-order approximation after all. Notice that nowhere does "relativity" explain any of this.
Poor Einstein. He always protested that he had absolutely nothing to do with the atomic bomb, aside from signing the letter to Roosevelt. Blame Charles-Augustin Coulomb instead.