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The bombs on Hiroshima and Nagasaki were dropped on August 6th and 9th respectively. According to this answer, the second bomb was tested once.

Must I assume that US leaders were well aware of the destruction they ordered? What have the leaders said in that regard? I have only found a quote by Truman "expect a rain of ruin from the air, the like of which has never been seen on this earth".

Scientists, such as Feynman, have written at length about the subject, striving to rationalise their deed. I want to understand, how well the decision makers could foresee the impact of their decision.

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    There was I think a great movie which I believe to be historically accurate about the Emperor of Japan recording a vinyl record or "album" as we used to call them in my days of Japan's surrender. There apparently was a spectacular fight to keep that record from being played on the Radio which failed thus announcing to all of Japan they were to surrender...which indeed Japan did do. In other words the Emperor knew the destructiveness of this weapon. – user14394 Aug 8 '16 at 18:37
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    seems like an extremely leading question, questioning the motivations of the decision makers on political and ethical grounds rather than the only grounds that made sense at the time: military requirements. Firebombings caused similar death and destruction but at far greater cost and risk to American troops. THAT was the consideration. – jwenting Aug 12 '16 at 21:28
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    @jwenting I cannot even remotely understand what you perceive as leading. The point is: scientists were (partly) aware. What about decision makers. Answers in both directions are possible. – Ludi Nov 28 '18 at 15:10
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    I think “aware” is rather vague here. At some point someone decided to build up one of the largest R&D project in history, so we can assume they expected a potent weapon. They specifically choose that city sizes, so we can assume they had a rough idea. If you ask for specifics then they had literally cheesepaper calculations only what they could expect in terms on energy, blast size, radiation damage etc - that is why they kept doing test explosions for decades after the war. – Greg Nov 28 '18 at 17:47
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    They were not really that ignorant even before the Hiroshima bomb. They had the Trinity test. Keep in mind that they had already carried out strategic bombing of Germany and Japan, so they had already had the experience of making the decision to kill large numbers of civilians. – Ben Crowell Feb 3 at 22:09
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The unfortunate addition of the word "perfectly" before aware means no, and it really depends on who you define as "decision makers" and what you mean by "aware".

First off, here is a great academic (but highly readable) blog run by a guy named Alex Wellerstein with lots of discussion about nuclear weapons in general, but with lots of emphasis on the decision to use the weapons in World War 2 in particular (obviously). It's especially great because he's got lots of contemporary documents that reflected how the participants thought at the time, as opposed to later when they are trying to smooth out their thoughts for historical purposes. I'll reference the titles of specific posts as I go for footnoting.

To answer the second question about awareness, many of the senior scientists and military officers involved in the Manhattan project certainly understood the damage of heat and blast (overpressure) could cause, because they used this when designing the bombs and setting the altimeters such that they could inflict the most possible damage from those effects, specifically on Japanese cities, which featured many buildings of light construction. See the post "The Trouble With Airbursts" and "The Height of the Bomb" for more info. As far as radiation sickness goes, certainly some of the scientists were aware, but Oppenheimer didn't seem to care about it, which meant General Groves knew nothing about it, and you can cut the farther chain above (Secretary of War Stimson and President Truman) from any knowledge whatsoever. See the post "Who Knew About Radiation Sickness, and When." As the post "To Demonstrate or Not to Demonstrate" discusses, people in Los Alamos themselves hadn't entirely come to appreciate that these would mean a truly new era of warfare until after the war. Especially for Truman, he understood he had a very powerful and destructive weapon he could use, but his understanding doesn't go much further than that. The post "The Kyoto Misconception" discusses how Truman seems to have been confused about how much damage the bomb would cause and what kind of targets it would be used on (Truman thought they would be used on purely military targets, not appreciating that Hiroshima and Nagasaki both were certainly not pure targets-they would have been firebombed long before if they had). The overall view could be summarized as they largely (if not entirely) thought of the A-Bomb as a weapon that combined the best of massive conventional payloads with incredible incendiary effects in one very efficient package that would be impossible to stop without massive effort from the defenders. They didn't fully realize how different it was until after the bombs. As "Hiroshima at 67: The Line We Crossed" notes, the line crossed wasn't one of using nuclear weaponry or not, it was one of non-precision targeting of cities-and that line had already been crossed with regards to Japan.

Finally, we can come back to the question of decision making, and in this case, who were the important decision makers, and the answer is mostly Groves and President Roosevelt (though how much he knew is an unknowable question since he died before the project yielded real results. It's noteworthy he inquired about using the bombs against Germany during the Battle of the Bulge, only to be told that they weren't ready and wouldn't be for some time). While the traditional view is that Truman was also important in the decision-making process, one fair thing that modern history has done a good job of noticing Truman didn't make a decision in the sense of either "Use the Bomb or Do [Insert Alternative Here]", it was more of a "Didn't Stop a Decision that had already been made before he came into office". As Wellerstein notes in a couple of places, Truman would probably never have thought of NOT using the bomb. His most important decision, as noted in both "The Kyoto Misconception" and "Why Nagasaki", was to stop the bombing after Nagasaki (although it didn't matter, since they wouldn't have had a 3rd shot available until much later anyway). Stimson's role is to screen out targets (as noted by removing Kyoto).

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    Your suggestion to read Who Knew About Radiation Sickness is fantastic. – axsvl77 Aug 9 '16 at 4:02
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    Always loved the Oppenheimer "I am become death" line upon seeing his little "Gadget" cook off. I don't think that was ever denied. The only other historically acurate descriptions came from the US Army reports which sent teams to the two sites to report on the actual damage. That's the only primary source of value on the subject that I am aware of. In other words "no one knew how destructive" otherwise there would have been no need to assess afterwards the damage and compile a report. – user14394 Aug 9 '16 at 4:46
  • Thank you, for all the information. I will read it carefully. And thanks for the criticism. Indeed, "perfectly" was a stupid addition, which could also have been interpreted as ill intentioned. I replaced it by "well". – Ludi Aug 9 '16 at 9:28
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Were US decision makers aware of the destructiveness of the Bomb of Nagasaki?

Must I assume that US leaders were well aware of the destruction they ordered?

Absolutely.

There might have been uncertainty about the effectiveness of the Little Boy (uranium, gun) design. It was untested, after all, and the effects of a nuclear airburst over a city were not yet well understood.

But Little Boy produced a yield of ~16kt, comparable to the ~20kt yield of the Trinity test, and there could have been little doubt that the effects of Fat Man dropped on another city would be comparable to the effects of Little Boy on Hiroshima.

(Which, given that there was a B-29 accompaning the Enola Gay for the expressed purpose of photographing the effects, and assuming there were recon flights in subsequent days as well, would be documented well enough.)

So, yes, the decision makers would have been well aware of the scale of destruction that would result from that second drop.

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    The Little Boy (ie Uranium) bomb was of a very simple design: Fire a cylinder of uranium down a tube with an explosive charge into a prepared hole in a uranium sphere. With only one or two moving parts it was a simple matter of proper machining, and it was not tested in advance because no-one doubted that the mechanism would work. The calculations – Pieter Geerkens Aug 10 '16 at 22:05
  • The plutonium bomb was a much more complicated design, with a sphere of explosive charges imploding a shell of distinct plutonium fragments simultaneously inwards, at just the right speed to not fizzle by igniting either too slowly or too quickly. There were serious doubts about whether the calculations had been done correctly. The purpose of the Trinity test was to verify that the imploding bomb could actually work as calculated. It was only incidently used to measure the yield, and only on a preliminary basis as they did not have time to build a proper city scape to get blown up. – Pieter Geerkens Aug 10 '16 at 22:08
  • Why build such a complicated plutonium bomb? because plutonium was a (nearly free) byproduct of the uranium enrichment process, that was produced in great excess. It was going to take several more months to enrich enough Uranium for a second Little Boy style bomb, and no-one expected the Japanese to surrender after a single bomb. – Pieter Geerkens Aug 10 '16 at 22:11
  • Feynman in his memoirs notes that there were whole buildings devoted to performing the calculations that enabled the Fat Man bomb to be properly designed. Feynman attracted everyone's attention when he and his team developed a way to run a dozen parallel calculations through the workflow in the same time as performing a single one. Without that speed-up probably no Fat Man bomb until at least summer 1946. – Pieter Geerkens Aug 10 '16 at 22:13
  • @PieterGeerkens: Inhowfar is this related to the question, or the answer? – DevSolar Aug 11 '16 at 4:47

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