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I remember hearing several times that the bombs dropped on Japan were a lot deadlier than expected. What were the original projections for casualties for both and how much less than the actual numbers were they?

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I think that the Americans had a pretty good idea of the immediate destruction these bombs would cause - the problem was with the lasting effects that nobody really knew about back then. – Wladimir Palant Nov 2 '11 at 7:31
I've heard the initial death toll was something like 100,000-200,000 for both (they were of similar deadliness). And the fallout due to radiation (i.e. premature deaths) over the following decades was about the same for each city. – Noldorin Nov 2 '11 at 13:59
@Noldorin: That figure was given by Richard Frank in Downfall, FWIW. I consider the lower limit to be way low. – David Thornley Nov 4 '11 at 2:03
Nagasaki was in fact less destructive than originally estimated because of the exact drop point and the local geography, or so I've read. – jwenting Jan 29 '13 at 7:13

I found Vincent C. Jones' 1985 book Manhattan, the Army and the atomic bomb. While it doesn't mention the death toll estimates, it does offer some insight on pages 531 and 532. In particular, it quotes Oppenheimer with the words:

the neutron effect . . . would be dangerous to life for a radius of at least two-thirds of a mile.

So Oppenheimer estimated the contaminated area with roughly 3.5 km². Also, if you look at the further discussion of the psychological effects and choice of targets ("a vital war plant . . . surrounded by workers' houses") - I think that it makes clear that the atomic bomb was considered to be just like a conventional bomb, merely with more destructive power. It was expected to completely destroy the plant and damage everything close to it. The expected radius of destruction couldn't have been more than half a mile (meaning an area of 2 km²).

Now let's compare to what actually happened. This military study reconstructs the events and cites a radius of total destruction of 1 mile for both Hiroshima and Nagasaki (meaning an area of 8 km²). It also mentions the contaminated area measured by Americans when they arrived there: 8.9 km² in Hiroshima and 1.5 km² in Nagasaki (with a note that the nuclear fallout in Nagasaki was mostly outside the city).

This document from 1946 essentially estimates the immediate casualties in Hiroshima to 70,000-80,000 people. Given the difference between estimated and actual destruction radius, the expected death toll most likely wasn't more than 20,000 people.

The information on Nagasaki is less definitive. I better link to Wikipedia, you can go through the sources yourself. The numbers here are somewhat smaller than with Hiroshima, probably by factor 1.5.

As to radioactive contamination, it is very hard to say anything definitive here. It is clear that Oppenheimer underestimated the contaminated area. It is also clear that there was no knowledge on the long-term consequences of radiation exposure in 1945. The information that we have now comes to a large part from studies performed in Hiroshima and Nagasaki. I'm not sure whether reliable numbers exist but this article lists another 36,000 deaths in Hiroshima until the end of 1945, significantly declining after that.

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They had a bit of an idea, at least where individuals are concerned, if not large populations. Most likely the issue was getting non-scientific leadership to grok the issue with what seemed to them to be just a really big explosive device. In Richard Feynman's first autobiography one of the anecdotes he mentioned was his attempts to get the military brass overseeing the project to take radiation protection for the workers seriously. – T.E.D. Jan 29 '13 at 15:13

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