"Small Target Bombing Probabilities"--Bombing Calculator, 1944

JF Ptak Science Books  Expansion of an earlier post from  2011 

I found this object in my paper-calculators box (moveable disk calculators made of paper, two going back to  Fr. A. Kircher in the 1680’s)—I’m not sure why it was there as it is not paper, though it is an interesting calculator.

[Images are greatly expanded in click mode.]

You can learn or re-learn an interesting lesson from it on bombing accuracy.

The “Small Target Bombing Probabilities” calculator was issued by the little-known (in the popular sense) Applied Mathematics Panel of the National Defense Research Council (NDRC)¹ in the early 1940’s during WWII. 
Marked “Restricted”, it calculated the number of bombs that would successfully be delivered given (1) the number of bombs, (2) the “aiming error”, and (3) target size. It would then generate results for “(a) the expected number of hits for the indicated number of bombs”, (b-e) the probability of at least one hit to four hits.

What is a little surprising to me was the number of bombs that didn’t find their target. For example, a 65,000 square foot target bombed with 1000 bombs and an aiming error factor of 2000 feet could expect to land 3-4 bombs on the target, with an 88% chance of landing at least two hits, 75% chance of landing three hits, and about 50% of landing at least four hits.  And so the necessity of large numbers of planes dropping a large number of bombs.  

Notes

1. The establishment of the NDRC was announced so: “It is announced by Science Service that the following committee has been appointed in the United States to correlate "scientific research on the mechanisms and devices of warfare": -- Nature 146, 191-191 (10 August 1940).

“Members included: Dr. Vannevar Bush (chairman), president of the Carnegie Institution of Washington, formerly dean of the faculty of engineering at the Massachusetts Institute of Technology; Prof. Richard C. Tolman (vice-chairman), dean of the graduate school and professor of physical chemistry and mathematical physics at the California Institute of Technology; . Dr. Irvin Stewart (secretary), formerly Federal Commissioner for Communications and chairman of the Committee on Scientific Aids to Learning; Rear Admiral Harold G. Bowen, director of the Naval Research Laboratory, Anacostia, D.C.; Conwiy P. Coe, U.S. Commissioner of Patents; Dr. Karl T. Compton, president of the Massachusetts Institute of Technology, formerly professor of physics at Princeton University; Dr. James B. Conant, president, formerly professor of organic chemistry, Harvard University; Dr. Frank B. Jewett, president of the Bell Telephone Laboratories; Brigadier General G. V. Strong, assistant chief of staff, U.S.”