Rational Action is back with the press. Part of my recent improvements involved figuring out what images I was going to use, which involved taking a day to run to the National Archives (living near Washington, DC has definite advantages). There I got some pictures that I remembered as cool-looking, but hadn’t previously bothered to get copies of. These related to experiments that the Applied Mathematics Panel (AMP), a wartime organization, did in 1944 in collaboration with the Mt. Wilson Observatory in Pasadena.
Staff setting up the experiment in a local school gymnasium
Now, however, I have many more photographs than I can possibly use, and the experiments they describe occupy only about two sentences in my book, so I thought I’d share them with you here.
A model of a B-29 equipped with lights representing its defensive armaments
The B-29 “Superfortress” was, for its time, an extraordinary feat of aeronautical engineering. A bomber of unprecedented range and speed, it made the United States’ devastating air raids on Japan possible. When it was rushed into service in 1944, it was still plagued by technical problems, and, moreover, little consideration had been put into how it should actually be used in combat. A lot of last-minute thought was put into the issue, and one of the groups consulted was AMP, which was a part of the National Defense Research Committee of the Office of Scientific Research and Development. AMP had been set up to provide mathematical assistance to other OSRD groups, and to the American military services, and it was led by mathematician and director of the natural sciences program at the Rockefeller Foundation, Warren Weaver.
B-29 models arranged to represent a squadron formation. The box with the dials controls the lights on the models.
AMP took a very broad view of the B-29 problem, and pitched to the Army Air Forces a number of different sorts of tests that would help determine what tactics would be best for the B-29. The Air Forces were not interested in most of the tests, but among the ones they did support was a set of experiments conducted in a school gymnasium near the Mt. Wilson Observatory, employing about 30 people, 20 of whom were borrowed from the observatory. The idea was to use lights attached to bombers to replicate the defensive fire of aircraft squadrons, and to use photocells to measure the patterns.
The experiments were conducted inside a spherical shell.
The objective was to determine what formations could best fend off a fighter attack, and to recommend firing tactics appropriate for such a formation. The mathematical equations yielded by a formal treatment of the problem were unwieldy.
The model experiment provided a means of measuring the values empirically.
Even without quantitative measurements, the experiments also proved useful as a visual demonstration, which itself could be sufficient to make choices between different formations. As Weaver wrote in his final report for AMP, “Early in this project it became obvious that one of its greatest contributions was that it furnished a method whereby one could see, simply and convincingly, a pattern of relationships otherwise so complicated and subtle as to provide topics for perpetual arguments. Two officers, urging different patterns for a formation, could set them up on this optical model, and could together directly examine the resulting pattern of fire power.”
Motion pictures were even made circling about the models showing how fire power varied through different angles. These films were sent to the Pacific Theater, as was a second model set, so that further experiments could be carried out closer to where decisions about the use of the B-29 were being made.
Of course, in recommending firing tactics, one also had to take into account the fact that both bombers and attacking fighters were moving, which was something that the models did not simulate.
Paths a fighter might take in pursuing and firing at a B-29.
Movement naturally made aiming a gun more difficult. While the rules of aiming could be built into mechanical “fire-control” devices, they could also be distilled into training regimens and simple rules for gunners.
Even these rules could be further simplified:
And, yes, if one was worried about a gunner’s memory, one could always translate the rules into naughty pictures.
All images are from the National Archives and Records Administration, Record Group 227, Records of the Applied Mathematics Panel: Studies and Notes, 1943-1946, Boxed 18 and 19, Study 128.