Differential analyser

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A differential analyser at the NACA Lewis Flight Propulsion Laboratory , 1951

Kay McNulty, Alyse Snyder, and Sis Stump operate the differential analyzer in the basement of the Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania, circa 1942-1945.

The differential analyser was a mechanical analog computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operationally.

Researches on solution of differential equations using mechanical devices started (discounting planimeters) at least as early as 1836, when the french physicist Gaspard-Gustave Coriolis designed a mechanical device to integrate differential equations of the first order. The analyser was invented in 1876 by James Thomson, brother of Lord Kelvin. Lord Kelvin advised Arthur Pollen to use an analyser for Pollen's fire-control system developed to control naval gunnery. This electrically driven analogue computer was ready by about 1912. Mechanical integrators for differential equations were also designed by the Italian mathematician Ernesto Pascal in 1913. A practical version of Thomson's differential analyzer was first constructed by H. W. Nieman and Vannevar Bush starting in 1927 at MIT. They published a full report on the device in 1931. D. R. Hartree of Manchester University brought the design to England, where he constructed his first model (with his student, Arthur Porter) in 1934. Over the next five years three more were added, at Cambridge University, Queen's University Belfast, and the Royal Aircraft Establishment in Farnborough. In the United States, differential analysers were built at Wright-Patterson Air Force Base and in the basement the Moore School of Electrical Engineering at the University of Pennsylvania in the early 1940s; the latter was used extensively in the assembly of artillery firing tables prior to the invention of the ENIAC, which, in many ways, was modeled after the differential analyser. Another - the UTEC - was constructed some years later at the University of Toronto, but it appears it saw little or no use.

With Samuel H. Caldwell (one of the initial contributors in the early 1930s), Bush attempted an electrical, rather than mechanical variation (1945), but the digital computer built elsewhere showed much greater promise and the project ceased. The differential analyser was used in the development of the bouncing bomb, used to attack German hydroelectric dams during World War II.^[1]

Differential analysers have also been used in the calculation of soil erosion by river control authorities. It was eventually rendered obsolete by electronic analog computers and later digital computers.

More recently, building differential analysers out of Meccano has become a popular project among serious Meccano hobbyists. An example on this is the Differential Analyzer built at Marshall University which is the only machine of its kind to be public in the United States or maybe even in the world. The use of this differential analyser is now also for educational purposes where the student not only solves a differential equation but becomes the calculator (one who calculates) and so understands better what a differential equation is.

A differential analyser is shown in operation in the 1950 film Destination Moon, the 1951 film When Worlds Collide, and the 1956 film Earth vs. the Flying Saucers.

The differential analyzer which was shown in (simulated) operations in the above-mentioned feature films was the one which was installed at UCLA. One unit of the many separable units there installed was preserved.

[edit] Notes

^ The machine built for this purpose (in 1935 at Cambridge University by J. B. Bratt largely from Meccano) is now in the Museum of Transport and Technology collection in Auckland, New Zealand, having been purchased in Britain in the 1950s for GBP 100. It was used in New Zealand for the design of the Benmore Hydro Dam.

[edit] Bibliography

(French) Gaspard-Gustave Coriolis Note sur un moyen de tracer des courbes données par des équations différentielles Journal de Mathématiques Pures et appliquées series I 1, 5-9 (1836).
An Integrating Machine having a new Kinematic Principle by James Thomson, Proceedings of the Royal Society, 24, 262-265 (1876).
Mechanical Integration of Linear Differential Equations of the Second Order with

Variable Coefficients by William Thomson, Proceedings of the Royal Society, 24, 269-271 (1876).

Mechanical Integration of the general Linear Differential Equation of any Order

with Variable Coefficients by William Thomson, Proceedings of the Royal Society, 24, 271-275 (1876).

(Italian) I miei integrafi per equazioni differenziali by Ernesto Pascal, Naples, B. Pellerano (1914).
Instrumental analysis by Vannevar Bush, Bull. Amer. Math. Soc. 42, 649-669 (1936).
A mathematical survey of computing devices with an appendix on an error analysis of differential analyzers by Beatrice Helen Worsley (Master Thesis, MIT,Cambridge, MA, 1947)
An electronic differential analyzer by A. B. MacNee (RLE, Technical Report, MIT, Cambridge, MA, 1948). Note that this is a paper on a very early electronic analogue computer, not a mechanical differntial analyser. It is included because the author felt that the only way to introduce such an innovation was as an electronic D. A.
The Differential Analyser by J Crank, Longmans Green & Co. 1947. The only book on setting up and operating a mechanical D. A.