differential analyzer

Thomson disc and sphere analyser for studying tides

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.

Research on solutions 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 report on the device during 1931. D. R. Hartree of Manchester University brought the design to England, where he constructed his first model (with his student, Arthur Porter) during 1934. During the next five years three more were added, at Cambridge University, Queen's University Belfast, and the Royal Aircraft Establishment in Farnborough.

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.

In Norway, the locally built Oslo Analyzer was finished during 1938, based on the same principles as the MIT machine. This machine had 12 integrators, and was the largest analyzer built for a period of four years.^[1]

In the United States, differential analysers were built at Wright-Patterson Air Force Base and in the basement of the Moore School of Electrical Engineering at the University of Pennsylvania during the early 1940s; the latter was used extensively in the computation 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 had little or no use.

With Samuel H. Caldwell (one of the initial contributors during the early 1930s), Bush attempted an electrical, rather than mechanical variation (1945), but the digital computer built elsewhere had 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.^[2]

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 with Meccano hobby parts has become a popular project among serious Meccano hobbyists. An example of 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 such that a 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.

Notes

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).
• James Thomson (1876). "An Integrating Machine having a new Kinematic Principle". Proceedings of the Royal Society 24: 262–5. doi:10.1098/rspl.1875.0033. 
• William Thomson (1876). "Mechanical Integration of Linear Differential Equations of the Second Order with Variable Coefficients". Proceedings of the Royal Society 24: 269–71. doi:10.1098/rspl.1875.0035. 
• William Thomson (1876). "Mechanical Integration of the general Linear Differential Equation of any Order with Variable Coefficients". Proceedings of the Royal Society 24: 271–5. doi:10.1098/rspl.1875.0036. 
• (Italian) I miei integrafi per equazioni differenziali by Ernesto Pascal, Naples, B. Pellerano (1914).
• Vannevar Bush (1936). "Instrumental analysis". Bull Amer Math Soc. 42 (10): 649–69. doi:10.1090/S0002-9904-1936-06390-1. http://projecteuclid.org/euclid.bams/1183499313. 
• 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 differential 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.

External links

Wikimedia Commons has media related to: Differential analysers

• Vannevar Bush bio which focuses on the Differential Analyzer
• The Differential Analyser Explained
• Tim Robinson's Meccano Differential Analyser
• "Meccano ‘Dam Busters’ computer stars at MOTAT". computerworld.co.nz. 2007-07-16. http://computerworld.co.nz/news.nsf/tech/7627BB58BAFE998DCC257317001AA6D1. Retrieved 2007-07-17.