Differential analyser

Source: Wikipedia, the free encyclopedia.
This article is about analogue differential analysers. For the digital implementation, see
Digital Differential Analyzer
.
Ball-and-disc integrator for studying tides.

The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration.[1] It was one of the first advanced computing devices to be used operationally.[2] The original machines could not add, but then it was noticed that if the two wheels of a rear differential are turned, the drive shaft will compute the average of the left and right wheels. Addition and subtraction are then achieved by using a simple gear ratio of 1:2; the gear ratio provides multiplication by two, and multiplying the average of two values by two gives their sum. Multiplication is just a special case of integration, namely integrating a constant function.[3]

History

Philadelphia, Pennsylvania
, c. 1942–1945.
A differential analyser at the NACA Lewis Flight Propulsion Laboratory, 1951

Research on solutions for differential equations using mechanical devices, discounting

Gaspard-Gustave Coriolis designed a mechanical device to integrate differential equations of the first order.[4]

The first description of a device which could integrate differential equations of any order was published in 1876 by

Lord Kelvin, which represents the invention of the differential analyser.[6]

One of the earliest practical uses of Thomson's concepts was a tide-predicting machine built by Kelvin starting in 1872–3. On Lord Kelvin's advice, Thomson's integrating machine was later incorporated into a fire-control system for naval gunnery being developed by Arthur Pollen, resulting in an electrically driven, mechanical analogue computer, which was completed by about 1912.[7] Italian mathematician Ernesto Pascal also developed integraphs for the mechanical integration of differential equations and published details in 1914.[8]

However, the first widely practical general-purpose differential analyser was constructed by Harold Locke Hazen and Vannevar Bush at MIT, 1928–1931, comprising six mechanical integrators.[9][10][11] In the same year, Bush described this machine in a journal article as a "continuous integraph".[12] When he published a further article on the device in 1931, he called it a "differential analyzer".[13] In this article, Bush stated that "[the] present device incorporates the same basic idea of interconnection of integrating units as did [Lord Kelvin's]. In detail, however, there is little resemblance to the earlier model." According to his 1970 autobiography, Bush was "unaware of Kelvin’s work until after the first differential analyzer was operational."[14] Claude Shannon was hired as a research assistant in 1936 to run the differential analyzer in Bush's lab.[15]

Science Museum
in London, alongside a complete Manchester machine.

In Norway, the locally built Oslo Analyser was finished during 1938, based on the same principles as the MIT machine. This machine had 12 integrators, and was the largest analyser built for a period of four years.[18]

In the United States, further differential analysers were built at the

digital computer built elsewhere had much greater promise and the project ceased.[21] In 1947, UCLA installed a differential analyser built for them by General Electric at a cost of $125,000.[22] By 1950, this machine had been joined by three more.[23] The UCLA differential analyzer appeared in 1951's When Worlds Collide
, where it was called "DA".

Early computer-and-plotter dating to 1944, solving complex equations again 70 years later.[24]

At

Osaka Imperial University (present-day Osaka University
) around 1944, a complete differential analyser machine was developed (illustrated) to calculate the movement of an object and other problems with mechanical components, and then draws graphs on paper with a pen. It was later transferred to the Tokyo University of Science and has been displayed at the school's Museum of Science in Shinjuku Ward. Restored in 2014 is one of only two still operational differential analyzers produced before the end of World War II.[24]

In Canada, a differential analyser was constructed at the

Beatrice Helen Worsley, but it appears to have had little or no use.[25]

A differential analyser may have been used in the development of the bouncing bomb, used to attack German hydroelectric dams during World War II.[26] Differential analysers have also been used in the calculation of soil erosion by river control authorities.[27]

The differential analyser was eventually rendered obsolete by

electronic analogue computers
and, later, digital computers.

Further information: Digital differential analyzer

Use of Meccano

MOTAT's Meccano differential analyser in use at the Cambridge University Mathematics Laboratory, c. 1937. The person on the right is Dr Maurice Wilkes, who was in charge of it at the time

The model differential analyser built at Manchester University in 1934 by Douglas Hartree and Arthur Porter made extensive use of

transmission lines.[29]

It is estimated that "about 15 Meccano model Differential Analysers were built for serious work by scientists and researchers around the world".[30]

See also

Notes

  1. ^ Irwin, William (July 2009). "The Differential Analyser Explained". Auckland Meccano Guild. Archived from the original on 2018-11-24. Retrieved 2010-07-21.{{cite web}}: CS1 maint: bot: original URL status unknown (link) Archived
  2. ^ "Invention of the modern computer". Encyclopædia Britannica. www.britannica.com. Retrieved 2010-07-26.
  3. ^ John von Neumann, The Computer and the Brain, Part 1, p.3, Yale University Press, The Silliman Memorial Lectures Series, 1958
  4. Coriolis, Gaspard-Gustave (1836). "Note sur un moyen de tracer des courbes données par des équations différentielles". Journal de Mathématiques Pures et Appliquées
    . series I 1 (in French): 5–9.
  5. ISBN 0-404-06422-1
    .
  6. doi:10.1098/rspl.1875.0036
    .
  7. ISBN 0-00-216298-9
    .
  8. ^ Pascal, Ernesto (1914). Miei Integrafi per Equazioni Differenziali (in Italian). Naples: B. Pellerano. See also Integraph.
  9. ^ Karl L. Wildes and Nilo A. Lindgren, A Century of Electrical Engineering and Computer Science at MIT, 1882-1982 (Cambridge, Massachusetts: MIT Press, 1985), pages 90-92.
  10. S2CID 10075776
    .. Hartree, D.R. (September 1940), op. cit.
  11. ^ Bush's differential analyser used mechanical integrators. The output of each integrator was intended to drive other parts of the machine; however, the output was too feeble to do so. Hazen recognized that a "torque amplifier", which had been invented in 1925 by Henry W. Nieman and which was intended to allow workers to control heavy machinery, could be used to provide the necessary power. See: Stuart Bennett, A History of Control Engineering 1930-1955 (London, England: Peter Peregrinus Ltd., 1993), page 103. See also Nieman's U.S. patents: (1) "Servo mechanism", U.S. patent no. 1,751,645 (filed: 28 January 1925; issued: 25 March 1930); (2) "Servo mechanism", U.S. patent no. 1,751,647 Archived 2018-08-07 at the Wayback Machine (filed: 8 January 1926; issued: 25 March 1930); (3) "Synchronous amplifying control mechanism", U.S. patent no. 1,751,652 Archived 2014-06-28 at the Wayback Machine (filed: 8 January 1926; issued: 25 March 1930).
  12. doi:10.1016/S0016-0032(27)90097-0
    ..
  13. doi:10.1016/S0016-0032(31)90616-9
    ..
  14. ^ Robinson, Tim (June 2005), op. cit., citing Bush, Vannevar (1970). "Pieces of the Action". New York NY: Morrow. {{cite journal}}: Cite journal requires |journal= (help).
  15. ISBN 978-0-00-742311-8
    .
  16. ^ Robinson, Tim (June 2005), op. cit., Hartree, D.R. (September 1940), op. cit. Hartree and Porter wrote about the model in their paper "The Construction and Operation of a Model Differential Analyser". Memoirs and Proceedings of the Manchester Literary & Philosophical Society. 79: 51–74. 1935..
  17. ^ Robinson, Tim (2005-12-07). "Other Differential Analyzers". Tim Robinson's Meccano Computing Machinery web site. Retrieved 2010-07-24. Includes summaries of "Meccano Differential Analyzers" and "Full Scale Differential Analyzers".
  18. doi:10.1109/85.539912
    .
  19. ^ Randell, Brian (ed.), The Origins of Digital Computers Selected Papers (3rd edition, 1982), Berlin, Heidelberg, New York: Springer-Verlag. p. 297. Google Books. Retrieved 25 July 2010.
  20. ^ Bunch, B. & Hellemans, A., The History of Science and Technology: A Browser's Guide to the Great Discoveries, Inventions, and the People who Made Them, from the Dawn of Time to Today (2004), New York: Houghton Mifflin, p. 535. Google Books. Retrieved 25 July 2010.
  21. S2CID 1737953. Archived from the original
    (PDF) on 2013-09-21. Retrieved 2010-07-25.
  22. ^ "UCLA's Bush Analyzer Retires to Smithsonian" (Google News). Computerworld. 1978-01-09. Retrieved 2010-07-22.
  23. ^ "The Thinking Machine". UCLA Engineering. Archived from the original on 2010-07-10. Retrieved 2010-07-22.
  24. ^ a b Hisatoshi Kabata (2014), "Early computer dating to 1944 solving complex equations again after long 'reboot'", The Asahi Shimbun/Technology, archived from the original on 2016-03-04
  25. S2CID 13499528. Retrieved 2010-07-24. [Worsley's] research was suggested by Samuel H. Caldwell, of MIT's electrical engineering department, who had helped Vannevar Bush design recent analyzers. … Over six weeks during summer 1948, Worsley constructed a differential analyzer using Meccano…, based on Douglas Hartree and Arthur Porter's 1935 article. Constructed from about CAD$75 worth of Meccano, the analyzer was minimally modified from the original design but offered slight improvements to the electrical power distribution system, the design of the torque amplifiers, and the output pen support. Unfortunately, there is no information regarding what use, if any, the analyzer was put to or why Worsley built it For more on Beatrice Worsley, see UTEC
    .
  26. ^ Irwin, William (2009-07). Op. cit. "It is rumoured that a differential analyser was used in the development of the "bouncing bomb" by Barnes Wallis for the "Dam Busters" attack on the Ruhr valley hydroelectric dams in WW2. This was first mentioned in MOTAT [New Zealand] literature in 1973. However after extensive enquiries and literature searches over the last few years, no evidence can be found that the [differential analyser held by MOTAT Archived 2018-02-26 at the Wayback Machine, nor any other differential analyser, was used for this purpose. Considering the secrecy surrounding war time activities at the time it could still be possible, but most people from that era are now deceased. Two remaining personalities still alive from that era were consulted, namely Arthur Porter and Maurice Wilkes, but neither could substantiate the rumour."
  27. ISBN 9781862076631
    .
  28. ^ a b (Hartree & Porter 1934–1935),"Differential Analyser". Auckland Meccano Guild. Retrieved 2010-07-21.
  29. ^ Cairns, W. J., Crank, J., & Lloyd, E. C. Some Improvements in the Construction of a Small Scale Differential Analyser and a Review of Recent Applications, Armament Research Department Theoretical Research Memo. No. 27/44, 1944 (see Robinson, Tim (2008-06-07). "Bibliography". Tim Robinson's Meccano Computing Machinery web site. Retrieved 2010-07-26.). The memorandum is now in The National Archives, UK: "Piece reference DEFE 15/751". The National Archives. Retrieved 2010-07-26. For the "Armament Research Department", see Fort Halstead, and cf. the entry for 1944 in "MoD History of Innovation" (PDF). Ploughshare Innovations Ltd. Retrieved 2010-07-26.
  30. ^ Irwin, William (2009-07). Op. cit. "It is estimated by Garry Tee of Auckland University that about 15 Meccano model Differential Analysers were built for serious work by scientists and researchers around the world." For Garry Tee, see "Computing History Displays: The Displays" (php). University of Auckland. Retrieved 2010-07-22.

Bibliography

External links

Wikimedia Commons has media related to Differential analysers.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Differential_analyser&oldid=1224740474"