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]
Research on solutions for differential equations using mechanical devices, discounting planimeters, started 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.[4]
The first description of a device which could integrate differential equations of any order was published in 1876 by James Thomson, who was born in Belfast in 1822, but lived in Scotland from the age of 10.[5] Though Thomson called his device an "integrating machine", it is his description of the device, together with the additional publication in 1876 of two further descriptions by his younger brother, 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]
Douglas Hartree of Manchester University brought Bush's design to England, where he constructed his first "proof of concept" model with his student, Arthur Porter, during 1934. As a result of this, the university acquired a full scale machine incorporating four mechanical integrators in March 1935, which was built by Metropolitan-Vickers, and was, according to Hartree, "[the] first machine of its kind in operation outside the United States".[16] During the next five years three more were added, at Cambridge University, Queen's University Belfast, and the Royal Aircraft Establishment in Farnborough.[17] One of the integrators from this proof of concept is on display in the History of Computing section of the 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 Ballistic Research Laboratory in Maryland and in the basement of the Moore School of Electrical Engineering at the University of Pennsylvania during the early 1940s.[19] The latter was used extensively in the computation of artillery firing tables prior to the invention of the ENIAC, which, in many ways, was modelled on the differential analyser.[20] Also in the early 1940s, with Samuel H. Caldwell, one of the initial contributors during the early 1930s, Bush attempted an electrical, rather than mechanical, variation, but 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.
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]
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 Meccano parts: this meant that the machine was less costly to build, and it proved "accurate enough for the solution of many scientific problems".[28] A similar machine built by J.B. Bratt at Cambridge University in 1935 is now in the Museum of Transport and Technology (MOTAT) collection in Auckland, New Zealand.[28] A memorandum written for the British military's Armament Research Department in 1944 describes how this machine had been modified during World War II for improved reliability and enhanced capability, and identifies its wartime applications as including research on the flow of heat, explosive detonations, and simulations 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]
↑ 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
↑ Pollen, Anthony (1980). The Great Gunnery Scandal – The Mystery of Jutland. Collins. p.23. ISBN0-00-216298-9.
↑ Pascal, Ernesto (1914). Miei Integrafi per Equazioni Differenziali (in Italian). Naples: B. Pellerano. See also Integraph.
↑ 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.
↑ 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. 1,751,647Archived 2018-08-07 at the Wayback Machine (filed: 8 January 1926; issued: 25 March 1930); (3) "Synchronous amplifying control mechanism", U.S. patent no. 1,751,652Archived 2014-06-28 at the Wayback Machine (filed: 8 January 1926; issued: 25 March 1930).
↑ Bush, V. (October 1931). "The differential analyzer. A new machine for solving differential equations". Journal of the Franklin Institute. 212 (4): 447–488. doi:10.1016/S0016-0032(31)90616-9..
↑ 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).
↑ Gleick, James (2011). The Information: A History, a Theory, a Flood (ebook). Patheon. p.342/1102. ISBN978-0-00-742311-8.
↑ 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..
↑ 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".
↑ Holst, P.A. (Oct–Dec 1996). "Svein Rosseland and the Oslo analyzer". IEEE Annals of the History of Computing. 18 (4): 16–26. doi:10.1109/85.539912.
↑ 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.
↑ 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.
↑ Campbell, Scott M. (October–December 2003). "Beatrice Helen Worsley: Canada's Female Computer Pioneer"(PDF). IEEE Annals of the History of Computing. IEEE Computer Society. 25 (4): 53–4. doi:10.1109/MAHC.2003.1253890. S2CID13499528. 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.
↑ 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 MOTATArchived 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."
↑ Hally, Mike (2005), Electronic Brains: Stories from the Dawn of the Computer Age, Granta, p.xx, ISBN9781862076631 .
↑ 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.
↑ 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.
Thomson, William (1876). "Mechanical Integration of Linear Differential Equations of the Second Order with Variable Coefficients". Proceedings of the Royal Society. 24 (164–170): 269–71. doi:10.1098/rspl.1875.0035. S2CID62694536.
Hartree, D. R.; Porter, Porter (1934–1935), "The construction and operation of a model differential analyser", Memoirs and Proceedings of the Manchester Literary and Philosophical Society, 79: 51–73, reprinted as a pamphlet July 1935
Crank, J. (1947). The Differential Analyser, London: Longmans, Green (this is the only book that describes how to set up and operate a mechanical differential analyser).
MacNee, A.B. (1948). An electronic differential analyzer (RLE, Technical Report 90, MIT. Note that this paper describes a very early electronic analogue computer, not a mechanical differential analyser: it is included because the author clearly felt that the only way to introduce such an innovation was to describe it as an "electronic differential analyser").
An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude.
The history of computing hardware covers the developments from early simple devices to aid calculation to modern day computers.
Vannevar Bush was an American engineer, inventor and science administrator, who during World War II headed the U.S. Office of Scientific Research and Development (OSRD), through which almost all wartime military R&D was carried out, including important developments in radar and the initiation and early administration of the Manhattan Project. He emphasized the importance of scientific research to national security and economic well-being, and was chiefly responsible for the movement that led to the creation of the National Science Foundation.
Meccano is a brand of model construction system created in 1898 by Frank Hornby in Liverpool, England. The system consists of reusable metal strips, plates, angle girders, wheels, axles and gears, and plastic parts that are connected using nuts and bolts. It enables the building of working models and mechanical devices.
An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output.
Douglas Rayner Hartree was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the construction of a differential analyser using Meccano.
A computer is a machine that can be programmed to automatically carry out sequences of arithmetic or logical operations (computation). Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. The term computer system may refer to a nominally complete computer that includes the hardware, operating system, software, and peripheral equipment needed and used for full operation; or to a group of computers that are linked and function together, such as a computer network or computer cluster.
Differential equations, in particular Euler equations, rose in prominence during World War II in calculating the accurate trajectory of ballistics, both rocket-propelled and gun or cannon type projectiles. Originally, mathematicians used the simpler calculus of earlier centuries to determine velocity, thrust, elevation, curve, distance, and other parameters.
Samuel Hawks Caldwell was an American electrical engineer, known for his contributions to the early computers.
A digital differential analyzer (DDA), also sometimes called a digital integrating computer, is a digital implementation of a differential analyzer. The integrators in a DDA are implemented as accumulators, with the numeric result converted back to a pulse rate by the overflow of the accumulator.
The MADDIDA was a special-purpose digital computer used for solving systems of ordinary differential equations. It was the first computer to represent bits using voltage levels and whose entire logic was specified in Boolean algebra. Invented by Floyd Steele, MADDIDA was developed at Northrop Aircraft Corporation between 1946 and 1949 to be used as a guidance system for the Snark missile. No guidance system, however, resulted from the work on the MADDIDA, and rather it was used for aeronautical research. In 1952, the MADDIDA became the world's top-selling commercial digital computer, six units having been sold.
The Oslo Analyzer was a mechanical analog differential analyzer, a type of computer, built in Norway from 1938 to 1942. It was the largest computer of its kind in the world when completed.
Designed by Vannevar Bush after he became director of the Carnegie Institution for Science in Washington DC, the Rockefeller Differential Analyzer (RDA) was an all-electronic version of the Differential Analyzer, which Bush had built at the Massachusetts Institute of Technology between 1928 and 1931.
Beatrice Helen Worsley was the first female Canadian computer scientist. She received her Ph.D. degree from the University of Cambridge with Maurice Wilkes as adviser, the first Ph.D. granted in what would today be known as computer science. She wrote the first program to run on EDSAC, co-wrote the first compiler for Toronto's Ferranti Mark 1, wrote numerous papers in computer science, and taught computers and engineering at Queen's University and the University of Toronto for over 20 years before her death at the age of 50.
The following is a timeline of scientific computing, also known as computational science.
The ball-and-disk integrator is a key component of many advanced mechanical computers. Through simple mechanical means, it performs continual integration of the value of an input. Typical uses were the measurement of area or volume of material in industrial settings, range-keeping systems on ships, and tachometric bombsights. The addition of the torque amplifier by Vannevar Bush led to the differential analysers of the 1930s and 1940s.
A torque amplifier is a mechanical device that amplifies the torque of a rotating shaft without affecting its rotational speed. It is mechanically related to the capstan seen on ships. Its most widely known use is in power steering on automobiles. Another use is on the differential analyser, where it was used to increase the output torque of the otherwise limited ball-and-disk integrator. The term is also applied to some gearboxes used on tractors, although this is unrelated. It differs from a torque converter, in which the rotational speed of the output shaft decreases as the torque increases.
From 1929 to the late 1960s, large alternating current power systems were modelled and studied on AC network analyzers or transient network analyzers. These special-purpose analog computers were an outgrowth of the DC calculating boards used in the very earliest power system analysis. By the middle of the 1950s, fifty network analyzers were in operation. AC network analyzers were much used for power-flow studies, short circuit calculations, and system stability studies, but were ultimately replaced by numerical solutions running on digital computers. While the analyzers could provide real-time simulation of events, with no concerns about numeric stability of algorithms, the analyzers were costly, inflexible, and limited in the number of buses and lines that could be simulated. Eventually powerful digital computers replaced analog network analyzers for practical calculations, but analog physical models for studying electrical transients are still in use.
The general purpose analog computer (GPAC) is a mathematical model of analog computers first introduced in 1941 by Claude Shannon. This model consists of circuits where several basic units are interconnected in order to compute some function. The GPAC can be implemented in practice through the use of mechanical devices or analog electronics. Although analog computers have fallen almost into oblivion due to emergence of the digital computer, the GPAC has recently been studied as a way to provide evidence for the physical Church–Turing thesis. This is because the GPAC is also known to model a large class of dynamical systems defined with ordinary differential equations, which appear frequently in the context of physics. In particular it was shown in 2007 that the GPAC is equivalent, in computability terms, to Turing machines, thereby proving the physical Church–Turing thesis for the class of systems modelled by the GPAC. This was recently strengthened to polynomial time equivalence.
Floyd George Steele was an American physicist, engineer, and computer designer who grew up in Brush, Colorado. He is known for leading the design team at Northrup that developed the MADIDDA, an early digital computer.
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