Editing Analog computer (section)

==Timeline of analog computers==
{{See also|History of computing hardware#Analog computers}}

===Precursors===
{{See also|Timeline of computing hardware before 1950}}

This is a list of examples of early computation devices considered precursors of the modern computers. Some of them may even have been dubbed 'computers' by the press, though they may fail to fit modern definitions.

[[File:Antikythera Fragment A (Front).webp|thumb|The [[Antikythera mechanism]], dating from between 200 BC and 80 BC, was an early analog computer.|alt=|260x260px]]
The [[Antikythera mechanism]], a type  of device used to determine the positions of [[Astronomical object|heavenly bodies]] known  as an [[orrery]], was  described as an early mechanical analog computer by British physicist, information scientist, and historian of science [[Derek J. de Solla Price]].<ref name="djclP">{{cite web|archiveurl=https://web.archive.org/web/20080428070448/http://www.antikythera-mechanism.gr/project/general/the-project.html|archivedate=28 April 2008|url-status=dead|url=http://www.antikythera-mechanism.gr/project/general/the-project.html|date=28 April 2008|title=The Antikythera Mechanism Research Project|accessdate=1 July 2007}}</ref> It was discovered in 1901, in the [[Antikythera wreck]] off the Greek island of [[Antikythera]], between [[Kythera]] and [[Crete]], and has been dated to {{circa|150~100 BC}}, during the [[Hellenistic period]]. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later.

Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use.
The [[planisphere]] was first described by [[Ptolemy]] in the 2nd century AD. The [[astrolabe]] was invented in the [[Hellenistic civilization|Hellenistic world]] in either the 1st or 2nd centuries BC and is often attributed to [[Hipparchus]]. A combination of the planisphere and [[dioptra]], the astrolabe was effectively an analog computer capable of working out several different kinds of problems in [[spherical astronomy]].

The [[Sector (instrument)|sector]], a calculating instrument used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots, was developed in the late 16th century and found application in gunnery, surveying and navigation.

The [[planimeter]] was a manual instrument to calculate the area of a closed figure by tracing over it with a mechanical linkage.

[[File:Sliderule 2005.png|thumb|A [[slide rule]]. The sliding central slip is set to 1.3, the cursor to 2.0 and points to the multiplied result of 2.6.|alt=|260x260px]]
The [[slide rule]] was invented around 1620–1630, shortly after the publication of the [[history of logarithms|concept of the logarithm]]. It is a hand-operated analog computer for doing multiplication and division. As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as [[transcendental function]]s such as logarithms and exponentials, circular and hyperbolic trigonometry and other [[Function (mathematics)|functions]]. Aviation is one of the few fields where slide rules are still in widespread use, particularly for solving time–distance problems in light aircraft.

In 1831–1835, mathematician and engineer [[Giovanni Plana]] devised a [[Cappella dei Mercanti (Turin)#Perpetual calendar|perpetual-calendar machine]], which, through a system of pulleys and cylinders, could predict the [[perpetual calendar]] for every year from AD&nbsp;0 (that is, 1&nbsp;BC) to AD&nbsp;4000, keeping track of leap years and varying day length.<ref name="1eYEV">{{Cite web|title=An Amazing Perpetual Calendar, Hidden in an Italian Chapel|first1=A J|last1=Oliveira|url=http://www.atlasobscura.com/places/planas-perpetual-calendar|access-date=2020-09-07|website=Atlas Obscura|language=en}}</ref>

The [[tide-predicting machine]] invented by [[William Thomson, 1st Baron Kelvin|Sir William Thomson]] in 1872 was of great utility to navigation in shallow waters. It used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location.

The [[differential analyser]], a mechanical analog computer designed to solve [[differential equation]]s by [[integral|integration]], used wheel-and-disc mechanisms to perform the integration. In 1876 [[James Thomson (engineer)|James Thomson]] had already discussed the possible construction of such calculators, but he had been stymied by the limited output torque of the [[ball-and-disk integrator]]s. Several systems followed, notably those of Spanish [[engineer]] [[Leonardo Torres Quevedo]], who built various [[Leonardo Torres Quevedo#Analogue calculating machines|analog machines]] for solving real and complex roots of [[polynomial]]s;<ref>{{Cite journal |last=Torres |first=Leonardo |author-link=Leonardo Torres Quevedo |date=1895-10-10 |title=Memória sobre las Máquinas Algébricas |url=https://quickclick.es/rop/pdf/publico/1895/1895_tomoI_28_01.pdf |journal=Revista de Obras Públicas |language=es |issue=28 |pages=217–222}}</ref><ref name="MaquinasAlgebricasLTQ">Leonardo Torres. ''[https://books.google.com/books?id=Eo0NAQAAIAAJ Memoria sobre las máquinas algébricas: con un informe de la Real academia de ciencias exactas, fisicas y naturales]'', Misericordia, 1895.</ref><ref name="Gomez-JaureguiGutierrez-GarciaGonzález-RedondoIglesiasManchadoOtero2022">{{Cite journal |last1=Gomez-Jauregui |first1=Valentin |last2=Gutierrez-Garcia |first2=Andres |last3=González-Redondo |first3=Francisco A. |last4=Iglesias |first4=Miguel |last5=Manchado |first5=Cristina |last6=Otero |first6=Cesar |date=2022-06-01 |title=Torres Quevedo's mechanical calculator for second-degree equations with complex coefficients|journal=[[Mechanism and Machine Theory]] |publisher=[[International Federation for the Promotion of Mechanism and Machine Science|IFToMM]] |volume=172 |issue=8|page=104830 |doi=10.1016/j.mechmachtheory.2022.104830|s2cid=247503677 |doi-access=free |hdl=10902/24391 |hdl-access=free }}</ref> and Michelson and Stratton, whose Harmonic Analyser performed Fourier analysis, but using an array of 80 springs rather than Kelvin integrators. This work led to the mathematical understanding of the [[Gibbs phenomenon]] of overshoot in Fourier representation near discontinuities.<ref name="GdfNz">Ray Girvan, [http://www.scientific-computing.com/scwmayjun03computingmachines.html "The revealed grace of the mechanism: computing after Babbage"] {{webarchive |url=https://web.archive.org/web/20121103094710/http://www.scientific-computing.com/scwmayjun03computingmachines.html |date=November 3, 2012}}, ''Scientific Computing World'', May/June 2003</ref> In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output. The [[torque amplifier]] was the advance that allowed these machines to work. Starting in the 1920s, [[Vannevar Bush]] and others developed mechanical differential analyzers.

===Modern era===
[[File:Analog Computing Machine GPN-2000-000354.jpg|thumb| Analog computing machine at the [[Lewis Flight Propulsion Laboratory]] {{Circa|1949}}.|alt=|260x260px]]
[[File:Heathkit Analog Computer.jpg|thumb|Heathkit EC-1 educational analog computer|alt=|260x260px]]
The [[Dumaresq]] was a mechanical calculating device invented around 1902 by Lieutenant [[John Saumarez Dumaresq|John Dumaresq]] of the [[Royal Navy]]. It was an analog computer that related vital variables of the fire control problem to the movement of one's own ship and that of a target ship. It was often used with other devices, such as a [[Vickers range clock]] to generate range and deflection data so the gun sights of the ship could be continuously set. A number of versions of the Dumaresq were produced of increasing complexity as development proceeded.

By 1912, [[Arthur Pollen]] had developed an electrically driven mechanical analog computer for [[fire-control system]]s, based on the differential analyser. It was used by the [[Imperial Russian Navy]] in [[World War I]].<ref>{{Cite journal |last=Clymer |first=Arthur Ben |date=1993 |title=The Mechanical Analog Computers of Hannibal Ford and William Newell |journal=IEEE Annals of the History of Computing |volume=15 |issue=2 |pages=19–34 |url=http://web.mit.edu/STS.035/www/PDFs/Newell.pdf |access-date=11 February 2023|doi=10.1109/85.207741|s2cid=6500043 }}</ref>

Starting in 1929, [[Network analyzer (AC power)|AC network analyzers]] were constructed to solve calculation problems related to electrical power systems that were too large to solve with [[numerical method]]s at the time.<ref name="G12GE">Thomas Parke Hughes ''Networks of power: electrification in Western society, 1880–1930'' JHU Press, 1993 {{ISBN|0-8018-4614-5}} page 376</ref> These were essentially scale models of the electrical properties of the full-size system. Since network analyzers could handle problems too large for analytic methods or hand computation, they were also used to solve problems in nuclear physics and in the design of structures. More than 50 large network analyzers were built by the end of the 1950s.

[[World War II]] era gun [[Director (military)|directors]], [[gun data computer]]s, and [[bomb sight]]s used mechanical analog computers. In 1942 [[Helmut Hölzer]] built a fully electronic analog computer at [[Peenemünde Army Research Center]]<ref name="HsrYN">James E. Tomayko, ''Helmut Hoelzer's Fully Electronic Analog Computer''; In: ''IEEE Annals of the History of Computing'', Vol. 7, No. 3, pp. 227–240, July–Sept. 1985, {{doi|10.1109/MAHC.1985.10025}}</ref><ref name="LQl0b">{{Cite book |url=https://books.google.com/books?id=L6BfBgAAQBAJ&q=Hoelzer%201942&pg=PT138 |title=The Rocket and the Reich: Peenemunde and the Coming of the Ballistic Missile Era |last=Neufeld |first=Michael J. |year=2013 |publisher=Smithsonian Institution |isbn=9781588344663 |pages=138 |language=en}}</ref><ref name="hOc4c">{{Cite book |url=https://books.google.com/books?id=y1DpBQAAQBAJ&q=Hoelzer%201941&pg=PA38 |title=Analog Computing |last=Ulmann |first=Bernd |date=2013-07-22 |publisher=Walter de Gruyter |isbn=9783486755183 |pages=38 |language=en}}</ref> as an embedded control system (''mixing device'') to calculate [[V-2 rocket]] trajectories from the accelerations and orientations (measured by [[gyroscope]]s) and to stabilize and guide the missile.{{sfnp|Neufeld|2013|p=106}}<ref name="u9qok">{{cite journal |title=Helmut Hoelzer |first=James E. |last=Tomayko |date=1 July 1985 |journal=IEEE Annals of the History of Computing |volume = 7 |issue=3 |pages=227–240 |doi=10.1109/MAHC.1985.10025 |s2cid=15986944}}</ref> Mechanical analog computers were very important in [[Fire control system|gun fire control]] in World War II, the Korean War and well past the Vietnam War; they were made in significant numbers.

In the period 1930–1945 in the Netherlands, [[Johan van Veen]] developed an analogue computer to calculate and predict tidal currents when the geometry of the channels are changed. Around 1950, this idea was developed into the [[Deltar]], a [[hydraulic analogy]] computer supporting the closure of estuaries in the southwest of the Netherlands (the [[Delta Works]]).

The [[FERMIAC]] was an analog computer invented by physicist [[Enrico Fermi]] in 1947 to aid in his studies of neutron transport.<ref name="bwwka">Metropolis, N. [http://www.fas.org/sgp/othergov/doe/lanl/pubs/00326866.pdf "The Beginning of the Monte Carlo Method."] Los Alamos Science, No. 15, p. 125</ref> [[Project Cyclone]] was an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems.<ref name="qU5NQ">Small, J. S. "The analogue alternative: The electronic analogue computer in Britain and the USA, 1930–1975" Psychology Press, 2001, p. 90</ref> Project Typhoon was an analog computer developed by RCA in 1952. It consisted of over 4,000 electron tubes and used 100 dials and 6,000 plug-in connectors to program.<ref name="1serv">Small, J. S. "The analogue alternative: The electronic analogue computer in Britain and the USA, 1930–1975" Psychology Press, 2001, p. 93</ref> The [[MONIAC Computer]] was a hydraulic analogy of a national economy first unveiled in 1949.<ref name="iSjwP">{{Cite journal |last=Bissell |first=C. |date=2007-02-01 |title=Historical perspectives – The Moniac A Hydromechanical Analog Computer of the 1950s|journal=IEEE Control Systems Magazine |volume=27 |issue=1 |pages=69–74 |doi=10.1109/MCS.2007.284511 |s2cid=37510407 |issn=1066-033X |url=http://oro.open.ac.uk/7942/1/04064850.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://oro.open.ac.uk/7942/1/04064850.pdf |archive-date=2022-10-09 |url-status=live}}</ref>

Computer Engineering Associates was spun out of [[Caltech]] in 1950 to provide commercial services using the "Direct Analogy Electric Analog Computer" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems") developed there by Gilbert D. McCann, Charles H. Wilts, and [[Bart N. Locanthi|Bart Locanthi]].<ref name="ZOi9Q">{{cite web |url=http://me100.caltech.edu/history/nastran.htm |title=History – Accounts |website=me100.caltech.edu}}</ref><ref name="jXkDw">{{cite web |url=https://books.google.com/books?id=X0UYAAAAIAAJ&q=caltech+analog-computer |title=Analog simulation: solution of field problems |first=Walter J. |last=Karplus |date=1958  |publisher=McGraw-Hill |via=Google Books}}</ref>

Educational analog computers illustrated the principles of analog calculation. The [[Heathkit]] EC-1, a $199 educational analog computer, was made by the Heath Company, US {{circa|1960}}.<ref name="HGxrP">{{cite book |last=Petersen |first=Julie K. |title=Fiber optics illustrated dictionary |publisher=CRC Press |year=2003 |page=441 |isbn= 978-0-8493-1349-3}}</ref> It was programmed using patch cords that connected nine [[operational amplifier]]s and other components.<ref name="fujYP">{{cite web |url=http://www.computerhistory.org/VirtualVisibleStorage/artifact_main.php?tax_id=01.03.05.00 |title=Heathkit EC - 1 Educational Analog Computer |publisher=Computer History Museum |access-date=9 May 2010|archive-url=https://web.archive.org/web/20100520214445/http://www.computerhistory.org/VirtualVisibleStorage/artifact_main.php?tax_id=01.03.05.00 |archive-date=2010-05-20 |url-status=dead}}</ref> [[General Electric]] also marketed an "educational" analog computer kit of a simple design in the early 1960s consisting of two transistor tone generators and three potentiometers wired such that the frequency of the oscillator was nulled when the potentiometer dials were positioned by hand to satisfy an equation. The relative resistance of the potentiometer was then equivalent to the formula of the equation being solved. Multiplication or division could be performed, depending on which dials were inputs and which was the output. Accuracy and resolution was limited and a simple slide rule was more accurate. However, the unit did demonstrate the basic principle.

Analog computer designs were published in electronics magazines. One example is the PEAC (Practical Electronics analogue computer), published in ''Practical Electronics'' in the January 1968 edition.<ref name="PE Jan 1968">[https://worldradiohistory.com/UK/Practical-Electronics/60s/Practical-Electronics-1968-01.pdf] Practical Electronics, January 1968</ref> Another more modern hybrid computer design was published in ''Everyday Practical Electronics'' in 2002.<ref name="EPE hybrid">[http://www.epemag3.com/lib/free_projects/general/1102-%20EPE%20Hybrid%20Computer%20-%20Part%201.pdf EPE Hybrid Computer - Part 1] (November 2002), [http://www.epemag3.com/lib/free_projects/general/1202-%20EPE%20Hybrid%20Computer%20-%20Part%202.pdf Part 2] (December 2002), ''Everyday Practical Electronics''</ref> An example described in the EPE hybrid computer was the flight of a [[VTOL|VTOL aircraft]] such as the [[Harrier jump jet]].<ref name="EPE hybrid" /> The altitude and speed of the aircraft were calculated by the analog part of the computer and sent to a PC via a digital microprocessor and displayed on the PC screen.

In industrial [[process control]], analog loop controllers were used to automatically regulate temperature, flow, pressure, or other process conditions. The technology of these controllers ranged from purely mechanical integrators, through vacuum-tube and solid-state devices, to emulation of analog controllers by microprocessors.