An analog computer is a form of computer that uses the continuously changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically, as their numerical values change. As an analog computer does not use discrete values, but rather continuous values, processes cannot be reliably repeated with exact equivalence, as they can with Turing machines. Unlike digital signal processing, analog computers do not suffer from the quantization noise, but are limited by analog noise.

Analog computers were widely used in scientific and industrial applications where digital computers of the time lacked sufficient performance. Analog computers can have a very wide range of complexity. Slide rules and nomographs are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated.[1] Systems for process control and protective relays used analog computation to perform control and protective functions.

The advent of digital computing made simple analog computers obsolete as early as the 1950s and 1960s, although analog computers remained in use in some specific applications, like the flight computer in aircraft, and for teaching control systems in universities. More complex applications, such as synthetic aperture radar, remained the domain of analog computing well into the 1980s, since digital computers were insufficient for the task.

Setup

Setting up an analog computer required scale factors to be chosen, along with initial conditions—that is, starting values. Another essential was creating the required network of interconnections between computing elements. Sometimes it was necessary to re-think the structure of the problem so that the computer would function satisfactorily. No variables could be allowed to exceed the computer's limits, and differentiation was to be avoided, typically by rearranging the "network" of interconnects, using integrators in a different sense.

Running an electronic analog computer, assuming a satisfactory setup, started with the computer held with some variables fixed at their initial values. Moving a switch released the holds and permitted the problem to run. In some instances, the computer could, after a certain running time interval, repeatedly return to the initial-conditions state to reset the problem, and run it again.

Precursors

See also: Timeline of computing hardware 2400 BC–1949

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

The south-pointing chariot, invented in ancient China during the first millennium BC, can be considered the earliest analog computer. It was a mechanical-geared wheeled vehicle used for to discern the southern cardinal direction.

 

The Antikythera mechanism, dating between 150 and 100 BC, was an early analog computer.

The Antikythera mechanism was an orrery and is claimed to be an early mechanical analog computer, according to Derek J. de Solla Price.[2] It was designed to calculate astronomical positions. 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 100 BC. 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 a star chart invented by Abū Rayḥān al-Bīrūnī in the early 11th century.[3] The astrolabe was invented in the 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. An astrolabe incorporating a mechanical calendar computer[4][5] and gear-wheels was invented by Abi Bakr of Isfahan, Persia in 1235.[6] Abū Rayhān al-Bīrūnī invented the first mechanical geared lunisolar calendar astrolabe,[7] an early fixed-wired knowledge processing machine[8] with a gear train and gear-wheels,[9] circa 1000 AD. The castle clock, a hydropowered mechanical astronomical clock invented by Al-Jazari in 1206, was the first programmable analog computer.[10][11][12]

The 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.

 

A slide rule

The slide rule was invented around 1620–1630, shortly after the publication of the 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 functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other 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.

The tide-predicting machine invented by 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 equations by integration, used wheel-and-disc mechanisms to perform the integration. In 1876 Lord Kelvin had already discussed the possible construction of such calculators, but he had been stymied by the limited output torque of the ball-and-disk integrators.[13] 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

 

Analog computing machine at the Lewis Flight Propulsion Laboratory circa 1949.

 

Heathkit EC-1 educational analog computer

The Dumaresq was a mechanical calculating device invented around 1902 by Lieutenant John Dumaresq of the Royal Navy. It was an analog computer which 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 systems, based on the differential analyser. It was used by the Imperial Russian Navy in World War I.[citation needed]

Starting in 1929, AC network analyzers were constructed to solve calculation problems related to electrical power systems that were too large to solve with numerical methods at the time.[14] 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 directors, gun data computers, and bomb sights used mechanical analog computers. In 1941 Helmut Hölzer built a fully electronic general-purpose analog computer at Peenemünde Army Research Center.[15] Mechanical analog computers were very important in gun fire control in World War II, The Korean War and well past the Vietnam War; they were made in significant numbers.

The FERMIAC was an analog computer invented by physicist Enrico Fermi in 1947 to aid in his studies of neutron transport.[16] Project Cyclone was an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems.[17] Project Typhoon was an analog computer developed by RCA in 1952. It consisted of over 4000 electron tubes and used 100 dials and 6000 plug-in connectors to program.[18] The MONIAC Computer was a hydraulic model of a national economy first unveiled in 1949.[19]

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 Locanthi.[20][21]

Educational analog computers illustrated the principles of analog calculation. The Heathkit EC-1, a $199 educational analog computer, was made by the Heath Company, USA c. 1960.[22] It was programmed using patch cords that connected nine operational amplifiers and other components.[23] General Electric also marketed an "educational" analog computer kit of a simple design in the early 1960s consisting of a two transistor tone generator 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 considered 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.

In industrial process control, thousands of 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.

Analog–digital hybrids

Analog computing devices are fast, digital computing devices are more versatile and accurate, so the idea is to combine the two processes for the best efficiency. An example of such hybrid elementary device is the hybrid multiplier where one input is an analog signal, the other input is a digital signal and the output is analog. It acts as an analog potentiometer upgradable digitally. This kind of hybrid technique is mainly used for fast dedicated real time computation when computing time is very critical as signal processing for radars and generally for controllers in embedded systems.

In the early 1970s analog computer manufacturers tried to tie together their analog computer with a digital computer to get the advantages of the two techniques. In such systems, the digital computer controlled the analog computer, providing initial set-up, initiating multiple analog runs, and automatically feeding and collecting data. The digital computer may also participate to the calculation itself using analog-to-digital and digital-to-analog converters.

The largest manufacturer of hybrid computers was Electronics Associates. Their hybrid computer model 8900 was made of a digital computer and one or more analog consoles. These systems were mainly dedicated to large projects such as the Apollo program and Space Shuttle at NASA, or Ariane in Europe, especially during the integration step where at the beginning everything is simulated, and progressively real components replace their simulated part.[citation needed]

Only one company was known as offering general commercial computing services on its hybrid computers, CISI of France, in the 1970s.

The best reference in this field is the 100,000 simulations runs for each certification of the automatic landing systems of Airbus and Concorde aircraft.[citation needed]

After 1980, purely digital computers progressed more and more rapidly and were fast enough to compete with analog computers. One key to the speed of analog computers was their fully parallel computation, but this was also a limitation. The more equations required for a problem, the more analog components were needed, even when the problem wasn't time critical. "Programming" a problem meant interconnecting the analog operators; even with a removable wiring panel this was not very versatile. Today there are no more big hybrid computers, but only hybrid components.[citation needed] this some information about analog computers