Analog computer - Knowledge

1960:(VLSI) technology, Yannis Tsividis' group at Columbia University has been revisiting analog/hybrid computers design in standard CMOS process. Two VLSI chips have been developed, an 80th-order analog computer (250 nm) by Glenn Cowan in 2005 and a 4th-order hybrid computer (65 nm) developed by Ning Guo in 2015, both targeting at energy-efficient ODE/PDE applications. Glenn's chip contains 16 macros, in which there are 25 analog computing blocks, namely integrators, multipliers, fanouts, few nonlinear blocks. Ning's chip contains one macro block, in which there are 26 computing blocks including integrators, multipliers, fanouts, ADCs, SRAMs and DACs. Arbitrary nonlinear function generation is made possible by the ADC+SRAM+DAC chain, where the SRAM block stores the nonlinear function data. The experiments from the related publications revealed that VLSI analog/hybrid computers demonstrated about 1–2 orders magnitude of advantage in both solution time and energy while achieving accuracy within 5%, which points to the promise of using analog/hybrid computing techniques in the area of energy-efficient approximate computing. In 2016, a team of researchers developed a compiler to solve 65: 1584:("op amps"), named because they perform mathematical operations. Op amps are a particular type of feedback amplifier with very high gain and stable input (low and stable offset). They are always used with precision feedback components that, in operation, all but cancel out the currents arriving from input components. The majority of op amps in a representative setup are summing amplifiers, which add and subtract analog voltages, providing the result at their output jacks. As well, op amps with capacitor feedback are usually included in a setup; they integrate the sum of their inputs with respect to time. 410: 641: 195: 1569: 1050: 428: 1714: 29: 1988: 699: 1838: 1653: 1385: 1470:, which summed the individual harmonic components. Another category, not nearly as well known, used rotating shafts only for input and output, with precision racks and pinions. The racks were connected to linkages that performed the computation. At least one U.S. Naval sonar fire control computer of the later 1950s, made by Librascope, was of this type, as was the principal computer in the Mk. 56 Gun Fire Control System. 298: 1449: 1598:, one motive for using higher frequencies for the calculator (instead of the actual power frequency) was that higher-quality inductors could be more easily made. Many general-purpose analog computers avoided the use of inductors entirely, re-casting the problem in a form that could be solved using only resistive and capacitive elements, since high-quality capacitors are relatively easy to make. 1042:. Either problem can cause the circuit to produce an incorrect simulation of the physical system. (Modern digital simulations are much more robust to widely varying values of their variables, but are still not entirely immune to these concerns: floating-point digital calculations support a huge dynamic range, but can suffer from imprecision if tiny differences of huge values lead to 629: 1936:. The American company Comdyna manufactured small analog computers. At Indiana University Bloomington, Jonathan Mills has developed the Extended Analog Computer based on sampling voltages in a foam sheet. At the Harvard Robotics Laboratory, analog computation is a research topic. Lyric Semiconductor's error correction circuits use analog probabilistic signals. 594:

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.

691:. In the circuit, the (simulated) stiffness of the spring, for instance, can be changed by adjusting the parameters of an integrator. The electrical system is an analogy to the physical system, hence the name, but it is much less expensive than a mechanical prototype, much easier to modify, and generally safer. 1310:

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

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Electronic analog computers typically have front panels with numerous jacks (single-contact sockets) that permit patch cords (flexible wires with plugs at both ends) to create the interconnections that define the problem setup. In addition, there are precision high-resolution potentiometers (variable

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Essentially, the whole mechanism, called a component integrator, was a variable-speed drive with one motion input and two outputs, as well as an angle input. The angle input varied the ratio (and direction) of coupling between the "motion" input and the outputs according to the sine and cosine of the

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A special type of integrator, used at a point where only moderate accuracy was needed, was based on a steel ball, instead of a disc. It had two inputs, one to rotate the ball, and the other to define the angle of the ball's rotating axis. That axis was always in a plane that contained the axes of two

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In the 1950s to 1970s, digital computers based on first vacuum tubes, transistors, integrated circuits and then micro-processors became more economical and precise. This led digital computers to largely replace analog computers. Even so, some research in analog computation is still being done. A few

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Functions of two variables were provided by three-dimensional cams. In one good design, one of the variables rotated the cam. A hemispherical follower moved its carrier on a pivot axis parallel to that of the cam's rotating axis. Pivoting motion was the output. The second variable moved the follower

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at the time. 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

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Typically, a pinion-operated rack moving parallel to the (trig.-defined) opposite side would position a slide with a slot coincident with the hypotenuse. A pivot on the rack let the slide's angle change freely. At the other end of the slide (the angle, in trig. terms), a block on a pin fixed to the

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Although the basic technology for analog computers is usually operational amplifiers (also called "continuous current amplifiers" because they have no low frequency limitation), in the 1960s an attempt was made in the French ANALAC computer to use an alternative technology: medium frequency carrier

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However, the difference between these systems is what makes analog computing useful. Complex systems often are not amenable to pen-and-paper analysis, and require some form of testing or simulation. Complex mechanical systems, such as suspensions for racing cars, are expensive to fabricate and hard

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The Simulation Council (or Simulations Council) was an association of analog computer users in US. It is now known as The Society for Modeling and Simulation International. The Simulation Council newsletters from 1952 to 1963 are available online and show the concerns and technologies at the time,

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Multiplication was done by mechanisms based on the geometry of similar right triangles. Using the trigonometric terms for a right triangle, specifically opposite, adjacent, and hypotenuse, the adjacent side was fixed by construction. One variable changed the magnitude of the opposite side. In many

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Analog computing devices are fast; digital computing devices are more versatile and accurate. The idea behind an analog-digital hybrid 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,

620:, 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. 593:

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

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In the early 1970s, analog computer manufacturers tried to tie together their analog computers with a digital computers 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

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Electronic analog computers have drawbacks: the value of the circuit's supply voltage limits the range over which the variables may vary (since the value of a variable is represented by a voltage on a particular wire). Therefore, each problem must be scaled so its parameters and dimensions can be

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Considering that accurately controlled rotational speed in analog fire-control computers was a basic element of their accuracy, there was a motor with its average speed controlled by a balance wheel, hairspring, jeweled-bearing differential, a twin-lobe cam, and spring-loaded contacts (ship's AC

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Coordinate conversion from polar to rectangular was done by a mechanical resolver (called a "component solver" in US Navy fire control computers). Two discs on a common axis positioned a sliding block with pin (stubby shaft) on it. One disc was a face cam, and a follower on the block in the face

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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

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Integration with respect to another variable was done by a rotating disc driven by one variable. Output came from a pick-off device (such as a wheel) positioned at a radius on the disc proportional to the second variable. (A carrier with a pair of steel balls supported by small rollers worked

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Rectilinear-coordinate outputs (both sine and cosine, typically) came from two slotted plates, each slot fitting on the block just mentioned. The plates moved in straight lines, the movement of one plate at right angles to that of the other. The slots were at right angles to the direction of

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Many small computers dedicated to specific computations are still part of industrial regulation equipment, but from the 1950s to the 1970s, general-purpose analog computers were the only systems fast enough for real time simulation of dynamic systems, especially in the aircraft, military and

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The second input variable in this type of multiplier positions a slotted plate perpendicular to the adjacent side. That slot contains a block, and that block's position in its slot is determined by another block right next to it. The latter slides along the hypotenuse, so the two blocks are

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cam's groove set the radius. The other disc, closer to the pin, contained a straight slot in which the block moved. The input angle rotated the latter disc (the face cam disc, for an unchanging radius, rotated with the other (angle) disc; a differential and a few gears did this correction).

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Although they did not accomplish any computation, electromechanical position servos (aka. torgue amplifiers) were essential in mechanical analog computers of the "rotating-shaft" type for providing operating torque to the inputs of subsequent computing mechanisms, as well as driving output

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Analog computers were widely used in scientific and industrial applications even after the advent of digital computers, because at the time they were typically much faster, but they started to become obsolete as early as the 1950s and 1960s, although they remained in use in some specific

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To provide the product as an output, a third element, another slotted plate, also moves parallel to the (trig.) opposite side of the theoretical triangle. As usual, the slot is perpendicular to the direction of movement. A block in its slot, pivoted to the hypotenuse block positions it.

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Electronic analog computers are especially well-suited to representing situations described by differential equations. Historically, they were often used when a system of differential equations proved very difficult to solve by traditional means. As a simple example, the dynamics of a

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Differentiation with respect to time is not frequently used, and in practice is avoided by redefining the problem when possible. It corresponds in the frequency domain to a high-pass filter, which means that high-frequency noise is amplified; differentiation also risks instability.

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The electronic circuit can also be made to run faster or slower than the physical system being simulated. Experienced users of electronic analog computers said that they offered a comparatively intimate control and understanding of the problem, relative to digital simulations.

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A pair of rollers "above" and "below" the pick-off plane were mounted in rotating holders that were geared together. That gearing was driven by the angle input, and established the rotating axis of the ball. The other input rotated the "bottom" roller to make the ball rotate.

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Integrating with respect to another variable is the nearly exclusive province of mechanical analog integrators; it is almost never done in electronic analog computers. However, given that a problem solution does not change with time, time can serve as one of the variables.

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was an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems. 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. The

287:, 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. 1902:

is composed of four basic components: DC and AC magnitudes, frequency, and phase. The real limits of range on these characteristics limit analog computers. Some of these limits include the operational amplifier offset, finite gain, and frequency response,

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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

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When compensated for temperature, the forward voltage drop of a transistor's base-emitter junction can provide a usably accurate logarithmic or exponential function. Op amps scale the output voltage so that it is usable with the rest of the computer.

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Benjamin Cramer; Sebastian Billaudelle; Simeon Kanya; Aron Leibfried; Andreas Grübl; Vitali Karasenko; Christian Pehle; Korbinian Schreiber; Yannik Stradmann; Johannes Weis; Johannes Schemmel; View ORCID ProfileFriedemann Zenke (25 January 2022).

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Online, there is a remarkably clear illustrated reference (OP 1140) that describes the fire control computer mechanisms. For adding and subtracting, precision miter-gear differentials were in common use in some computers; the Ford Instrument

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resistors) for setting up (and, when needed, varying) scale factors. In addition, there is usually a zero-center analog pointer-type meter for modest-accuracy voltage measurement. Stable, accurate voltage sources provide known magnitudes.

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On the patch panel, various connections and routes can be set and switched to configure the machine and determine signal flows. This allows users to flexibly configure and reconfigure the analog computing system to perform specific tasks.

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movement pick-off rollers, quite similar to the mechanism of a rolling-ball computer mouse (in that mechanism, the pick-off rollers were roughly the same diameter as the ball). The pick-off roller axes were at right angles.

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The precision of the analog computer readout was limited chiefly by the precision of the readout equipment used, generally three or four significant figures. (Modern digital simulations are much better in this area. Digital

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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.

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These are just general blocks that can be found in a typical analog computing machine. The actual configuration and components may vary depending on the specific implementation and the intended use of the machine.

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At any distance along the adjacent side, a line perpendicular to it intersects the hypotenuse at a particular point. The distance between that point and the adjacent side is some fraction that is the product of

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can provide any desired degree of precision.) However, in most cases the precision of an analog computer is absolutely sufficient given the uncertainty of the model characteristics and its technical parameters.

317:. 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 1622:

Any physical process that models some computation can be interpreted as an analog computer. Some examples, invented for the purpose of illustrating the concept of analog computation, include using a bundle of

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Other readout mechanisms, not directly part of the computation, included internal odometer-like counters with interpolating drum dials for indicating internal variables, and mechanical multi-turn limit stops.

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Analog computing machines also feature a patch panel or patch field. A patch panel is a physical structure on which connectors or contacts are placed to interconnect various components and modules within the

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Modulators convert information into analog signals that can be transmitted through a communication channel, and demodulators perform the reverse transformation, recovering the original data from modulated

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Analog computers often have a complicated framework, but they have, at their core, a set of key components that perform the calculations. The operator manipulates these through the computer's framework.

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During World War II, a similar mechanism converted rectilinear to polar coordinates, but it was not particularly successful and was eliminated in a significant redesign (USN, Mk. 1 to Mk. 1A).

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Filters are used to modify the spectrum of signals by suppressing or amplifying specific frequencies. They allow the isolation or suppression of certain signal components depending on the computational

1086:, with its 231R Analog Computer (vacuum tubes, 20 integrators) and subsequently its EAI 8800 Analog Computer (solid state operational amplifiers, 64 integrators). Its challenger was Applied Dynamics of 389:; 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 2364: 1466:

Most practical mechanical analog computers of any significant complexity used rotating shafts to carry variables from one mechanism to another. Cables and pulleys were used in a Fourier synthesizer, a

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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.

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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.

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Guo, Ning; Huang, Yipeng; Mai, Tao; Patil, S.; Cao, Chi; Seok, Mingoo; Sethumadhavan, S.; Tsividis, Y. (1 September 2015). "Continuous-time hybrid computation with programmable nonlinearities".

447:. 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 1463:

While a wide variety of mechanisms have been developed throughout history, some stand out because of their theoretical importance, or because they were manufactured in significant quantities.

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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.

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Electrical elements such as inductors and capacitors used in electrical analog computers had to be carefully manufactured to reduce non-ideal effects. For example, in the construction of

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where the continuous and periodic rotation of interlinked gears drives the second, minute and hour needles in the clock. More complex applications, such as aircraft flight simulators and

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Referring to the mechanism's frame, the location of the pin corresponded to the tip of the vector represented by the angle and magnitude inputs. Mounted on that pin was a square block.

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Adders and multipliers perform arithmetic operations on analog signals. They can be used for mathematical operations such as addition, multiplication, integration, and differentiation.

687:(op amps) and some passive linear components to form a circuit that follows the same equations as the mechanical system being simulated. All measurements can be taken directly with an 393:

of overshoot in Fourier representation near discontinuities. In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output. The

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Patch panels can be presented as a physical panel with connectors or, in more modern systems, as a software interface that allows virtual management of signal connections and routes.

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Amplifiers are used to boost analog signals and maintain their amplitudes throughout the system. They amplify weak input signals and compensate for signal losses during transmission.

1058: 1349:, or Ariane in Europe, especially during the integration step where at the beginning everything is simulated, and progressively real components replace their simulated parts. 1615:—special circuits of various combinations of resistors and diodes to provide the nonlinearity. Typically, as the input voltage increases, progressively more diodes conduct. 2174: 1820:

In some analog computer designs, multiplication is much preferred to division. Division is carried out with a multiplier in the feedback path of an Operational Amplifier.

1008: 613:. 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. 2771: 1512:

cases, this variable changed sign; the hypotenuse could coincide with the adjacent side (a zero input), or move beyond the adjacent side, representing a sign change.

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Feedback and control blocks are used to maintain the stability and accuracy of the analog computing machine. They may include regulation systems and error correction.

1337:. 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 531:

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

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this device is designed to present the results of analog computations in a convenient form for the user or to transmit the obtained data to other systems.

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are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated. Complex mechanisms for

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By contrast, it is very inexpensive to build an electrical equivalent of a complex mechanical system, to simulate its behavior. Engineers arrange a few

1038:. Improperly scaled variables can have their values "clamped" by the limits of the supply voltage. Or if scaled too small, they can suffer from higher 2349:

Gomez-Jauregui, Valentin; Gutierrez-Garcia, Andres; González-Redondo, Francisco A.; Iglesias, Miguel; Manchado, Cristina; Otero, Cesar (1 June 2022).

325:. Aviation is one of the few fields where slide rules are still in widespread use, particularly for solving time–distance problems in light aircraft. 1283:, etc. These devices allow for the visualization of analog signals and the representation of the results of measurements or mathematical operations. 2837: 2409: 2257: 1217:

Analog computing machines can use various forms of information storage, such as capacitors or inductors, to store intermediate results and memory.

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can also be viewed as a form of analog computer, and their technology was originally based in part on electronic analog computer technology. The

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Analog computer designs were published in electronics magazines. One example is the PEAC (Practical Electronics analogue computer), published in

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within semiconductor devices. For commercially available electronic components, ranges of these aspects of input and output signals are always

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especially well. A roller, its axis parallel to the disc's surface, provided the output. It was held against the pair of balls by a spring.)

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Output devices in analog machines can vary depending on the specific goals of the system. For example, they could be graphical indicators,

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Small, J. S. "The analogue alternative: The electronic analogue computer in Britain and the USA, 1930–1975" Psychology Press, 2001, p. 93

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Small, J. S. "The analogue alternative: The electronic analogue computer in Britain and the USA, 1930–1975" Psychology Press, 2001, p. 90

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Large collection of electronic analog computers with lots of pictures, documentation and samples of implementations (some in German)

249:. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later. 3049:

Cowan, G.E.R.; Melville, R.C.; Tsividis, Y. (1 February 2005). "A VLSI analog computer/Math co-processor for a digital computer".

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In the 1970s, every large company and administration concerned with problems in dynamics had an analog computing center, such as:

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had already discussed the possible construction of such calculators, but he had been stymied by the limited output torque of the

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of a set of points; and strings tied together as a model of finding the shortest path in a network. These are all described in

382: 218:, was described as an early mechanical analog computer by British physicist, information scientist, and historian of science 174: 3107: 3066: 2755: 2775: 1034:

represented using voltages that the circuit can supply —e.g., the expected magnitudes of the velocity and the position of a

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The best reference in this field is the 100,000 simulation runs for each certification of the automatic landing systems of

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Arbitrary functions of one variable were provided by cams, with gearing to convert follower movement to shaft rotation.

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for every year from AD 0 (that is, 1 BC) to AD 4000, keeping track of leap years and varying day length.

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automatically feeding and collecting data. The digital computer may also participate to the calculation itself using

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were constructed to solve calculation problems related to electrical power systems that were too large to solve with

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Memoria sobre las máquinas algébricas: con un informe de la Real academia de ciencias exactas, fisicas y naturales

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Interfaces provide means of interaction with the machine, for example, for parameter control or data transmission.

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These are blocks that generate analog signals, such as voltage or current, to represent input data and operations.

2169: 2158: 2153: 1130: 645: 276:, the astrolabe was effectively an analog computer capable of working out several different kinds of problems in 3317: 2732: 1863: 1722: 1678: 1406: 1067: 294:

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

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was an analog computer invented by physicist Enrico Fermi in 1947 to aid in his studies of neutron transport.

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Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use. The

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connect (4) Ashley, J. R. Introduction to Analog Computation (New York: John Wiley & Sons, Inc. , 1963).

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Other computing elements include analog multipliers, nonlinear function generators, and analog comparators.

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power frequency was not necessarily accurate, nor dependable enough, when these computers were designed).

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functions and calculations can be constructed to a limited precision (three or four digits) by designing

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The use of electrical properties in analog computers means that calculations are normally performed in

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to modify. And taking precise mechanical measurements during high-speed tests adds further difficulty.

305:. The sliding central slip is set to 1.3, the cursor to 2.0 and points to the multiplied result of 2.6. 2861:(1) Truitt, T. D., and A. E. Rogers. Basics of Analog Computers (New York: John F. Rider, Inc., 1960). 2342: 1352:

Only one company was known as offering general commercial computing services on its hybrid computers,

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in World War II, the Korean War and well past the Vietnam War; they were made in significant numbers.

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Havranek, Bill (1 August 1966). "The role of a hybrid computer in supersonic transport simulation".

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positioned at a distance from the (trig.) adjacent side by an amount proportional to the product.

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ISSCC. 2005 IEEE International Digest of Technical Papers. Solid-State Circuits Conference, 2005

2870:(2) Johnson, C. L. Analog Computer Techniques (New York: McGraw-Hill Book Company, Inc., 1956). 2284: 1976: 1968: 1814: 1736:

Key mechanical components might include rotating shafts for carrying data within the computer,

440: 322: 3144: 2351:"Torres Quevedo's mechanical calculator for second-degree equations with complex coefficients" 2625: 2143: 2128: 2091: 1961: 1757: 1718: 1581: 1334: 1083: 1079: 684: 586: 520:) and to stabilize and guide the missile. Mechanical analog computers were very important in 463: 359: 355: 314: 207: 199: 110:

represent varying quantities symbolically and by discrete values of both time and amplitude (

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is striking in terms of mathematics. They can be modeled using equations of the same form.

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machine (computer) that uses the continuous variation aspect of physical phenomena such as

8: 3334:– an analog computer for the analysis of electric power systems (advertisement from 1955) 2373: 2350: 2044: 1991: 1717:

A 1960 Newmark analogue computer, made up of five units. This computer was used to solve

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in the January 1968 edition. Another more modern hybrid computer design was published in

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A.K. Dewdney. "On the Spaghetti Computer and Other Analog Gadgets for Problem Solving",

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The Analogue Alternative. The Electronic Analogue Computer in Britain and USA, 1930-1975

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data-transmission devices such as large torque-transmitter synchros in naval computers.

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These are examples of analog computers that have been constructed or practically used:

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computer supporting the closure of estuaries in the southwest of the Netherlands (the

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Typical electronic analog computers contain anywhere from a few to a hundred or more

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Jackson, Albert S., "Analog Computation". London & New York: McGraw-Hill, 1960.

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such as logarithms and exponentials, circular and hyperbolic trigonometry and other

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Educational analog computers illustrated the principles of analog calculation. The

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ESSCIRC Conference 2015 - 41st European Solid-State Circuits Conference (ESSCIRC)

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Analog circuit for the dynamics of a spring-mass system (without scaling factors)

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The Rocket and the Reich: Peenemunde and the Coming of the Ballistic Missile Era

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along the axis of the cam. One practical application was ballistics in gunnery.

1138: 3058: 2926: 2713: 1933: 1804: 1799: 1628: 1452: 1338: 868: 528: 329: 165:) well into the 1980s, since digital computers were insufficient for the task. 150: 111: 3298: 3347: 2684: 2163: 1908: 1899: 1767: 1342: 1262: 605:

in 2002. An example described in the EPE hybrid computer was the flight of a

578:

EC-1, a $ 199 educational analog computer, was made by the Heath Company, US

455: 398: 98: 3306:

Chris Bissell, The Open University, Milton Keynes, UK Accessed February 2007

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was the advance that allowed these machines to work. Starting in the 1920s,

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in universities. Perhaps the most relatable example of analog computers are

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Large collection of old analog and digital computers at Old Computer Museum

3191: 2951: 2138: 1608: 1288: 1272: 688: 485: 427: 41: 3259: 1779:

The core mathematical operations used in an electric analog computer are:

1713: 2080: 1904: 1632: 1501: 1227: 1188: 971:{\displaystyle {\ddot {y}}=-{\tfrac {d}{m}}{\dot {y}}-{\tfrac {c}{m}}y-g} 540: 467: 253: 227: 81: 49: 1971:, and in 2021 a group of researchers have shown that a specific type of 1747:(2-D and 3-D), mechanical resolvers and multipliers, and torque servos. 28: 2383: 2059: 2055: 2038: 1987: 1937: 1737: 1631:; a board, a set of nails, and a rubber band as a model of finding the 1516:

frame defined the vertex between the hypotenuse and the adjacent side.

1409: in this section. Unsourced material may be challenged and removed. 513: 497: 444: 439:

was a mechanical calculating device invented around 1902 by Lieutenant

386: 310: 302: 291: 269: 118: 93: 45: 2450: 2115:'s Ring Modulator was actually a moderate-accuracy analog multiplier. 698: 559:

was a hydraulic analogy of a national economy first unveiled in 1949.

336:, which, through a system of pulleys and cylinders, could predict the 3314: 2432:"The Mechanical Analog Computers of Hannibal Ford and William Newell" 2179: 2096: 2086: 1809: 1733:

Key hydraulic components might include pipes, valves and containers.

1624: 1280: 1242: 1184: 1165: 665: 517: 366:, used wheel-and-disc mechanisms to perform the integration. In 1876 261: 133:

used analog computation to perform control and protective functions.

89: 3283: 3274:

in "Archaeology: High tech from Ancient Greece", François Charette,

1837: 1652: 1384: 458:

had developed an electrically driven mechanical analog computer for

313:

was invented around 1620–1630, shortly after the publication of the

3234:, by A.K. Dewdney, published by W.H. Freeman & Company (1988), 2112: 2070: 1788: 1783: 1364: 673: 669: 575: 436: 375: 363: 146: 122: 1898:

In general, analog computers are limited by non-ideal effects. An

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trajectories from the accelerations and orientations (measured by

16:

Computation machine that uses continuously varying data technology

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An analog computing machine consists of several main components:

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in either the 1st or 2nd centuries BC and is often attributed to

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Networks of power: electrification in Western society, 1880–1930

2201:"Gears of war: When mechanical analog computers ruled the waves" 1448: 1057: 3293: 2064: 2009: 1360: 1212: 633: 532: 482:

50 large network analyzers were built by the end of the 1950s.

215: 68:

TR-10 desktop analog computer of the late 1960s and early 1970s

53: 2407:"The revealed grace of the mechanism: computing after Babbage" 202:, dating between 150 and 100 BC, was an early analog computer. 1134: 656:

The similarity between linear mechanical components, such as

649: 235: 2285:"An Amazing Perpetual Calendar, Hidden in an Italian Chapel" 664:(viscous-fluid dampers), and electrical components, such as 3310:

German computer museum with still runnable analog computers

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Analog computers can have a very wide range of complexity.

57: 3304:

A great disappearing act: the electronic analogue computer

3013: 2977: 2035:'s Analogue Calculating Machines based on "fusee sans fin" 585:. It was programmed using patch cords that connected nine 2831:"System Description EAI 8800 Scientific Computing System" 2014: 628: 462:, based on the differential analyser. It was used by the 1572:

Switching board of EAI 8800 analog computer (front view)

401:

and others developed mechanical differential analyzers.

36:(BIF) that describes the components and controls of the 3148:"Surrogate gradients for analog neuromorphic computing" 702:

OME P2, 1952, a French electronic analog computer from

210:, a type of device used to determine the positions of 2571: 948: 921: 895:. For analog computing, the equation is programmed as 3048: 2175:

Voskhod Spacecraft "Globus" IMP navigation instrument

2119:

and the common use of analog computers for missilry.

1979:

was able to work with analog neuromorphic computers.

1016: 984: 901: 877: 853: 829: 809: 789: 721: 374:. Several systems followed, notably those of Spanish 175:

History of computing hardware § Analog computers

3245:

Universiteit van Amsterdam Computer Museum. (2007).

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Key electrical/electronic components might include:

1030:(position), one inverter, and three potentiometers. 2590:Tomayko, James E. (1 July 1985). "Helmut Hoelzer". 1022: 1002: 970: 883: 859: 835: 815: 795: 775: 2501:Helmut Hoelzer's Fully Electronic Analog Computer 2229: 1932:universities still use analog computers to teach 358:, a mechanical analog computer designed to solve 3345: 3089: 1563: 562:Computer Engineering Associates was spun out of 2733:"Analog simulation: solution of field problems" 2507:, Vol. 7, No. 3, pp. 227–240, July–Sept. 1985, 168: 161:, remained the domain of analog computing (and 3327:Harvard Robotics Laboratory Analog Computation 1437: 776:{\displaystyle m{\ddot {y}}+d{\dot {y}}+cy=mg} 623: 3340:– Type LC-1 WWII Navy PV-1 "Balance Computor" 2806: 2804: 2772:"Heathkit EC - 1 Educational Analog Computer" 2233:Holographic Visions: A History of New Science 2258:"The Antikythera Mechanism Research Project" 1500:movement. Each plate, by itself, was like a 527:In the period 1930–1945 in the Netherlands, 504:built a fully electronic analog computer at 2790: 1866:. Unsourced material may be challenged and 1681:. Unsourced material may be challenged and 19:For the Atari 8-bit computer magazine, see 2946: 2944: 2801: 2626:"The Beginning of the Monte Carlo Method." 644:EAI 8800 Analog computing system used for 500:used mechanical analog computers. In 1942 186:Timeline of computing hardware before 1950 3181: 3171: 2774:. Computer History Museum. Archived from 2382: 2372: 2198: 1886:Learn how and when to remove this message 1701:Learn how and when to remove this message 1425:Learn how and when to remove this message 1304: 1094:and non dissipative reversible circuits. 1078:In the 1960s, the major manufacturer was 431:Heathkit EC-1 educational analog computer 328:In 1831–1835, mathematician and engineer 3272:Biruni's eight-geared lunisolar calendar 3230:, 250(6):19–26, June 1984. Reprinted in 2912: 2745: 2530:. Smithsonian Institution. p. 138. 1986: 1712: 1567: 1447: 1056: 1048: 697: 639: 627: 426: 408: 296: 193: 63: 27: 2941: 2735:. McGraw-Hill – via Google Books. 2730: 2655: 2592:IEEE Annals of the History of Computing 2589: 2577: 2523: 2505:IEEE Annals of the History of Computing 2439:IEEE Annals of the History of Computing 2314:"Memória sobre las Máquinas Algébricas" 2223: 704:Société d'Electronique et d'Automatisme 272:. A combination of the planisphere and 106:the problem being solved. In contrast, 3346: 2902:. London: Routledge. pp. 119–178. 2550: 2429: 2308: 2041:, aircraft weight and balance computer 385:for solving real and complex roots of 3198: 3124: 3083: 3042: 3020: 3006: 2992: 2962: 2906: 2897: 2891: 2823: 2764: 2739: 2724: 2706: 2649: 2640: 2631: 2618: 2583: 2544: 2517: 2493: 2472: 2211:from the original on 8 September 2018 1982: 1504:, known to steam engine enthusiasts. 1061:Damped motion of a spring-mass system 2702:from the original on 9 October 2022. 2399: 2374:10.1016/j.mechmachtheory.2022.104830 2282: 2276: 2250: 2192: 2083:, and related fire control computers 1864:adding citations to reliable sources 1831: 1679:adding citations to reliable sources 1646: 1528:the magnitude of the opposite side. 1407:adding citations to reliable sources 1378: 222:. It was discovered in 1901, in the 2843:from the original on 9 October 2022 2798:Practical Electronics, January 1968 2748:Fiber optics illustrated dictionary 803:as the vertical position of a mass 13: 2628:Los Alamos Science, No. 15, p. 125 1967:Analog computers are also used in 1754:precision resistors and capacitors 1524:the distance from the vertex, and 1374: 415:Lewis Flight Propulsion Laboratory 14: 3375: 3265: 2557:. Walter de Gruyter. p. 38. 2199:Gallagher, Sean (17 March 2014). 2166:series of WW II German bombsights 1241:Patch panels are used to control 715:can be described by the equation 3278:444, 551–552(30 November 2006), 3053:. Vol. 1. pp. 82–586. 3000:"Kirchhoff-Lukasiewicz Machines" 1836: 1743:, disc/ball/roller integrators, 1651: 1383: 413:Analog computing machine at the 3332:The Enns Power Network Computer 3206:"Simulation Council newsletter" 3138: 2952:"Basic Fire Control Mechanisms" 2882: 2873: 2864: 2855: 2656:Bissell, C. (1 February 2007). 2260:. 28 April 2008. Archived from 2170:Signal (electrical engineering) 2159:General purpose analog computer 2154:Field-programmable analog array 1721:and is currently housed at the 1394:needs additional citations for 1149: 1131:French Atomic Energy Commission 646:hardware-in-the-loop simulation 508:as an embedded control system ( 506:Peenemünde Army Research Center 137:applications, such as aircraft 3338:Librascope Development Company 2819:Everyday Practical Electronics 2551:Ulmann, Bernd (22 July 2013). 2423: 2302: 1827: 1723:Cambridge Museum of Technology 1068:arbitrary-precision arithmetic 603:Everyday Practical Electronics 1: 3354:History of computing hardware 3220: 3014:"Harvard Robotics Laboratory" 2665:IEEE Control Systems Magazine 2023:Ishiguro Storm Surge Computer 1951: 1642: 1478:contained about 160 of them. 1275:, graphic recording devices, 579: 417: 404: 239: 179: 34:Bombardier's Information File 3100:10.1109/ESSCIRC.2015.7313881 2811:EPE Hybrid Computer - Part 1 2524:Neufeld, Michael J. (2013). 2356:Mechanism and Machine Theory 1958:very-large-scale integration 1476:Mark I Fire Control Computer 1329:The largest manufacturer of 1324:digital-to-analog converters 1143:British Aircraft Corporation 169:Timeline of analog computers 7: 2746:Petersen, Julie K. (2003). 2731:Karplus, Walter J. (1958). 2430:Clymer, Arthur Ben (1993). 2323:(in Spanish) (28): 217–222. 2122: 2109:Analog (audio) synthesizers 2006:Central Fire Control System 1564:Electronic analog computers 1438:Mechanical analog computers 1003:{\displaystyle -{\dot {y}}} 624:Electronic analog computers 260:in the 2nd century AD. The 10: 3380: 3132:"Analog computing returns" 3059:10.1109/ISSCC.2005.1493879 2927:10.1177/003754976600700213 2750:. CRC Press. p. 441. 2418:Scientific Computing World 2236:. OUP Oxford. p. 90. 2230:Johnston, Sean F. (2006). 1926: 1629:a model of sorting numbers 1596:AC power network analyzers 1441: 334:perpetual-calendar machine 183: 172: 18: 2412:November 3, 2012, at the 2321:Revista de Obras Públicas 2033:Leonardo Torres y Quevedo 2004:Boeing B-29 Superfortress 1994:simulator analog computer 1973:artificial neural network 1356:of France, in the 1970s. 372:ball-and-disk integrators 2898:Small, James S. (2001). 2185: 1956:With the development of 319:transcendental functions 315:concept of the logarithm 238:, and has been dated to 226:off the Greek island of 159:synthetic-aperture radar 3173:10.1073/pnas.2109194119 2677:10.1109/MCS.2007.284511 2604:10.1109/MAHC.1985.10025 2513:10.1109/MAHC.1985.10025 1964:using analog circuits. 1913:temperature coefficient 1468:tide-predicting machine 1457:tide-predicting machine 1108:(Huntsville, Houston), 632:Polish analog computer 379:Leonardo Torres Quevedo 345:tide-predicting machine 256:was first described by 220:Derek J. de Solla Price 3315:Analog computer basics 1995: 1977:spiking neural network 1969:neuromorphic computing 1962:differential equations 1758:operational amplifiers 1726: 1719:differential equations 1582:operational amplifiers 1573: 1460: 1305:Analog–digital hybrids 1062: 1054: 1024: 1004: 972: 885: 861: 837: 817: 797: 777: 707: 685:operational amplifiers 653: 637: 589:and other components. 587:operational amplifiers 432: 424: 360:differential equations 306: 203: 69: 61: 52:to aid the pilot of a 3320:6 August 2009 at the 3232:The Armchair Universe 2339:, Misericordia, 1895. 2144:Differential equation 2129:Analog neural network 2092:Torpedo Data Computer 1990: 1934:control system theory 1716: 1571: 1451: 1335:Electronic Associates 1221:Feedback and control: 1084:Princeton, New Jersey 1080:Electronic Associates 1060: 1052: 1044:numerical instability 1025: 1005: 973: 886: 862: 838: 818: 798: 778: 701: 643: 631: 599:Practical Electronics 464:Imperial Russian Navy 430: 412: 356:differential analyser 300: 208:Antikythera mechanism 200:Antikythera mechanism 197: 67: 56:aircraft in dropping 31: 3094:. pp. 279–282. 2714:"History – Accounts" 2478:Thomas Parke Hughes 2067:, economic modelling 1860:improve this section 1791:with respect to time 1675:improve this section 1403:improve this article 1277:TV connection module 1014: 982: 899: 875: 851: 827: 807: 787: 719: 475:AC network analyzers 460:fire-control systems 381:, who built various 264:was invented in the 3289:The first computers 3228:Scientific American 3164:2022PNAS..11909194C 2312:(10 October 1895). 2058:, for example, the 2045:Mechanical computer 1774:function generators 1613:function generators 1444:Mechanical computer 1254:Hardware interfaces 1088:Ann Arbor, Michigan 845:damping coefficient 449:Vickers range clock 349:Sir William Thomson 278:spherical astronomy 149:, and for teaching 2980:on 1 December 2017 2970:"Analog Computers" 2499:James E. Tomayko, 2028:Kerrison Predictor 1996: 1983:Practical examples 1940:are still used as 1727: 1574: 1461: 1063: 1055: 1020: 1000: 968: 957: 930: 881: 857: 833: 813: 793: 773: 713:spring-mass system 708: 654: 638: 494:gun data computers 473:Starting in 1929, 433: 425: 338:perpetual calendar 307: 247:Hellenistic period 204: 155:mechanical watches 70: 62: 3109:978-1-4673-7470-5 3068:978-0-7803-8904-5 2817:(December 2002), 2813:(November 2002), 2757:978-0-8493-1349-3 2718:me100.caltech.edu 2451:10.1109/85.207741 2333:Leonardo Torres. 2134:Analogical models 1917:parasitic effects 1896: 1895: 1888: 1711: 1710: 1703: 1435: 1434: 1427: 1320:analog-to-digital 1075:aerospace field. 1023:{\displaystyle y} 997: 956: 941: 929: 911: 884:{\displaystyle g} 860:{\displaystyle c} 836:{\displaystyle d} 816:{\displaystyle m} 796:{\displaystyle y} 752: 734: 537:hydraulic analogy 479:numerical methods 266:Hellenistic world 243: 150~100 BC 224:Antikythera wreck 139:flight simulators 131:protective relays 108:digital computers 78:analogue computer 3371: 3364:Greek inventions 3359:Analog computers 3248:Analog Computers 3214: 3213: 3208:. 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