A page from the Bombardier's Information File (BIF) that describes the components and controls of the Norden bombsight. The Norden bombsight was a highly sophisticated optical/mechanical analog computer used by the United States Army Air Force during World War II, the Korean War, and the Vietnam War to aid the pilot of a bomber aircraft in dropping bombs accurately.

An analog computer (spelled analogue in British English) is a form of computer that uses electrical^[1], mechanical or hydraulic phenomena to model the problem being solved. More generally an analog computer uses one kind of physical quantity to represent the behavior of another physical system, or mathematical function. Modeling a real physical system in a computer is called simulation. Image File history File links Download high resolution version (536x733, 146 KB)Here is an excerpt from the Bombardiers Information File (BIF) that describes the components and controls of the Norden Bombsight. ... Image File history File links Download high resolution version (536x733, 146 KB)Here is an excerpt from the Bombardiers Information File (BIF) that describes the components and controls of the Norden Bombsight. ... The Norden bombsight A page from the Bombardiers Information File (BIF) that describes the components and controls of the Norden Bombsight. ... Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000... Combatants United Nations:  Republic of Korea,  Australia,  Belgium,  Luxembourg,  Canada,  Colombia,  Ethiopia,  France,  Greece,  Luxembourg,  Netherlands,  New Zealand,  Philippines,  South Africa,  Thailand,  Turkey,  United Kingdom,  United States Medical staff:  Denmark,  Australia,  Italy,  Norway,  Sweden Communist states:  Democratic People’s Republic of Korea,  Peoples Republic of China,  Soviet Union Commanders... Combatants Republic of Vietnam United States Republic of Korea Thailand Australia New Zealand The Philippines National Front for the Liberation of South Vietnam Democratic Republic of Vietnam People’s Republic of China Democratic Peoples Republic of Korea Strength US 1,000,000 South Korea 300,000 Australia 48,000... The B-17 Flying Fortress is one of the most recognizable and famous bombers of World War II. A bomber is a military aircraft designed to attack ground targets, primarily by dropping bombs. ... The Massive Ordnance Air Blast (MOAB) bomb produced in the United States. ... This article is about the machine. ... Lightning strikes during a night-time thunderstorm. ... Wind turbines The scientific definition of a machine is any device that transmits or modifies energy. ... Hydraulics is a branch of science and engineering concerned with the use of liquids to perform mechanical tasks. ... This article is about the general term. ...

[edit] Timeline of analog computers

• The Antikythera mechanism is the earliest known mechanical analog computer. 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.
• Al-Biruni invented the first mechanical geared calendar computer, circa 1000 AD.^[2]
• The slide rule is a hand-operated analog computer for doing multiplication and division, invented around 1620–1630, shortly after the publication of the concept of the logarithm.
• The differential analyser, a mechanical analog computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. Invented in 1876, they were first built in the 1920s and 1930s.
• World War II era gun directors and bomb sights used mechanical analog computers.
• General Precision Systems electronic analog computer c. 1950 was a very adaptable machine, that could be configured to solve a range of problems.
• The MONIAC Computer was a hydraulic model of a national economy built in the early 1950s
• Heathkit EC-1 An educational analog computer made by the Heath Company, USA c. 1960.

The Antikythera mechanism (main fragment). ... Antikythera (Αντικύθηρα) is a Greek island with a land mass of 20 square kilometers, 38 kilometers south-east of Kythira. ... (September 15, 973 in Kath, Khwarezm – December 13, 1048 in Ghazni) was a Persian[1][2][3] Muslim polymath[4] of the 11th century, whose experiments and discoveries were as significant and diverse as those of Leonardo da Vinci or Galileo, five hundred years before the Renaissance; al-Biruni was... Spur gears found on a piece of farm equipment A gear is a wheel with teeth around its circumference, the purpose of the teeth being to mesh with similar teeth on another mechanical device -- possibly another gear wheel -- so that force can be transmitted between the two devices in a... A page from the Hindu calendar 1871-72. ... A typical 10 inch student slide rule (Pickett N902-T simplex trig). ... The differential analyser was a mechanical analog computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. ... Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000... A bombsight is a device used by bomber aircraft to assist in the task of accurately dropping bombs on a ground target. ... Moniac Computer The MONIAC (Monetary National Income Automatic Computer) also known as the Phillips Hydraulic Computer and the Financephalograph, was created in 1949 by the New Zealander economist Bill Phillips to model the national economic processes of the United Kingdom, while Phillips was a student at the London School of... Heathkits were products of the Heath Company, Benton Harbor, Michigan. ...

[edit] Electronic analog computers

The similarity between linear mechanical components, such as springs and dashpots, and electrical components, such as capacitors, inductors, and resistors is striking in terms of mathematics: They can be modeled using equations that are of essentially the same form. Helical or coil springs designed for tension A spring is a flexible elastic object used to store mechanical energy. ... A dashpot is a mechanical device, a damper which resists motion via viscous friction. ... See Capacitor (component) for a discussion of specific types. ... An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ... Resistor symbols (non-European) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ...

However, the difference between these systems is what makes analog computing useful. If one considers a simple mass-spring system, constructing the physical system would require buying the springs and masses. This would be proceeded by attaching them to each other and an appropriate anchor, collecting test equipment with the appropriate input range, and finally, taking (somewhat difficult) measurements.

The electrical equivalent can be constructed with a few operational amplifiers (Op amps) and some passive linear components; all measurements can be taken directly with an oscilloscope. In the circuit, the (simulated) 'mass of the spring' can be changed by adjusting a potentiometer. The electrical system is an analogy to the physical system, hence the name, but it is less expensive to construct, safer, and easier to modify. Also, an electronic circuit can typically operate at higher frequencies than the system being simulated. This allows the simulation to run faster than real time, for quicker results. An operational amplifier or op-amp is an electronic circuit module (normally built as an integrated circuit, but occasionally with discrete transistors or vacuum tubes) which has a non-inverting input (+), an inverting input (-) and one output. ... Illustration showing the interior of a cathode-ray tube for use in an oscilloscope. ... The present popular usage of the term potentiometer (or pot for short) describes an electrical device which has a user-adjustable resistance. ...

The drawback of the mechanical-electrical analogy is that electronics are limited by the range over which the variables may vary. This is called dynamic range. They are also limited by noise levels. Dynamic range is a term used frequently in numerous fields to describe the ratio between the smallest and largest possible values of a changeable quantity. ... In science, and especially in physics and telecommunication, noise is fluctuations in and the addition of external factors to the stream of target information (signal) being received at a detector. ...

These electric circuits can also easily perform other simulations. For example, voltage can simulate water pressure and amperes can simulate water flow in terms of cubic metres per second. International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... Water pressure is the pressure in any system for supplying water, usually a domestic water system, although the term is used in other contexts as well, such as a municipal water system. ... Current can be measured by a galvanometer, via the deflection of a magnetic needle in the magnetic field created by the current. ... The cubic meter (symbol m³) is the SI derived unit of volume. ...

There is a lack of understanding about electrical systems that sometimes leads to the terms analog and digital having seemingly confusing and somewhat dubious meanings. Analog systems are sometimes understood only as continuous, time variant electrical systems. From the above discussion this is not correct, since discontinuous functions may also be modeled. In fact, digital also has a precise technical definition. In the context of circuits, it refers to the use of discrete electrical voltage levels as codes for symbols and the manipulation of these symbols in the operation of the digital computer. The electronic analog computer manipulates the physical quantities of (waveforms) of volts or amperes. Consequently, the precision of the analog computer readout (of rational numbers) is limited only by the quantization of the readout equipment used (generally three or four places). The digital computer precision must necessarily be finite, but the precision of its result is limited only by time. Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. ...

[edit] Analog digital hybrid computers

There is an intermediate device, a hybrid computer, in which a digital computer is combined with an analog computer. Hybrid computers are used to obtain a very accurate but imprecise 'seed' value, using an analog computer front-end, which is then fed into a digital computer iterative process to achieve the final desired degree of precision. With a three or four digit, highly accurate numerical seed, the total digital computation time necessary to reach the desired precision is dramatically reduced, since many fewer iterations are required. Or, for example, the analog computer might be used to solve a non-analytic differential equation problem for use at some stage of an overall computation (where precision is not very important). In any case, the hybrid computer is usually substantially faster than a digital computer, but can supply a far more precise computation than an analog computer. It is useful for real-time applications requiring such a combination (e.g., a high frequency phased-array radar or a weather system computation). Polish Hybrid computer WAT 1001 Hybrid computers are made by combining features of analog computers and digital computers. ... ... A Center for Correct, Usable, Reliable, Auditable, and Transparent Elections ACCURATE was established by a group of computer scientists, psychologists and policy experts to address problems with electronic voting. ... Iteration is the repetition of a process, typically within a computer program. ... In Wikipedia, precision has the following meanings: In engineering, science, industry and statistics, precision characterises the degree of mutual agreement among a series of individual measurements, values, or results - see accuracy and precision. ... Realtime redirects here. ... A giant phased-array radar in Alaska In telecommunication, a phased array is a group of antennas in which the relative phases of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern of the array is reinforced in a desired direction and...

Polish Analog computer ELWAT.

Image File history File links Download high resolution version (887x492, 81 KB) Please see the file description page for further information. ... Image File history File links Download high resolution version (887x492, 81 KB) Please see the file description page for further information. ...

[edit] Mechanisms

In analog computers, computations are often performed by using properties of electrical resistance, voltages and so on. For example, a simple two variable adder can be created by two current sources in parallel. The first value is set by adjusting the first current source (to say x milliamperes), and the second value is set by adjusting the second current source (say y milliamperes). Measuring the current across the two at their junction to signal ground will give the sum as a current through a resistance to signal ground, i.e., x+y milliamperes. (See Kirchhoff's current law) Other calculations are performed similarly, using operational amplifiers and specially designed circuits for other tasks. It has been suggested that this article or section be merged with Voltage source. ... Milli (symbol m) is an SI prefix in the SI system of units denoting a factor of 10-3, or 1/1,000. ... Current can be measured by a galvanometer, via the deflection of a magnetic needle in the magnetic field created by the current. ... Kirchhoffs circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. ... A 741 operational amplifier in a TO-5 metal can package An operational amplifier, usually referred to as an op-amp for brevity, is a DC-coupled high-gain electronic voltage amplifier with Differential Inputs and, usually, a single output. ...

The use of electrical properties in analog computers means that calculations are normally performed in real time (or faster), at a significant fraction of the speed of light, without the relatively large calculation delays of digital computers. This property allows certain useful calculations that are comparatively "difficult" for digital computers to perform— for example numerical integration. These computers can integrate— essentially calculating the integral of a (nondiscrete) voltage waveform, usually by means of a capacitor, which accumulates charge over time. It has been suggested that Real-time computing be merged into this article or section. ... See Capacitor (component) for a discussion of specific types. ...

Nonlinear functions and calculations can be constructed to a limited precision (three or four digits) by designing function generators— special circuits of various combinations of capacitance, inductance, resistance, in combination with diodes (e.g., Zener diodes) to provide the nonlinearity. Generally, a nonlinear function is simulated by a nonlinear waveform whose shape varies with voltage (or current). For example, as voltage increases, the total impedance may change as the diodes successively permit current to flow. To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... It has been suggested that this article or section be merged with signal generator. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... Zener diode schematic symbol A Zener diode is a type of diode that permits current to flow in the forward direction like a normal diode, but also in the reverse direction if the voltage is larger (not equal to, but larger) than the rated breakdown voltage known as Zener knee... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ...

Any physical process which 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 spaghetti as a model of sorting numbers; a board, a set of nails, and a rubber band as a model of finding the convex hull 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 A.K. Dewdney (see citation below). Cooked spaghetti in a bowl. ... Convex hull: elastic band analogy In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X. // For planar objects, i. ...

[edit] Components

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

Key hydraulic components might include pipes, valves or towers; mechanical components might include gears and levers; key electrical components might include:

• potentiometers
• operational amplifiers
• integrators
• fixed-function generators

The core mathematical operations used in an electric analog computer are: The present popular usage of the term potentiometer (or pot for short) describes an electrical device which has a user-adjustable resistance. ... A 741 operational amplifier in a TO-5 metal can package An operational amplifier, usually referred to as an op-amp for brevity, is a DC-coupled high-gain electronic voltage amplifier with Differential Inputs and, usually, a single output. ... An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in calculus. ... It has been suggested that this article or section be merged with signal generator. ...

• summation
• inversion
• exponentiation
• logarithm
• integration with respect to time
• differentiation with respect to time
• multiplication and division

Differentiation with respect to time is not frequently used. It corresponds in the frequency domain to a high-pass filter, which means that high-frequency noise is amplified. For evaluation of sums in closed form see evaluating sums. ... The additive inverse, or opposite, of a number n is the number which, when added to n, yields zero. ... Exponentiation is a mathematical operation, written an, involving two numbers, the base a and the exponent n. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... The integral of f(x) from a to b is the area above the x-axis and below the curve y = f(x), minus the area below the x-axis and above the curve, for x in the interval [a,b]. Integration is a core concept of advanced mathematics, specifically... For a non-technical overview of the subject, see Calculus. ... In mathematics, multiplication is an elementary arithmetic operation. ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ...

[edit] Limitations

In general, analog computers are limited by real, non-ideal effects. An analog signal 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 noise floor, non-linearities, temperature coefficient, and parasitic effects within semiconductor devices, and the finite charge of an electron. Incidentally, for commercially available electronic components, ranges of these aspects of input and output signals are always figures of merit. In signal theory, the noise floor is the measure of the signal created from the sum of all the noise sources and unwanted signals within a measurement system. ... Non-linearity is a slight distortion of a single frequency into multiple frequencies within the human or mammalian auditory system. ... The temperature coefficient is the relative change of a physical property when the temperature is changed by 1 K (kelvin). ... Microelectronics is a subfield of electronics. ... For other uses, see Electron (disambiguation). ... A Figure of merit is a quantity used to characterize the performance of a device relative to other devices of the same type. ...

Analog computers, however, have been replaced by digital computers for almost all uses. It may be stretching a point to regard some physical simulations such as wind tunnels as analog computers, because the data so obtained must then also be scaled, for example, for Reynolds number and Mach number. There is a point of view in physics based on information processing which attempts to map the physical processes to computations. Thus, from these points of view, the wind tunnel data gathering is either an experiment or a computation. NASA wind tunnel with the model of a plane A wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects. ... In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. ... An F/A-18 Hornet breaking the sound barrier. ... In general, information processing is the changing (processing) of information in any manner detectable by an observer. ... Process (lat. ... Look up computation in Wiktionary, the free dictionary. ... In the scientific method, an experiment (Latin: ex- periri, of (or from) trying) is a set of observations performed in the context of solving a particular problem or question, to support or falsify a hypothesis or research concerning phenomena. ... Look up computation in Wiktionary, the free dictionary. ...

[edit] Current research

While digital computation is extremely popular, research in analog computation is being done by a handful of people worldwide. In the United States, Jonathan Mills from Indiana University, Bloomington, Indiana has been working on research using Extended Analog Computers. At the Harvard Robotics Laboratory, analog computation is a research topic.

[edit] Practical examples

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

• Antikythera mechanism
• astrolabe
• differential analyzer
• Kerrison Predictor
• mechanical integrator
• MONIAC Computer (hydraulic model of UK economy)
• nomogram
• Norden bombsight
• operational amplifier
• planimeter
• Rangekeeper
• slide rule
• Torpedo Data Computer
• Tide predictors
• Torquetum
• Water integrator

Analog synthesizers can also be viewed as a form of analog computer, and their technology was originally based on electronic analog computer technology. The Antikythera mechanism (main fragment). ... A 16th century astrolabe. ... The differential analyser was a mechanical analog computer invented by Vannevar Bush in 1927. ... The Kerrison Predictor was one of the first fully-automated anti-aircraft predictors, fire control systems which would attempt to predict the correct aim at a plane based on simple inputs like the observed speed and angle to the target. ... Moniac Computer The MONIAC (Monetary National Income Automatic Computer) also known as the Phillips Hydraulic Computer and the Financephalograph, was created in 1949 by the New Zealander economist Bill Phillips to model the national economic processes of the United Kingdom, while Phillips was a student at the London School of... Smith chart which shows how the complex impedance of a transmission line varies along its length This article is about the graphical devices called nomograms. ... The Norden bombsight A page from the Bombardiers Information File (BIF) that describes the components and controls of the Norden Bombsight. ... A 741 operational amplifier in a TO-5 metal can package An operational amplifier, usually referred to as an op-amp for brevity, is a DC-coupled high-gain electronic voltage amplifier with Differential Inputs and, usually, a single output. ... A planimeter is a technical drawing instrument used to measure the surface area of an arbitrary two-dimensional shape. ... Figure 1: The Ford Mk 1A Ballistic Computer. ... A typical 10 inch student slide rule (Pickett N902-T simplex trig). ... The Torpedo Data Computer was an early electromechanical analog computer used for torpedo fire-control in American submarines during WWII. German U-boats used a similar torpedo fire control computer. ... The Torquetum or Turquet is a medieval astronomical instrument designed to take and convert measurements made in three sets of coordinates: Horizon, equatorial, and ecliptic. ... The Water Integrator was an early analog computer built in the Soviet Union in 1936. ... An analog synthesizer is a synthesizer that uses analog circuits and analog computer techniques to generate sound electronically. ...

[edit] Real computers

Computer theorists often refer to idealized analog computers as real computers (because they operate on the set of real numbers). Digital computers, by contrast, must first quantize the signal into a finite number of values, and so can only work with the rational number set (or, with an approximation of irrational numbers). In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. ... In mathematics, a rational number is a number which can be expressed as a ratio of two integers. ...

These idealized analog computers may in theory solve problems that are intractable on digital computers; however as mentioned, in reality, analog computers are far from attaining this ideal, largely because of noise minimization problems. Moreover, given unlimited time and memory, the (ideal) digital computer may also solve real number problems. Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ... This article is about the machine. ...

[edit] See also

Wikimedia Commons has media related to:

Category:Analog computer

• signal (information theory)
• signal (computing)
• set theory
• computability theory
• differential equation
• dynamical system
• chaos theory
• slide rule
• analogue models
• Antikythera mechanism

Other types of computers: Image File history File links Commons-logo. ... In information theory, a signal is the sequence of states of a communications channel that encodes a message. ... A signal is a limited form of inter-process communication used in Unix, Unix-like, and other POSIX-compliant operating systems. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In computer science, computability theory is the branch of the theory of computation that studies which problems are computationally solvable using different models of computation. ... A simulation of airflow into a duct using the Navier-Stokes equations A differential equation is a mathematical equation for an unknown function of one or several variables which relates the values of the function itself and of its derivatives of various orders. ... The Lorenz attractor is an example of a non-linear dynamical system. ... A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under specific conditions exhibit dynamics that are sensitive to initial conditions (popularly referred to as the butterfly effect). ... A typical 10 inch student slide rule (Pickett N902-T simplex trig). ... The Antikythera mechanism (main fragment). ...

• DNA computer
• Molecular computer
• Quantum computer
• Wetware computer
• Digital computer

People associated with analog computer development: DNA computing is a form of computing which uses DNA and molecular biology, instead of the traditional silicon-based computer technologies. ... Molecular computers are massively parallel computers taking advantage of the compuational power of molecules. ... The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers. ... An organic computer based on living neurons and ganglions. ... ...

• George A. Philbrick

George A. Philbrick was responsible, through his company George A. Philbrick Researches, for the commercialization and wide adoption of operational amplifiers, a now-ubiquitous component of analog electronic systems, and the invention and commercialization of electronic analog computers based on the operational amplifier principle. ...

[edit] Notes

[edit] References

• A.K. Dewdney. "On the Spaghetti Computer and Other Analog Gadgets for Problem Solving", Scientific American, 250(6):19-26, June 1984. Reprinted in The Armchair Universe, by A.K. Dewdney, published by W.H. Freeman & Company (1988), ISBN 0-7167-1939-8.

• Universiteit van Amsterdam Computer Museum. (2007). Analog Computers.

[edit] External links

• Introduction to Analog-/Hybrid-Computing (PDF file)
• Example programs for Analog Computers (PDF file)
• A great disappearing act: the electronic analogue computer Chris Bissell, The Open University, Milton Keynes, UK Accessed February 2007
• Lots of documentation about analog computers as well as detailed descriptions of some historic machines
• German computer museum with still runnable analog computers
• Analog computer basics
• Lecture 20: Analog vs Digital (in a series of lectures on "History of computing and information technology")
• Analog computer trumps Turing model
• Jonathan W. Mills's Analog Notebook
• Indiana University Extended Analog Computer
• Harvard Robotics Laboratory Analog Computation
• Large collection of analog and digital computers