A page from the Bombardier's Information File (BIF) that describes the components and controls of the Norden bombsight. The Norden bombsight was a Bombsight used by the United States Army Air Forces during World War II, and the United States Air Force in the 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. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including The Korean War refers to a period of military conflict between North Korean and South Korean regimes with major hostilities lasting from June 25 1950 until the The Vietnam War, also known as the Second Indochina War, or the Vietnam Conflict, occurred in Vietnam, Laos and Cambodia A bomber is a Military aircraft designed to attack ground and sea targets primarily by dropping Bombs on them A bomb is any of a range of devices that typically rely on the Exothermic Chemical reaction of an Explosive material to produce an extremely

An analog computer (spelled analogue in British English) is a form of computer that uses continuous physical phenomena such as electrical^[1], mechanical, or hydraulic quantities to model the problem being solved. A computer is a Machine that manipulates data according to a list of instructions.

Timeline of analog computers

• The Antikythera mechanism is believed to be the earliest known mechanical analog computer. The Antikythera mechanism (ˌæntɪkɪˈθɪərə an-ti-ki- theer -uh is an ancient mechanical Calculator (also described as the first known " mechanical ^[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. Antikythera (Αντικύθηρα (ˌæntɪkɪˈθɪərə an-ti-ki-theer-uh ˌɑndiˈkiθirɑˌɑndiˈkiθirɑ ahn-dee-kee-thee-rah is a Greek Island Devices of the level of complexity as the Antikythera mechanism would not reappear until a thousand years later.

• The astrolabe was invented in the Hellenistic world in either the first or second centuries BCE and is often attributed to Hipparchus. The astrolabe is a historical Astronomical instrument used by classical astronomers, Navigators This article focuses on the cultural aspects of the Hellenistic age for the historical aspects see Hellenistic period. Hipparchus ( Greek; ca 190 BC &ndash ca 120 BC was a Greek Astronomer, Geographer, and Mathematician of the Hellenistic 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. A dioptra is a classical astronomical and surveying instrument dating from the 3rd century BCE. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study

• Muslim astronomers later produced many different types of astrolabes and used them for over a thousand different problems related to astronomy, astrology, horoscopes, navigation, surveying, timekeeping, Qibla (direction of Mecca), Salah (prayer), etc. The astrolabe is a historical Astronomical instrument used by classical astronomers, Navigators This is a sub-article of History of science in the Islamic World and Astrology. The mariner's astrolabe, also called sea astrolabe, is not an Astrolabe proper but rather a graduated circle with an Alidade used to measure Surveying is the technique and science of accurately determining the terrestrial or three-dimensional space Position of points and the distances and angles between For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Qiblah ( ar قبلة, also transliterated as Kiblah) is an Arabic word for the direction that should be faced when a Muslim prays during Mecca ˈmɛkə also spelled Makkah ˈmækə (in full Makkah Al-Mukarramah (Arabic mækːæ(t ælmʊkarˑamæ مكّة المكرمة, literally Honored Ṣalāt ( Arabic: صلاة‎, pl ṣalawāt, Qur'anic Arabic: صلوة ṣalawah) (also munz in Pashto and ^[3]

• Abū Rayhān al-Bīrūnī invented the first mechanical geared lunisolar calendar astrolabe,^[4] an early fixed-wired knowledge processing machine^[5] with a gear train and gear-wheels,^[6] circa 1000 AD. This is the page for mechanical Gears For other uses see Gear (disambiguation For the gear-like device used to drive a roller chain see Sprocket A lunisolar calendar is a Calendar in many Cultures whose date indicates both the Moon phase and the time of the solar Year. A wire is a single usually cylindrical, elongated string of drawn Metal. A machine is any device that uses Energy to perform some activity A gear train is a set or system of Gears arranged to transfer rotational Torque from one part of a mechanical system to another This is the page for mechanical Gears For other uses see Gear (disambiguation For the gear-like device used to drive a roller chain see Sprocket

• The Planisphere was a star chart astrolabe also invented by Abū Rayhān al-Bīrūnī in the early 11th century. A star chart is a map of the Night sky. Astronomers divide these into grids to easily use them ^[7][8]

• The Equatorium was an astrometic calculating instrument invented by Abū Ishāq Ibrāhīm al-Zarqālī (Arzachel) in Islamic Spain circa 1015. An equitorium (plural equitoria) was an astronomical calculating instrument. Astrometry is the branch of Astronomy that relates to precise measurements and explanations of the positions and movements of Stars and other celestial bodies Al-Andalus (الأندلس was the Arabic name given to those parts of the Iberian Peninsula governed by Muslims or

• An astrolabe incorporating a mechanical calendar computer and gear-wheels was invented by Abi Bakr of Isfahan in 1235. The astrolabe is a historical Astronomical instrument used by classical astronomers, Navigators The word Calendar consist of two words 1 Cal ( in Pashto means Year in Hindi and Persian is Sal- also means Year This is the page for mechanical Gears For other uses see Gear (disambiguation For the gear-like device used to drive a roller chain see Sprocket Esfahān or Isfahan (historically also rendered as Ispahan or Hispahan, Old Persian: Aspadana, Middle Persian: Spahān ^[9]

A slide rule

• 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 slide rule, also known as a slipstick, is a mechanical Analog computer.

• The differential analyser, a mechanical analog computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. The differential analyser was a mechanical Analog computer designed to solve Differential equations by integration, using wheel-and-disc mechanisms to perform Invented in 1876 by James Thomson (engineer), they were first built in the 1920s and 1930s. James Thomson ( February 16, 1822 - May 8, 1892) was an Irish Engineer and Physicist whose reputation would have

• By 1912 Arthur Pollen had developed an electrically driven mechanical analog computer for fire-control system, based on the differential analyser. Arthur Joseph Hungerford Pollen ( 13 September, 1866 &ndash 28 January, 1937) was a writer on naval affairs in the early 1900s who recognised Note the term " fire control " may also refer to means of stopping a fire such as sprinkler systems A fire-control system The differential analyser was a mechanical Analog computer designed to solve Differential equations by integration, using wheel-and-disc mechanisms to perform It was used by the Imperial Russian Navy in World War I. The Imperial Russian Navy refers to the Tsarist Fleets prior to the Bolshevik Revolution. World War I (abbreviated WWI; also known as the First World War, the Great War, and the War to End All

• World War II era gun directors and bomb sights used mechanical analog computers. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including A bombsight is a device used by Bomber aircraft to assist in the task of accurately dropping Bombs on a ground target

• 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. ^[10][11]

• 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. Heathkits were products of the Heath Company Benton Harbor Michigan. 1960.

Electronic analog computers

Polish analog computer AKAT-1

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. 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. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors An inductor is a passive electrical component designed to provide Inductance in a circuit |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| | They can be modeled using equations that are of essentially the same form.

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. An operational amplifier, often called an op-amp, is a DC - coupled high- Gain electronic voltage amplifier with differential An oscilloscope (commonly abbreviated to scope or O-scope) is a type of Electronic test equipment that allows signal Voltages to be viewed In the circuit, the (simulated) 'mass of the spring' can be changed by adjusting a potentiometer. A potentiometer is a three-terminal Resistor with a sliding contact that forms an adjustable Voltage divider. 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.

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. 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 such as in Sound They are also limited by noise levels. In Science, and especially in Physics and Telecommunication, noise is fluctuations in and the addition of external factors to the stream of target

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. Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical Fluid pressure is the Pressure at some point within a Fluid, such as water or air The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second CM3 redirects here If you were looking for the 3rd game in the Cooking Mama series abbreviated as CM3 see here.

A digital system uses discrete electrical voltage levels as codes for symbols. The manipulation of these symbols is the method of operation of the digital computer. The electronic analog computer manipulates the physical quantities of waveforms, (voltage or current). The precision of the analog computer readout is limited chiefly by the precision of the readout equipment used, generally three or four significant figures. The digital computer precision must necessarily be finite, but the precision of its result is limited only by time. A digital computer can calculate many digits in parallel, or obtain the same number of digits by carrying out computations in time sequence.

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 computers that comprise features of Analog computers and Digital Computers The digital component normally serves as the controller and A computer is a Machine that manipulates data according to a list of instructions. Hybrid computers are used to obtain a very accurate but not exact '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. Iteration means the act of repeating Mathematics Iteration in mathematics may refer to the process of iterating a function, or to the techniques used 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. In Computer science, real-time computing (RTC is the study of hardware and software systems that are subject to a "real-time constraint"—i g. , a high frequency phased-array radar or a weather system computation). This article is about general theory and electromagnetic phased array

Polish Analog computer ELWAT.

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. A current source is an electrical or electronic device that delivers or absorbs electric current 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). "Milli" redirects here for the village in Azerbaijan see Birinci Milli; for similar-sounding words see Millie. The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second 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. For other laws named after Gustav Kirchhoff, see Kirchhoff's laws. An operational amplifier, often called an op-amp, is a DC - coupled high- Gain electronic voltage amplifier with differential

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. Analog computers can integrate a voltage waveform, usually by means of a capacitor, which accumulates charge over time. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors

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. This article describes the use of the term nonlinearity in mathematics A function generator is a piece of Electronic test equipment or Software used to generate electrical Waveforms These waveforms can be either repetitive Capacitance is a measure of the amount of Electric charge stored (or separated for a given Electric potential. In Electrical circuits, any Electric current i produces a Magnetic field and hence generates a total Magnetic flux \Phi acting Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is g. , Zener diodes) to provide the nonlinearity. A Zener diode is a type of Diode that permits current in the forward direction like a normal diode but also in the reverse direction if the voltage is larger 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. Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal Alternating current (AC

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. Spaghetti is a long thin cylindrical Pasta of Italian origin A variety of pasta dishes are based on it from spaghetti with cheese and pepper or garlic and In Mathematics, the convex hull or convex envelope for a set of points X in a Real Vector space V is the minimal Convex These are all described in A. K. Dewdney (see citation below).

Components

A 1960 Newmark analogue computer, made up of five units. This computer was used to solve differential equations and is currently housed at the Cambridge Museum of Technology. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the

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:

• 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. A potentiometer is a three-terminal Resistor with a sliding contact that forms an adjustable Voltage divider. An operational amplifier, often called an op-amp, is a DC - coupled high- Gain electronic voltage amplifier with differential An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in Calculus. A function generator is a piece of Electronic test equipment or Software used to generate electrical Waveforms These waveforms can be either repetitive In mathematics the additive inverse, or opposite, of a Number n is the number that when added to n, yields zero. In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change In Mathematics, especially in elementary Arithmetic, division is an arithmetic operation which is the inverse of Multiplication. It corresponds in the frequency domain to a high-pass filter, which means that high-frequency noise is amplified.

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. 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 This article describes the use of the term nonlinearity in mathematics The temperature coefficient is the relative change of a physical property when the Temperature is changed by 1  K. Microelectronics is a subfield of Electronics. Microelectronics as the name suggestsis related to the study and manufacture or Microfabrication, of electronic The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J Incidentally, for commercially available electronic components, ranges of these aspects of input and output signals are always figures of merit. 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. 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 and Heat transfer, the Reynolds number \mathrm{Re} is a Dimensionless number that gives a measure of the Ratio Mach number (\mathrm{Ma} or M (generally ˈmɑːk sometimes /ˈmɑːx/ or /ˈmæk/ is the speed of an object moving through air or any Fluid There is a point of view in physics based on information processing which attempts to map the physical processes to computations. Information processing is the change (processing of Information in any manner detectable by an observer. Computation is a general term for any type of Information processing. Thus, from these points of view, the wind tunnel data gathering is either an experiment or a computation. In scientific inquiry an experiment ( Latin: Ex- periri, "to try out" is a method of investigating particular types of research questions or Computation is a general term for any type of Information processing.

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.

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
• thermostat
• Tide predictors
• Torpedo Data Computer
• 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 (ˌæntɪkɪˈθɪərə an-ti-ki- theer -uh is an ancient mechanical Calculator (also described as the first known " mechanical The astrolabe is a historical Astronomical instrument used by classical astronomers, Navigators The differential analyser was a mechanical Analog computer designed to solve Differential equations by integration, using wheel-and-disc mechanisms to perform The Kerrison Predictor was one of the first fully-automated Anti-aircraft predictors, Fire-control systems which would attempt to Predict the This article is about the graphical devices called nomograms For a description of the Japanese puzzle see Nonogram. The Norden bombsight was a Bombsight used by the United States Army Air Forces during World War II, and the United States Air Force in the An operational amplifier, often called an op-amp, is a DC - coupled high- Gain electronic voltage amplifier with differential A planimeter is a Measuring instrument used to measure the area of an arbitrary two-dimensional shape Rangekeepers were electromechanical fire control computers used primarily during the early part of the 20th century The slide rule, also known as a slipstick, is a mechanical Analog computer. A thermostat is a device for regulating the Temperature of a System so that the system's temperature is maintained near a desired setpoint The Torpedo Data Computer (TDC was an early Electromechanical Analog computer used for Torpedo fire-control on American The torquetum or turquet is a medieval astronomical instrument designed to take and convert measurements made in three sets of coordinates Horizon equatorial and 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

Real computers

Computer theorists often refer to idealized analog computers as real computers (because they operate on the set of real numbers). In Computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision Real numbers They are given this name because In Mathematics, the real numbers may be described informally in several different ways 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 Mathematics, a rational number is a number which can be expressed as a Ratio of two Integers Non-integer rational numbers (commonly called fractions

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. Computational complexity theory, as a branch of the Theory of computation in Computer science, investigates the problems related to the amounts of resources A computer is a Machine that manipulates data according to a list of instructions. Moreover, given unlimited time and memory, the (ideal) digital computer may also solve real number problems.

See also

• Signal (electrical engineering)
• Signal (computing)
• Differential equation
• Dynamical system
• Chaos theory
• Slide rule
• Analogical models
• Antikythera mechanism

Other types of computers:

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

People associated with analog computer development:

• George A. Philbrick

Notes

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.

External links

• Introduction to Analog-/Hybrid-Computing (PDF file)
• Example programs for Analog Computers (PDF file)
• Large collection of old analog and digital computers at Old Computer Museum
• 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