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The ball-and-disk integrator is a key component of many advanced mechanical computers. Through simple mechanical means, it performs continual integration of the value of an input. Typical uses were the measurement of area or volume of material in industrial settings, range-keeping systems on ships, and tachometric bombsights. The addition of the torque amplifier by Vannevar Bush led to the differential analysers of the 1930s and 1940s.
The basic mechanism consists of two inputs and one output. The first input is a spinning disk, generally electrically driven, and using some sort of governor to ensure that it turns at a fixed rate. The second input is a movable carriage that holds a bearing against the input disk, along its radius. The bearing transfers motion from the disk to an output shaft. The axis of the output shaft is oriented parallel to the rails of the carriage. As the carriage slides, the bearing remains in contact with both the disk & the output, allowing one to drive the other.
The spin rate of the output shaft is governed by the displacement of the carriage; this is the "integration." When the bearing is positioned at the center of the disk, no net motion is imparted; the output shaft remains stationary. As the carriage moves the bearing away from the center and towards the edge of the disk, the bearing, and thus the output shaft, begins to rotate faster and faster. Effectively, this is a system of two gears with an infinitely variable gear ratio; when the bearing is nearer to the center of the disk, the ratio is low (or zero), and when the bearing is nearer to the edge, it is high. [1]
The output shaft can rotate either "forward" or "backward," depending on the direction of the bearing's displacement; this is a useful property for an integrator.
Consider an example system that measures the total amount of water flowing through a sluice: A float is attached to the input carriage so the bearing moves up and down with the level of the water. As the water level rises, the bearing is pushed farther from the center of the input disk, increasing the output's rotation rate. By counting the total number of turns of the output shaft (for example, with an odometer-type device), and multiplying by the cross-sectional area of the sluice, the total amount of water flowing past the meter can be determined.
The basic concept of the ball-and-disk integrator was first described by James Thomson, brother of William Thomson, 1st Baron Kelvin. William used the concept to build the Harmonic Analyser in 1886. This system was used to calculate the coefficients of a Fourier series representing inputs dialled in as the positions of the balls. The inputs were set to measured tide heights from any port being studied. The output was then fed into a similar machine, the Harmonic Synthesiser, which spun several wheels to represent the phase of the contribution from the sun and moon. A wire running along the top of the wheels took the maximum value, which represented the tide in the port at a given time. [2] Thomson mentioned the possibility of using the same system as a way to solve differential equations, but realized that the output torque from the integrator was too low to drive the required downstream systems of pointers. [2]
A number of similar systems followed, notably those of Leonardo Torres Quevedo, a Spanish physicist who built several machines for solving real and complex roots of polynomials; [3] and Michelson and Stratton, whose Harmonic Analyser performed Fourier analysis, but using an array of 80 springs rather than Kelvin integrators. This work led to the mathematical understanding of the Gibbs phenomenon of overshoot in Fourier representation near discontinuities. [2]
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By the turn of the 20th century, naval ships were starting to mount guns with over-the-horizon range. At these sorts of distances, spotters in the towers could not accurately estimate range by eye, leading to the introduction of ever more complex range finding systems. Additionally, the gunners could no longer directly spot the fall of their own shot, relying on the spotters to do this and relay this information to them. At the same time the speed of the ships was increasing, consistently breaking the 20 knot barrier en masse around the time of the introduction of the Dreadnought in 1906. Centralized fire control followed in order to manage the information flow and calculations, but calculating the firing proved to be very complex and error prone.
The solution was the Dreyer table , which used a large ball-and-disk integrator as a way to compare the motion of the target relative to the ship, and thereby calculate its range and speed. Output was to a roll of paper. The first systems were introduced around 1912 and installed in 1914. Over time, the Dreyer system added more and more calculators, solving for the effects of wind, corrections between apparent and real wind speed and direction based on the ships motion, and similar calculations. By the time the Mark V systems were installed on later ships after 1918, the system might have as many as 50 people operating it in concert.
Similar devices soon appeared in other navies and for other roles. The US Navy used a somewhat simpler device known as the Rangekeeper, but this also saw continual modification over time and eventually turned into a system of equal or greater sophistication to the UK versions. A similar calculator formed the basis of the Torpedo Data Computer, which solved the more demanding problem of the very long engagement times of torpedo fire.
A well-known example is the Norden bombsight which used a slight variation on the basic design, replacing the ball with another disk. In this system the integrator was used to calculate the relative motion of objects on the ground given the altitude, airspeed, and heading. By comparing the calculated output with the actual motion of objects on the ground, any difference would be due to the effects of wind on the aircraft. Dials setting these values were used to zero out any visible drift, which resulted in accurate wind measurements, formerly a very difficult problem.
Ball disk integrators were used in the analog guidance computers of ballistic missile weapon systems as late as the mid 1970s. The Pershing 1 missile system utilized the Bendix ST-120 inertial guidance platform, combined with a mechanical analog computer, to achieve accurate guidance. The ST-120 provided accelerometer information for all three axes. The accelerometer for forward movement transmitted its position to the ball position radial arm, causing the ball fixture to move away from the disk center as acceleration increased. The disk itself represents time and rotates at a constant rate. As the ball fixture moves further out from the center of the disk, the ball spins faster. The ball speed represents the missile speed, the number of ball rotations represent distance traveled. These mechanical positions were used to determine staging events, thrust termination, and warhead separation, as well as "good guidance" signals used to complete the arming chain for the warhead. The first known use of this general concept was in the V-2 missile developed by the Von Braun group at Peenemünde. See PIGA accelerometer. It was later refined at Redstone Arsenal and applied to the Redstone rocket and subsequently Pershing 1.
An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude.
A cam is a rotating or sliding piece in a mechanical linkage used especially in transforming rotary motion into linear motion. It is often a part of a rotating wheel or shaft that strikes a lever at one or more points on its circular path. The cam can be a simple tooth, as is used to deliver pulses of power to a steam hammer, for example, or an eccentric disc or other shape that produces a smooth reciprocating motion in the follower, which is a lever making contact with the cam. A cam timer is similar, and were widely used for electric machine control before the advent of inexpensive electronics, microcontrollers, integrated circuits, programmable logic controllers and digital control.
An accelerometer is a tool that measures proper acceleration. Proper acceleration is the acceleration of a body in its own instantaneous rest frame; this is different from coordinate acceleration, which is acceleration in a fixed coordinate system. For example, an accelerometer at rest on the surface of the Earth will measure an acceleration due to Earth's gravity, straight upwards of g ≈ 9.81 m/s2. By contrast, accelerometers in free fall will measure zero.
An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output.
A fire-control system (FCS) is a number of components working together, usually a gun data computer, a director and radar, which is designed to assist a ranged weapon system to target, track, and hit a target. It performs the same task as a human gunner firing a weapon, but attempts to do so faster and more accurately.
A cycloidal drive or cycloidal speed reducer is a mechanism for reducing the speed of an input shaft by a certain ratio. Cycloidal speed reducers are capable of relatively high ratios in compact sizes with very low backlash.
A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical raceway for ball bearings which act as a precision screw. As well as being able to apply or withstand high thrust loads, they can do so with minimum internal friction. They are made to close tolerances and are therefore suitable for use in situations in which high precision is necessary. The ball assembly acts as the nut while the threaded shaft is the screw.
A friction drive or friction engine is a type of transmission that utilises two wheels in the transmission to transfer power from the engine to the driving wheels. The system is naturally a continuously variable transmission; by moving the two disks' positions, the output ratio changes continually. Although once used in early automobiles, today the system is most commonly used on scooters, mainly go-peds, in place of a chain and gear system. It is mechanically identical to a ball-and-disk integrator, but intended to handle higher torque levels.
Rangekeepers were electromechanical fire control computers used primarily during the early part of the 20th century. They were sophisticated analog computers whose development reached its zenith following World War II, specifically the Computer Mk 47 in the Mk 68 Gun Fire Control system. During World War II, rangekeepers directed gunfire on land, sea, and in the air. While rangekeepers were widely deployed, the most sophisticated rangekeepers were mounted on warships to direct the fire of long-range guns.
The Mark 1, and later the Mark 1A, Fire Control Computer was a component of the Mark 37 Gun Fire Control System deployed by the United States Navy during World War II and up to 1991 and possibly later. It was originally developed by Hannibal C. Ford of the Ford Instrument Company. and William Newell. It was used on a variety of ships, ranging from destroyers to battleships. The Mark 37 system used tachymetric target motion prediction to compute a fire control solution. It contained a target simulator which was updated by further target tracking until it matched.
The Stabilised Automatic Bomb Sight (SABS) was a Royal Air Force bombsight used in small numbers during World War II. The system worked along similar tachometric principles as the more famous Norden bombsight, but was somewhat simpler, lacking the Norden's autopilot feature.
The D-37C (D37C) is the computer component of the all-inertial NS-17 Missile Guidance Set (MGS) for accurately navigating to its target thousands of miles away. The NS-17 MGS was used in the Minuteman II (LGM-30F) ICBM. The MGS, originally designed and produced by the Autonetics Division of North American Aviation, could store multiple preprogrammed targets in its internal memory.
A mechanical computer is a computer built from mechanical components such as levers and gears rather than electronic components. The most common examples are adding machines and mechanical counters, which use the turning of gears to increment output displays. More complex examples could carry out multiplication and division—Friden used a moving head which paused at each column—and even differential analysis. One model, the Ascota 170 accounting machine sold in the 1960s calculated square roots.
A PIGA is a type of accelerometer that can measure acceleration and simultaneously integrates this acceleration against time to produce a speed measure as well. The PIGA's main use is in Inertial Navigation Systems (INS) for guidance of aircraft and most particularly for ballistic missile guidance. It is valued for its extremely high sensitivity and accuracy in conjunction with operation over a wide acceleration range. The PIGA is still considered the premier instrument for strategic grade missile guidance, though systems based on MEMS technology are attractive for lower performance requirements.
Ship gun fire-control systems (GFCS) are analogue fire-control systems that were used aboard naval warships prior to modern electronic computerized systems, to control targeting of guns against surface ships, aircraft, and shore targets, with either optical or radar sighting. Most US ships that are destroyers or larger employed gun fire-control systems for 5-inch (127 mm) and larger guns, up to battleships, such as Iowa class.
An inertial navigation system (INS) is a navigation device that uses motion sensors (accelerometers), rotation sensors (gyroscopes) and a computer to continuously calculate by dead reckoning the position, the orientation, and the velocity of a moving object without the need for external references. Often the inertial sensors are supplemented by a barometric altimeter and sometimes by magnetic sensors (magnetometers) and/or speed measuring devices. INSs are used on mobile robots and on vehicles such as ships, aircraft, submarines, guided missiles, and spacecraft. Other terms used to refer to inertial navigation systems or closely related devices include inertial guidance system, inertial instrument, inertial measurement unit (IMU) and many other variations. Older INS systems generally used an inertial platform as their mounting point to the vehicle and the terms are sometimes considered synonymous.
Strain wave gearing is a type of mechanical gear system that uses a flexible spline with external teeth, which is deformed by a rotating elliptical plug to engage with the internal gear teeth of an outer spline.
An inertial measurement unit (IMU) is an electronic device that measures and reports a body's specific force, angular rate, and sometimes the orientation of the body, using a combination of accelerometers, gyroscopes, and sometimes magnetometers. When the magnetometer is included, IMUs are referred to as IMMUs. IMUs are typically used to maneuver modern vehicles including motorcycles, missiles, aircraft, including unmanned aerial vehicles (UAVs), among many others, and spacecraft, including satellites and landers. Recent developments allow for the production of IMU-enabled GPS devices. An IMU allows a GPS receiver to work when GPS-signals are unavailable, such as in tunnels, inside buildings, or when electronic interference is present.
The Course Setting Bomb Sight (CSBS) is the canonical vector bombsight, the first practical system for properly accounting for the effects of wind when dropping bombs. It is also widely referred to as the Wimperis sight after its inventor, Harry Wimperis.
A torque amplifier is a mechanical device that amplifies the torque of a rotating shaft without affecting its rotational speed. It is mechanically related to the capstan seen on ships. Its most widely known use is in power steering on automobiles. Another use is on the differential analyser, where it was used to increase the output torque of the otherwise limited ball-and-disk integrator. The term is also applied to some gearboxes used on tractors, although this is unrelated. It differs from a torque converter, in which the rotational speed of the output shaft decreases as the torque increases.