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Proportional navigation
Proportional navigation is a guidance law used in some form or another by most homing air target missiles. It is based on the fact that two vehicles are on a collision course when their direct Line-of-Sight does not change direction. PN dictates that the missile velocity vector should rotate at a rate proportional to the rotation rate of the line of sight and in the same direction.
An = N' * L' * V
Where An is the acceleration perpendicular to missile velocity vector, N’ is the proportionality constant (dimensionless), L’ is the line of sight rate, and V is the velocity.
For example, if the line of sight rotates slowly from north to east, the missile should turn to the right by a certain factor faster than the LOS-rate. This factor is called the Navigation Constant K_nav.
via Proportional navigation – Wikipedia, the free encyclopedia.
CORDIC
CORDIC (digit-by-digit method, Volder’s algorithm) (for COordinate Rotation DIgital Computer) is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. It is commonly used when no hardware multiplier is available (e.g., simple microcontrollers and FPGAs) as the only operations it requires are addition, subtraction, bitshift and table lookup.
The modern CORDIC algorithm was first described in 1959 by Jack E. Volder. It was developed at the aeroelectronics department of Convair to replace the analog resolver in the B-58 bomber’s navigation computer, although it is similar to techniques published by Henry Briggs as early as 1624. John Stephen Walther at Hewlett-Packard further generalized the algorithm, allowing it to calculate hyperbolic and exponential functions, logarithms, multiplications, divisions, and square roots.
Originally, CORDIC was implemented using the binary numeral system. In the 1970s, decimal CORDIC became widely used in pocket calculators, most of which operate in binary-coded-decimal BCD rather than binary. CORDIC is particularly well-suited for handheld calculators, an application for which cost (eg, chip gate count has to be minimised) is much more important than is speed. Also the CORDIC subroutines for trigonometric and hyperbolic functions can share most of their code.
CORDIC is generally faster than other approaches when a hardware multiplier is unavailable (e.g., in a microcontroller based system), or when the number of gates required to implement the functions it supports should be minimized (e.g., in an FPGA). On the other hand, when a hardware multiplier is available (e.g., in a DSP microprocessor), table-lookup methods and power series are generally faster than CORDIC. These days, CORDIC algorithm is used extensively for various biomedical applications, especially in the FPGA domain.
SoftFloat: A software implementation of the IEEE 754 Floating Point Specification
This program is often used to provide verification sequences when designing floating point unit (FPU) hardware IP blocks:
SoftFloat is a free, high-quality software implementation of the IEC/IEEE Standard for Binary Floating-point Arithmetic. (IEC is the International Electrotechnical Commission, an international standards body.) SoftFloat is completely faithful to the IEEE Standard, while at the same time being relatively fast. All functions dictated by the standard are supported except for conversions to and from decimal. SoftFloat fully implements the four most common floating-point formats: single precision (32 bits), double precision (64 bits), extended double precision (80 bits), and quadruple precision (128 bits). All required rounding modes, exception flags, and special values are supported.
Preferred Number
In industrial design, product developers must choose numerous lengths, distances, diameters, volumes, and other characteristic quantities. While all of these choices are constrained by considerations of functionality, usability, compatibility, safety or cost, there usually remains considerable leeway in the exact choice for many dimensions. Preferred numbers (also called preferred values) are standard guidelines for choosing exact product dimensions within such constraints.
They serve two purposes:
1. Using preferred numbers increases the probability that other designers will make exactly the same choice. This is particularly useful where the chosen dimension affects compatibility. For example, if the inner diameters of cooking pots or the distances between screws in wall fixtures are chosen from a series of preferred numbers, then it will be more likely that old pot lids and wall-plug holes can be reused when the original product is replaced.
2. Preferred numbers are chosen such that when a product is manufactured in many different sizes, these will end up roughly equally spaced on a logarithmic scale. They therefore help to minimize the number of different sizes that need to be manufactured or kept on stock.
Barn (unit of measure)
A barn (symbol b) is a unit of area. While the barn is not an SI unit, it is accepted (although discouraged) for use with the SI. Originally used in nuclear physics for expressing the cross sectional area of nuclei and nuclear reactions, today it is used in all fields of high energy physics to express the cross sections of any scattering process. A barn is approximately equal to the cross sectional area of a uranium nucleus. The symbol b is also used by the IEEE to represent the bit.
The etymology is clearly whimsical—the unit is said to be “as big as a barn” compared to the typical cross sections for nuclear reactions. During wartime research on the atomic bomb, American physicists who were bouncing neutrons off uranium nuclei described the uranium nucleus as “big as a barn.” Physicists working on the project adopted the name barn for a unit equal to 10-24 square centimetres, about the size of a uranium nucleus. Initially they hoped the American slang name would obscure any reference to the study of nuclear structure; eventually, the word became a standard unit in particle physics.
Mendenhall Order
The Mendenhall Order marked a decision to change the fundamental standards of length and mass of the United States from the customary standards based on those of England to metric standards. It was issued on April 5, 1893 by Thomas Corwin Mendenhall, superintendent of the U.S. Coast and Geodetic Survey, with the approval of the United States Secretary of the Treasury, John Griffin Carlisle. The order was issued as the Survey’s Bulletin No. 26 – Fundamental Standards of Length and Mass.
In 1866 the Congress passed a law which allowed, but did not require, the use of the metric system. Included in the law was a table of conversion factors between the traditional and metric units. The U.S. Coast and Geodetic Survey Office of Weights and Measures had on hand a number of metric standards, and selected the iron “Committee Meter” and the platinum “Arago Kilogram” to be the national standards for metric measurement; the standard yard and pound previously mentioned continued to be the standards for customary measurements.
A series of conferences in France between 1870 and 1875 lead to the signing of the “Metric Convention” in 1875, and to the permanent establishment of the International Bureau of Weights and Measures, abbreviated BIPM after the French name. The BIPM made meter and kilogram standards for all the countries that signed the treaty; the two meters and two kilograms allocated to the United States arrived in 1890, and were adopted as national standards.
The imperial standard yard of 1855 was found to be unstable and shortening by measurable amounts. Also, the mint pound was found to be “likewise unfit for use.” For several years before the Mendenhall order was actually issued, the Office of Weights and Measures was “practically forced” to use the metric standards because of their superior stability, and because they were better designed for carrying out precision comparisons. The Office found that the conversion tables in the 1866 law were satisfactory and used them to derive customary length and mass from the metric standards. The conversions were 1 yard = 3600/3937 meter and 1 pound = 0.4535924277 kilogram. The Mendenhall order amounted to a formal announcement of a change that had already occurred.
Avoirdupois
The avoirdupois system is a system of weights (or, properly, mass) based on a pound of sixteen ounces. It is the everyday system of weight used in the United States. It is still widely used by many people in Canada and the United Kingdom despite the official adoption of the metric system, including the compulsory introduction of metric units in shops. It is considered more modern than the alternative troy or apothecary or the medieval English mercantile and Tower systems.
The word avoirdupois is from French and Middle English (Anglo-French) avoir de pois, “goods of weight” or “goods sold by weight”, and from Old French aveir de peis, literally “goods of weight”, from aveir, “property, goods” (from aveir, “to have”, from Latin habere, “to have, to hold, to possess property”) de, “from” (from the Latin) peis, “weight”, from Latin pensum, “weight”. This term originally referred to a class of merchandise: aveir de peis, “goods of weight”, things that were sold in bulk and were weighed on large steelyards or balances. Only later did it become identified with a particular system of units used to weigh such merchandise. The imaginative orthography of the day and the passage of the term through a series of languages (Latin, Anglo-French and English) has left many variants of the term, such as haberty-poie and haber de peyse.
Apothecaries’ System
The apothecaries’ system of mass is an obsolete system formerly used by apothecaries (now called pharmacists or chemists) in English-speaking countries. The system is related to the English avoirdupois and troy systems, as they use the same mass for a grain. Sometimes “ap” is added to the front of the unit to identify it as part of the apothecaries’ system (the abbreviation for avoirdupois is “av”). Similar systems had been in use in other European countries.
During the first half of the 20th century, the apothecaries’ system was replaced by the metric system. In the United States, it is still occasionally used, for example with prescribed medicine being sold in six ounce (℥ vi) bottles. An old maxim related to the problem involved in apothecary weight calculations when converting from avoirdupois weight — a grain is a grain is a grain — the pound weight in each system being different. The apothecary would buy the drugs by avoirdupois and compound and dispense by apothecary weight. Another anomaly, when converting grains to metric weight, 60 mg was considered the same as 64 mg or 65 mg = 1 gr.
Steradian
A graphical representation of 1 steradian.
The steradian (symbol: sr) is the SI unit of solid angle. It is used to describe two-dimensional angular spans in three-dimensional space, analogous to the way in which the radian describes angles in a plane. The name is derived from the Greek stereos for “solid” and the Latin radius for “ray, beam”.
Steradian – Wikipedia, the free encyclopedia
Grad Angle
The grad is a unit of plane angle, equivalent to 1⁄400 of a full circle, dividing a right angle in 100. It is also known as gon, grade, or gradian (not to be confused with grade of a slope, gradient, or radian). One grad equals 9⁄10 of a degree or pi⁄200 of a radian. In continental Europe, the term centigrade was in use for one hundredth of a grade, and the term myriograde was in use for one ten-thousandth of a grade. This was one reason for the adoption of the term Celsius to replace Centigrade as the unit of temperature.
One advantage of this unit is that right angles are easy to add and subtract in mental arithmetic. If one is traveling on a course of 117 grad clockwise from due North, say, then the direction from ones left is instantly convertible into 17 grads; while the direction from ones right is 217 grads; and the direction from behind one is 317 grads. A disadvantage is that the common angles of 30° and 60° in geometry must be expressed in fractions 33 1⁄3 grad and 66 2⁄3 grad, respectively.