Horsepower

Horsepower is a unit of measurement of power, or the rate at which work is done. There are many different types of horsepower. Two common definitions being used today are the mechanical horsepower, about 745.7 watts, the metric horsepower, 735.5 watts. The term was adopted in the late 18th century by Scottish engineer James Watt to compare the output of steam engines with the power of draft horses, it was expanded to include the output power of other types of piston engines, as well as turbines, electric motors and other machinery. The definition of the unit varied among geographical regions. Most countries now use the SI unit watt for measurement of power. With the implementation of the EU Directive 80/181/EEC on January 1, 2010, the use of horsepower in the EU is permitted only as a supplementary unit; the development of the steam engine provided a reason to compare the output of horses with that of the engines that could replace them. In 1702, Thomas Savery wrote in The Miner's Friend: So that an engine which will raise as much water as two horses, working together at one time in such a work, can do, for which there must be kept ten or twelve horses for doing the same.

I say, such an engine may be made large enough to do the work required in employing eight, fifteen, or twenty horses to be maintained and kept for doing such a work… The idea was used by James Watt to help market his improved steam engine. He had agreed to take royalties of one third of the savings in coal from the older Newcomen steam engines; this royalty scheme did not work with customers who did not have existing steam engines but used horses instead. Watt determined; the wheel was 12 feet in radius. Watt judged. So: P = W t = F d t = 180 l b f × 2.4 × 2 π × 12 f t 1 m i n = 32, 572 f t ⋅ l b f m i n. Watt defined and calculated the horsepower as 32,572 ft⋅lbf/min, rounded to an 33,000 ft⋅lbf/min. Watt determined that a pony could lift an average 220 lbf 100 ft per minute over a four-hour working shift. Watt judged a horse was 50% more powerful than a pony and thus arrived at the 33,000 ft⋅lbf/min figure. Engineering in History recounts that John Smeaton estimated that a horse could produce 22,916 foot-pounds per minute.

John Desaguliers had suggested 44,000 foot-pounds per minute and Tredgold 27,500 foot-pounds per minute. "Watt found by experiment in 1782 that a'brewery horse' could produce 32,400 foot-pounds per minute." James Watt and Matthew Boulton standardized that figure at 33,000 foot-pounds per minute the next year. A common legend states that the unit was created when one of Watt's first customers, a brewer demanded an engine that would match a horse, chose the strongest horse he had and driving it to the limit. Watt, while aware of the trick, accepted the challenge and built a machine, even stronger than the figure achieved by the brewer, it was the output of that machine which became the horsepower. In 1993, R. D. Stevenson and R. J. Wassersug published correspondence in Nature summarizing measurements and calculations of peak and sustained work rates of a horse. Citing measurements made at the 1926 Iowa State Fair, they reported that the peak power over a few seconds has been measured to be as high as 14.9 hp and observed that for sustained activity, a work rate of about 1 hp per horse is consistent with agricultural advice from both the 19th and 20th centuries and consistent with a work rate of about 4 times the basal rate expended by other vertebrates for sustained activity.

When considering human-powered equipment, a healthy human can produce about 1.2 hp and sustain about 0.1 hp indefinitely. The Jamaican sprinter Usain Bolt produced a maximum of 3.5 hp 0.89 seconds into his 9.58 second 100-metre dash world record in 2009. When torque T is in pound-foot units, rotational speed is in rpm and power is required in horsepower: P / hp = T / × N / rpm 5252 The constant 5252 is the rounded value of /; when torque T is in inch pounds: P

Engineering

Engineering is the application of knowledge in the form of science and empirical evidence, to the innovation, construction and maintenance of structures, materials, devices, systems and organizations. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, types of application. See glossary of engineering; the term engineering is derived from the Latin ingenium, meaning "cleverness" and ingeniare, meaning "to contrive, devise". The American Engineers' Council for Professional Development has defined "engineering" as: The creative application of scientific principles to design or develop structures, apparatus, or manufacturing processes, or works utilizing them singly or in combination. Engineering has existed since ancient times, when humans devised inventions such as the wedge, lever and pulley; the term engineering is derived from the word engineer, which itself dates back to 1390 when an engine'er referred to "a constructor of military engines."

In this context, now obsolete, an "engine" referred to a military machine, i.e. a mechanical contraption used in war. Notable examples of the obsolete usage which have survived to the present day are military engineering corps, e.g. the U. S. Army Corps of Engineers; the word "engine" itself is of older origin deriving from the Latin ingenium, meaning "innate quality mental power, hence a clever invention."Later, as the design of civilian structures, such as bridges and buildings, matured as a technical discipline, the term civil engineering entered the lexicon as a way to distinguish between those specializing in the construction of such non-military projects and those involved in the discipline of military engineering. The pyramids in Egypt, the Acropolis and the Parthenon in Greece, the Roman aqueducts, Via Appia and the Colosseum, Teotihuacán, the Brihadeeswarar Temple of Thanjavur, among many others, stand as a testament to the ingenuity and skill of ancient civil and military engineers.

Other monuments, no longer standing, such as the Hanging Gardens of Babylon, the Pharos of Alexandria were important engineering achievements of their time and were considered among the Seven Wonders of the Ancient World. The earliest civil engineer known by name is Imhotep; as one of the officials of the Pharaoh, Djosèr, he designed and supervised the construction of the Pyramid of Djoser at Saqqara in Egypt around 2630–2611 BC. Ancient Greece developed machines in both military domains; the Antikythera mechanism, the first known mechanical computer, the mechanical inventions of Archimedes are examples of early mechanical engineering. Some of Archimedes' inventions as well as the Antikythera mechanism required sophisticated knowledge of differential gearing or epicyclic gearing, two key principles in machine theory that helped design the gear trains of the Industrial Revolution, are still used today in diverse fields such as robotics and automotive engineering. Ancient Chinese, Greek and Hungarian armies employed military machines and inventions such as artillery, developed by the Greeks around the 4th century BC, the trireme, the ballista and the catapult.

In the Middle Ages, the trebuchet was developed. Before the development of modern engineering, mathematics was used by artisans and craftsmen, such as millwrights, clock makers, instrument makers and surveyors. Aside from these professions, universities were not believed to have had much practical significance to technology. A standard reference for the state of mechanical arts during the Renaissance is given in the mining engineering treatise De re metallica, which contains sections on geology and chemistry. De re metallica was the standard chemistry reference for the next 180 years; the science of classical mechanics, sometimes called Newtonian mechanics, formed the scientific basis of much of modern engineering. With the rise of engineering as a profession in the 18th century, the term became more narrowly applied to fields in which mathematics and science were applied to these ends. In addition to military and civil engineering, the fields known as the mechanic arts became incorporated into engineering.

Canal building was an important engineering work during the early phases of the Industrial Revolution. John Smeaton was the first self-proclaimed civil engineer and is regarded as the "father" of civil engineering, he was an English civil engineer responsible for the design of bridges, canals and lighthouses. He was a capable mechanical engineer and an eminent physicist. Using a model water wheel, Smeaton conducted experiments for seven years, determining ways to increase efficiency. Smeaton introduced iron gears to water wheels. Smeaton made mechanical improvements to the Newcomen steam engine. Smeaton designed the third Eddystone Lighthouse where he pioneered the use of'hydraulic lime' and developed a technique involving dovetailed blocks of granite in the building of the lighthouse, he is important in the history, rediscovery of, development of modern cement, because he identified the compositional requirements needed to obtain "hydraulicity" in lime.

Physics

Physics is the natural science that studies matter, its motion, behavior through space and time, that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, its main goal is to understand how the universe behaves. Physics is one of the oldest academic disciplines and, through its inclusion of astronomy the oldest. Over much of the past two millennia, chemistry and certain branches of mathematics, were a part of natural philosophy, but during the scientific revolution in the 17th century these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, the boundaries of physics which are not rigidly defined. New ideas in physics explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics enable advances in new technologies.

For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have transformed modern-day society, such as television, domestic appliances, nuclear weapons. Astronomy is one of the oldest natural sciences. Early civilizations dating back to beyond 3000 BCE, such as the Sumerians, ancient Egyptians, the Indus Valley Civilization, had a predictive knowledge and a basic understanding of the motions of the Sun and stars; the stars and planets were worshipped, believed to represent gods. While the explanations for the observed positions of the stars were unscientific and lacking in evidence, these early observations laid the foundation for astronomy, as the stars were found to traverse great circles across the sky, which however did not explain the positions of the planets. According to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, all Western efforts in the exact sciences are descended from late Babylonian astronomy.

Egyptian astronomers left monuments showing knowledge of the constellations and the motions of the celestial bodies, while Greek poet Homer wrote of various celestial objects in his Iliad and Odyssey. Natural philosophy has its origins in Greece during the Archaic period, when pre-Socratic philosophers like Thales rejected non-naturalistic explanations for natural phenomena and proclaimed that every event had a natural cause, they proposed ideas verified by reason and observation, many of their hypotheses proved successful in experiment. The Western Roman Empire fell in the fifth century, this resulted in a decline in intellectual pursuits in the western part of Europe. By contrast, the Eastern Roman Empire resisted the attacks from the barbarians, continued to advance various fields of learning, including physics. In the sixth century Isidore of Miletus created an important compilation of Archimedes' works that are copied in the Archimedes Palimpsest. In sixth century Europe John Philoponus, a Byzantine scholar, questioned Aristotle's teaching of physics and noting its flaws.

He introduced the theory of impetus. Aristotle's physics was not scrutinized until John Philoponus appeared, unlike Aristotle who based his physics on verbal argument, Philoponus relied on observation. On Aristotle's physics John Philoponus wrote: “But this is erroneous, our view may be corroborated by actual observation more than by any sort of verbal argument. For if you let fall from the same height two weights of which one is many times as heavy as the other, you will see that the ratio of the times required for the motion does not depend on the ratio of the weights, but that the difference in time is a small one, and so, if the difference in the weights is not considerable, that is, of one is, let us say, double the other, there will be no difference, or else an imperceptible difference, in time, though the difference in weight is by no means negligible, with one body weighing twice as much as the other”John Philoponus' criticism of Aristotelian principles of physics served as an inspiration for Galileo Galilei ten centuries during the Scientific Revolution.

Galileo cited Philoponus in his works when arguing that Aristotelian physics was flawed. In the 1300s Jean Buridan, a teacher in the faculty of arts at the University of Paris, developed the concept of impetus, it was a step toward the modern ideas of momentum. Islamic scholarship inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further placing emphasis on observation and a priori reasoning, developing early forms of the scientific method; the most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn al-Haytham, in which he conclusively disproved the ancient Greek idea about vision, but came up with a new theory. In the book, he presented a study of the phenomenon of the camera obscura (his thousand-year-old

Orientation (geometry)

In geometry the orientation, angular position, or attitude of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies. Namely, it is the imaginary rotation, needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement, it may be necessary to add an imaginary translation, called the object's location. The location and orientation together describe how the object is placed in space; the above-mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, its location does not change when it rotates. Euler's rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis; this gives one common way of representing the orientation using an axis–angle representation. Other used methods include rotation quaternions, Euler angles, or rotation matrices.

More specialist uses include Miller indices in crystallography and dip in geology and grade on maps and signs. The orientation is given relative to a frame of reference specified by a Cartesian coordinate system. In general the position and orientation in space of a rigid body are defined as the position and orientation, relative to the main reference frame, of another reference frame, fixed relative to the body, hence translates and rotates with it. At least three independent values are needed to describe the orientation of this local frame. Three other values are All the points of the body change their position during a rotation except for those lying on the rotation axis. If the rigid body has rotational symmetry not all orientations are distinguishable, except by observing how the orientation evolves in time from a known starting orientation. For example, the orientation in space of a line, line segment, or vector can be specified with only two values, for example two direction cosines. Another example is the position of a point on the earth described using the orientation of a line joining it with the earth's center, measured using the two angles of longitude and latitude.

The orientation of a plane can be described with two values as well, for instance by specifying the orientation of a line normal to that plane, or by using the strike and dip angles. Further details about the mathematical methods to represent the orientation of rigid bodies and planes in three dimensions are given in the following sections. In two dimensions the orientation of any object is given by a single value: the angle through which it has rotated. There is only one fixed point about which the rotation takes place. Several methods to describe orientations of a rigid body in three dimensions have been developed, they are summarized in the following sections. The first attempt to represent an orientation was owed to Leonhard Euler, he imagined three reference frames that could rotate one around the other, realized that by starting with a fixed reference frame and performing three rotations, he could get any other reference frame in the space. The values of these three rotations are called Euler angles.

These are three angles known as yaw and roll, Navigation angles and Cardan angles. Mathematically they constitute a set of six possibilities inside the twelve possible sets of Euler angles, the ordering being the one best used for describing the orientation of a vehicle such as an airplane. In aerospace engineering they are referred to as Euler angles. Euler realized that the composition of two rotations is equivalent to a single rotation about a different fixed axis. Therefore, the composition of the former three angles has to be equal to only one rotation, whose axis was complicated to calculate until matrices were developed. Based on this fact he introduced a vectorial way to describe any rotation, with a vector on the rotation axis and module equal to the value of the angle. Therefore, any orientation can be represented by a rotation vector that leads to it from the reference frame; when used to represent an orientation, the rotation vector is called orientation vector, or attitude vector.

A similar method, called axis–angle representation, describes a rotation or orientation using a unit vector aligned with the rotation axis, a separate value to indicate the angle. With the introduction of matrices, the Euler theorems were rewritten; the rotations were described by orthogonal matrices referred to as rotation matrices or direction cosine matrices. When used to represent an orientation, a rotation matrix is called orientation matrix, or attitude matrix; the above-mentioned Euler vector is the eigenvector of a rotation matrix. The product of two rotation matrices is the composition of rotations. Therefore, as before, the orientation can be given as the rotation from the initial frame to achieve the frame that we want to describe; the configuration space of a non-symmetrical object in n-dimensional space is SO × Rn. Orientation may be visualized by attaching a basis of tangent vectors to an object; the direction in which each vector points determines its orientation. Another way to describe rotations is using rotation quaternions called versors.

They are equivalent to rotation matrices and rotation vectors. With respect to rotation vectors, they can be more converted to and from matri

Omega

Omega is the 24th and last letter of the Greek alphabet. In the Greek numeric system/Isopsephy, it has a value of 800; the word means "great O", as opposed to omicron, which means "little O". In phonetic terms, the Ancient Greek Ω is a long open-mid o, comparable to the vowel of British English raw. In Modern Greek, Ω represents the same sound as omicron; the letter omega is transcribed ō or o. As the last letter of the Greek alphabet, Omega is used to denote the last, the end, or the ultimate limit of a set, in contrast to alpha, the first letter of the Greek alphabet. Ω was not part of the early Greek alphabets. It was introduced in the late 7th century BC in the Ionian cities of Asia Minor to denote the long half-open, it is a variant of omicron, broken up with the edges subsequently turned outward. The Dorian city of Knidos as well as a few Aegean islands, namely Paros and Melos, chose the exact opposite innovation, using a broken-up circle for the short and a closed circle for the long /o/.

The name Ωμέγα is Byzantine. The modern lowercase shape goes back to the uncial form, a form that developed during the 3rd century BC in ancient handwriting on papyrus, from a flattened-out form of the letter that had its edges curved further upward. In addition to the Greek alphabet, Omega was adopted into the early Cyrillic alphabet. See Cyrillic omega. A Raetic variant is conjectured to be at the origin or parallel evolution of the Elder Futhark ᛟ. Omega was adopted into the Latin alphabet, as a letter of the 1982 revision to the African reference alphabet, it has had little use. See Latin omega; the uppercase letter Ω is used as a symbol: In chemistry: For oxygen-18, a natural, stable isotope of oxygen. In physics: For ohm – SI unit of electrical resistance. Unicode has a separate code point for the ohm sign, but it is included only for backward compatibility, the Greek uppercase omega character is preferred. In statistical mechanics, Ω refers to the multiplicity in a system; the solid angle or the rate of precession in a gyroscope.

In particle physics to represent the Omega baryons. In astronomy, Ω refers to the density of the universe called the density parameter. In astronomy, Ω refers to the longitude of the ascending node of an orbit. In mathematics and computer science: In complex analysis, the Omega constant, a solution of Lambert's W function In differential geometry, the space of differential forms on a manifold. A variable for a 2-dimensional region in calculus corresponding to the domain of a double integral. In topos theory, the subobject classifier of an elementary topos. In combinatory logic, the looping combinator, In group theory, the omega and agemo subgroups of a p-group, Ω and ℧ In group theory, Cayley's Ω process as a partial differential operator. In statistics, it is used as total set of possible outcomes. In number theory, Ω is the number of prime divisors of n. In notation related to Big O notation to describe the asymptotic behavior of functions. Chaitin's constant; as part of logo or trademark: The logo of Omega Watches SA.

Part of the original Pioneer logo. Part of the Badge of the Supreme Court of the United Kingdom. Part of the mission patch for STS-135, as it was the last mission of the Space Shuttle program; the logo of the God of War video game series based on Greek mythology. In God of War, it is revealed; the logo of E-123 Omega, a Sonic the Hedgehog character. The logo of the Heroes of Olympus series, based on Greek mythology; the logo of the Ultramarines in Warhammer 40,000 The logo of Primal Groudon, the version mascot of Pokémon Omega Ruby. The logo of Darkseid in DC comics One of the logos of professional wrestler Kenny Omega Other The symbol of the resistance movement against the Vietnam-era draft in the United States Year or date of death Used to refer to the lowest-ranked wolf in a pack In eschatology, the symbol for the end of everything In molecular biology, the symbol is used as shorthand to signify a genetic construct introduced by a two-point crossover Omega Particle in the Star Trek universe The final form of NetNavi bosses in some of the Mega Man Battle Network games The personal symbol for Death, as worn by Death in the Discworld series by Terry Pratchett The symbol to represent Groudon in Pokémon Omega Ruby and Alpha Sapphire A secret boss in the Final Fantasy series called Omega Weapon.

A character from the series Doctor Who called Omega, believed to be one of the creators of the Time Lords on Gallifrey. The minuscule letter ω is used as a symbol: Biochemistry and chemistry: Denotes the carbon atom furthest from the carboxyl group of a fatty acid In biochemistry, for one of the RNA polymerase subunits In biochemistry, for the dihedral angle associated with the peptide group, involving the backbone atoms Cα-C'-N-Cα In biology, for the fitness. In genomics, as a measure of evolution at the protein level Physics Angular velocity or angular frequency In computational fluid dynamics, the specific turbulence dissipation rate In meteorology, the change of pressure with respect to time of a parcel o

Cycle per second

The cycle per second was a once-common English name for the unit of frequency now known as the hertz. The plural form was used written cycles per second, cycles/second, c.p.s. c/s, ~, or, just cycles. The term comes from the fact that sound waves have a frequency measurable in their number of oscillations, or cycles, per second. With the organization of the International System of Units in 1960, the cycle per second was replaced by the hertz, or reciprocal second, "s−1" or "1/s". Symbolically, "cycle per second" units are "cycle/second", while hertz is "Hz" or "s−1". For higher frequencies, kilocycles, as an abbreviation of kilocycles per second were used on components or devices. Other higher units like megacycle and less kilomegacycle were used before 1960 and in some documents; these have modern equivalents such as kilohertz and gigahertz. The rate at which aperiodic or stochastic events occur may be expressed in becquerels, not hertz, since although the two are mathematically similar, by convention hertz implies regularity where becquerels implies the requirement of a time averaging operation.

Thus, one becquerel is one event per second on average, whereas one hertz is one event per second on a regular cycle. Cycle can be a unit for measuring usage of reciprocating machines presses, in which cases cycle refers to one complete revolution of the mechanism being measured. Derived units include cycles per day and cycles per year. Revolutions per minute Cycles per instruction Heinrich Hertz Instructions per cycle Instructions per second MKS system of units a predecessor of the SI set of units Normalized frequency Radian per second

System of measurement

A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have been important and defined for the purposes of science and commerce. Systems of measurement in use include the International System of Units, the modern form of the metric system, the imperial system, United States customary units; the French Revolution gave rise to the metric system, this has spread around the world, replacing most customary units of measure. In most systems, length and time are base quantities. Science developments showed that either electric charge or electric current could be added to extend the set of base quantities by which many other metrological units could be defined. Other quantities, such as power and speed, are derived from the base set: for example, speed is distance per unit time. A wide range of units was used for the same type of quantity: in different contexts, length was measured in inches, yards, rods, furlongs, nautical miles, leagues, with conversion factors which were not powers of ten.

Such arrangements were satisfactory in their own contexts. The preference for a more universal and consistent system only spread with the growth of science. Changing a measurement system has substantial financial and cultural costs which must be offset against the advantages to be obtained from using a more rational system; however pressure built up, including from scientists and engineers for conversion to a more rational, internationally consistent, basis of measurement. In antiquity, systems of measurement were defined locally: the different units might be defined independently according to the length of a king's thumb or the size of his foot, the length of stride, the length of arm, or maybe the weight of water in a keg of specific size itself defined in hands and knuckles; the unifying characteristic is. Cubits and strides gave way to "customary units" to meet the needs of merchants and scientists. In the metric system and other recent systems, a single basic unit is used for each base quantity.

Secondary units are derived from the basic units by multiplying by powers of ten, i.e. by moving the decimal point. Thus the basic metric unit of length is the metre. Metrication is complete or nearly complete in all countries. US customary units are used in the United States and to some degree in Liberia. Traditional Burmese units of measurement are used in Burma. U. S. units are used in limited contexts in Canada due to the large volume of trade. A number of other jurisdictions have laws mandating or permitting other systems of measurement in some or all contexts, such as the United Kingdom – whose road signage legislation, for instance, only allows distance signs displaying imperial units – or Hong Kong. In the United States, metric units are used universally in science in the military, in industry, but customary units predominate in household use. At retail stores, the liter is a used unit for volume on bottles of beverages, milligrams, rather than grains, are used for medications; some other standard non-SI units are still in international use, such as nautical miles and knots in aviation and shipping.

Metric systems of units have evolved since the adoption of the first well-defined system in France in 1795. During this evolution the use of these systems has spread throughout the world, first to non-English-speaking countries, to English speaking countries. Multiples and submultiples of metric units are related by powers of ten and their names are formed with prefixes; this relationship is compatible with the decimal system of numbers and it contributes to the convenience of metric units. In the early metric system there were the metre for length and the gram for mass; the other units of length and mass, all units of area and derived units such as density were derived from these two base units. Mesures usuelles were a system of measurement introduced as a compromise between the metric system and traditional measurements, it was used in France from 1812 to 1839. A number of variations on the metric system have been in use; these include gravitational systems, the centimetre–gram–second systems useful in science, the metre–tonne–second system once used in the USSR and the metre–kilogram–second system.

The current international standard metric system is the International System of Units It is an mks system based on the metre and second as well as the kelvin, ampere and mole. The SI includes two classes of units which are agreed internationally; the first of these classes includes the seven SI base units for length, time, electric current, luminous intensity and amount of substance. The second class consists of the SI derived units; these derived. All other quantities are expressed in terms of SI derived units. Both imperial units and US customary units derive from earlier English units. Imperial units were used in the former British Empire and