Tacheometry
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Tacheometry
Tacheometry (; from Greek for "quick measure") is a system of rapid surveying, by which the horizontal and vertical positions of points on the earth's surface relative to one another are determined without using a chain or tape, or a separate levelling instrument. Instead of the pole formerly employed to mark a point, a staff similar to a level staff is used. This is marked with heights from the base or foot, and is graduated according to the form of tacheometer in use. The horizontal distance is inferred from the vertical angle included between two well-defined points on the staff and the known vertical distance between them. Alternatively, also by readings of the staff indicated by two fixed stadia wires in the diaphragm (reticle) of the telescope. The difference of height is computed from the angle of depression or elevation of a fixed point on the staff and the horizontal distance already obtained. The azimuth angle is determined as formerly. Thus, all the measurements req ...
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Tacheometry (; from Greek for "quick measure") is a system of rapid surveying, by which the horizontal and vertical positions of points on the earth's surface relative to one another are determined without using a chain or tape, or a separate levelling instrument. Instead of the pole formerly employed to mark a point, a staff similar to a level staff is used. This is marked with heights from the base or foot, and is graduated according to the form of tacheometer in use. The horizontal distance is inferred from the vertical angle included between two well-defined points on the staff and the known vertical distance between them. Alternatively, also by readings of the staff indicated by two fixed stadia wires in the diaphragm (reticle) of the telescope. The difference of height is computed from the angle of depression or elevation of a fixed point on the staff and the horizontal distance already obtained. The azimuth angle is determined as formerly. Thus, all the measurements requi ...
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Surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales. Surveyors work with elements of geodesy, geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages, and the law. They use equipment, such as total stations, robotic total stations, theodolites, GNSS receivers, retroreflectors, 3D scanners, LiDAR sensors, radios, inclinometer, handheld tablets, optical and digital levels, subsurface locators, d ...
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Stadia Mark
Stadia marks, also called stadia lines or stadia hairs, are crosshairs on the reticle of a theodolite or other surveying instrument that allow stadiametric rangefinding. Etymology The term stadia mark derives from the obsolete unit of distance, the stadion, derived from the Greek measurement of a stadium.Early Units of Measurement and the Nautical Mile, Commander Alton B. Moody, U.S.N.R. (U.S. Navy Hydrographic Office), pp 162-170, The Journal of Navigation / Volume 5 / Issue 3 / July 1952 . Several different stadia were defined, such as the Greek stadion and Egyptian stadion. Usage A typical surveyor's instrument reticle has two pairs of stadia marks. One pair are on the horizontal centreline and the other on the vertical cross hair. Each functions in the same manner and are placed for measuring on either axis. The stadia marks are set a specific length apart. This length is chosen so that there is a fixed, integer ratio between the difference of the rod readings and the d ...
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Surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales. Surveyors work with elements of geodesy, geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages, and the law. They use equipment, such as total stations, robotic total stations, theodolites, GNSS receivers, retroreflectors, 3D scanners, LiDAR sensors, radios, inclinometer, handheld tablets, optical and digital levels, subsurface locators, d ...
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Theodolite
A theodolite () is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching. It consists of a moveable telescope mounted so it can rotate around horizontal and vertical axes and provide angular readouts. These indicate the orientation of the telescope, and are used to relate the first point sighted through the telescope to subsequent sightings of other points from the same theodolite position. These angles can be measured with accuracies down to microradians or seconds of arc. From these readings a plan can be drawn, or objects can be positioned in accordance with an existing plan. The modern theodolite has evolved into what is known as a total station where angles and distances are measured electronically, and ...
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Stadia Mark
Stadia marks, also called stadia lines or stadia hairs, are crosshairs on the reticle of a theodolite or other surveying instrument that allow stadiametric rangefinding. Etymology The term stadia mark derives from the obsolete unit of distance, the stadion, derived from the Greek measurement of a stadium.Early Units of Measurement and the Nautical Mile, Commander Alton B. Moody, U.S.N.R. (U.S. Navy Hydrographic Office), pp 162-170, The Journal of Navigation / Volume 5 / Issue 3 / July 1952 . Several different stadia were defined, such as the Greek stadion and Egyptian stadion. Usage A typical surveyor's instrument reticle has two pairs of stadia marks. One pair are on the horizontal centreline and the other on the vertical cross hair. Each functions in the same manner and are placed for measuring on either axis. The stadia marks are set a specific length apart. This length is chosen so that there is a fixed, integer ratio between the difference of the rod readings and the d ...
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Total Station
A total station (TS) or total station theodolite (TST) is an electronic/optical instrument used for surveying and building construction. It is an electronic transit theodolite integrated with electronic distance measurement (EDM) to measure both vertical and horizontal angles and the slope distance from the instrument to a particular point, and an on-board computer to collect data and perform triangulation calculations. Robotic or motorized total stations allow the operator to control the instrument from a distance via remote control. In theory, this eliminates the need for an assistant staff member as the operator holds the retroreflector and controls the total station from the observed point. In practice however, an assistant surveyor is often needed when the surveying is being conducted in busy areas such as on a public carriageway or construction site. This is to prevent people from disrupting the total station as they walk past, which would neccesitate resetting the tripo ...
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Rangefinder
A rangefinder (also rangefinding telemeter, depending on the context) is a device used to measure distances to remote objects. Originally optical devices used in surveying, they soon found applications in other fields, such as photography and in the military. They were specially useful for finding the range of a target, such as in naval gunnery and anti-aircraft artillery. The word ''telemeter'' is derived . Designs The first rangefinder telemeter was invented by James Watt in 1769 and put to use in 1771 in surveying canals. Watt called his instrument a micrometer, a term now used with a different meaning in engineering (the micrometer screw gauge). It consisted of two parallel hairs in the focal plane of a telescope eyepiece crossing an upright hair. At the point to be measured, two sliding targets on a surveyor's rod were adjusted to align with the hairs in the telescope. The distance to the rod could then be determined from the distance between the targets on the ro ...
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Surveying Instruments
Instruments used in surveying include: * Alidade * Alidade table * Cosmolabe * Dioptra * Dumpy level * Engineer's chain * Geodimeter * Graphometer * Groma (surveying) * Laser scanning * Level * Level staff * Measuring tape * Plane table * Pole (surveying) * Prism (surveying) (corner cube retroreflector) * Prismatic compass (angle measurement) * Ramsden surveying instruments * Ranging rod * Surveyor's chain * Surveyor's compass * Tachymeter (surveying) * Tape (surveying) * Tellurometer * Theodolite ** Half theodolite ** Plain theodolite ** Simple theodolite ** Great theodolite ** Non-transit theodolite ** Transit theodolite ** Seconds theodolite ** Electronic theodolite ** Mining theodolite ** Suspension theodolite ** Traveling theodolite ** Pibal theodolite ** Registering theodolite ** Gyro-theodolite ** Construction theodolite ** Photo-theodolite ** Robotic theodolite ** Vernier theodolite * Total station * Transit (surveying) * Tripod (surveying) * Universal instr ...
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Trigonometry
Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation. Trigonometry is known for its many identities. These trigonometric identities are commonly used for rewriting trigonometrical expressions with the aim to simplify an expression, to find a more useful form of an expression, or to solve an equation. History Sumerian astronomers studied angle measure, using a division of circles into 360 degrees. They, and later the Babylonians, studied the ratios of the sides of ...
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Isosceles Triangle
In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids. The mathematical study of isosceles triangles dates back to ancient Egyptian mathematics and Babylonian mathematics. Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the pediments and gables of buildings. The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs an ...
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Invar
Invar, also known generically as FeNi36 (64FeNi in the US), is a nickel–iron alloy notable for its uniquely low coefficient of thermal expansion (CTE or α). The name ''Invar'' comes from the word ''invariable'', referring to its relative lack of expansion or contraction with temperature changes. The discovery of the alloy was made in 1895 by Swiss physicist Charles Édouard Guillaume for which he received the Nobel Prize in Physics in 1920. It enabled improvements in scientific instruments. Properties Like other nickel/iron compositions, Invar is a solid solution; that is, it is a single-phase alloy. In one commercial version it consists of approximately 36% nickel and 64% iron. The invar range was described by Westinghouse scientists in 1961 as "30–45 atom per cent nickel". Common grades of Invar have a coefficient of thermal expansion (denoted α, and measured between 20 °C and 100 °C) of about 1.2 × 10−6  K−1 (1.2  ppm/°C), while ...
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