Tacheometry
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Tacheometry (; from Greek for "quick measure") is a system of rapid
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 ca ...
, 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 requisite to locate a point both vertically and horizontally with reference to the point where the tacheometer is centred are determined by an observer at the instrument without any assistance beyond that of a person to hold the level staff. The ordinary methods of surveying with a theodolite,
chain A chain is a serial assembly of connected pieces, called links, typically made of metal, with an overall character similar to that of a rope in that it is flexible and curved in compression but linear, rigid, and load-bearing in tension. A c ...
, and levelling instrument are fairly satisfactory when the ground is relatively clear of obstructions and not very precipitous, but it becomes extremely cumbersome when the ground is covered with bush, or broken up by ravines. Chain measurements then become slow and liable to considerable error; the levelling, too, is carried on at great disadvantage in point of speed, though without serious loss of accuracy. These difficulties led to the introduction of tacheometry. In western countries, tacheometry is primarily of historical interest in surveying, as professional measurement nowadays is usually carried out using total stations and recorded using data collectors. Location positions are also determined using GNSS. Traditional methods and instruments are still in use in many areas of the world and by users who are not primarily surveyors.


Tacheometer

A ''tachymeter'' or ''tacheometer'' is a type of theodolite used for rapid
measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
s and determines, electronically or electro-optically, the distance to target. The principles of action are similar to those of rangefinders.


Stadia measurements

Other forms of tacheometry in surveying include the use of
stadia rod {{short description, Graduated rod used to measure differences between heights A level staff, also called levelling rod, is a graduated wooden or aluminium rod, used with a levelling instrument to determine the difference in height between points ...
s with theodolites or
plane-table A plane table (plain table prior to 1830) is a device used in surveying site mapping, exploration mapping, coastal navigation mapping, and related disciplines to provide a solid and level surface on which to make field drawings, charts and maps. ...
alidades.Raymond Davis, Francis Foote, Joe Kelly, ''Surveying, Theory and Practice'', McGraw-Hill Book Company, 1966 LC 64-66263 These use
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, t ...
s on the instrument's reticle to measure the distance between two points on the stadia rod (the stadia interval). This is converted to distance from the instrument to the stadia rod by multiplying the stadia interval by the ''stadia interval factor''. If the stadia rod is not at the same elevation as the instrument, the value must be corrected for the angle of elevation between the instrument and the rod. The formula most widely used for finding the distances is: d = ks + c Here, s is the stadia interval (top intercept minus bottom intercept); k and c are multiplicative and additive constants. Generally, the instrument is made so that k = 100 and c = 0 exactly, to simplify calculations.


Subtense bars

Another device used in tacheometry is the ''subtense bar''. This is a rigid rod, usually of a material insensitive to change in temperature such as invar, of fixed length (typically ). The subtense bar is mounted on a tripod over the station to which the distance is desired. It is brought to level, and a small telescope on the bar enables the bar to be oriented perpendicular to the line of sight to the angle measuring station. A theodolite is used to measure the angle between indicators on the two ends of the subtense bar. The distance from the telescope to the subtense bar is the height of an
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 versio ...
formed with the theodolite at the upper vertex and the subtense bar length at its base, determined by trigonometry.


References

{{Reflist Surveying Surveying instruments Measuring instruments Length, distance, or range measuring devices