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 ...

, 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 {{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 ...

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 A reticle, or reticule also known as a graticule, is a pattern of fine lines or markings built into the eyepiece of an optical device such as a telescopic sight, spotting scope, theodolite, optical microscope or the screen of an oscillos ...

) of the

telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to obse ...

. 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 An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north. Mathematicall ...

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 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 ...

chain A chain is a wikt:series#Noun, 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 (physics), compression but line (g ...

, and

levelling Levelling or leveling (American English; see spelling differences) is a branch of surveying, the object of which is to establish or verify or measure the height of specified points relative to a datum. It is widely used in geodesy and cartogra ...

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

ravine A ravine is a landform that is narrower than a canyon and is often the product of streambank erosion. In western countries, tacheometry is primarily of historical interest in surveying, as professional measurement nowadays is usually carried out using

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 ...

s and recorded using data collectors. Location positions are also determined using

GNSS A satellite navigation or satnav system is a system that uses satellites to provide autonomous geo-spatial positioning. It allows satellite navigation devices to determine their location (longitude, latitude, and altitude/elevation) to high p ...

. 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

used for rapid measurements and determines, electronically or electro-optically, the distance to target. The principles of action are similar to those of

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 an ...

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. ...

alidade An alidade () (archaic forms include alhidade, alhidad, alidad) or a turning board is a device that allows one to sight a distant object and use the line of sight to perform a task. This task can be, for example, to triangulate a scale map on sit ...

s.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, ...

s on the instrument's

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 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 lac ...

, 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

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 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. ...

References

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