Tacheometry is a rapid surveying method that uses a tacheometer, a specialized theodolite, to determine horizontal and vertical positions without relying on a chain, tape, or separate levelling instrument. Instead of a usual pole, a staff similar to a level staff is used, marked with heights for quick measurements. Traditional surveying methods become cumbersome in rough terrain with bush or ravines, where chain measurements are slow and error-prone. While tacheometry has mostly historical significance in western countries, replaced by electronic total stations and GNSS technology, it remains useful in some regions and for non-professional users.
Use
The horizontal distance S is inferred from the vertical angle subtended between two well-defined points on the staff and the known distance 2L 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 Δh is computed from the angle of depression z or angle of elevation α of a fixed point on the staff and the horizontal distance S already obtained.
The azimuth angle is determined as normally. 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.3
Specialized equipment
Stadia rod
Other forms of tacheometry in surveying include the use of a level staff known as a stadia rod with a theodolite or plane-table alidade.4 These use stadia marks 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 = k s + c {\displaystyle d=ks+c}Here, s {\displaystyle s} is the stadia interval (top intercept minus bottom intercept); k {\displaystyle k} and c {\displaystyle c} are multiplicative and additive constants. Generally, the instrument is made so that k = 100 {\displaystyle k=100} and c = 0 {\displaystyle c=0} exactly, to simplify calculations.
Subtense bar
Another device used in tacheometry to measure distance between the measuring station and a desired point is the subtense bar.5 This is a rigid rod, usually of a material insensitive to change in temperature such as invar, of fixed length (typically 2 metres (6.6 ft)). 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. Since the subtense bar is always 2m. The formula for the subtense bar is:
Horizontal distance = cot(θ/2)A theodolite is used to measure the horizontal 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 formed with the theodolite at the upper vertex and the subtense bar length at its base, determined by trigonometry.
Wild brand subtense barTacheometer
A tachymeter or tacheometer is a type of theodolite used for rapid measurements and in modern form determines, electronically or electro-optically, the distance to target. The principles of action are similar to those of rangefinders.
References
One or more of the preceding sentences incorporates text from a publication now in the public domain: Airy, Wilfrid (1911). "Tacheometry". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 26 (11th ed.). Cambridge University Press. pp. 341–344. /wiki/Public_domain ↩
One or more of the preceding sentences incorporates text from a publication now in the public domain: Airy, Wilfrid (1911). "Tacheometry". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 26 (11th ed.). Cambridge University Press. pp. 341–344. /wiki/Public_domain ↩
One or more of the preceding sentences incorporates text from a publication now in the public domain: Airy, Wilfrid (1911). "Tacheometry". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 26 (11th ed.). Cambridge University Press. pp. 341–344. /wiki/Public_domain ↩
Raymond Davis, Francis Foote, Joe Kelly, Surveying, Theory and Practice, McGraw-Hill Book Company, 1966 LC 64-66263 ↩
Raymond Davis, Francis Foote, Joe Kelly, Surveying, Theory and Practice, McGraw-Hill Book Company, 1966 LC 64-66263 ↩