Tacheometry (/ˌtækiˈɒmᵻtri/; 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 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 man to hold the staff.
The ordinary methods of surveying with a theodolite, chain, 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[edit]
A tachymeter or tacheometer is a type of theodolite used for rapid measurements and determines, electronically or electro-optically, the distance to target. The principles of action are similar to those of rangefinders.
Stadia measurements[edit]
Other forms of tacheometry in surveying include the use of stadia rods with theodolites or plane-table alidades.[1] 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
Here, s is the stadia interval (top intercept minus bottom intercept); k and c are additive and multiplicative constants. Generally, the instrument is made so that k = 100 and c = 0 exactly, to simplify calculations.
Subtense bars[edit]
Another device used in tacheometry is the subtense bar.[1] This is a rigid rod, usually of a material insensitive to change in temperature such as invar, of fixed length (typically two metres). 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 formed with the theodolite at the upper vertex and the subtense bar length at its base, determined by trigonometry.
Tacheometry is the branch of Surveying in which we determine the horizontal and vertical distances with the angular measurements with an instrument , Tachemometer. It is not so accurate method of finding the horizontal distances as the Chaining is, but it is most suitable for carrying out the surveys to find the distances in the hilly area where other methods are quite difficult being carried out. It is generally used to locate contours, hydrographic surveys and laying out routes of highways, railways etc.
The instruments required for carrying out the Tacheometric survey are:
(1) A Tacheometer (2) A Stadia Rod.
- Tacheometer: Tacheometer is more or less a Theodolite installed with a stadia diaphragm. Stadia diaphragm is equiped with three horizontal hairs and one vertical hair. So we can take three vertical staff reading at the same instruments setting, lower most hair reading, central hair reading and the top hair reading. The difference between the lower hair reading and the upper hair reading gives the staff intercept(s).
The Tacheometer with the analactic lens are famous because their additive constant is 0. There is one concave lens introduced between the eye piece and the object piece to eliminate the additive constant of the instrument. It simplifies the calculations.
Methods of Tacheometric Survey:
(A) Stadia Hair Method
- Fixed Hair Method
- Movable Hair Method
(B) Tangential Method
(A)Stadia Hair Method:
- As the name suggests in this method theodolite with the stadia diaphragm is used to find out the staff intercept between the lower and upper hairs and also the central hair reading is noted.
Principle of Stadia hair method is that the ratio of the length of perpendicular to the base is constant in case of similar triangles.
- Fixed Hair Method: In the fixed hair method the cross hairs of the diaphragm are kept at a constant distance apart and the staff intercept varies with the horizontal and vertical position of the staff with respect to the Theodolite.
- Movable Hair Method: In this method the staff intercept between the lower hair and the upper hair is kept constant by moving the horizontal cross hairs in the vertical plane.
Formula to carry out calculation works:
Case:
(a) Staff held vertical:
 |
| Tacheometry -Staff held vertical |
D = (f/i).s+ (f+d)
where, f/i = multiplying constant
s = staff intercept between the bottom and top hair
f+d = Additive constant
D = Horizontal distance between the staff station and the observer's position
(b) Inclined sights staff held vertical:
D = (f/i).s. cos^2A + (f+d) cosA
V = {(f/i).s.} .[{sin(2A)}/2] + (f+d) sinA
Where A is the angle of elevation or angle of depression.
(c) Inclined sights upwards, staff held normal:
D = [(f/i).s+ (f+d)]cosA - h.sinA ; V= [(f/i).s+ (f+d)].sinA
h= central hair reading.
R.L. of staff = H.I. + [(f/i).s+ (f+d)].sinA - hcosA
(d) Inclined sights downwards, staff held normal:
D = [(f/i).s+ (f+d)]cosA - h.sinA ; V= [(f/i).s+ (f+d)].sinA
R.L. of staff = H.I. + [(f/i).s+ (f+d)].sinA - hcosA
(B)Tangential Method:
In Tangential method only central hair reading is noted down and generally two angular observations are taken to calculate the horizontal and vertical distances.
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Reference: Surveying Vol-1 Dr. B.C.Punmia
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