Saturday, March 31, 2018

Tacheometry (Surveying) - Theory and Formulae


Tacheometry is the branch of Surveying in which we determine the horizontal and vertical distances between points by taking some angular measurements with the help of an instrument caled Tacheometer. 

This 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 equipped with three horizontal hairs and one vertical hair. So we can take three vertical staff reading at the same instruments setting, lowermost 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 zero. There is one concave lens introduced between the eyepiece and the object piece to eliminate the additive constant of the instrument. It simplifies the calculations.
Methods of Tacheometric Survey:

(A) Stadia Hair Method
  1. Fixed Hair Method
  2. 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.

  1. 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.
  2. 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:

(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 - h.cosA

(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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