To determine the horizontal distances by Tacheometric Surveying when the line of sight is horizontal.

Object: To determine the horizontal distance by tacheometric surveying when the line of sight is horizontal.

Equipment:

Digital theodolite, tripod stand, leveling staff, prismatic compass, ranging rods, and plum bob.

Theory:

Tacheometric Surveying (Tacheometry):

It is the branch of surveying in which horizontal and vertical distances are determine by taking angular observations and stadia readings with help of an instrument known as tacheometer. In this survey chaining operation is completely eliminated.

Tacheometer:

It is a transit theodolite, fitted with stadia lines (or stadia diaphragm) and an additional convex lens in the telescope of a tachometer.

Lens formula is 1/f = 1/p + 1/q From figure

1/f = 1/u + 1/v

Since, i/s = v/u => v = iu/s 1/f = 1/u + s/iu

1/f = 1/u(1 + s/i) u= f(1 + s/i)

u+d = f(1 + s/i) + d D = (f/i)s + (f+d)

Procedure:

1. Mark station A then mark North with help of prismatic compass at station A.
   
2. Set the instrument at station A and done the temporary adjustment.
   
3. Horizontal clamp is kept fixed and vertical clamp loosened, then set telescope at 90˚ with the help of vertical clamp and vertical screw.
   
4. Now the vertical clamp is tightly fixed and horizontal clamp is loosened and telescope is directed towards north and bisect the ranging rod.
   
5. Horizontal clamp is fixed and set horizontal angle as 0˚ by using reset button.
   
6. Now loose the horizontal clamp and telescope is directed towards B and bisect the ranging rod at B.
   
7. Note the H.A. displayed at display screen, which is the bearing of line AB.
   
8. Now hold the staff rod on station B and note the stadia readings that is uppers stadia, lower stadia and central stadia readings.
   
9. Horizontal distance of AB is calculated by using distance formula ( D = (f/i)s + (f+d) ).
   
10. Repeat the above process for bearings and distances of lines BC, CD, DE, EF and FA.
    
11. Find the latitude by using LCosθ and departure by using LSinθ (where L is distance of line and θ is bearing of that line).
    
12. Let the coordinates of point A as (0, 0).
    
13. And find the coordinates of other stations by adding latitudes and departures in coordinates of station A.
    
14. The coordinates are arranged in determinant form as follows.
    

1. Sum of products along the solid line,
   

∑P = (Y1.X2+Y2.X3+Y3.X4+Y4.X5+Y5.X1)

1. Sum of products along the dotted lines,
   

∑Q = (X1.Y2+X2.Y3+X3.Y4+X4.Y5+X5.Y1)

1. Now area is calculated by following formula, Area = 1/2 x (∑P – ∑Q)
   

Observations:

Area Calculations:

∑P = ……………………………

∑Q = …………………………..

Area = 1/2 x (∑P – ∑Q)

Area = 1/2 x (……………. – ……………..) = ………………