DETERMINATION OF THE MULTIPLYING CONSTANTS BY STADIA METHOD

 APPARATUS:- Tachometer withstand, Ranging rods, Peg, Arrows, Tape, etc.

THEORY:- Tachometer is a branch of angular surveying in which the horizontal and vertical distances of points are obtained. The method is very rapid and convenient.  The tachometer is the combination of transit theodolite and stadia diaphragm.  The stadia diaphragm essentially consists of one stadia hair above the other at an equal distance below the horizontal crosshair.

PRINCIPLE OF TACHOMETER:-

The Principle underlying tachometer is as follows.

If  ‘C’ and ‘D’  be two points and if a Tachometer is a set up at ‘C’, the     horizontal distance of ‘D’ from ‘C’ and elevation of ‘D’ with respect to the instrument axis at ‘C’ can be obtained from,

1) The vertical angle from ‘D’ to ‘C’.

2)      The angle subtended at ‘C’ by a known distance on the staff held at ‘D’. this principle is utilized in different ways in the ten above methods and consequently, the methods of observation and reduction are different.

PROCEDURE:-

By stadia methods, both constants are determined by field observation as given under.

1)      Measure the distance of 200m. long on fairly level ground and drawing pegs at the same interval say 50m.

2)   Place the instrument on instrument station ‘O’.

3)      Keep the staff on the pegs and observe the corresponding staff readings for three wires which results in “s”. The difference between the top wire reading the bottom wire reading gives the value of “s”

4)      Knowing the value of ‘D’ & ‘S’ ( D is the horizontal distance of the staff station say M from instant station O which we can measure by tape.) for different point a number of the simultaneous equation can be formed.  Subtracting the values of ‘D’ & ‘S’  in the equation the simultaneous solution of successive pairs of equation will give the value of ‘K’ and ‘C’ and average if this can be found.

                                                D = { f / I } S + ( f  + d )

            K = f /  I & C = f + d

                                                      D = Ks + C

                                                      C = f = d = D1 – [(D2-D1) / (S2 – S1)] S1

                                                      K = f / I = (D2 – D1) / (S2 – S1)

FIGURE :- 

 

 

Instrument station	Staff reading on	Distance (m)	Stadia reading
			Lower	Upper

OBSERVATION:-

INST STN.	STAFF STN	DISTA-NCE FROM ‘O’	STAFF READING			STAFF INST	VALUE OF (f / I)	AV (f / I)	VALUE OF (f + d)	AV (f + d)
			TOP	MID	BOTTOM

 

RESULT:-    The respective values of the multiplying constants f / I and f + d are found to be ……….

PRECAUTIONS:- The multiplying constants should be 100.  The axial horizontal line

should be exactly midway between the other two lines.  The telescope should be truly analytic.  The telescope should be powerful having a magnification of 20 to 30  diameters principle of stadia in tachometry is that the ratio of perpendicular to the base is constant in similar isosceles triangles.  Depending upon this concept we determine the distance and elevation to horizontal sight.

 

FIELD MEASUREMENT(Fixed Hair):-

 

Inst. Stn.	Staff Stn.	Staff Reading			Staff Intercept	Value of	Value of	Horiz. dist. from	Instru- ment	Staff	Remarks
		Top	Middle	Lower		f / i	f + d	instrument	R. L.	R.L.

 

FIELD MEASUREMENT BY TANGENTIAL:-

 

Instrument	Staff	Stadia reading		Staff	Vertical	Instrument	Staff
Station	Station	Upper	Lower	Intercept	Angle	R. L.	R. L.