tacheometry surveying II

TACHEOMETRIC SURVEYING

Objectives:
1. To plot the plan of the area by the help of tacheometric survey.

Instruments required:
1. Transit Theodolite
2. Stadia rods (staff)
3. Ranging rods
4. Pegs and hammer
5. Tape
6. Prismatic compass
7. Plumb bob

Theory
Tacheometry
Tacheometry (or Tachemetry or Telemetry) is a branch of angular surveying in which the horizontal and vertical distances of points are obtained by optical means as opposed to the ordinary slower process of measurements by tape or chain. The method is very rapid and convenient. Although the accuracy of Tacheometry in general compares unfavorably with that of chaining, it is best adopted in obstacles such as steep and broken ground, deep ravines, stretches of water or swamp and so on, which make chaining difficult or impossible. The accuracy attained is such that under favorable conditions the error will not exceed 1/1000, and if the purpose of a survey does not require greater accuracy, the method is unexcelled. The primary object of Tacheometry is the preparation of contoured maps or plans requiring both the horizontal as well as vertical control. Also, on surveys of higher accuracy, it provides a check on distances measured with the tape.

Instruments for tacheometry
An ordinary transit theodolite fitted with a stadia diaphragm is generally used for tacheometric survey. The stadia diaphragm essentially consists of one stadia hair above and the other an equal distance below the horizontal cross-hair, the stadia hairs being mounted in the same ring and in the same vertical plane as the vertical and horizontal cross-hairs.

Fig.1.5. Stadia diaphragm
Stadia method for tacheometric measurement
This is the most common method in tacheometry. In this method, observation is made with the help of a stadia diaphragm having stadia wires at fixed or constant distance apart. The readings on the staff corresponding to all the three wires are taken. The staffs intercepts, i.e. the difference of the readings corresponding to top and bottom stadia wires will therefore, depend on the distance of the staff from the instrument. When the staff intercepts is more than the length of the staff, only half intercept is read. For inclined sights, readings may be taken by keeping the staff either vertical or normal to the line of sight.

Principle of stadia method
The stadia method is based on the principle that the ratio of the perpendicular to the base is constant in similar isosceles triangles.
In Fig. 1.6, let two rays OA and OB be equally inclined to the central ray OC. Let A2B2, A1B1 and AB be the staff intercepts,
Then OC2A2B2 = OC1A1B1 = OCAB = constant = OC2 × AC
= 12 tan β2 = 12 cot β2

Fig. 1.6.


Fig. 1.7. Principle of stadia method
Let A, C and B = the points cut by the three line of sight corresponding to the three wires.
Also, a, c and b = top, axial and bottom hairs of the diaphragm.
ab = i = interval between the stadia hairs (stadia interval)
AB = s = staff intercept
d = distance of the vertical axis of the instrument from O
D = horizontal distance of the staff from the vertical axis of the instrument
M = center of the instrument corresponding to the vertical axis
Now, from figure,
FCAB = OFa'b' = fi
Or, FC = fi AB = fi s
Also, distance from the axis to the staff is given by
D = FC + ( f + d ) = fi s + ( f + d ) = k s + C
Above equation is known as the distance equation.
The constant k = fi is known as the multiplying constant or stadia interval factor and the constant C = ( f + d ) is known as the additive constant of the instrument.
Using a Plano-convex lens called anallatic or anallactic lens at the vertical axis (at point M), the values of k and C are made 100 and 0 for simplicity of calculation.


Distance and elevation formula

Fig. 1.8
We know, distance of the staff from the instrument is given as
D = k A'B' + C
= k s cos α + C
Then, the horizontal distance is given as
H = D cos α
H = k s cos2 α + C cos α
Also, elevation of the line of sight from the instrument is
V = k s cos α sin α + C sin α
V = k s sin 2α + C sin α
Thus, elevation of the staff station is given by
R.L. of staff station Y = R.L. of instrument station X + H.I. + V − h