This article throws light upon the fixed hair method and moveable hair method of stadia system of tacheometry.
1. Fixed Hair Method of Stadia Tacheometry:
While finding the horizontal distance between an instrument station and a point and the elevation of a point with respect to the instrument station, the line of sight may be horizontal or inclined depending upon their position in the vertical plane.
Case I:
When the line of sight is horizontal and the staff is held vertical, In this case the horizontal distance from the axis of the instrument to the staff station is:
R.L. of the station = R.L of instrument axis — Staff reading on the central hair i.e. axial hair reading.
Case II:
When the line of sight is inclined. When the ground is rough and horizontal sights are not possible, inclined sights have to be taken, in this case the staff may be held either vertical or normal to the line of sight. In general, the method of holding the staff vertically is most commonly adopted because the staff can be held vertically easily and the formulate involved are simpler.
(i) When the staff is held vertically.
In figures 10.5:
Let, O = the instrument — station.
O’ = the position of the instrument axis.
P = the staff station.
ADVERTISEMENTS:
A, C, and B = the points on the staff cut by the hairs of the diaphragm.
∠CO’Q= the inclination to the line of the sight to the horizontal.
AB= S = the staff intercept.
PC= h =the reading with the central hair i.e. the axial reading.
ADVERTISEMENTS:
O’C= L = the inclined distance along the line of sight from the instrument axis O to the point C.
O Q = D = the horizontal distance from the instrument axis to the staff station P.
QC= V = the vertical distance from the instrument axis to the point C.
Through C draw AB perpendicular to O C cutting OA and O B at A and B respectively.
ADVERTISEMENTS:
The inclined distance L
The value of D can be obtained by expressing AB in term in the staff intercept AB (i.e S):
Thus in s AA’C and CB’B angles, AA’C and CB are equal to (90° +α) and (90°-α) respectively .The angle α beings very small, angles AA^C and CB^B may considered to be practically equal to 90°.
Knowing the value of V, the R.L. of the staff attain may be calculated as under:
When is an angle of elevation (Fig. 10.5):
R.L. of staff station P = R.L. of instrument axis + V — h (Eqn. 10.5)
When is an angle of depression:
R.L. of staff station P = R.L. of instrument axis — V — h (Eqn. 10.6)
Note:
The horizontal distance D is the same whether the angle is in elevation or in depression.
The various notations in the above figures are the same as in figures 10.5 and 10.6.
Let us consider the case when is an angle elevation (Fig. 10.7) Let a horizontal line drawn through C meet the vertical line drawn through P at C.
Note:
When θ is small, h sin θ may be neglected and h cos θ taken equal to h
2. Moveable Hair Method of Stadia Tacheometry:
In this method the instruments used are:
(i) A theodolite equipped with a diagram fig. 10.9, the axial wire of which is fixed in the optical axis of the telescope and the stadia wires can be moved by means of two finely threaded micrometer screws, and
(ii) A staff provided with two vanes or targets at some known distance apart, say 3m and 6m. A third vane is fixed exactly midway or levelling purposes.
While observing with the instrument, the middle vane or target is first bisected with the axial wire and the micrometre screws are then simultaneously turned to move the stadia wires to intercept the distance between the targets. The distance through which either wire is moved from the middle one is measured by turns made by the micrometre screws, the whole turns being read on a scale and the fractional parts of a turns on the graduated drums of the micrometre screws.
Thus the distance through which the stadia wires are moved is given by the sum of the micrometre readings.
It may be observed dial in this method, the staff intercept (S) is constant and the stadia interval is variable.
When the line of sight is horizontal, the horizontal distance D is given by:
On comparing this equation with the equation 10.12, it is observed that i of the equation has replaced by nP in the equation 10.12.
Therefore the various formulae for distance and elevations in different cases may be derived as before by substituting nP for i.