# METHOD OF TACHEOMETRIC SURVEY

Upendra Kumar

THERE ARE TWO METHOD OF TACHEOMETRY SURVEY

2.Tangential Method.

i. Fixed Hair Method:- This method of tacheometry is most commonly used. In this method, the stadia hair interval is fixed. When a staff is sighted through the telescope, a certain length of the staff is intercepted by the stadia lines and from this value of the staff intercept, the distance from the instrument to the staff station may be determined.

The measurement in tacheometry on fixed hair method has three types.

Case I:-When the line of sight is horizontal and the staff held verticle TACHOMETER

O= Optical center of object-glass.

A₁,A₂,C= Reading on the staff.

a₁,a₂ and c₁=Bottom, top and central hair on the diaphragm.

a₁,a₂=i= length of the image.

A₁,A₂= staff intercept.

F= Focus

V= Vertical of the instrument.

f= Focal length of the object-glass.

d= distance between the optical center and the vertical axis of the instrument.

u= Distance between optical center and staff.

v=Distance between optical center and image.

In the triangle a₁Oa₂=A₁OA₂

i/s=v/u                                                                                                     (1)

or v= iu/s

we know that property of lenses

1/v+1/u=1/f                                                                                              (2)

putting the value of v in equation (2)

or           1/iu/s+1/u=1/f

or             {1/u{s/i+1}=1/f

or            u= {s/i+1}f                                                                           (3)

D=           u+d

D=          {s/i+1}f +d

= s/if+f+d

= f/i*s+(f+d)                                                                                        (4)

Hence ,

Horizontal distance (D) of the staff from the vertical axis of the instrument is given by

D=f/i*s+(f+d)

Elevation of the staff station
= Elevation of the instrument axis-Axial hair reading

Case II:- When the line of collimation is inclined to the horizontal and the staff is held vertically. HORIZONTAL METHOD

Let A=The instrument station

A'= The position of the instrument axis.
P=  The staff station.
D, C, B=The points on the staff cut by the hairs of the diaphragm.
CA'K=𝞱=The inclination of the line of collimation A'C to the horizontal.
DB =S=The staff intercept.
A'C=L= The distance along the line of collimation from the instrument axis A' to point C.
A'K=D= The horizontal distance from the vertical axis of the instrument to the staff station P.
KC=V=The vertical distance from the instrument axis to point C.

In the above picture

Draw a line D'B' on the line A'C
The angle 𝛃 is small it may be neglected

From formula (4)
L= f/i D'B'+(f+d)
= f/i✖S cos𝞱
Horizontal Distance A'K=D=L cos𝞱
= f/i✖S cos  ²𝞱 +(f+d) cos𝞱
Vertical distance KC=V=L sin𝞱
V=f/iS sin𝞱cos𝞱+(f+d)sin𝞱

Case II:-When the line of collimation is inclined to the horizontal and the staff is held normal to the line of collimation.

In the above picture.

A'C= the line of collimation at an angle 𝞱 to the horizontal.
DB=S= the staff intercept.
Draw a line CC1
angle CPC1=angle CA'K=𝞱
Then CC1=hsin𝞱
PC1=PCcosCPC1=hcos𝞱
L=f/i*S+(f+d)
Horizontal distance
D=f/i*Scos𝞱+(f+d)cos𝞱+hsin𝞱
vertical distance V= L sin𝞱
=f/i Ssin𝞱+(f+d)sin𝞱

2.Tangential Method.  :-

This method is used when the telescope is not fitted with a stadia diaphragm. The horizontal and vertical distances of the staff station from the instrument station may be computed from observations taken to two vanes or targets on the staff at a known distance(S).
Solve the triangle BA'K and triangle CA'K
BK=Dtan∝1
CK=Dtan∝2
S=D(tan∝1-tan∝2)
D=S/(tan∝1-tan∝2)
V=Dtan∝2