method of tangential tacheometry

The method of tangential tacheometry can be used:

• When staff is held much away from the instrument making it difficult to read it.
• When the diaphragm doesnot have stadia hairs.

In tangential tacheometry, horizontal and vertical distance from the instruments to the staff position are computed from the observed vertical angles to two targets fixed at a distance `S` on the staff.

Depending upon the vertical angles, the following three cases may arises:

• Both vertical angles may be elevation angle.
• Both vertical angles may be depression angles.
• One elevation angle and other depression angle.

Let,

`S`=Distance between targets

`V`=Vertical distance between lowest target(staff reading) and axis of instruments.

`h`=Height of lower staff reading above the staff station

Now, from triangle `OAP'` and `OBP'`,we get,

`V+S=D*tan alpha_1` and

`V=D*tan alpha_2`

Thus,`V....

The method of tangential tacheometry can be used:

• When staff is held much away from the instrument making it difficult to read it.
• When the diaphragm doesnot have stadia hairs.

In tangential tacheometry, horizontal and vertical distance from the instruments to the staff position are computed from the observed vertical angles to two targets fixed at a distance `S` on the staff.

Depending upon the vertical angles, the following three cases may arises:

• Both vertical angles may be elevation angle.
• Both vertical angles may be depression angles.
• One elevation angle and other depression angle.

CASE(i):

Let,

`S`=Distance between targets

`V`=Vertical distance between lowest target(staff reading) and axis of instruments.

`h`=Height of lower staff reading above the staff station

Now, from triangle `OAP'` and `OBP'`,we get,

`V+S=D*tan alpha_1` and

`V=D*tan alpha_2`

Thus,`V+S-V=D*(tan alpha_1-tan alpha_2)`

Or, `D=S/(tan alpha_1-tan alpha_2)`,

Where `S=D*tan alpha_1-tan alpha_2`

Thus, RL of staff station= RL of instrument axis+V-h

CASE(ii)

Here,

`V-S=D*tan alpha_2` and

`V=D*tan alpha_1`

Thus,`V-(V-S)=D(tan alpha_1-tan alpha_2)`

Or, `D=S/(tan alpha_1-tan alpha_2)`,

Where `S=D*tan alpha_1-tan alpha_2`

Also,

`V=(S*tan alpha_1)/(tan alpha_1-tan alpha_2`

Thus, RL of staff station=RL of instrument axis-V-h

CASE (iii):

Here,

`S-V=D*tan alpha_1` and

`V=D*tan alpha_2`

Thus,`(S-V)+V=D(tan alpha_1+tan alpha_2)`

Or, `D=S/(tan alpha_1+tan alpha_2)`,

Where `S=D*tan alpha_1- tan alpha_2`

Also,

`V=(S*tan alpha_2)/(tan alpha_1+tan alpha_2`

Thus, RL of staff station=RL of instrument axis-V-h

DISADVANTAGES OF TANGENTIAL METHOD:

Tangential Method has the following disadvantages:

1. It is rigorous method which requires more time that means it is slow method.
2. It involves more computations for reducing distances and elevations.
3. Minimum two vertical angles are required to be observed for computations.
4. During observing vertical angles, instruments may be unnoticeable disturbed.
5. Staff (targets) is assumed to be perfectly vertical.