What is theodolite || Parts of theodolite || Surveying Function of theodolite, parts of theodolite

Theodolite Surveying

* Theodolite is used for measuring horizontal and vertical angles. It may be used for prolonging a

line, levelling and even for measuring distances indirectly (tacheometry).

* Main parts of a theodolite are telescope, vertical circle, vernier frame, standards (A-frame) upper

 

plate, lower plate, plate level, levelling head, magnetic compass, tripod, plumb hob and shifting

head.

* Fundamental axes of theodolite are:

1. Vertical axis 2. Trunnion axis

3. Line of collimation 4. Altitude level axis

5. Axis of plate level

A theodolite is said to be in proper condition, if the following conditions are satisfied:

1. The axis of the plate is perpendicular to the vertical axis.

2. The trunnion axis is perpendicular to the vertical axis.

3. The line of collimation is perpendicular to the trunnion axis.

4. The axis of the altitude level is parallel to the line of collimation.

* Temporary adjustment involves setting up, levelling and focussing.

* To get more accurate results in measuring angle take readings by method of repetition and face left

as well as face right.

* In the method of repetition the following errors are eliminated:

1. Errors due to inaccurate graduations

2. Errors due to eccentricity of vernier

3. Errors due to the line of sight and trunnion axis being out of adjustment

4. Errors due to inaccurate bisection.

However, the following errors are not eliminated:

1. Error due to dip

2. Error due to displacement of signal

3. Error due to non-verticality of vertical axis

* In the field theodolite is used to measure direct angle or deflection angle. Direct angles are the

horizontal angles measured clockwise from the preceding line to the following lines. The angle

made by a survey line with the prolongations of the previous line is known as deflected angle.

* Theodolite traversing may be done by the

1. Included angle method

2. Direct angle method or

3. Deflection angle method

Trigonometric Levelling

* This is the method of levelling in which difference between elevation of two points is found by

measuring vertical angles and horizontal distances.

* If base of the object is accessible, the distance of the object and vertical angle to the object may be

measured to find the RLof the object.

* If base line is inaccessible single plane method or double plane method may be used to find RL of

inaccessible object.

 PERMANENT ADJUSTMENTS OFDUMPYLEVEL AND THEODOLITE

* Requirements of dumpy level:

1. The axis of the bubble tube should be perpendicular to the vertical axis.

2. The horizontal cross hair should be in the plane perpendicular to the vertical axis is

perpendicular to vertical axis.

3. The line of sight collimination should be parallel to the axis of bubble tube.

* Required permanent adjustments in theodolite

1. The plate level axis is perpendicular to vertical axis.

2. The horizontal axis is perpendicular to vertical axis.

3. The line of sight coincides with the optical axis of the telescope.

4. The axis of the altitude level is parallel to the line of sight.

5. When the line of sight is horizontal, vertical circle vernier should read zero.

Computation of Areas

* Note 1 hectare = 100 m × 100 m = 1 × 10

4 m2

1 square kilometre = 1000 × 1000 m = 1 × 10

6 m2 = 100 hectare

* Computation from plotted plans is suitable at planning stage but while executing the works

computations of areas from field notes is ideal.

* If boundary of the area has irregular shape, major portion is calculated by dividing area into regular

figures and the smaller areas around the boundary is determined from several offsets taken from

survey lines close to boundary.

* Areas from offsets taken at regular intervals may be found by

1. Mid-ordinate rule:

A =

where oi are mid-ordinates of n number of intervals of size d.

2. Average ordinate rules:

Area =

where n is number of ordinates over L = (n – 1) d length.

3. Area by trapezoidal rule: In this method, area of each segment is calculated as a trapezoid. If d

is the regular interval and total ordinates are n

Area =

4. Simson’s Rule: In this the boundary line is assumed parabolic. If d is the interval and n is the

odd number of ordinates

Area = [(O1 + On + 4 (O2 + O4 + … + On–1

) + 2 (O3 + O5 +… On–2

)]

If there are even number of ordinates, use Simpson’s rule upto n – 1 ordinates and for last

segment use trapezoidal rule.

* Area from coordinates

If (xi

, yi

) are the coordinates of n stations of a closed figure

Area = [(y1

(xn – x2

) + y2

(x1 – x3

) + y3

(x2 – x4

) + … + yn

(xn–1 – x1

)]

* Computing area from maps: methods used are

1. Give and take method

2. Subdivision into squares

3. Subdivision into trapezoids

4. Using planimeter. In this case

Area = M (F – I ± 10 N + C )

where M = Multiplying constant

F = Final reading

I = Initial reading

N = Number of complete revolutions of the disc. Plus sign, if the zero mark of the dial passes the

index mark in clockwise direction and minus if it passes in anticlockwise direction.

C = Area of zero circle. This is added only when the anchor point is inside the area.

M and C are marked by manufacturers on the tracing arm. One can determine them by measuring

area of known simple figures also.

Computation of Volumes

The methods employed are

1. From cross-sections

2. From spot levels

3. From contours

1. From cross sections The first step in computation of volumes is to determine the cross-sectional

areas.

(a) Level sections:

A = (b + nh) h

Fig. 3.1 Level section

(b) Two-level section

A =

Fig. 3.2 Two-level section

(c) Side hill two-level section:

Area of cutting A1 =

Area of filling A2 =

Fig. 3.3 Side hill two-level section

(d) Three-level section:

A =

Fig. 3.4 Three-level section

* If cross sections are found at regular intervals volume by trapezoidal rule is

V =

Volume by prismoidal rule is

V = [(A1 + An

) + 4 (A2 + A4 + … + An – 1

) + 2 (A3 + A5 + …)]

It needs odd number of sections.

2. From spot levels If a pit of area A is made and the depth of four corners from earth surface is h1

,

h2

, h3 and h4

, then

Volume of earth work =

3. Volumes from contours If h is contour interval and area measured between a set of consecutive

contours are A1

, A2

,… A4

, then by trapezoidal rule

V = h

Volume by prismoidal rule is

V = [(A1 + A4

) + 4 (A2 + A4 + … + An – 1

) + 2 (A3 + A5 + …)]

where n is odd number.

Minor Instruments

1. For levelling: hand level, burel hand level

2. For taking horizontal and vertical sights:

Abney level, Indian pattern clinometer, Delisle’s clinometer, Foot rule clinometer, Ceylon ghat tracer.

3. Sextants: These are the instruments, which make use of optical principle to measure an angle in

single observation. Two types of sextants are nautical sextant and box sextant.

4. Pentagraphs: These are the instruments used to reduce or enlarge the maps.

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