Surveying - II Lab Manual

1

1. MEASUREMENT OF ANGLES (HORIZONTAL & VERTICAL) A. MEASUREMENT OF HORIZONTAL ANGLE BY REPETITION METHOD AIM: To Measure the horizontal angle between the two given stations P and Q with

respect to instrument station O.

INSTRUMENTS:

Transit Vernier Theodolite and its accessories & Ranging Rods.

PROCEDURE: Let P and Q be the two given stations. It is required to measure the angle POQ by the method of

repetition where O is the station occupied by the theodolite as shown in fig. 1.

1. Set up the instrument over O and level it accurately (The instrument should be in face right

position and the telescope in the inverted position).

2. Set the reading on vernier A to 00 0' 0" exactly using upper clamp and upper tangent screw.

Loosen the lower clamp, direct the telescope to the station P and bisect P exactly using

lower clamp and lower tangent screw.

3. Unclamp the upper clamp screw, turn the telescope clockwise (Right swing) and bisect

station Q exactly by using the upper clamp and upper tangent screw.

4. Read both the verniers A and B and enter the readings in Table 1.

5. Leaving the verniers unchanged (with upper clamp screw clamped), unclamp the lower plate

and turn the telescope until the station P is attain again bisected accurately using lower

clamp and lower tangent screw.

O

P Q

Fig.1.

2

6. Release the upper clamp screw, turn the telescope clock-wise and again bisect the station Q

exactly using upper clamp and its slow motion screw. The verniers will read now twice the

value of angle POQ.

7. Repeat the process until the angle is measured for the required number of times (usually

three repetitions). Read both the verniers. The final reading is divided by the number of

repetitions to get the correct value of the angle POQ.

8. Change the face of the instrument. The telescope will be now in normal position and the

vertical circle will be in face left position. Repeat the whole series of observations in exactly

the same manner with left swing. The average of the two values of the angle thus obtained

gives a very precise value of angle POQ.

OBSERVATIONS & CALCULATIONS:

TABLE 1:

Inst.

at

Sight

to

Face Right Right Swing Face Left Left Swing

Remarks A B Mean Horz.

Angle A B Mean

Horz.

Angle 0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

O P

Q

P

Q

P

Q

Horizontal angle between P & Q = Final reading / No. of repetitions

RESULT: Horizontal angle between P and Q =

Note: 1. The reading while turning the telescope clock-wise increases. It decreases when

the telescope is turned anti-clockwise.

2. The initial reading in the case of left swing with left face will be 1800 00' 00" instead

of 00 00' 00" in right swing.

3. The experiment can be conducted for different initial reading other than zero and

different combinations of face and swing.

3

B. HORIZONTAL ANGLES BETWEEN GIVEN STATIONS BY THE METHOD

OF REITERATION

PROCEDURE:

Let A, B, C, D & E be the given stations and O be the station occupied by the theodolite as

shown in fig. 2. It is required to measure the angles AOB, BOC, COD, DOE and EOA by the

method of reiteration.

1. Set up and level the instrument over O.

2. Round 1. Inst. Face Right.

a) Set the leading vernier at 00 0' 0" exactly and clamp the upper clamp screw.

b) Turn the whole instrument round and strike A. A is now called the REFERENCE

OBJECT (R.O.)

c) Without touching the lower clamp strict B, C, D, E and A in succession, swinging the

inst. to the right, and note the corresponding angles and enter in Table 2.

The first and the las t readings for A may not agree. If the difference is not too

great record both readings. The final reading of the R.O. must never be assumed. If

the difference is too great reject the entire round.

3. Round 2. Inst. Face Left.

a) Relevel and recentre the inst. if necessary

b) Set the leading vernier at 1800 0' 0" exactly and clamp the plate.

c) Turn the whole inst. round and strike the R.O.

d) Without touching the lower clamp again strike E, D, C, B and A in succession,

swinging the inst. to the left and note the angels correspondingly.

O

E

D

C B

A

Fig. 2.

4


TABLE 2:

Inst.

at

Sight

to



Angle A B Mean

Horz.

Angle 0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

O A

B

C

D

E

A

Correction =

Corrected horizontal angles are AOB =

BOC =

COD =

DOE =

EOA =

Note: 1. Follow the form. It is essential that from whatever side the stations A, B, C, D and E

are approached, they must never be over-ridden, i.e., passed.

2. It is desirable to see A, B, C, D and E are arranged in such a way that at least one

angle is too small and one angle is too large and the rest in between so as to gain

practice in measuring angles of different magnitudes.

5

C. MEASUREMENT OF VERTICAL ANGLE

PROCEDURE:

Let the instrument be set up and leveled over B. It is required to measure the angle of

elevation AOA1 and angle of depression AOA2 where OA1 plane containing axis of the telescope

as shown in fig. 3. The instrument is to be levelled with respect to the altitude bubble also.

1. Round 1. Instrument Face Right

a) By the clip screw bring the altitude bubble to the centre of its run, if necessary

b) Loosen the vertical circle clamp and direct the telescope towards the object A1 and

when it is sighted approximately, clamp the vertical circle and bisect A1 exactly by

using the tangent screw.

c) Read both the verniers C and D, and enter the readings in Table 3. The mean of two

readings gives the angle of elevation ( ) AOA1.

d) Down the telescope and make it horizontal with the help of clop screw. Repeat the

steps b & c to set the angle of depression ( ) AOA2.

2. Round 2. Instrument Face Left

a) If necessary, by the clip screw, bring the altitude bubble to the centre of its run

again.

b) Follow the sane procedure used for Round 1 Face right to obtain the angles & .

3. The average of the two values (Face right and Face left) thus obtained, gives the value of

the required angle free from instrumental errors.

A1

A

A2

G

B

O

Fig. 3.

6


TABLE 3:

Inst.

at

Sight

to


Remarks C D Mean Vert.

Angle C D Mean

Vert.

Angle 0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

O A

A1

A2

Note: It is desirable that a number of vertical angles of varying magnitude above and below the

horizon are measured for practice.

RESULT:

Angle of elevation ( ) =

Angle of depression ( ) =

7

2. THEODOLITE TRAVERSING (GALES TRAVERSE TABLE) AIM: To plot the given traverse by theodolite traversing with the help of Gales traverse table.

INSTRUMENTS:

Theodolite and its accessories, Ranging Rods & Tape

PROCEDURE:

It is required to plot a closed traverse ABCDE as shown in fig. 4.

1. Set up the theodolite instrument over station A and level it accurately. Set the horizontal

angle to zero and fix line of sight towards arbitrary meridian.

2. Direct the telescope towards station B and observe the bearing of the line AB. Set the

back bearing by adding or subtracting 1800. Enter the readings in Table 4.

3. Shift the instrument from station A to station B and level it accurately and sight to A with

the help of lower clamp screw. From the station B, observe the bearing of the line BC.

4. Repeat the step 2 & 3 same for the successive lines and observe the bearings of CD, DE

and EA.

C

N

E D

B

A

Fig. 4

8


1. From the observed bearings, compute the interior angles of the traverse.

2. Add all the included angles. Check that the if included angles must be equal to (2n 4)

right angles, where n is the number of sides of a traverse.

3. If not, find out the error in angle and distribute the error equally to all the sides.

4. Calculate the whole circle bearings of the other lines from the observed bearing of the

first line and the corrected included angles.

5. From the whole circle bearings of the lines, deduce the reduced bearings (R.B.) of the

lines and determine the quadrants in which the lines lie.

6. From the given lengths and the calculated reduced bearings of the lines, compute their

latitudes and departures (consecutive coordinates)

7. Add, all northings and all southings and find the difference between the two sums.

Similarly obtain the difference between the sum of all eastings and the sum of all

westings.

8. Obtain the corrected consecutive coordinates by taking corrections to latitudes and

departures either by Bowditchs rule / Transit rule given below.

a) Bowditchs Rule,

Correction to latitude or departure of any side =

(Total error in latitude or departure

length of that side) /

perimeter of traverse

b) Transit rule,

Correction to latitude of any side =

(Total error in latitude latitude of that

side) / Arithmetical sum of all latitudes

Correction to departure of any side =

(Total error in departure departure of

that side) / Arithmetical sum of all

departure

9. From the corrected consecutive coordinates, obtain the independent coordinates of the

lines, so that they are all positive, the whole of the traverse thus lying in the first

quadrant (N.E.)

10. Finally, plot the traverse by taking independent coordinates.

9

TABLE 4:

Inst.

stn.

Sight

to Line

Length

(m)

Obs.

bearings

(W.C.B.)

Inc.

angles Correc.

Correc.

bearings

(W.C.B.)

R.B. Quadrant

Cons. Coord.

Correc.

Correc.

Cons.

coordinates

Ind.

coordinates Remarks

Lat. Dep.

N

+

S

E

+

W

N

+

S

E

+

W

N

+

S

E

+

W

N S

RESULT:

A closed traverse ABCDEA is plotted with the values obtained in Gales traverse.

9

10

3. DISTANCE BETWEEN TWO INACCESSIBLE STATIONS

AIM:

To determine the distance between two in accessible points by horizontal

angle observations with both faces.

INSTRUMENTS:

Transit Vernier Theodolite and its accessories & Ranging Rods.

PROCEDURE:

It is required to find the horizontal distance between two in accessible points P & Q as

shown in fig. 5.

1. Select base line CD of suitable length so that all points are intervisible.

2. Set up theodolite at C and level it.

3. Keep face left, and 00 0' 0" on vernier. A Bisect P exactly using lower clamp and lower

tangent screw. Release upper clamp and take right swing and bisect point Q exactly

using upper tangent screw. Read both the Verniers A and B and get the mean which

gives the angle PCQ ( 1). Enter the readings in Table 5. Release upper clamp, turn the

telescope towards D and bisect it exactly using upper tangent screw and vertical circle

tangent screw. Read both verniers A and B and get the mean, which gives the angle PCD

( 2). Knowing angle, PCQ & PCD the angle QCD ( 3) can be found. Change the face of

the instrument at C and repeat the whole process. Arrive at average values of angles 1,

2 & 3.

4. Now shift the instrument to the point D. Set up over it and level it.

Keep 00 0' 0" on A vernier, bisect exactly point C using lower clamp and lower tangent

screw and also vertical circle clamp and vertical circle tangent screw. Keep the

instrument in the face right position. Release upper tangent screw. Note the two vernier

readings A and B. The mean value gives the angle CDP ( 4).

Release upper clamp, turn the telescope towards point Q and bisect exactly using upper

tangent screw. Read the two vernier readings and take mean value which gives angle

CDQ ( 5). From the known mean value of angle CDQ and CDP, angle PDQ ( 6) can be

computed.

11


TABLE 5:

Inst.

at

Sight

to



Angle A B Mean

Horz.

Angle 0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

C

D

P

Q

D

C

P

Q

Distance CD (measured) =

CD / sin 7 = PC / sin 4

PC = (CD sin 4) / sin 7

From triangle QCD

CD / sin 8 = QC / sin 5

QC = (CD sin 5) / sin 8

From triangle CPQ

PQ2 = PC

2 + QC

2 2 PC. QC. Cos 1

From which PQ is calculated.

RESULT:

Horizontal distance between two inaccessible P & Q = m

8 7

6

5

4 2 3 1

D C

Q P

Fig. 5

12

4. TRIGONOMETRICAL LEVELLING : BASE ACCESSIBLE

AIM:

To find the elevation of the top of a spire/tower/building (Q) using the

principle of trignometerical levelling.

INSTRUMENTS:

Transit Vernier Theodolite and its accessories, Tape & Levelling Staff.

PROCEDURE:

It is required to find the elevation (R.L.) of the top of a tower Q from the instrument

station P as shown in fig. 6.

1. Set up theodolite at P and level it accurately with respect to the altitude bubble. See that

the vertical circle reads 00 0' 0" when the line of sight is horizontal.

2. Direct the telescope towards Q and bisect it accurately, clamp both the plates. Read the

vertical angle 1 and enter the readings in Table 6.

3. Plunge the telescope and sight to the same point Q and take the vertical angle ( 1).

Calculate the average of the vertical angles measured in both faces.

4. With the vertical vernier set to zero reading and the altitude bubble in the centre of its

run take the reading on the levelling staff kept at A.B.M. Let it be S.

Q1 S

A.B.M.

A

Q

P

D

h

Fig. 6

13


TABLE 6:

Inst.

at

Sight

to

Face Right Right Swing Face Left Left Swing Staff

intercepts

(m)


Angle C D Mean

Vert.

Angle 0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

P

Q S R.L. of

A.B.M.

Distance between the instrument station (P) and the given point (Q) = D = m

From triangle QAQ1, h = D tan

R.L. of Q = R.L. of A.B.M. + S + h

RESULT:

R.L. of the given point Q =

14

5. TRIGONOMETRICAL LEVELLING : BASE INACCESSIBLE

(SINGLE PLANE METHOD)

AIM:

To find the elevation of the top of a building Q using the principle of

trignometerical levelling with the instrument stations having their vertical axes in the

same plane as the object.

INSTRUMENTS:

Transit Vernier Theodolite and its accessories, Tape & Levelling Staff.

PROCEDURE:

It is required to find the elevation (R.L.) of the top of a building Q from the instrument

stations P & R as shown in fig. 7.

1. Set up theodolite at P and level it accurately with respect to the altitude bubble. See that

the vertical circle reads 00 0' 0" when the line of sight is horizontal.

2. Direct the telescope towards Q and bisect it accurately, clamp both the plates. Read the

vertical angle 1 and enter the readings in Table 7.

3. Transit the telescope so that the line of sight is reversed. Mark the instrument station R

on the ground along the line of sight. Measure the distance between P & R accurately.

Let it be b repeat the steps (2) and (3) for both face observations. The mean values

should be adopted in the calculations.

4. With the vertical vernier set to zero reading and the altitude bubble in the centre of its

run take the reading on the levelling staff kept at A.B.M. Let it be S1.

5. Shift the instrument to R and set up the theodolite there. Measure the vertical angle 2

to Q with both face observations.

6. Repeat step (4) and R and to the same A.B.M. Let the reading at R be S 2.

15


TABLE 7:

Inst.

at

Sight

to

Face Right Right Swing Face Left Left Swing Staff

intercepts Remarks C D Mean

Vert.

Angle C D Mean

Vert.

Angle 0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

P

R

Q

Q

S1

S2

R.L. of

A.B.M.

Horizontal distance between P & R = b = m

h1 h2 = S2 S1 = S

D = S b tan 2 / (tan 1 tan 2)

h = D tan 1

R.L. of Q = R.L. of A.B.M. + S1 + h1

or

R.L. of Q = R.L. of A.B.M. + S2 + h2

Note : use + sign if S2 > S1 and use ve sign if S2 < S1 in the expression of D.

RESULT:

R.L. of the given point Q =

Q1

Q'

Q"

A.B.M.

S2 S

S1

B 2

A 1

Q

R P

b D

h1 h2

Fig. 7

16

6. TRIGONOMETRICAL LEVELLING : BASE INACCESSIBLE

(TWO PLANE METHOD)

AIM:

To find the R.L. of the top of an object, when the base of the object is

inaccessible and the instrument stations are not in the same vertical plane as the

elevated object (double plane method) by Trigonometrical levelling.

INSTRUMENTS:

Transitmeter, Theodolite and its accessories, Levelling Staff, Tape, Ranging Rod & Pegs.

PROCEDURE:

Let P and R be the two instrument stations which are not in the same vertical plane as

that of the elevated object Q as shown in fig. 8. P and R are should be selected such that the

triangle PQR is a well conditioned triangle.

It is required to find out the elevation of the top of an object Q.

1. Set up the instrument at P and level it accurately with respect to the altitude bubble.

Bisect the point Q and measure the angle of elevation 1. Enter the readings in Table 8.

2. Sight to point R with reading on horizontal circle as zero and measure the horizontal

angle RPQ1 ( 1) from P.

3. Take a back sight S on the staff kept at A.B.M.

4. Shift the instrument to R and measure 2 and 2 from R.

5. Measure the distance between two instrument stations R and P (equals to b)

17


TABLE 8:

S.

No

Inst.

Stn

Sight

to

Horizontal circle

reading

Avg.

Horz.

angle

Vertical circle

reading Dist.

(m)

Staff

reading Remarks

A

0 ' "

B

0 ' "

Mean

0 ' "

C

0 ' "

D

0 ' "

Mean

0 ' "

0 ' "

P

R

Q

R

Q

P

S

(from P)

S

(from R)

R.L. of

A.B.M.

R.L. of

A.B.M.

From triangle AQQ' h1 = D tax 1

From triangle PRQ1, angle PQ1R = 3 = 1800 ( 1 + 2)

By applying sine rule,

(PQ1 / sin 2) = (RQ1 / sin 1) = (RP / sin 3)

PQ1 = D = b sin 1 / sin ( 1 + 2)

And RQ1 = b sin 1 / sin ( 1 + 2)

h1 = D tan 1 or h2 = RQ1 tan 2

R.L. of Q = R.L. of A.B.M. + S + h1

Or

R.L. of Q = R.L. of A.B.M. + S (from B) + h2

RESULT:

R.L. of the given station Q = m

2

1

1

2

A

P

S

b

R

B

Q

Q'

Q"

Q1

A.B.M.

h1 h2

3

Fig. 8

D

18

7. TACHEOMETRY (STADIA HAIR METHOD)

AIM:

To find the R.L. of an elevated object, when the line of sight is inclined and the

staff is held vertical by using Tacheometry (Stadia Hair method).

INSTRUMENTS:

Tachometer and its accessories (Theodolite), Tape, Pegs & Levelling Staff.

PROCEDURE:

It is required to find the R.L. of an elevated object (Q). It may be the top of building /

water tank / top of hill point.

1. Set up theodolite (also called as tachometer) over a station P. Level the instrument

accurately.

2. Keep a levelling staff over a point (Q) in vertical position.

3. Direct the telescope towards the levelling staff and take the stadia hair readings (top,

central & bottom). Also take the vertical angle ( ) corresponding to the central hair

reading and enter the readings in Table 9.

Q

Q'

B'

B

D

C

D'

A

P

A.B.M.

S1

D

h

V

L

Fig. 9

19

4. Make the telescope horizontal by keep 0

0 0' 0" in the vertical circle take back sight S1 on

A.B.M.


TABLE 9:

Inst.

at

Sight

to

Face Right Right Swing Face Left Left Swing Axial

readings

(Staff

intercepts)


Angle C D Mean

Vert.

Angle 0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

P

Q

A.B.M

R.L. of

A.B.M.

Horizontal Distance = D = K.S. Cos2

+ C. Cos

Vertical Distance = V = K.S. Sin2 / 2 + C. Cos

R.L. of the staff station P = R.L. of B.M. + S1 + V h

Where S is the difference between top and bottom axial readings.

RESULT:

R.L. of the given staff station Q = m.

Note: Take the values of tacheometric constants K & C are 100 & zero respectively.

20

8. TACHEOMETRY (TANGENTIAL METHOD)

AIM:

To find the R.L. of an elevated object using Tacheometry (tangential method).

INSTRUMENTS:

Tachometer and its accessories, Levelling Staff, Ranging Rod & Tape.

PROCEDURE:

It is required to find the R.L. of an elevated object Q as shown in fig. 10.

1. Set up the theodolite instrument over the station P and level it accurately.

2. Keep a levelling staff vertically over the point Q.

3. Mark any two vanes or targets on the levelling staff with a known distance say 0.5 m or

1.0 m.

4. Direct the telescope towards the leveling staff and observe the vertical angles made by

the two targets (say 1 and 2) with respect to the horizontal and enter the readings in

Table 10.

5. Keep a levelling staff over a known A.B.M. and take the staff reading (S1).

A

S

r

1 2

Q

Q'

B

C

P

A.B.M.

S1

D

V

Fig. 10

21


TABLE 10:

Inst.

at

Sight

to

Face Right Right Swing Face Left Left Swing Central

hair

readings


Angle C D Mean

Vert.

Angle 0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

P

C

B

A.B.M

R.L. of

A.B.M.

Vertical angle to the upper vane ( 1) =

Vertical angle to the lower vane ( 2) =

Difference between the two vanes (S) = difference of two central hair

readings taken

Staff reading on A.B.M. (S1) =

Height of the lower vane above foot of the staff = r =

Horizontal distance from the instrument station P to the staff station Q = D = S/(tan 1 tan 2)

Vertical distance from the instrument axis to the lower vane = V = D tan 2

R.L. of the staff station P = R.L. of A.B.M. + S1 + V r

RESULT:

R.L. of the given station Q = m

Note: Use + if 1 > 2, use if 1 < 2

22

9. GRADIENT BETWEEN TWO STATIONS BY TACHEOMETRIC

LEVELING

AIM:

To find the gradient between the two stations by Tacheometric levelling.

INSTRUMENTS:

Tachometer and its accessories, Levelling Staff & Tape

PROCEDURE:

It is required to find the gradient between the A.B.M. and elevated object Q s shown in

fig. 10 (refer the experiment 8). After finding out the horizontal distance, vertical distance, R.L.

of the staff station Q adopt the following procedure further to find the gradient.

1. When the instrument is at P, measure the horizontal angle QPR ( 1) as shown in fig. 11

and enter the readings in Table 11.

2. Shift the instrument to point R (A.B.M.) and take the horizontal angle QRP ( 2).

3. Measure the distance between the instrument station P and R (A.B.M.) let it be b.

3

2

1 b

D

d

R

(A.B.M.)

Fig. 11

P

Q

23


TABLE 11:

Inst.

at

Sight

to



Angle A B Mean

Horz.

Angle 0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

0 ' "

P

R

Q

R

Q

P

R.L. of

A.B.M.

Let d be the distance between R & Q

3 = 1800 ( 1 + 2)

Applying sine rule for the triangle PRQ,

b / sin 3 = D / sin 2 = d / sin 1

calculate d

Gradient from B.M. to Q = Difference in elevation between A.B.M. and elevated object

Q / Horizontal distance

= (R.L. of Q R.L. of B.M.) / d

RESULT:

The gradient between the two stations =

24

10. CURVE TRACING (SIMPLE OFFSET METHOD)

AIM:

To set a simple curve by simple offset method (Linear).

INSTRUMENTS:

Chain / Tape, Pegs & Ranging Rods.

PROCEDURE:

1. Locate the tangent points T1 & T2 and find out their chainage. Calculate the length (c) of

the first sub-chord so that the first peg is the full station.

2. With zero mark at T1 spread the chain (or tape) along the first tangent to point A, on it

such that T1 A1 = C = length of the first sub chord as shown in fig 12.

3. With T1 as centre and T1 A1 as radius, swing the chain such that the arc A1 A = calculate

offset O1. Fix the point A on the curve.

4. Spread the chain along T1 A and pull it straight in this direct on to a point B2 such that

the zero of the chain is at A and the distance AB2 = C = length or the normal chord.

5. With zero of the chain centered at A and AB2 as radius, swing the chain to a point B such

that B2B = O2 = length of the second offset. Fix the point B on the curve.

6. Spread the chain along AB and repeat the spreads (4) and (5) till the point of tangency

(T2) is reached. All intermediate offsets will be equal to C2/R, while the last offset will be

equal to c'/2R (C + c').

25

CALCULATIONS:

Length of I offset O1 = C12 / 2R

II offset O2 = C2 / 2R (C1 + C2)

O3 = C3 / 2R (C2 + C3)

On = Cn / 2R (Cn-1 + Cn)

RESULT:

A simple curve of radius R is set by offset method.

Note: 1. The last point so fixed must coincide with the point of tangency (T2) fixed originally by

measurements from the vertex.

2. If the closing error is more, curve must be reset.

3. If the error is less, it should be distributed to all the point by moving them side ways

by an amount proportional to the square of their distance from the point T1.

D

B1B

O2

A' O1 A

T1 C3

C2

C1

D D 2

O

R R

Fig. 12

26

11. CURVE SETTING (DEFLECTION ANGLE METHOD)

AIM:

To set a simple curve by Rankines method of deflect ion angles

INSTRUMENTS:

Transit Vernier Theodolite and its accessories, Arrows, Tape & Ranging Rods.

PROBLEM:

Two tangents intersect at chainage 592m, the deflection angle being 200 40'. Calculate

the necessary data for setting out a simple curve of 150m radius, if it is intended to set out the

curve by Rankines method of deflection angles. Peg interval being 20 m.

Details of the Curve:

Radius of curve R = 150 m

Deflection angle = 200 40'

Chainage of intersection = 592 m

Length of tangent (T) = R tan ( /2) = () 27.35 m

Chainage of T1 = 564.65 m

Length of curve (L) = ( R / 180) = (+) 54.10 .

Chainage of T2 = 618.75

Length of normal chord = 20 m

Length of 1st sub chord = 570 564.65 = 5.35 m

Length of last sub chord = 618.75 610 = 8.75 m

No. of normal chords = 2 nos.

Tangential angle for 1st sub chord 1 = 1718.9 (C1/R) minutes

= (1718.9 5.35 ) / 150

= 61.30' = 10 1' 18"

Tangential for normal chord = 2 = 3

= 1718.9 (20 / 150)

= 100.269' = 10 40' 16"

27

Inst.

at

Sight

to

Length of sub

chord

(m)

Tangential

angle ( ) 0 ' "

Total tangential

angle ( ) 0 ' "

Theodolite

reading 0 ' "

T1 1st Pt

2nd

3rd

4th

5.35

20

20

8.75

1 1 18

4 59 28

8 48 38

10 28 54

1 1 18

5 59 28

8 48 38

10 28 54

1 1 20

4 59 40

8 48 40

10 29 0

PROCEDURE:

1. Set the theodolite at the point of curve T1 as shown in fig. 13. Level it with both plates

clamped to zero, direct the theodolite to bisect the point of intersection (V). The line of

sight in this direction is that of the rear tangent.

2. Release both lower and upper clamp screws and set angle 1 (deflection angle for first

point on the curve) on the vernier. The line of sight is directed towards first point of the

curve.

3. With zero and of tape pinned on T1 and an arrow held at a distance of the first sub-chord

length along it, swing the tape around T1 till the arrow is bisected by the cross hairs.

Thus the first point is fixed on the curve.

4. Set the second deflection angle 2 on the vernier so that the line of sight is directed

towards second point.

5. With the zero end of the tape pinned at the established first point on the curve, and

arrow held at distance of 20m along it, swing the tape till the arrow is bisected by cross -

hairs, thus fixing the second point on the curve.

6. Repeat the steps (4) and (5) till the last point T2 is reached.

The last point so located must coincide with the point of tangency (T2) fixed

independently by measurements from the point of intersection. If the discrepancy is

small, last few pegs may be adjusted. If it is more the whole curve should be reset.

28

RESULT:

Simple curve of radius 150m is set in the field.

Note: 1. The curve can be set as a left hand curve or a right hand curve.

2. The example given is not necessarily for practice. A different example can be taken

depending on local conditions.

4

3 2

1

O

V

R = 150m

B A

T2 T1

200 40'

Fig. 13

29

12. GLOBAL POSITIONING SYSTEM (GPS)

INTRODUCTION:

GPS, which stands for Global Positioning System, is the only system today able to show

us our exact position on the eartn any time, in any weather, anywhere. It is one of the history's

most exciting and revolutionary development which was developed to meet military needs of the

Department of Defence; but new ways to use its capabilities are continually being found.

What is GPS ?

GPS is a collection of 24 satellites which orbit 12000 miles above the earth's surface,

constantly transmitting the precise the time and their position in space. They provide highly

accurate worldwide positioning and navigation information 24 hours a day; as they are

continuously monitored by ground stations located worldwide. The satellites transmit signals that

can be detected by any one with GPS receiver. As GPS receiver is either on (or near) earth's

surface; and thus listen in on the information received from three to twelve satellites and from

that determine the precise location of the receiver, as well as how fast and in what direction it is

moving.

How GPS works ?

The principle behind GPS is the measurment of distance (or range) between the reciever

and satellites. The working can be explained like this: If we know our exact distance from a

satellite in space, we know we are somewhere on a surface of an imaginary sphere with radius

equal to the satelite radius. If we know our exact distance from the two satellites: than we are

located some where on the line where two spheres intesect. And if we take the third

measurement, there are only two possible points where we could be located. One of these is

usually impossible, and the GPS receivers elliminate that impossible location using mathematical

methods.

What GPS uses to determine location on Earth ?

GPS uses the triangulation of signals from the satellites to determine location on earth.

GPS satellites know their locations in space and receivers can determine their distance from the

satellite by using the travel time of radio message from the satellite to the receiver.

After calculating its relative position to atleast three or four satellites, a GPS receiver can calculate

its position using triangulation. GPS satellites have four highly accurate atomic clocks on board.

30

They also use the database (frequently updated from the earth) of the current and expected

positions for all the satellites in determining the location on the earth.

What are the elements of GPS?

GPS has three parts : The Space Segment, The User Segment and The Control Segment.

Space Segment:

The Space segment consists of 24 operational satellites in six orbital planes (four

satellites in each plane). The satellite operate in circular 20200 Km orbits at an inclination angle

of 55 degrees and with a 12-hour period. The satellite orbits repeat almost the same ground

track (as the earth turns beneath them) once each day. The orbit altitude is such that the

satellites repeat the same track and configuration over any point approximately each 24 hours.

This constellation provides the user with between five and eight Space Vehicles visible from any

point on the earth.

User Segment:

The user segment consists of antennas and receivers - processors that provide

positioning, velocity and precise timing to the user. GPS receivers convert Space Vehicles signals

into position, velocity, and time estimates. Four satellites are required to compute the four

dimensions of X, Y, Z (position) and Time. GPS receivers are used for navigation, positioning,

time dissemination, and other research. Navigation in three dimensions is the primary function of

GPS. Navigation receivers are made for aircraft, ships, ground vehicles, and for hand carrying by

individuals. Precise positioning is possible using GPS receivers at reference locations providing

corrections and relative positioning data for remote receivers. Surveying, geodetic control, and

plate tectonic studies are examples. Time and frequency dissemina tion, based on the precise

clocks on board the SVs and controlled by the monitor stations.

GPS can be used to measure atmospheric parameters.

Control Segment:

The Control Segment consists of a system of tracking stations located around the world.

The control segment in addition of having five Monitor Stations also consists of three Ground

Antennas, and Master Control Station (MCS) located at Schriever Air Force Base (formerly Falcon

AFB) in Colorado. The monitor stations passively track all satell ites in view, accumulating ranging

data. This information is processed at the MCS to determine satellite orbits and to update each

satellite's navigation message. Updated information is transmitted to each satellite via the Ground

Antenna.

31

What are the capabilities of GPS ?

GPS, worldwide satallite based radio navigation system was developed to meet the

military needs. But, new ways to use its capabilities are rapidly being explored. They are as

follows:

During construction of the tunnel under the English Channel.

GPS is helping to save lives. Many police, fire and emergency medical service units are

using GPS receivers to determine the police car, fire truck or ambulance nearest to

emergency, enabling the quickest position response in life or death situations.

Automobile manufacturers are offering moving map display guided by GPS receivers.

GPS technologies are also used for outdoor adventures like hiking, biking, hunting and

boating. GPS is an excellent tool to help you to locate specific position.

GPS products have been also explored in surveying and natural mapping.

It is also monitored for land use planning, urban planning and zoning.

Relief workers could have used photographs by GPS to track refugee movements to plan

delivery of food supplies.

There can be various other purposes like environmental analysis, oil and gas explorations,

agricultural monitoring, insurance and risk management, emergency preparedness and

disaster assessment and so on.

What are the positioning services used by GPS ?

Standard Positioning Service (SPS):

The standard positioning and timing service which is available to all GPS users on a

continuous, worldwide basis with no direct charge .SPS is provided on GPS L1 frequency which a

coarse aquisition code and a navigation data message.

SPS Predictable Accuracy

100 meter horizontal accuracy

156 meter vertical accuracy

340 nanoseconds time accuracy

These GPS accuracy figures are from the 1999 Federal Radionavigation Plan. The figures

are 95% accuracies, and express the value of two standard deviations of radial error from the

actual antenna position to an ensemble of position estimates made under specified satellite

elevation angle (five degrees) and PDOP (less than six) conditions. For horizontal accuracy figures

95% is the equivalent of 2drms (two-distance root-mean-squared), or twice the radial error

standard deviation. For vertical and time errors 95% is the value of two-standard deviations of

vertical error or time error. Receiver manufacturers may use other accuracy measures. Root-

32

mean-square (RMS) error is the value of one standard deviation (68%) of the error in one, two or

three dimensions. Circular Error Probable (CEP) is the value of the radius of a circle, centered at

the actual position that contains 50% of the position estimates. Spherical Error Probable (SEP) is

the spherical equivalent of CEP, that is the radius of a sphere, centered at the actual position,

that contains 50% of the three dimension position estimates. As opposed to 2drms, drms, or RMS

figures, CEP and SEP are not affected by large blunder errors making them an overly optimistic

accuracy measure.

Precise Posit ioning Service (PPS):

The precise positioning service (PPS) is a highly accurate military positioning, velocity and

timing service which will be available on continuous worldwide basis to the authorized user with

cryptographic equipments and keys and specially receivers. Government agencies and selected

civil users specially approved by the government can use the PPS.

PPS Predictable Accuracy

22 meter Horizontal accuracy

27.7 meter vertical accuracy

200 nanosecond time accuracy

33

13. MICRO-OPTIC THEODOLITE

INTRODUCTION:

Micro Optic theodolite is a kind of precision angle-measuring instrument. It plays a very

important role in geodetic survey and engineering measurement, therefore it is widely used in

third-order triangulation, building, roadwork, pipe laying, tunnelling, mining, cadastral survey as

well as machine tooling and installation, etc. The lease count of micro-optic theodolite is 1".

Main Parts of theodolite (Refer figures 14, 15, 16, 17 & 18):

1. Objective 2. Illumination mirror 3. Press button

4. Cover for index error adjusting screw 5. Optical sight

6. Lever 7. Vertical clamp 8. Bayonet ring

9. Eyepiece of microscope 10. Eyepiece of telescope

11. Focussing sleeve 12. Adjustment screw 13. Plate level

14. Circle drive 15. Horizontal clamp 16. Foot screw

17. Optical plummet 18. Cover 19. Horizontal drive

20. Circular bubble 21. Adjustment screw 22. Horz. circle drive

23. Vertical drive 23. Change-over knob 24. Micrometer knob

25. Adjustment screw 26. Hole 27. Positioning pin

28. Clamping screw

Fig. 14

34

Fig. 15 Fig. 16

Fig. 17 Fig. 18

35

Method of Operat ion:

This instrument can be used with a three-groove tribach or a socket tribach. Since the

circle drive knob (22) is embedded into the tribach, it is necessary that the positioning pin (28)

pass through the hold (27) in the tribach before the alidade fits into the tribach. Only by this, the

circle drive can be set properly. Slacken the clamping on tribach before lifting out the alidade

screw (29).

1. Centering:

a) Centering with the plumb bob

Extend tripod legs so that instrument will be at comfortable height. Tread tripod shoes firmly

into ground.

Open the container. Lift out instrument, place on tripod and with one hand still holding the

instrument, attach by means of tripod fixing screw. Rotate the footscrews (16) to centre the

circular bubble, slacken central fixing screw and move over tripod plate until plumb bob is

exactly over ground mark. Retighten fixing screw.

The instrument can be centered under a plumb bob suspended from a roof or ceil ing point,

by lining up the tips of the plumb bob with the small point at the centre of the optical sight.

Before doing this the instrument must be levelled-up and the telescope horizontal (900

0' 0").

b) Centering with the optical plummet:

For precision centering, the optical plummet is used. Turn eyepiece (17,18) of optical

plummet until cross hairs are in focus. Slacken tripod fixing screw and move instrument over

tripod plate until cross hairs coincides with ground mark. Turn the alidade through 1800 and

check centering. Re-centre and relevel if necessary.

2. Levelling up:

a) Levelling up with the plate level:

With horizontal clamp open, turn alidade so that plate level (13) is parallel to the line joining

any two footscrews A and B, by equal and opposite rotations. Turn the footscrew until the

plate bubble is in centre of its run. Turn the alidade through 900 in clockwise direction and

centre the bubble with the third footscrew C. turn the alidade once again so that the plate

level is parallel to the first 2 footscrews A and B and check if the bubble is in centre. Rotate

the alidade by 180 deg. and check if the bubble is in centre of its run. Repeat the procedure

till the bubble is in centre of its run in all four positions of the alidade. The plate level must

be protected from direct sun rays as these may cause the bubble to run off. Note if the

bubble is out by more than 1/2 division, then only adjustment is required, if not, adjustment

is not required.

36

b) Levelling up with the automatic index:

Provided the instrument set-up is very stable. It is possible to level up with the assistance of

the automatic index. With this method, levelling up to about 1" 2" is possible, it is

especially useful for horizontal angle measurement with steep sights and for plumbing. Level

up with plate level then proceed as follows:

i. With alidade in any position, tighten vertical clamp and then read vertical circle.

Vertical clamp and drive must not be touched.

ii. Turn alidade through 1800, read vertical circle, compute the mean, of the vertical

circle readings taken in steps a and b. Now, set micrometer to give the minutes

and seconds of this mean reading.

iii. Turn alidade until telescope is parallel to the line joining any two footscrews, A and B.

Turn A and B very carefully, by equal and opposite rotations, until the circle

graduation lines in top window of reading microscope coincide. That is until mean

vertical circle reading calculated in step b is set.

iv. Turn alidade through 900, turn footscrew C until circle graduation lines coincides.

v. Repeat until graduation lines are in coincidence for all positions of the alidade, i.e.

until vertical circle reading remains constant.

3. Sighting

a) Focussing:

Point telescope to sky or an uniformly light surface. Turn eyepiece (10) until cross hairs are

sharp and black. The dioptric scale now indicates the correct setting for the observers eye.

Note reading for future setting. Slacken horizontal and vertical calmps. Point telescope to

target by means of optical sight. Tighten clamps. Look through telescope eyepiece and turn

focussing sleeve (11) until target is seen. Set cross hairs close to target by turning sleeve

until target image is sharp and free from parallax. If there is parallax remove by adjusting

the focussing slightly. During observation, no further focussing is allowed.

4. Circle Reading:

Both the horizontal circle and vertical circle are read in the microscope. The illumination

mirrors (2, 14, 17) directs light to the circles. The change-over knob is used to select the

required circle. In the left window is the micrometer scale. Turn the eyepiece (9) of microscope

until the reading is sharp and black.

a) Horizontal circle reading:

Slacken horizontal and vertical clamps (7, 26 & 15), turn the alidade. Point telescope to

target by means of optical sight (5). Tighten clamps. Set cross hairs close to target by

turning horizontal and vertical drives (19, 22 & 23).

37

Turn the change-over knob to its stop, so that the white line on the knob is horizontal. Open

and turn the mirrors towards the light so that the field o f view of the reading microscope is

evenly illuminated.

The eyepiece of the reading microscope is turned until the circle graduation lines are in focus.

The cover is then opened and the circle drive (14, 22) turned until the required reading

appears. The cover is now closed to prevent any accidental displacement of the circle.

The micrometer knob (25) must now be turned until the graduation lines coincide exactly

when the micrometer scale is turned. To avoid damage do not exert to much pressure, on

the micrometer knob (25).

Note: The last turn of the knob should be clockwise.

In the central part of the top window are seen the whole degree numbers. Below this is the

number for tens of minutes. In the left part of the screen the micrometer scale is seen the

numbers for minutes are on the left of the scale and tens of seconds on the right of the scale.

The value of one scale interval is 1".

From the fig. 19 the reading in the horizontal circle is 1500 01' 54"

Reading in the top window 1500 00'

Reading in the left window 1' 54"

b) Vertical Circular Reading:

Turn the change-over knob anticlockwise to its stop until the white line is vertical, open and

turn the illumination mirrors towards the light so that the field of view of reading microscope

is evenly illuminated. The vertical circle is read in exactly the same way as the horizontal

circle.

1 5

2 0

149 150 151

0

Fig. 19

38

From the fig. 20 the reading in the vertical circle is 740 47' 16"

Reading in the top window 740 40'

Reading in the left window 07' 16"

7 1

7 2

74 75

4

Fig. 20

Micro-meter

scale

Vernier scale

Documents

Surveying - II Lab Manual