1. MEASUREMENT OF HORIZONTAL ANGLES BY REPITITION METHOD USING A THEODOLITE

AIM: To measure horizontal angles at a point by the method of repetition.

BASIC CONCEPT: The method of repetition of measuring horizontal angle is used for very accurate work. In this

method the angle is divided into the number of repetitions to get the value of the angle. The method of

repetitions consists in measuring the horizontal angle clockwise by any number of times. Generally six repetitions

are made, out of which half of the repetition are made with the telescope normal and the other half with the

telescope inverted. By this process very accurate measurement of angles can be made.

APPARATUS:

1. Theodolite

2. Tripod

3. Ranging Rods

PROCEDURE:

(i)Let an angle AOB is to be measured. The theodolite is set up over station O. All the temporary adjustments are

made.

(ii)Let the first observation be taken with face left. The lower clamp is tightened and upper clamp is loosened.

(iii)The telescope is turned clockwise such that that the vernier A is set to 0 and vernier B to approximately

180.The upper clamp is then tightened. By operating the tangent screw verniers A and B are set exactly on 0

and 180 respectively.

(iv)The lower clamp is then loosened and the telescope is directed to the object A located at the left. The ranging

rod at A is bisected roughly. The lower clamp is tightened and by operating the tangent screw the ranging rod at

A is accurately bisected.

(v)Keeping the lower clamp at fixed condition, the upper clamp is loosened and the telescope is turned clockwise

by roughly bisecting the ranging rod at B. The upper clamp is fixed and tangent screw is operated to get the

correct bisection of ranging rod at B.

(vi)The readings on vernier A, the angle is noted directly. In the case of vernier B, the angle is obtained by

subtracting the initial reading from the final reading. The readings are tabulated.

(vii)Keeping the verniers unchanged, unclamp the lower plate and turn the telescope in clockwise direction and

the object A is bisected using lower clamp and tangent screw.

(viii)Now the upper clamp is released, and the telescope turned clockwise and the station B is bisected again

using the upper clamp and the tangent screw. The verniers will read now, the twice of the angle.

(ix)The process is repeated (usually three) until the requested repetition is over.

(x)Then the face is changed. Now the telescope will be inverted. The whole procedure is repeated.

(xi)The average of the two values of angles gives the precise value of angle AOB.

Face:Left Swing:Clockwise

Mean:

Face:Right Swing:Clockwise

Mean:

RESULT: The included angle AOB is measured as:

A B Difference

Vernier A 0

Vernier B 180

Vernier A

Vernier B

Vernier A

Vernier B

A B Difference

Vernier A 0

Vernier B 180

Vernier A

Vernier B

Vernier A

Vernier B

2. MEASUREMENT OF HORIZONTAL ANGLES BY REITERATION METHOD USING A THEODOLITE

AIM: To measure the horizontal angles at a point by the method of reiteration.

BASIC CONCEPT: In this method several angles subtended at a point are measured successively and finally the

horizon is closed.(Closing the horizon is the process of measuring the angles around a point to obtain a check on

their sum, which should be equal to 360).It is known as direction method or method of series.

APPARATUS:

1.Thedolite

2.Tripod

3.Ranging Rod

PROCEDURE:

(i)The instrument is set at O and initial adjustments are made accurately.

(ii)The vernier is set to zero. The telescope is directed to A and bisected using the lower clamp and tangent screw.

The vernier reading is noted.

(iii)The upper clamp is loosened and the telescope is turned clockwise and the object B is bisected accurately.

Both the verniers are noted and the average value gives the angle AOB>

(iv)Similarly the objects C,D and E are bisected successively and reading both the verniers at every bisection.

(v)Finally the horizon is closed by sighting the ranging rod at A.

(vi)Now the vernier A should read 360.If not, the error is noted, and distributed equally if the error is

small.Otherwise the whole process is repeated.

(vii)It should be noted that the lower clamp remain undisturbed during the revolution of the telescope.

(viii)The face is changed,i.e.the telescope is transited such that it is upside down and is swung through 180

(ix)The vernier is set to 0 or any other degree(say 60)

(x)The horizontal angles are measured in the same manner.

(xi)The mean of the two results is taken as the exact value.

Face:Left Swing:Right

A B C D E A

Vernier A 0

Vernier B 180

AOB=

BOC=

COD=

=

EOA=

Face:Right Swing:Right

A B C D E A

Vernier A 0

Vernier B 180

AOB=

BOC=

COD=

=

EOA=

RESULT:

The angles are measured as

AOB=

BOC=

COD=

=

EOA=

3. MEASUREMENT OF VERTICAL ANGLES AND DETERMINATION OF HEIGHT OF AN

OBJECT USING THEODOLITE SURVEY

Aim: To measure the height of the object (building)

APPARATUS

1.Theodolite

2.Tripod

3.Tape

PROCEDURE:

(i)Level the instrument with reference to the plate level

(ii)Keep the altitude level parallel to any two foot screws and bring the bubble central. Rotate the telescope

through 90 till the altitude bubble is on the third screw. Bring the bubble to the centre with the third foot screw.

(iii)Repeat step (ii) till the bubble is central in both the positions.

(iv)Now rotate the instrument through 180. The bubble should remain in the centre of its run, provided it is in

correct adjustment. The vertical axis will then be truly vertical. If not, it needs permanent adjustment.

(v)In the same way, the instrument should be leveled with reference to the altitude bubble.

(vi)The vertical vernier is set to zero exactly by using clamp and tangent screws.

(vii)The bubble of the altitude level is brought to the centre of its run by means of the clip screws. Thus the line of

collimation is made horizontal.

(viii)The distance D is measured by chain or tape or found out by the stadia method.

(ix)The angle of elevation and angle of depression are measured.

(x)A BS reading is taken on the BM. Let it be h1.

(xi)Now h2=D tan and h3=D tan

(xii)Total height H=h2+h3

(xiii)HI=BM+h1.

(xiv)R.L of P=BM+h1+h2

Face:-Left Face:-Right Mean C D C D

RESULT:

(i)The height of the building is

(ii)The R.L. of the top of the building is

4. HEIGHTS AND DISTANCES

(SINGLE PLANE METHOD USING THEODOLITE)

AIM:- To find the heights and distance of the object using single plane method, the foot of the object being

inaccessible.

APPARATUS:

1.Thedolite

2.Tripod

3.Levelling Staff

4.Tape

PROCEDURE:

(I)Set up the theodolite at P and level it accurately with respect to the altitude bubble.

(ii)Direct the telescope towards Q and bisect it accurately. Clamp both the plates. Read the vertical angle 1.

(iii)Transit the telescope so that the line of sight is reversed. Mark the second instrument station R on the ground

with the help of ranging rod. Measure the distance RP accurately.

(iv) Repeat steps (ii) and (iii) for both face observations. The mean values should be adopted.

(iv) With the vertical vernier set to zero reading, take the reading on the staff kept at the nearby B.M. Take the

staff reading on B.M.(s1)

(v)Shift the instrument to R and set up the theodolite there. Measure the vertical angle 2 to Q with both face

observations.

(vi)With the vertical vernier set to zero reading, take the reading on the staff kept on B.M(s2).

Instrument station

Vertical angle

Face:-Left Face:-Right Mean C D C D

P 1 R 2

s1= ______ s2=_______

B point is at higher elevation than A

h1=D tan 1

h2=(b+D)tan 2

h1-h2=difference in level of instrument axes=s2-s1=s

s=D tan 1-(b+D)tan 2

s + b tan 2

D=

tan 1 tan 2

h1=D tan 1

R.L of Q=R.L of B.M+s1+h1

A point is at higher elevation than B

b tan 2 -s

D=

tan 1 tan 2

h1=D tan 1

R.L of Q=R.L of B.M+s1+h1

R

PQ''

Q'

Q

BA

1

2S1

s

S2

h1

h2

RESULT:

(I)The horizontal distance between instrument station P and Q=

(ii)R.L of Q=

5. HEIGHTS AND DISTANCES

(DOUBLE PLANE METHOD USING THEODOLITE)

AIM:- To find the heights and distance of the object using double plane method, the foot of the object being

inaccessible.

APPARATUS:

1.Thedolite

2.Tripod

3.Levelling Staff

4.Tape

PROCEDURE:

(i)Let P and R be the two instrument stations not in the same vertical plane as that of Q.

(ii)Set up the theodolite at P and level it accurately with respect to the altitude bubble.

(iii)Direct the telescope towards Q and bisect it accurately. Clamp both the plates. Read the vertical angle 1.

(iii)Loosen the upper plate and direct the telescope towards R and note the angle 1.

(iv) Repeat steps (ii) and (iii) for both face observations. The mean values should be adopted.

(iv) With the vertical vernier set to zero reading, take the reading on the staff kept at the nearby B.M. Take the

staff reading on B.M.(s)

(v)Shift the instrument to R and set up the theodolite there. Measure the vertical angle 2 to Q and the horizontal

angle is measured with both face observations.

Instrument station

Vertical angle

Face:-Left Face:-Right Mean C D C D

P 1 R 2

Instrument station

Horizontal angle

Face:-Left Face:-Right Mean

A B A B

P RPQ1(1)

R PRQ1(2)

s=___________

b sin 2

PQ1=D=

sin(1+2)

b sin 1

RQ1=

sin(1+2)

h1=D tan 1

R.L. of Q=R.L. of B.M. + s + h1

RESULT:

(I)The horizontal distance between instrument station P and Q=

(ii)R.L of Q=

6. CLOSED TRAVERSE

(Included Angle Method)

AIM : To conduct a traverse and do the closed traverse computations. APPARATUS:

1.Theodolite

2.Tripod

3.Ranging Rod

Included Angle Method :

This method is most suitable for closed traverse. The traverse may be taken in clockwise or anticlockwise order.

Generally a closed traverse is taken in the anticlockwise direction. In this method the bearing of the initial line is

taken. After this the included angles of the traverse are measured. These angles may be exterior or interior.

Procedure:

(i)The theodolite is set-up and centred over A. The plate bubble is levelled.

(ii)Vernier A is set at 0 and vernier B at 180.The upper clamp is fixed.

(iii)The telescope is oriented along the north line with the help of tubular compass fitted to the instrument. Then

the magnetic bearing of AB is measured.

(iv)Again vernier A is set at 0 and the upper clamp is kept fixed. The lower clamp is loosened and the ranging rod

at E is bisected. Now this clamp is tightened and the upper one is opened.

(v)By turning the telescope clockwise,the ranging rod at B is bisected. The readings on the verniers are noted.

(vi) is obtained in this fashion.

(vii)The face of the instrument is changed and is measured once more. The mean of the two observations

gives the correct value of .

(viii)Similarly the other angles are measured by centring the theodolite at B,C,D and E.

(ix)The arithmetic check is applied as follows:

(2n-4)90=Sum of interior angles.

(x)If there is any error, the error is distributed among the angles.

NE

D

C

B

A

Face:-Left Swing: Right

Inst at Sight To Angle Angle

A E 0 = B

B A 0 = C

C B 0 = D

D C 0 = E

E D 0 = A

Face:-Right Swing:Right

Inst at Sight To Angle Angle

A E 0 = B

B A 0 = C

C B 0 = D

D C 0 = E

E D 0 = A

Result:-

Thus the closed traverse is conducted and the internal angles are computed.

7. OPEN TRAVERSE

(Deflection Angle Method)

AIM:- To conduct a traverse and do the open traverse computations.

APPARATUS:

1.Theodolite

2.Tripod

3.Ranging Rod

Procedure:

(i) This method is suitable for open traverse and is mostly employed in the survey of rivers, coast lines,

roads, railways,etc.

(ii) Suppose an open traverse starts from A. The following procedure is adopted

(iii) The theodolite is setup at A, and then centred and levelled. After this, the bearing of the line AB is

measured in the usual manner.

(iv) The theodolite is now shifted and centred over B. The plate bubble is levelled and vernier A set at 0.Then

a backsight is taken on A.

(v) The telescope is transited and by turning it clockwise the ranging rod at C is bisected. The vernier

readings are taken.

(vi) Then the deflection angle 1 is determined. It is the average value of the angles obtained from verniers A and B.

(vii) Similarly the other deflection angles 2 and 3 are measured. (viii) A field book is prepared in which the deflection angles and offsets are clearly noted.

Diagram:

AB

C

1

2

Result:-

Thus the open traverse is conducted and the deflection angles are computed.

8. EVALUATION OF CONSTANTS OF A TACHEOMETER

AIM: To evaluate the tacheometric constants of a tacheometer.

BASIC CONCEPT: The principle of stadia tacheometry is based on the principle of isosceles triangles. As per this

property of isosceles triangles the ratio of the distance of the base from the apex and the length of the base is

always constant.

FORMULA: D=KS+C

APPARATUS:

(i)Tacheometer

(ii)Tripod

(iii)Levelling staff

(iv)Tape

(v)Peg

Procedure

(i)Set the instrument station at O and temporary adjustments are made.

(ii)From the instrument stations two pegs are driven into the ground at 5m,20m distances and are named as P

and Q. The staff intercepts at P and Q are noted.

(iii)Solving two equations, the multiplying constant K and additive constant C are computed.

Instrument at Distance

Sight to Face:-Left Face:-Right Staff Intercept Top Hair Bottom Hair Top Hair Bottom Hair

O D1= P s1= D2= Q s2=

CALCULATION:

(I)D1=KS1+C1

(II)D2=KS2+C2

D1S2-D2S1

C=

S2-S1

D1-D2

K=

S1-S2

RESULT:

The constants of the given tacheometer are determined and they are found to be

(i)Multiplying Constant K=

(ii)Additive Constant C=

9. AREA OF A POLYGON

AIM: To find the area of the polygon

APPARATUS:

1.Tacheometer

2.Tripod

3.Ranging Rod

4.Tape

PROCEDURE:

1. Set up the tacheometer at 0.

2. Now the horizontal angles AOB, , , , are measured.

3. Measure the distance OA,OB,OC,OD,OE with the help of a tape.

4. The area of the individual triangle is (ab sin C)/2 and the individual areas are added to obtain the area of the

polygon.

Diagram:

O

B

CD

E

Result:

The area of the polygon is

10. TANGENTIAL TACHEOMETRY

AIM: To find the distance and RL of given field points from the given station by the method of tangential

tacheometry.

BASIC CONCEPT:

In this method stadia hairs are not used to bisect the staff for observations. Two vanes at a constant distance

apart are fixed on the staff. Each vane is bisected by the cross-hairs and the staff reading and vertical angle

corresponding to each vanes are recorded.

APPARATUS:

1. Tacheometer

2. Tripod

3. Levelling Staff

NOTATIONS:

P=Position of the instrument

R,S,T=Staff station

M=Position of instrument axis

A,B=Position of top vane and bottom vane

S=distance between the vanes-staff intercept

1=Angle of elevation corresponding to A

2=Angle of elevation corresponding to B

D=Horizontal distance between P and R,S,T ie..MR,MS,MT

V=Vertical intercept between the lower vane and the horizontal line of sight

h=Height of the instrument=MP

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

PROCEDURE:

1. Let R,S,T be the three fixed points on the ground.

2. Set up the instrument at P.

3. Sight the staff placed at each of these points and find out the staff intercepts(S).

4. Note the vertical angles to the top vane and the bottom of the field points.

5. Repeat the steps 3 and 4 for another point, and determine S and vertical angle for other points also.

Instrument station

Staff Station

Top Hair Reading

Bottom Hair Reading

Staff Intercept

1 2 D V

P R

S

T

(i) Both angles are angles of elevation:

s

D=

tan 1 tan 2

V=D tan 2

Elevation of R = (Elevation of station P + h) + V r.

h

a1a2

A

Bs

r

V

DP

Q'

Q

M

Tangential Method:-Both Angles are angles of elevation

(ii) Both angles are angles of depression:

s

D=

tan 2 tan 1

V=D tan 2

Elevation of S = (Elevation of station P + h) - V r.

D

s

r

VP

M

hQ'

A

B

Q

a1a2

Tangential Method:-Both Angles are angles of depression

(iii)One Angle of Elevation and other of Depression:

s

D=

tan 1 + tan 2

V=D tan 2

Elevation of T = (Elevation of station P + h) - V r.

D

P

M

h

a1a2 s

V

rQ

B

Q'

Tangential Method:-One Angle of elevation and the other of depression

RESULT:

The distance and R.L of given points are found to be =

11.STADIA TACHEOMETRY

AIM: To find the distance and RL of given field points from the given station by the method of stadia

tacheometry.

BASIC CONCEPT:

It is the most prevalent method for tacheometric surveying. In this method, the telescope of the theodolite is

equipped with two additional cross hairs, one above and the other below the main horizontal hair at equal

distance. These additional cross hairs are known as stadia hairs. This is also known as tacheometer.

APPARATUS:

1. Tacheometer

2. Tripod

3. Levelling Staff

PROCEDURE:

1. Let P and Q be the two points on the sloping ground.

2. Set up the theodolite at the point M.

3. Place the leveling staff over the point N and hold it upright.

4. Sight the staff placed at the point and observe the vertical angle () and also the staff intercept (s) which is the

difference between the top hair reading and the bottom hair reading.

Instrument station

Staff Station

Top Hair Reading

Middle Hair Reading

Bottom Hair Reading

Staff Intercept(s)

HD VD

M N

CALCULATION:

Horizontal distance between M and N=HD=ks(cos )2 + C cos

Vertical distance between M and N=VD=HD tan

R.L of Point N=R.L of M+H.I+VD-Middle Hair Reading.

RESULT:

The distance and R.L of given points are found to be =

12. SUBTENSE BAR METHOD

AIM:To measure the distance and elevation on sloping ground by subtense bar.

BASIC CONCEPT: The principle of subtense method is just the reverse of the stadia principle. Here the staff

intercept S forms the fixed base and the tacheometric angle changes according with the staff position.

APPARATUS:

1. Theodolite

2. Tripod

3. Ranging Rod

PROCEDURE:

1. Let P and Q be the two points on the sloping ground.

2. Set up the theodolite at the point P.

3. Place the subtense bar at Q such that the subtense bar is perpendicular to the line of sight.

4. Note the horizontal angle between the ends of bar A & B from the instrument station().

5. Also record the vertical angle of the midpoint of the bar C().

CALCULATION:

(i) Distance between P & Q = (D)= S/2 cot (/2) x cos

Where S=3m (normally) is bar distance (AB)

(ii) R.L of Q= R.L of P +H.I+h-height of the subtense bar.

Where h=S/2 cot (/2)xsin

RESULT:

(i)Distance between P and Q=

(ii)R.L of Q=

13. TANGENTIAL CONTOURING (RADIAL)

Aim: To prepare the contour plan for the given area by radial method using tacheometer.

BASIC CONCEPT: A tacheometer is a thedolite fitted with stadia diaphragm so that staff reading against all the

three hairs may be taken. The staff intercepts which is vertical distance between the top and bottom hair of the

staff image is determined. After determining the staff intercept there is no need to measure the horizontal

distance, since the tacheometer gives both the horizontal and vertical distances.

APPARATUS:

(i)Tacheometer

(ii)Tripod

(iii)Levelling Staff

PROCEDURE:

(i)Set the instrument at a convenient place.

(ii)Set the zero reading on horizontal.

(iii)Sight the staff and determine the staff reading. Note the vertical angle .

(iv)On each radial line, readings may be taken on leveling staff kept at different points. The point must be so

chosen that approximate vertical difference in elevation between two consective points is less than the contour

interval.

(v)Set up another angle on horizontal scale and repeat the steps (iii)&(iv)

Radial Position 1 2 3 4 5 6

Top Reading

Middle Reading

Bottom Reading

Staff Intercept

Vertical Reading

D= ks(cos )2 + C cos

V= D tan

RESULT: The contour plan for the given area is plotted.

14. Determination of horizontal distance between two inaccessible points and also the difference in R.L

between the the top of those two points.

Aim:To determine the horizontal distance between two inaccessible points and also the difference in R.L

between the the top of those two points.

APPARATUS:

(i)Tacheometer

(ii)Tripod

(iii)Levelling Staff

PROCEDURE:

(i)Select a base line AB = b m approximately parallel to PQ.

(ii)Set up the instrument over station A and do all temporary adjustments and a ranging rod at B.

(iii)Keep Face left and swing right..

(iv)Loose the upper clamp .Bring the vernier A to 0.Loose the lower clamp and bisect the top point P. Note down

the vertical angle 1.

(v)Loose the upper clamp and bisect the top point Q. Note the angles in vernier A and B.

(vi)Bisect the ranging rod at B and note the angles in vernier A and B.

(vii)Similarly do the experiment by keeping face right and swing right.

(viii)Keep a common Bench Mark for stations A and B say Q and note the staff middle hair reading by keeping

the telescope vertical angle at 0.

(ix)Similarly do the experiment by keeping the instrument at B and the ranging rod at A.

Instrument at

Sight to

Face:Left Swing:Right Face:Right Swing:Right

A B Mean Horizontal Angle

A B Mean Horizontal Angle

A

P

Q

B

B

A

P

Q

PAQ =

QAB =

=

PBQ =

1(At station A by focusing P)=

2(At station B by focusing Q)=

s1=(Staff reading on BM at station A)=

s2=(Staff reading on BM at station B)=

= PAQ + QAB

QBA = + PBQ

Bearing of Line PA=0(Assumed)

Bearing of line AP=180

Bearing of Line AB=180+PAB

Bearing of line BA=Bearing of line AB-180

Bearing of line BQ=Bearing of line BA+ ABQ

Sine Rule

=

PBA

APB

APB = 180 - -

PA= ___m.

AB=___ m

=

QAB

AQB

AQB = 180 - -

QB=____ m

Line Bearing Latitude=L cos Departure=L sin

PA

AB

BQ

Lat =0

Lat Pa + Lat AB + Lat BQ + Lat QP =0

Lat QP= ______

Dep =0

Dep PA + Dep AB + Dep BQ + Dep QP= 0

Dep QP=_______

Length of the line PQ=2 + 2

R.L of point P = R.L of BM + s1 + PA tan 1

R.L of point Q=R.L of BM + s2 + BQ tan 2

Difference in elevation between P and Q = R.l of point P R.L of point Q

RESULT:

(i)The distance PQ=

(ii)Difference in R.L between P and Q=

15.SETTING OUT A SIMPLE CIRCULAR CURVE

(SINGLE THEODOLITE METHOD)(OR)

(RANKINES METHOD OF TANGENTIAL (OR DEFLECTION) ANGLES)

AIM:To trace out a simple circular curve using single theodolite method

BASIC CONCEPT: A curve connecting two intersecting straights have a constant radius all through is known as

simple circular curve. It is tangential to the two straights at the joining ends. In this curve means locating various

points at equal and convenient distances along the length of the curve.

APPARATUS:

(i)Theodolite

(ii)Tripod

(iii)20 m chain

(iv)Ranging Rod

(v)Arrows

PROCEDURE:

(i)Set the thedolite at the point of curve(T1).With both plates clamped to zero, direct the theodolite to bisect the

point of intersection (V).The line of sight is thus in the direction of the rear tangent.

(ii)Release the vernier plate and set the angle 1 on the vernier. The line of sight is thus directed along chord T1A.

(iii)With the zero end of the tape pointed at T1 and an arrow held at a distance T1A=c along it,swing the tape

around T1 till the arrow is bisected by the cross hairs. Thus the first point A is fixed.

(iv)Set the second deflection angle 2 on the vernier so that the line of sight is directed along T1B.

(v)With the zero end of the tape pinned at A, and an arrow held at distance AB=C along it,swing the tape around

A till the arrow is bisected by the croos hairs,thus fixing the point B.

(vi)Repeat steps (iv) and (v) till the last point T2 is reached.

CALCULATION:

(I)For chord of 20 m length,

20:2R = D:360

R=1146/D metres

Where R=Radius of the curve

D=Degree of the curve

(ii)Length of the curve

l=

180

(or)

l=20

l=length of the curve

=Intersection angle or the external deflection angle

1=1=

40

2=1+2 =

40 +

2

Where 1,2,.n=Total tangential angles or the deflection angles to the points.

1,2,.n=The tangential angles

RESULT:

A simple circular curve has been set using the calculation data on the field using single theodolite method.

16. SETTING OUT A SIMPLE CIRCULAR CURVE

(DOUBLE THEODOLITE METHOD)

AIM:To trace out a simple circular curve using double theodolite method

APPARATUS:

(i)Theodolite

(ii)Tripod

(iii)20 m chain

(iv)Ranging Rod

(v)Arrows

PROCEDURE:

(i)Set up one transit at P.C (T1) and the other at P.T.(T2)

(ii)Clamp both the plates of each transit to zero reading.

(iii)With the zeo reading, direct the line of sight of the transit at T1 towards V. Similarly, direct the line of sight of

the other transit at T2 towards T1 when the reading is zero. Both the transits are thus correctly oriented.

(iv)Set the reading of each of the transits to the deflection angle(B1) for the first point A. The line of sight of both

the theodlites are thus directly towards A along T1A and T2A respectively.

(v)Move a ranging rod or an arrow in such a way that it is bisected simultaneously by cross hairs of both the

instruments. Thus point A is fixed.

(vi)To fix the second point C,set reading B2 on both the instruments and bisect the ranging rod.

(vii)Repeat steps (4) and (5) for location of all the points.

The method is expensive since two instruments and two surveyors are required.However this method is most

accurate since each point is fixed independently of the others.An error in setting out one point is not carried right

through the curve as in the method of tangential angles.

CALCULATION:

(I)For chord of 20 m length,

20:2R = D:360

R=1146/D metres

Where R=Radius of the curve

D=Degree of the curve

(ii)Length of the curve

l=

180

(or)

l=20

l=length of the curve

B=Intersection angle or the external deflection angle

1=1=

40

B2=B1+2 =

40 +

2

Where B1,B2,.Bn=Total tangential angles or the deflection angles to the points.

1,2,.n=The tangential angles

B

B1

B2A C

T1 T2

V

B2B1

RESULT:

A simple circular curve has been set using the calculation data on the field using double theodolite method.

17. SETTING OUT A TRANSITION CURVE

Problem:-A road bend which deflects 80 is to be designed for a maximum speed of 100 km per hour, a maximum

centrifugal ratio of and a maximum rate to the change of acceleration of 30 cm/sec3, the curve consisting of a

circular arc combined with two cubic spirals. Calculate(a) the radius of the circular arc, (b) the requisite length of

transition (c) the total length of the composite curve, and (d) the chainages of the beginning and end of transition

curve, and of the junctions of the transition curves with the circular arc if the chainage of the P.I is 42862 metres.

Aim:-To set out the given transition curve and the circular curve

Introduction:-

A transition or easement curve is a curve of varying radius introduced between a straight and a circular curve, or

between two branches of a compound curve or reverse curve.

The functions of a transition curve are:-

(i) To accomplish gradually the transition from the tangent to the circular curve, so that the curvature is increased

gradually from zero to a specified value.

(ii) To provide a medium for the gradual introduction or change of the required super elevation.

Apparatus:

(i) Theodolite

(ii)Tripod

(iii)Ranging Rod

(iv)Arrows

Calculation:

V=100 kmph

v=100x1000

6060 = 27.78 m/sec.

Centrifugal ratio = 2

=

1

4 (given)

R=4 2

=

4(27.78)2

9.81 = 314.68 315 m

The length of the transition curve is given by

L=3

=

(27.78)3

0.3 315 = 226.9 m 227 m

s =

2 radians = 1719

min = 1719

227

315 = 203848

Central angle for the circular curve c = - 2s

= 80 - 411736 = 38 42 24

Length of the circular curve = c

180

= 3153842 24"

180 = 212.8 m

Total length of the composite curve= 212.8 + (2x227) = 666.8 m

Shift s = 2

24 =

(227)2

24(315) = 6.82 m

Total tangent length =(R+s)tan +

2 = (315 + 6.82) tan 80 +

227

2 = 1938.6 m

Chainage of P.I = 42862.0

Deduct tangent length = 1938.6

Chainage of T1 = 40923.4

Add length of transition curve = 227.0

Chainage of junction = 41150.4

Add length of circular curve = 212.8

Chainage of the other junction = 41363.2

Add length of transition = 227.0

Chainage of T2 = 41590.2

Diagram:

Formula:

(i)The deflection angles for the transition curve

= 573 2

minutes

= 1719

minutes

Procedure:

(i)Locate the tangent point T by measuring back the tangent length from the P.I(V). Similarly, locate the other

tangent point T by measuring along the forward tangent the length from the P.I.

(ii)Set the theodolite at T and direct the line of sight towards V when the reading is zero.

(iii)Release the vernier plate and set the vernier to the first deflection angle (1) thus directing the line of sight to

the first peg on the transition curve.

(iv)With the zero end of the tape pinned at T, swing the length of the tape equal to the length of the first chord

till the arrow held at that distance along the tape is bisected by the line of sight. The first peg is thus fixed.

(v)Set the angle 2 on the circle so that the line of sight is directed to the second point. With the zero of the tape

pinned at T hold an arrow at a distance equal to the length of the second chord and swing it till bisected by the

line of sight, thus fixing the second point.

(vi)Repeat the procedure until the last point D is set out. For every point, the chord distance is measured from

the point T and not from the previous point as is done in a circular curve. Check the position of D by measuring

the offset DD2=2

6 = 4s.

(vii)To set out the circular curve, shift the theodolite to the junction point D. To orient the theodolite with

reference to the common tangent DD1 , direct the line of sight towards DT with the reading equal to

(360-2

3 ) for a right hand curve. Since DTV =

1

3 DD1V=

1

3 , we have D1DT=

2

3 . When the theodolite is

rotated in azimuth by an angle 2

3 ( till zero reading is obtained on the circle), the line of sight will be directed

along DD1. On transiting the theodolite now, the line of sight is directed along the tangent D1D with reference to

which the deflection angles of the circular curve have been calculated.

(viii)When the line of sight is thus correctly oriented, the reading on the circle will be zero. To locate the first peg

on the circular curve, the first deflection angle 1 is set out on the curve as usual.

(ix)Set out the circular curve in the usual way till the junction point D is reached, the position of which may be

checked by measuring the offset (=4s) to the second tangent at the point.

(x)Set out the other transition curve from T as before.

Result:

Thus the transition curve and the circular curve is set out.

18. AZIMUTH BY THE EX-MERIDIAN OBSERVATION ON THE SUN

General :

The required altitude and the horizontal angles are those to the suns centre. Hence the hairs should be set

tangential to the two limbs simultaneously. The opposite limbs are then observed by changing the face as shown

in figure.

Procedure :

1. Set the instrument over the station mark and leveling very accurately.

2. Clamp both the plates to zero and sight the reference mark (RM).

3. Turn to the sun and observe and altitude and horizontal angle with the sun in quadrant 1 of the cross hair system.

The motion in the azimuth is slow and the vertical hair is kept in contact by the upper tangent screw, the sun

being allowed to make contact with the horizontal hair the line of observation is also noted.

4. Using two tangential screw as quickly as possible, bring the sun in to the quadrant 3 of the cross hairs and again

read the horizontal and vertical angles. Observe also the chronometer time.

5. Turn to the RM. Reverse the face and take another side to RM.

6. Take two more observations of the sun precisely in the same way as in steps 3 and 4 above, but this time with the

sun is quadrant 2 and 4. Note the time of each observations.

7. Finally bisect the RM to see that the reading is zero.

During the above four observations (two with face left and two with face right)

8. The declination is taken for the corresponding date and the latitude is taken for the corresponding place.

Diagram:

Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4

Calculation: The azimuth (A) can be calculated by one of the following expressions :

sin 1

2 A =

sin().sin ()

sin .sin he following expressions:-

where s = 1

2 (p+c+z)

where c=co-latitude=90-

p=co-declination=90-

z=Corrected co-altitude of star=90-

Correction for refraction:

Correction for refraction (in seconds) = 58 cot

Correction for refraction is always subtractive.

Correction for Parallax:

Correction for parallax= +8.8 cos

Where = Observed Altitude

Correction for parallax is always additive.

Face:Left Swing:Right

Inst at

Sight to

Ver A Ver B Mean Ver C Ver D Mean Note

O RM 0 0 0 180 0 0 0 0 0

Sun 1st Quadrant

Sun 3rd Quadrant

Horizontal Angle (1) Observed altitude()

Face:Right Swing:Right

Inst at

Sight to

Ver A Ver B Mean Ver C Ver D Mean Note

O RM 0 0 0 180 0 0 0 0 0

Sun 2nd Quadrant

Sun 4th Quadrant

Horizontal Angle (1) Observed altitude()

Result:-

(i)Azimuth of the sun=

(ii)Azimuth of the reference meridian=

18. AZIMUTH BY THE EX-MERIDIAN OBSERVATION ON THE SUN