TheodoliTheodolitete

Traversing Traversing with theodolitewith theodolite Er Raju Sharma Er Raju Sharma

(Lecturer) (Lecturer)

Department - Department - civil engineering civil engineering

(yamuna (yamuna polytechnic for engineeringpolytechnic for engineering))

YamunanagarYamunanagar

Traversing with Traversing with theodolitetheodolite Traverse may be define as series of Traverse may be define as series of

connected lines from the frame work connected lines from the frame work having the direction and length.theodolite having the direction and length.theodolite is used to find out direction of lines and is used to find out direction of lines and measuring tape is used for measuring measuring tape is used for measuring length in case of theodolite traversing.length in case of theodolite traversing.

There are mainly two method for plotting There are mainly two method for plotting traversing.traversing.

By measurement of angles between two By measurement of angles between two successive lines (by direct observation of successive lines (by direct observation of angle)angle)

By direct observing the bearing of the By direct observing the bearing of the surveysurvey line line..

Traversing by direct Traversing by direct anglesangles

In this method the angle between the In this method the angle between the successive line are measured and the successive line are measured and the bearing of the starting line is bearing of the starting line is observed. The bearing of the observed. The bearing of the remaining lines are then found from remaining lines are then found from the observed bearing and the the observed bearing and the measured angles. Traversing by this measured angles. Traversing by this method is done eithermethod is done either

By the method of included angles.By the method of included angles. By the method of direct anglesBy the method of direct angles By the method of deflection anglesBy the method of deflection angles

(a) (a) Traversing by method of Traversing by method of included anglesincluded angles

In a closed traverse the angle measured In a closed traverse the angle measured either interior or exterior according as either interior or exterior according as the traverse is run in a counter clockwise the traverse is run in a counter clockwise direction .genrally closed traverse in anti direction .genrally closed traverse in anti –counter clockwise direction. the angle –counter clockwise direction. the angle can be measured by repetition so as to can be measured by repetition so as to desired degree of accuracy is obtained.desired degree of accuracy is obtained.

Procedure :Procedure : for running the traverse for running the traverse ABCDEFGABCDEFG

Set up the theodolite at 1Set up the theodolite at 1STST station A and station A and observed the bearing of the line AB.observed the bearing of the line AB.

`̀2. then measure the angle 2. then measure the angle

GAB. Shift the instrument to GAB. Shift the instrument to each of the successive each of the successive station B,C etc. and measure station B,C etc. and measure the angles ABC,BCD etc.the angles ABC,BCD etc.

3. Measure the line AB,BC,CD 3. Measure the line AB,BC,CD etc. and take offset to locate etc. and take offset to locate the required detailthe required detail

after this check is applied for after this check is applied for interiors angles it is (2n-interiors angles it is (2n-4)x90º,4)x90º,

And for exterior angles it is And for exterior angles it is (2n+4)x90º(2n+4)x90º

n = number of sides of the n = number of sides of the traversetraverse

A

G

F E

D

C

B

N

S

By the method of direct anglesBy the method of direct angles : : this method is used for open traverse. set up the this method is used for open traverse. set up the theodolite at the starting station P and observe theodolite at the starting station P and observe the bearing of line PQ . Shift the theodolite to Q. the bearing of line PQ . Shift the theodolite to Q. set the venier A to zero, take a back sight on the set the venier A to zero, take a back sight on the preceding station P.unclamp the upper plate, turn preceding station P.unclamp the upper plate, turn the telescope clockwise, take a foresight on the the telescope clockwise, take a foresight on the following station R, and read both verniers. the following station R, and read both verniers. the mean of two vernier reading is the required angle mean of two vernier reading is the required angle PQR. take other angles in the similar manner. PQR. take other angles in the similar manner. chain the line and take the necessary offsets.chain the line and take the necessary offsets.

P

S

N

Q

R

S

T

By the method of deflection angle:By the method of deflection angle:

This method is also used in open traverse. this This method is also used in open traverse. this is ,much suitable when the survey line makes small is ,much suitable when the survey line makes small deflection angles with each other survey roads deflection angles with each other survey roads railway, pipe line etc .set up the thedolite at the railway, pipe line etc .set up the thedolite at the starting point P and observed the bearing of line PQ. starting point P and observed the bearing of line PQ. shift the instrument to station Q. set the vernnier A to shift the instrument to station Q. set the vernnier A to zero and take a back sight on P. then transit the zero and take a back sight on P. then transit the telescope ,loosen the upper clamp ,turn the telescope telescope ,loosen the upper clamp ,turn the telescope clockwise and take a foresight on R. read both clockwise and take a foresight on R. read both verniers, the mean of these readings is the required verniers, the mean of these readings is the required deflection angles of QR from PQ. Also note down its deflection angles of QR from PQ. Also note down its direction. then set up the theodolite at each successive direction. then set up the theodolite at each successive station R,S,T etc. and observe the deflection angles.station R,S,T etc. and observe the deflection angles.

P

N

S

Q

RT

SØ 1 R

Ø 1 R

Traversing by direct observation of Traversing by direct observation of bearingbearing

There are following three method There are following three method direct method when the telescope is direct method when the telescope is

transited transited Direct method when the telescope is Direct method when the telescope is

not transitednot transited Back bearing methodBack bearing method

(a) Direct method when the telescope (a) Direct method when the telescope is transisitedis transisited Set up the theodolite at A and level it. Set up the theodolite at A and level it.

set the vernier A to zero. point the set the vernier A to zero. point the telescope towards the northtelescope towards the north

Loosen the upper clamp and bisect B Loosen the upper clamp and bisect B by using the upper clamp. read the by using the upper clamp. read the vernier A which gives the bearing of vernier A which gives the bearing of AB.AB.

Shift the instrument and set up at B.Shift the instrument and set up at B. With the help of lower clamp and With the help of lower clamp and

tangent screw ,back sight on A. transit tangent screw ,back sight on A. transit the telescope ,loosen the upper clamp the telescope ,loosen the upper clamp and turn the telescope and bisect and turn the telescope and bisect C ,with the help of upper clamp and C ,with the help of upper clamp and tangent screw ,read both verniers tangent screw ,read both verniers which gives the bearing of line BCwhich gives the bearing of line BC

Sift the instrument at ‘c’ and repeat Sift the instrument at ‘c’ and repeat the whole process.the whole process.

For check at the end FB and BB of line For check at the end FB and BB of line EA differ exactly by 180º.this will show EA differ exactly by 180º.this will show the correct observationthe correct observation

N

S

A

N

N

S

B

C

E D

Direct method when telescope is not Direct method when telescope is not transitedtransited

This is the same method as discussed in the This is the same method as discussed in the above the difference is that the telescope is above the difference is that the telescope is rotated about horizontal plane.rotated about horizontal plane.

Back bearing method :Back bearing method : set up the set up the instrument at A and observe the fore instrument at A and observe the fore bearing of line ABbearing of line AB

Shift the instrument and set it up at BShift the instrument and set it up at B Set the vernier A to back bearing of ABSet the vernier A to back bearing of AB With the vernier A kept clamped at the With the vernier A kept clamped at the

same reading, back sight on A by using the same reading, back sight on A by using the lower clamp and its tangent screw. when lower clamp and its tangent screw. when the line of sight is directed towards the the line of sight is directed towards the BA ,the instrument is in correct orientation.BA ,the instrument is in correct orientation.

Unclamp the upper plate and turn the Unclamp the upper plate and turn the telescope until c is sighted. bisect C exactly telescope until c is sighted. bisect C exactly by using the upper clamp and its tangent by using the upper clamp and its tangent screw.screw.

Read the vernier A which gives the bearing Read the vernier A which gives the bearing of BC of BC

Repeat the process at each of the Repeat the process at each of the subsequent stationsubsequent station

A

E D

N

N

N

S S

B

C

Latitude and departureLatitude and departure Both terms are introduced with plotting Both terms are introduced with plotting

the traverse. latitude and departure both the traverse. latitude and departure both are required for plotting the position of are required for plotting the position of different point different point w.r.tw.r.t yy-axis and -axis and xx- axis. y - axis. y axis and x axis are known as reference axis and x axis are known as reference line and are also known as the co-line and are also known as the co-ordinates.ordinates. N

S

EW

Reference axis- x axis

Reference axis- y axis DepartureEasting = +

Latitudenorthing=+

Latitude Southing= -ve

DepartureWesting= -ve

ØØ

Latitude and departureLatitude and departure

Latitude of line =Latitude of line =ll cos Ø cos Ø Departure of line = Departure of line = ll sin Ø sin Ø

If N 30 º S is the bearing of a any If N 30 º S is the bearing of a any given line N show that its latitude given line N show that its latitude and S shows departure of the line.and S shows departure of the line.

The following rules will be much useful while The following rules will be much useful while solving problems on traverse surveyingsolving problems on traverse surveying

If l is the length of a line and Ø is its If l is the length of a line and Ø is its reduced bearing. Then reduced bearing. Then

l

N

S

W E

L c

os

Ø=

la

titu

de

L sin Ø =departure

Ø

(i) Latitude = (i) Latitude = ll cos Ø cos Ø Departure = Departure = ll sin Ø sin Ø

(ii) Tan Ø= (ii) Tan Ø= departuredeparture latitudelatitude Ø = tan¯1 Ø = tan¯1 departuredeparture latitudelatitude

(iii) (iii) ll = = (latitude)²+(departure)² (a) l = latitude x sec ØØ (c) (c) ll = departure x cosec Ø = departure x cosec Ø

Q: 1 Q: 1 The coordinates of two The coordinates of two points A and B are as follows. points A and B are as follows. Find the length and bearing of Find the length and bearing of AB AB

Let Let l l = length of AB = length of AB

Ø = the reduced bearing of AB.Ø = the reduced bearing of AB.

LATITUDE of AB = 840.78 – 500.25= LATITUDE of AB = 840.78 – 500.25= 340.53340.53

DEPARTURE of AB = 315.60-640.75= DEPARTURE of AB = 315.60-640.75= -325.15-325.15

tan Ø = tan Ø = departure departure 325.15 325.15 = .9548= .9548

latitude 340.53latitude 340.53

Ø = 43º41’Ø = 43º41’

Since the latitude is +ve and the Since the latitude is +ve and the departure is –ve ,the line AB lies in departure is –ve ,the line AB lies in the fourth (N.W) quadrant.the fourth (N.W) quadrant.

R.B of AB = N 43º41’WR.B of AB = N 43º41’W

W.C.B of AB = 360-43º41’= W.C.B of AB = 360-43º41’= 316º19’ (ANS)316º19’ (ANS)

length of AB = (L²)+(D²) length of AB = (L²)+(D²)

470.83 m (ans)470.83 m (ans)

pointpointss

Co-ordinatesCo-ordinates

Northing Northing EastingEasting

A A 500.25500.25 640.75640.75

B B 840.78840.78 315.60315.60

a

b

500.25,640.75

840.78,315.60N

S

EW

Q : 2 the following are Q : 2 the following are the length and bearing the length and bearing of the sides of a closed of the sides of a closed traverse ABCDtraverse ABCD

Calculate the length and Calculate the length and bearing of line DA.bearing of line DA.

Let length of DA= Let length of DA= l ,l ,R.BR.B of line-Øof line-Ø

(i)(i) Convert the W.C.B to Convert the W.C.B to the R.Bthe R.B

R.B R.B of AB= 180º-140º of AB= 180º-140º 12’=S39º 48’E 12’=S39º 48’E

R.B R.B of BC=36º24’ of BC=36º24’ =N36º24’E=N36º24’E

R.B R.B of CD=of CD=360º-338º48’=N21º12’W360º-338º48’=N21º12’W

Line Line Length Length in in metersmeters

bearinbearingg

ABAB 78.278.2 140º1140º12’2’

BCBC 198.0198.0 36º 36º 24’24’

CDCD 37.837.8 338º 338º 48’48’

DADA ?? ??

(ii) find the latitude and departures of the lines (ii) find the latitude and departures of the lines from the known length and bearing of the lines.from the known length and bearing of the lines.

latitude of AB = 78.2 x cos39º48’ = -60.08(S)latitude of AB = 78.2 x cos39º48’ = -60.08(S) latitude of BC =198XCOS 36º 24’= +159.37 (N)latitude of BC =198XCOS 36º 24’= +159.37 (N)latitude of CD = 37.8x COS 21º 12’= 35.24 (N)latitude of CD = 37.8x COS 21º 12’= 35.24 (N)latitude of DA = latitude of DA = l l x cosØ = x cosØ = l l cosØcosØAlgebraic sum of the latitude( ∑ ) Algebraic sum of the latitude( ∑ ) = l cosØ+35.24+159.37-60.08= l cosØ+35.24+159.37-60.08 = l cosØ+ 134.53= l cosØ+ 134.53The traverse being closed ( ∑ ) should equal zeroThe traverse being closed ( ∑ ) should equal zero lcosØ+134.53 = 0lcosØ+134.53 = 0lcosØ= -134.53lcosØ= -134.53

Departure of AB = 78.2xsin 39º48’= +50.06 Departure of AB = 78.2xsin 39º48’= +50.06 (E)(E)

Departure of BC = 198xsin 36º24’ = +117.49 Departure of BC = 198xsin 36º24’ = +117.49 (E)(E)

Departure of CD = 37.8x sin 21º12’ = -13.6 Departure of CD = 37.8x sin 21º12’ = -13.6 (w)(w)

Departure of DA = lxsinØDeparture of DA = lxsinØ

Algebric sum of departure ( ∑ )Algebric sum of departure ( ∑ )

= l sinØ+50.06+117.49-13.67= l sinØ+50.06+117.49-13.67

= lsinØ + 153.88= lsinØ + 153.88 But ∑ D =0But ∑ D =0

lsinØ + 153.88 = 0lsinØ + 153.88 = 0

lsinØ = -153.88lsinØ = -153.88

(iii) since the latitude and departure of DA (iii) since the latitude and departure of DA are both –ve therefore, the line DA lies in are both –ve therefore, the line DA lies in the iii (SW) quardentthe iii (SW) quardent

now tanØ= now tanØ= departure departure 153.88 153.88

latitude 134.53latitude 134.53

=1.1438=1.1438

Ø =48º50’Ø =48º50’

hence reduced bearing of DA= S48º50’Whence reduced bearing of DA= S48º50’W

W.C.B of DA = 180º+ 48º50’=228º 50’W.C.B of DA = 180º+ 48º50’=228º 50’

length of DA = (lat) ²+(dep)² = length of DA = (lat) ²+(dep)² = 204.40m(ans)204.40m(ans)

Error in theodolite Error in theodolite surveyingsurveying These may be classified into 3 groups These may be classified into 3 groups

Instrumental error Instrumental error Personal error or observation errorPersonal error or observation error Natural errorNatural error Instrumental errorInstrumental error : (i) : (i) non adjustment of non adjustment of

plate levelplate level::if the adjustment of a plate is not proper as a if the adjustment of a plate is not proper as a

result, the horizontal circle is inclined and the result, the horizontal circle is inclined and the angles are measured in an inclined plane angles are measured in an inclined plane instead of horizontal plane. The error are instead of horizontal plane. The error are introduced in the measurement of both introduced in the measurement of both horizontal and vertical angles. the error is horizontal and vertical angles. the error is serious when the horizontal angles between serious when the horizontal angles between points at considerably different elevation are to points at considerably different elevation are to be measured. the error can be minimized by be measured. the error can be minimized by levlling the instrument with reference to be levlling the instrument with reference to be altitude bubble.altitude bubble.

(ii) (ii) The line of collimation not being The line of collimation not being perpendicular to the horizontal axis: perpendicular to the horizontal axis:

if line of collimation not perpendicular if line of collimation not perpendicular to the horizontal axis ,as a result of this to the horizontal axis ,as a result of this the horizontal angles when measured the horizontal angles when measured between points at widely different between points at widely different elevation will be incorrect elevation will be incorrect

the the error can be eliminated by reading error can be eliminated by reading angles on both the faces and taking the angles on both the faces and taking the mean of the observed readingmean of the observed reading

(iii(iii) the horizontal axis not being ) the horizontal axis not being perpendicular to the vertical axisperpendicular to the vertical axis

if the horizontal axis is not perpendicular if the horizontal axis is not perpendicular to the vertical axis, the line of collimation to the vertical axis, the line of collimation not revolved in a vertical plane when the not revolved in a vertical plane when the telescope is raised or lowerd. This causes telescope is raised or lowerd. This causes an angular error both in horizontal and an angular error both in horizontal and vertical angles.vertical angles.

the error can be the error can be eliminated by reading angles on both the eliminated by reading angles on both the faces and taking mean of the two values.faces and taking mean of the two values.

(iv) (iv) the line of collimation and the the line of collimation and the axis of telescope –level not being axis of telescope –level not being parallel to each otherparallel to each other

if this type of condition occurred ,the if this type of condition occurred ,the zero line of vertical verniers is not a zero line of vertical verniers is not a true line of reference and as a true line of reference and as a result ,an error is introduced in the result ,an error is introduced in the measurement of vertical anglemeasurement of vertical angle

the error can be eliminated the error can be eliminated by taking two observation of the angles, by taking two observation of the angles, one with the telescope normal and the one with the telescope normal and the other with the telescope inverted ,and other with the telescope inverted ,and taking mean of the two valuestaking mean of the two values

The inner and outer axis The inner and outer axis i.e i.e the axis of the axis of both upper and lower plate not being both upper and lower plate not being concentricconcentric

the error can be eliminated by reading the error can be eliminated by reading both verniers and averaging the two values.both verniers and averaging the two values.

The graduation being unequalThe graduation being unequal The error is eliminated by measuring the The error is eliminated by measuring the

angles several times on different parts of angles several times on different parts of the circle and taking mean of all.the circle and taking mean of all.

Vernier being eccentricVernier being eccentric The zero of the vernier will not be The zero of the vernier will not be

diametrically opposite to each other. an diametrically opposite to each other. an error will be introduced if only one vernier error will be introduced if only one vernier is read ,but it will cancel itself ,if both is read ,but it will cancel itself ,if both verniers are read and the mean taken.verniers are read and the mean taken.

The vertical hair not being exactly The vertical hair not being exactly verticalvertical

The error is minimised by using The error is minimised by using thethe portion of portion of the hair near the horizontal hair for bisecting the hair near the horizontal hair for bisecting the signal.the signal.

Personal errorPersonal error : : Inaccurate centeringInaccurate centering Inaccurate leveling Inaccurate leveling Working wrong tangent screwWorking wrong tangent screw SlipSlip ParallaxParallax Inaccurate bisection of the point sighted Inaccurate bisection of the point sighted

and non-verticality of the ranging rodand non-verticality of the ranging rod

Other error such as Other error such as mistake in setting the verniermistake in setting the vernier Mistake in reading the scale and the vernierMistake in reading the scale and the vernier Mistake in reading wrong vernierMistake in reading wrong vernier Mistake while booking the reading Mistake while booking the reading Natural error : Natural error : this error are due tothis error are due to High temperature causing irregular refractionHigh temperature causing irregular refraction Wind storm causing vibration of the instrumentWind storm causing vibration of the instrument The sun shining on the instrument The sun shining on the instrument These are negligible for ordinary survey. but the precise work These are negligible for ordinary survey. but the precise work

is usually performed under the most favorable atmosphere is usually performed under the most favorable atmosphere conditioncondition

Er Raju Sharma Er Raju Sharma

(Lecturer) (Lecturer) Department- Civil Department- Civil

EngineeringEngineering Yamuna polytechnic for Yamuna polytechnic for

EngineeringEngineering YamunanagarYamunanagar