Introduction Of Theodolite,traversing By Theodolite,error In Traversing 5w1111
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Theodolite Traversing with theodolite Er Raju Sharma Department - civil engineering Chandigarh University
Traversing with theodolite
Traverse may be define as series of connected lines from the frame work having the direction and length.theodolite is used to find out direction of lines and measuring tape is used for measuring length in case of theodolite traversing. There are mainly two method for plotting traversing. By measurement of angles between two successive lines (by direct observation of angle) By direct observing the bearing of the survey line.
Traversing by direct angles In this method the angle between the successive line are measured and the bearing of the starting line is observed. The bearing of the remaining lines are then found from the observed bearing and the measured angles. Traversing by this method is done either By the method of included angles. By the method of direct angles By the method of deflection angles
(a) Traversing by method of included angles
In a closed traverse the angle measured either interior or exterior according as the traverse is run in a counter clockwise direction .genrally closed traverse in anti –counter clockwise direction. the angle can be measured by repetition so as to desired degree of accuracy is obtained. Procedure : for running the traverse ABCDEFG Set up the theodolite at 1ST station A and observed the bearing of the line AB.
2. then measure the angle GAB. Shift the instrument to each of the ` successive station B,C etc. and measure the angles ABC,BCD etc. 3. Measure the line AB,BC,CD etc. and take offset to locate the required detail after this check is applied for interiors angles it is (2n-4)x90º, And for exterior angles it is (2n+4)x90º n = number of sides of the traverse
E
F D
N A
C
G
B
S
By the method of direct angles : this method is
used for open traverse. set up the theodolite at the starting station P and observe the bearing of line PQ . Shift the theodolite to Q. set the venier A to zero, take a back sight on the preceding station P.unclamp the upper plate, turn the telescope clockwise, take a foresight on the following station R, and read both verniers. the mean of two vernier reading is the required angle PQR. take other angles in the similar manner. chain the line and take the necessary offsets. N T P R S
Q
S
By the method of deflection angle:
This method is also used in open traverse. this is ,much suitable when the survey line makes small deflection angles with each other survey roads railway, pipe line etc .set up the thedolite at the starting point P and observed the bearing of line PQ. shift the instrument to station Q. set the vernnier A to zero and take a back sight on P. then transit the telescope ,loosen the upper clamp ,turn the telescope clockwise and take a foresight on R. read both verniers, the mean of these readings is the required deflection angles of QR from PQ. Also note down its direction. then set up the theodolite at each successive station R,S,T etc. and observe the deflection angles. N
Q
Ø1R
P R S
Ø1R S T
Traversing by direct observation of bearing
There are following three method direct method when the telescope is transited Direct method when the telescope is not transited Back bearing method
(a) Direct method when the telescope is transisited
Set up the theodolite at A and level it. set the vernier A to zero. point the telescope towards the north Loosen the upper clamp and bisect B by using the upper clamp. read the vernier A which gives the bearing of AB. Shift the instrument and set up at B. With the help of lower clamp and tangent screw ,back sight on A. transit the telescope ,loosen the upper clamp and turn the telescope and bisect C ,with the help of upper clamp and tangent screw ,read both verniers which gives the bearing of line BC Sift the instrument at ‘c’ and repeat the whole process. For check at the end FB and BB of line EA differ exactly by 180º.this will show the correct observation
N B N
N
C
A S
S E
D
Direct method when telescope is not transited
This is the same method as discussed in the above the difference is that the telescope is rotated about horizontal plane. Back bearing method : set up the instrument at A and observe the fore bearing of line AB Shift the instrument and set it up at B Set the vernier A to back bearing of AB With the vernier A kept clamped at the same reading, back sight on A by using the lower clamp and its tangent screw. when the line of sight is directed towards the BA ,the instrument is in correct orientation. Unclamp the upper plate and turn the telescope until c is sighted. bisect C exactly by using the upper clamp and its tangent screw. Read the vernier A which gives the bearing of BC Repeat the process at each of the subsequent station
N B N
N
C
A S
S E
D
Latitude and departure
Both are introduced with plotting the traverse. latitude and departure both are required for plotting the position of different point w.r.t y-axis and x- axis. y axis and x axis are known as reference line and are also known as the coordinates. Ø N Reference axis- y axis
Departure Westing= -ve W
Departure Easting = +
Reference axis- x axis
Latitude northing=+ E
Latitude Southing= -ve S
Latitude and departure
Latitude of line =l cos Ø Departure of line = l sin Ø
If N 30 º S is the bearing of a any given line N show that its latitude and S shows departure of the line.
The following rules will be much useful while solving problems on traverse surveying
If l is the length of a line and Ø is its reduced bearing. Then L cos Ø= latitude
N
l Ø
W
E
L sin Ø =departure S
(i) Latitude = l cos Ø Departure = l sin Ø
(ii) Tan Ø= departure latitude Ø = tan¯1 departure latitude (iii) l = (latitude)²+(departure)² (a) l = latitude x sec Ø (c) l = departure x cosec Ø
Q: 1 The coordinates of two points A
and B are as follows. Find the length and bearing of AB Let l = length of AB Ø = the reduced bearing of AB. LATITUDE of AB = 840.78 – 500.25= 340.53 DEPARTURE of AB = 315.60-640.75= -325.15
tan Ø = departure latitude
325.15 340.53
points
Northing Easting
= .9548
Ø = 43º41’ Since the latitude is +ve and the departure is – ve ,the line AB lies in the fourth (N.W) quadrant. R.B of AB = N 43º41’W W.C.B of AB = 360-43º41’= 316º19’ (ANS) length of AB = (L²)+(D²) 470.83 m (ans)
Co-ordinates
A
500.25
640.75
B
840.78
315.60
N
b a
W
840.78,315.60
500.25,640.75 E
Q : 2 the following are the length and bearing of the sides of a closed traverse ABCD Calculate the length and bearing of line DA. Let length of DA= l ,R.B of lineØ (i) Convert the W.C.B to the R.B R.B of AB= 180º-140º 12’=S39º 48’E R.B of BC=36º24’ =N36º24’E R.B of CD= 360º-338º48’=N21º12’W
Line AB BC CD DA
Length in meters 78.2 198.0 37.8 ?
bearing 140º12’ 36º 24’ 338º 48’ ?
(ii) find the latitude and departures of the lines from the known length and bearing of the lines.
latitude of AB = 78.2 x cos39º48’ = -60.08(S) latitude of BC =198XCOS 36º 24’= +159.37 (N) latitude of CD = 37.8x COS 21º 12’= 35.24 (N) latitude of DA = l x cosØ = l cosØ Algebraic sum of the latitude( ∑ ) = l cosØ+35.24+159.37-60.08 = l cosØ+ 134.53 The traverse being closed ( ∑ ) should equal zero lcosØ+134.53 = 0 lcosØ= -134.53
Departure of AB = 78.2xsin 39º48’= +50.06 (E) Departure of BC = 198xsin 36º24’ = +117.49 (E) Departure of CD = 37.8x sin 21º12’ = -13.6 (w) Departure of DA = lxsinØ
Algebric sum of departure ( ∑ ) = l sinØ+50.06+117.49-13.67 = lsinØ + 153.88 But ∑ D =0 lsinØ + 153.88 = 0 lsinØ = -153.88
(iii) since the latitude and departure of DA are both –ve therefore, the line DA lies in the iii (SW) quardent now tanØ= departure 153.88 latitude 134.53 =1.1438 Ø =48º50’ hence reduced bearing of DA= S48º50’W W.C.B of DA = 180º+ 48º50’=228º 50’ length of DA = (lat) ²+(dep)² = 204.40m(ans)
Error in theodolite surveying These may be classified into 3 groups Instrumental error Personal error or observation error Natural error Instrumental error : (i) non adjustment of plate level: if the adjustment of a plate is not proper as a result, the horizontal circle is inclined and the angles are measured in an inclined plane instead of horizontal plane. The error are introduced in the measurement of both horizontal and vertical angles. the error is serious when the horizontal angles between points at considerably different elevation are to be measured. the error can be minimized by levlling the instrument with reference to be altitude bubble.
(ii) The line of collimation not being perpendicular to the horizontal axis: if line of collimation not perpendicular to the horizontal axis ,as a result of this the horizontal angles when measured between points at widely different elevation will be incorrect the error can be eliminated by reading angles on both the faces and taking the mean of the observed reading
(iii) the horizontal axis not being perpendicular to the vertical axis if the horizontal axis is not perpendicular to the vertical axis, the line of collimation not revolved in a vertical plane when the telescope is raised or lowerd. This causes an angular error both in horizontal and vertical angles. the error can be eliminated by reading angles on both the faces and taking mean of the two values.
(iv) the line of collimation and the axis of telescope –level not being parallel to each other if this type of condition occurred ,the zero line of vertical verniers is not a true line of reference and as a result ,an error is introduced in the measurement of vertical angle the error can be eliminated by taking two observation of the angles, one with the telescope normal and the other with the telescope inverted ,and taking mean of the two values
The inner and outer axis i.e the axis of both upper and lower plate not being concentric the error can be eliminated by reading both verniers and averaging the two values. The graduation being unequal The error is eliminated by measuring the angles several times on different parts of the circle and taking mean of all. Vernier being eccentric The zero of the vernier will not be diametrically opposite to each other. an error will be introduced if only one vernier is read ,but it will cancel itself ,if both verniers are read and the mean taken.
The vertical hair not being exactly vertical The error is minimised by using the portion of the hair near the horizontal hair for bisecting the signal.
Personal error : Inaccurate centering Inaccurate leveling Working wrong tangent screw Slip Parallax Inaccurate bisection of the point sighted and non-verticality of the ranging rod
Other error such as mistake in setting the vernier Mistake in reading the scale and the vernier Mistake in reading wrong vernier Mistake while booking the reading Natural error : this error are due to High temperature causing irregular refraction Wind storm causing vibration of the instrument The sun shining on the instrument These are negligible for ordinary survey. but the precise work is usually performed under the most favorable atmosphere condition
Er Raju Sharma (Lecturer) Department- Civil Engineering
Traversing with theodolite
Traverse may be define as series of connected lines from the frame work having the direction and length.theodolite is used to find out direction of lines and measuring tape is used for measuring length in case of theodolite traversing. There are mainly two method for plotting traversing. By measurement of angles between two successive lines (by direct observation of angle) By direct observing the bearing of the survey line.
Traversing by direct angles In this method the angle between the successive line are measured and the bearing of the starting line is observed. The bearing of the remaining lines are then found from the observed bearing and the measured angles. Traversing by this method is done either By the method of included angles. By the method of direct angles By the method of deflection angles
(a) Traversing by method of included angles
In a closed traverse the angle measured either interior or exterior according as the traverse is run in a counter clockwise direction .genrally closed traverse in anti –counter clockwise direction. the angle can be measured by repetition so as to desired degree of accuracy is obtained. Procedure : for running the traverse ABCDEFG Set up the theodolite at 1ST station A and observed the bearing of the line AB.
2. then measure the angle GAB. Shift the instrument to each of the ` successive station B,C etc. and measure the angles ABC,BCD etc. 3. Measure the line AB,BC,CD etc. and take offset to locate the required detail after this check is applied for interiors angles it is (2n-4)x90º, And for exterior angles it is (2n+4)x90º n = number of sides of the traverse
E
F D
N A
C
G
B
S
By the method of direct angles : this method is
used for open traverse. set up the theodolite at the starting station P and observe the bearing of line PQ . Shift the theodolite to Q. set the venier A to zero, take a back sight on the preceding station P.unclamp the upper plate, turn the telescope clockwise, take a foresight on the following station R, and read both verniers. the mean of two vernier reading is the required angle PQR. take other angles in the similar manner. chain the line and take the necessary offsets. N T P R S
Q
S
By the method of deflection angle:
This method is also used in open traverse. this is ,much suitable when the survey line makes small deflection angles with each other survey roads railway, pipe line etc .set up the thedolite at the starting point P and observed the bearing of line PQ. shift the instrument to station Q. set the vernnier A to zero and take a back sight on P. then transit the telescope ,loosen the upper clamp ,turn the telescope clockwise and take a foresight on R. read both verniers, the mean of these readings is the required deflection angles of QR from PQ. Also note down its direction. then set up the theodolite at each successive station R,S,T etc. and observe the deflection angles. N
Q
Ø1R
P R S
Ø1R S T
Traversing by direct observation of bearing
There are following three method direct method when the telescope is transited Direct method when the telescope is not transited Back bearing method
(a) Direct method when the telescope is transisited
Set up the theodolite at A and level it. set the vernier A to zero. point the telescope towards the north Loosen the upper clamp and bisect B by using the upper clamp. read the vernier A which gives the bearing of AB. Shift the instrument and set up at B. With the help of lower clamp and tangent screw ,back sight on A. transit the telescope ,loosen the upper clamp and turn the telescope and bisect C ,with the help of upper clamp and tangent screw ,read both verniers which gives the bearing of line BC Sift the instrument at ‘c’ and repeat the whole process. For check at the end FB and BB of line EA differ exactly by 180º.this will show the correct observation
N B N
N
C
A S
S E
D
Direct method when telescope is not transited
This is the same method as discussed in the above the difference is that the telescope is rotated about horizontal plane. Back bearing method : set up the instrument at A and observe the fore bearing of line AB Shift the instrument and set it up at B Set the vernier A to back bearing of AB With the vernier A kept clamped at the same reading, back sight on A by using the lower clamp and its tangent screw. when the line of sight is directed towards the BA ,the instrument is in correct orientation. Unclamp the upper plate and turn the telescope until c is sighted. bisect C exactly by using the upper clamp and its tangent screw. Read the vernier A which gives the bearing of BC Repeat the process at each of the subsequent station
N B N
N
C
A S
S E
D
Latitude and departure
Both are introduced with plotting the traverse. latitude and departure both are required for plotting the position of different point w.r.t y-axis and x- axis. y axis and x axis are known as reference line and are also known as the coordinates. Ø N Reference axis- y axis
Departure Westing= -ve W
Departure Easting = +
Reference axis- x axis
Latitude northing=+ E
Latitude Southing= -ve S
Latitude and departure
Latitude of line =l cos Ø Departure of line = l sin Ø
If N 30 º S is the bearing of a any given line N show that its latitude and S shows departure of the line.
The following rules will be much useful while solving problems on traverse surveying
If l is the length of a line and Ø is its reduced bearing. Then L cos Ø= latitude
N
l Ø
W
E
L sin Ø =departure S
(i) Latitude = l cos Ø Departure = l sin Ø
(ii) Tan Ø= departure latitude Ø = tan¯1 departure latitude (iii) l = (latitude)²+(departure)² (a) l = latitude x sec Ø (c) l = departure x cosec Ø
Q: 1 The coordinates of two points A
and B are as follows. Find the length and bearing of AB Let l = length of AB Ø = the reduced bearing of AB. LATITUDE of AB = 840.78 – 500.25= 340.53 DEPARTURE of AB = 315.60-640.75= -325.15
tan Ø = departure latitude
325.15 340.53
points
Northing Easting
= .9548
Ø = 43º41’ Since the latitude is +ve and the departure is – ve ,the line AB lies in the fourth (N.W) quadrant. R.B of AB = N 43º41’W W.C.B of AB = 360-43º41’= 316º19’ (ANS) length of AB = (L²)+(D²) 470.83 m (ans)
Co-ordinates
A
500.25
640.75
B
840.78
315.60
N
b a
W
840.78,315.60
500.25,640.75 E
Q : 2 the following are the length and bearing of the sides of a closed traverse ABCD Calculate the length and bearing of line DA. Let length of DA= l ,R.B of lineØ (i) Convert the W.C.B to the R.B R.B of AB= 180º-140º 12’=S39º 48’E R.B of BC=36º24’ =N36º24’E R.B of CD= 360º-338º48’=N21º12’W
Line AB BC CD DA
Length in meters 78.2 198.0 37.8 ?
bearing 140º12’ 36º 24’ 338º 48’ ?
(ii) find the latitude and departures of the lines from the known length and bearing of the lines.
latitude of AB = 78.2 x cos39º48’ = -60.08(S) latitude of BC =198XCOS 36º 24’= +159.37 (N) latitude of CD = 37.8x COS 21º 12’= 35.24 (N) latitude of DA = l x cosØ = l cosØ Algebraic sum of the latitude( ∑ ) = l cosØ+35.24+159.37-60.08 = l cosØ+ 134.53 The traverse being closed ( ∑ ) should equal zero lcosØ+134.53 = 0 lcosØ= -134.53
Departure of AB = 78.2xsin 39º48’= +50.06 (E) Departure of BC = 198xsin 36º24’ = +117.49 (E) Departure of CD = 37.8x sin 21º12’ = -13.6 (w) Departure of DA = lxsinØ
Algebric sum of departure ( ∑ ) = l sinØ+50.06+117.49-13.67 = lsinØ + 153.88 But ∑ D =0 lsinØ + 153.88 = 0 lsinØ = -153.88
(iii) since the latitude and departure of DA are both –ve therefore, the line DA lies in the iii (SW) quardent now tanØ= departure 153.88 latitude 134.53 =1.1438 Ø =48º50’ hence reduced bearing of DA= S48º50’W W.C.B of DA = 180º+ 48º50’=228º 50’ length of DA = (lat) ²+(dep)² = 204.40m(ans)
Error in theodolite surveying These may be classified into 3 groups Instrumental error Personal error or observation error Natural error Instrumental error : (i) non adjustment of plate level: if the adjustment of a plate is not proper as a result, the horizontal circle is inclined and the angles are measured in an inclined plane instead of horizontal plane. The error are introduced in the measurement of both horizontal and vertical angles. the error is serious when the horizontal angles between points at considerably different elevation are to be measured. the error can be minimized by levlling the instrument with reference to be altitude bubble.
(ii) The line of collimation not being perpendicular to the horizontal axis: if line of collimation not perpendicular to the horizontal axis ,as a result of this the horizontal angles when measured between points at widely different elevation will be incorrect the error can be eliminated by reading angles on both the faces and taking the mean of the observed reading
(iii) the horizontal axis not being perpendicular to the vertical axis if the horizontal axis is not perpendicular to the vertical axis, the line of collimation not revolved in a vertical plane when the telescope is raised or lowerd. This causes an angular error both in horizontal and vertical angles. the error can be eliminated by reading angles on both the faces and taking mean of the two values.
(iv) the line of collimation and the axis of telescope –level not being parallel to each other if this type of condition occurred ,the zero line of vertical verniers is not a true line of reference and as a result ,an error is introduced in the measurement of vertical angle the error can be eliminated by taking two observation of the angles, one with the telescope normal and the other with the telescope inverted ,and taking mean of the two values
The inner and outer axis i.e the axis of both upper and lower plate not being concentric the error can be eliminated by reading both verniers and averaging the two values. The graduation being unequal The error is eliminated by measuring the angles several times on different parts of the circle and taking mean of all. Vernier being eccentric The zero of the vernier will not be diametrically opposite to each other. an error will be introduced if only one vernier is read ,but it will cancel itself ,if both verniers are read and the mean taken.
The vertical hair not being exactly vertical The error is minimised by using the portion of the hair near the horizontal hair for bisecting the signal.
Personal error : Inaccurate centering Inaccurate leveling Working wrong tangent screw Slip Parallax Inaccurate bisection of the point sighted and non-verticality of the ranging rod
Other error such as mistake in setting the vernier Mistake in reading the scale and the vernier Mistake in reading wrong vernier Mistake while booking the reading Natural error : this error are due to High temperature causing irregular refraction Wind storm causing vibration of the instrument The sun shining on the instrument These are negligible for ordinary survey. but the precise work is usually performed under the most favorable atmosphere condition
Er Raju Sharma (Lecturer) Department- Civil Engineering
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