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Chapter:
1. COMPUTATION AND PLOTTING OF A TRAVERSE
TITLE:
COMPUTATION AND PLOTTING OF A TRAVERSE
OBJECTIVES:
To learn the principles of running a closed field traverse
To enhance our knowledge in traversing procedure.
To enable us to get hands-on experience in setting up and working with the theodolite, levelling rod, tripod stand as well as other instruments and collect the data of the relevant field work .
To allow us to learn the basic correct method in traversing.
To enable us identify the error and make adjustments to the data by using the correct formula.
To learn how to compute a traverse and properly adjust the measured values of the traverse to achieve mathematical closure.
To determine the error of closure and compute the accuracy of work.
THEORY:
Traversing is the art of surveying in which a number of connected survey line forms of framework, where the direction and length of survey line are measured with the help of angle measuring instrument (compass, theodolite) and tape, EDM respectively.
A traverse which originates from a station and closes on the same station or runs between two station whose co-ordinate are already known is known as closed traverse.
For a closed traverse, sum of included interior angle is given by,
`(2n-4)*90^0`
The appropriate method usually adapted for balancing of traverse are:
Transit method and
Bowditch's method
According to transit method, the correction to latitude or departure of any side is given by
`(t\otal\ erro\r\ i\n\ latitude\ or\ departure\*\ latitude\ (departure) of\ t\h\at\ li\n\e)/(arithmetic\ s\um\ of\ latitude\ (departure)) `
According to Bowditch's method, the correction is given by,
`(t\otal\ erro\r\ i\n\ latitude\ or\ departure\*\ l\eng\th\ of\ t\h\at\ li\n\e)/(perimeter\ of\ traverse)`
The traverse station, which are the control points, can be plotted either by the angle and distance method or by the coordinate method.
APPARATUS REQUIRED:
Theodolite
Tripod
Ranging rod
Plumb bob
Arrows
Pegs
OBSERVATION TABLE:
Station | Line | Length | Angle | Bearing |
A | `98^0\ 3^'\ 30^('')` | |||
AB | `58` | `84^0\ 30^'\ 00^('')` | ||
B | `95^0\ 36^'\ 45^('')` | |||
BC | `58.37` | |||
C | `180^0\ 44^'\ 50^('')` | |||
CD | `46.99` | |||
D | `111^0\ 18^'\ 25^('')` | |||
DE | `57.1` | |||
E | `179^0\ 0^'\ 20^('')` | |||
EF | `39.35` | |||
F | `58^0\ 5^'\ 45^('')` | |||
FG | `83.85` | |||
G | `177^0\ 10^'\ 35^('')` | |||
GA | `65.98` | |||
A | `98^0\ 3^'\ 30^('')` |
CALCULATIONS:
Sum of interior angles (observed)`=900^0\0^'\10^('')`
Theoretical sum of interior angles is,
`=(2N-4)*900^0`
`=900^0\0^'\0^('')`
Error`=900^0\0^'\10^('')-900^0\0^'\0^('')`
`=0^0\0^'\10^('')`
Correction,`=-0^0\0^'\10^('')`
hence, the corrected angles are:
`angle A=98^0\3^'\29^('') `
`angle B=95^0\36^'\44^('') `
`angle C=180^0\44^'\48^('') `
`angle D=111^0\18^'\24^('') `
`angle E=179^0\0^'\18^('') `
`angle F=58^0\5^'\44^('') `
`angle G=177^0\10^'\33^('') `
Thus, sum of angles is,`=900^0\0^'\0^('')`
Now,
Bearing of line AB `=84^0\30^'\00^('') `
Bearing of line BC is,
`=(84^0\30^'\00^('')+180^0)+95^0\36^'\44^('')-360^0`
`=0^0\6^'\44^('')`
Bearing of line CD is,
`=(0^0\6^'\44^('')+180^0)+180^0\44^'\48^('')-360^0`
`=0^0\51^'\32^('')`
Bearing of line DE is,
`=(0^0\51^'\32^('')+180^0)+111^0\18^'\24^('')`
`=292^0\9^'\56^('')`
Bearing of line EF is,
`=(292^0\9^'\56^('')-180^0)+179^0\0^'\18^('')`
`=291^0\10^'\14^('')`
Bearing of line FG is,
`=(291^0\10^'\14^('')_180^0)+58^0\5^'\44^('')`
`=169^0\15^'\58^('')`
Bearing of line GA is,
`=(169^0\15^'\58^('')+180^0)+98^0\3^'\29^('')-360^0`
`=166^0\26^'\31^('')`
Bearing of line AB is,
`=(166^0\26^'\31^('')+180^0)+98^0\3^'\29^('')`
`=84^0\30^'\00^('')`
Hence, the calculated bearings are correct.
Line | Length | WCB | Latitude (`Lcostheta`) | Departure (`Lsintheta`) |
AB | `58` | `84^0\ 30^'\ 00^('')` | `5.559` | `57.733` |
BC | `58.37` | `0^0\ 6^'\ 44^('')` | `58.370` | `0.114` |
CD | `46.99` | `0^0\ 51^'\ 32^('')` | `46.985` | `0.704` |
DE | `57.1` | `292^0\ 9^'\ 56^('')` | `21.543` | `-52.880` |
EF | `39.35` | `291^0\ 10^'\ 14^('')` | `14.211` | `-36.694` |
FG | `83.85` | `169^0\ 15^'\ 58^('')` | `-82.383` | `15.617` |
GA | `65.98` | `166^0\ 26^'\ 31^('')` | `-64.141` | `15.468` |
`P=409.64` | `sumL=0.144` | `sumD=0.062` |
Now,
Error`=root()(sumL^2+sum D^2)=root()(0.144^2+0.062^2` `=0.157` Thus, Closing error is,`=e/p=0.157/409.64=1/2609.2` Hence, it is within permissible limit.
Total sum of latitude is,
`sum absL =293.192`
Total sum of departure is,
`=sum abs D=179.210`
Now, by transit rule, the correction is given by,
For Latitude,
Correction for AB is,
`=5.559 /293.192*0.144 `
`=0.003`
Correction for BC is,
`= 58.370/293.192*0.144`
`=0.029`
Correction for CD is,
`= 46.985/293.192*0.144`
`=0.023`
Correction for DE is,
`=21.543 /293.192*0.144`
`=0.011`
Correction for EF is,
`= 14.211/293.192*0.144`
`=0.007`
Correction for FG is,
`= 82.383/293.192*0.144`
`=0.040`
Correction for GA is,
`= 64.141/293.192*0.144`
`=0.031`
Since, the total error of latitude is positive, their correction is of negative sign.
Again, for Departure,
Correction for AB is,
`= 57.733/179.21*0.062`
`=0.020`
Correction for BC is,
`= 0.114/179.21*0.062`
`=0.000039 `
Correction for CD is,
`= 0.704/179.21*0.062`
`= 0.000244`
Correction for DE is,
`= 52.880/179.21*0.062`
`= 0.0183`
Correction for EF is,
`= 36.694/179.21*0.062`
`= 0.0127`
Correction for FG is,
`= 15.617/179.21*0.062`
`= 0.0054`
Correction for GA is,
`= 15.468/179.21*0.062`
`= 0.005317`
Since, the total error of departure is positive, their correction is of negative sign.
Line | Length | Latitude | Corrected Latitude | Departure | Corrected Departure |
AB | `58` | `5.559` | `5.556` | `57.733` | `57.713` |
BC | `58.37` | `58.370` | `58.341` | `0.114` | `0.114` |
CD | `46.99` | `46.985` | `46.962` | `0.704` | `0.704` |
DE | `57.1` | `21.543` | `21.532` | `-52.880` | `-52.898` |
EF | `39.35` | `14.211` | `14.211` | `-36.694` | `-36.707` |
FG | `83.85` | `-82.383` | `-82.423` | `15.617` | `15.612` |
GA | `65.98` | `-64.141` | `-64.172` | `15.468` | `15.462` |
P=409.64 | `sumL=0.00` | `sumD=0.00` |
Here , for corrected latitude and departure,
`sum absL =0` and,
`sum abs D =0`
Hence, these values are correct.
Station | Line | Length | Corrected Angle | WCB | Consecutive Latitude | Consecutive Departure | Independent Northing | Independent Easting |
A | `98^0\ 3^'\ 29^('')` | `500` | `500` | |||||
AB | `58` | `84^0\ 30^'\ 00^('')` | `5.556` | `57.713` | ||||
B | `95^0\ 36^'\ 44^('')` | `505.556` | `557.713` | |||||
BC | `58.37` | `0^0\ 6^'\ 44^('')` | `58.341` | `0.114` | ||||
C | `180^0\ 44^'\ 48^('')` | `563.897` | `557.827` | |||||
CD | `46.99` | `0^0\ 51^'\ 32^('')` | `46.962` | `0.704` | ||||
D | `111^0\ 18^'\ 24^('')` | `610.859` | `558.531` | |||||
DE | `57.1` | `292^0\ 9^'\ 56^('')` | `21.532` | `-52.898` | ||||
E | `179^0\ 0^'\ 18^('')` | `632.391` | `505.633` | |||||
EF | `39.35` | `291^0\ 10^'\ 14^('')` | `14.204` | `-36.707` | ||||
F | `58^0\ 5^'\ 44^('')` | `646.595` | `468.926` | |||||
FG | `83.85` | `169^0\ 15^'\ 58^('')` | `-82.423` | `15.612` | ||||
G | `177^0\ 10^'\ 33^('')` | `564.172` | `484.538` | |||||
GA | `65.98` | `166^0\ 26^'\ 31^('')` | `-64.172` | `15.462` | ||||
A | `98^0\ 3^'\ 29^('')` | `500` | `500` |
RESULTS:
Hence, the closed traverse was computed, adjusted and finally plotted.
SOURCE OF ERRORS:
Instrumental errors
Natural errors
Personal errors
Instrumental Errors:
Imperfect graduation.
Line of collimation not being perpendicular to trunnion Axis.
Horizontal axis not being perpendicular to the vertical axis.
Non-Parallelism of the axis of telescope level and line of collimation.
Natural Errors:
Unequal atmospheric refraction due to high temperature.
Unequal expansion of the various part of the instrument.
Unequal settlement of the tripod.
Poor visibility.
Strong wind producing vibration to the instrument
Personal Errors:
Inaccurate Leveling,
Inaccurate centering,
Improper use of tangent screw
Slip
Inaccurate bisection of signals
Non-verticality of ranging rod
PRECAUTIONS:
The instrumental errors, if any, should be minimised or eliminated by applying appropriate correction and adjustment.
Apparatus should be handled carefully.
One should be careful while taking/reading data.
The Arithmetic calculation should be checked.
One should be careful with the use of tangent screw.
The ranging rod should be bisected at minimum possible height.
DISCUSSIONS:
From this fieldwork, we learn to conduct a traverse survey by using theodolite. Throughout this survey, we were able to apply the technique and knowledge taught by our teacher.
CONCLUSIONS:
In conclusion, we had a great experience in hands on during our fieldwork, where we became able to compute and adjust the traverse with appropriate methods.
