Theodolite Traversing

 

Unit 4    Theodolite Traversing:

4.1 Traverse Definition, Purpose, Types and Equipment

Traversing is that type of survey in which no. of connected survey lines form a framework and the direction or angle of survey lines are measured with an angle measurement instrument  like theodolite, total station and the length of the line are measured with tape or EDM (Electronic Distance Measurement).

Theodolite traversing is a type of survey in which direction or angle of survey lines are measured with theodolite and length by tape.

A traverse is a series of connected straight lines of known length, each joining two points on the ground and related to one another by known angles between the lines. Straight lines between the consecutive stations are traverse legs. And the points defining end of traverse lines are traverse station.

There are two types of traverse:

1) Closed traverse

a) Geometrically closed and

b) Linked traverse

2) Open Traverse

 

1) Closed traverse

A traverse originated from a known position (Co-ordinate) and also terminates to known position (Co-ordinate) is called closed traverse.

If the starting and last point is same then it is called closed loop or geometrically closed traverse.

If a traverse starts from a known point and ends at another known point then it is called linked traverse.

 

2) Open Traverse

Open traverse starts from a point whose position may be known or unknown but ends to the point whose position is not known.

# Purpose of traversing

-        To locate the control points in the area to be surveyed.

-        For photogrammetric survey.

-        To determination the boundary area

-        To calculate the areas within the boundaries.

-        To locate contour points for highway, railways, tunnel, etc.

-        To find the contour points for calculation of earthwork quantity.

-        To establish the boundary of property

-        To provide the control points for chain survey, plane tabling or photogrammetric survey.

-        To fix the alignment of roads, canals, rivers, boundary, etc with better accuracy.

-        To ascertain the co-ordinates of boundary of pillars of forest, international borders. In case of pillars get disturbed their position can be re-laid with the help of co-ordinate.

4.2   Traverse Field Works

Field work for theodolite traverse are as follows :

i) Reconnaissance (Recci)

ii) Selection and marking of stations.

iii) Measurement of length of traverse legs.

vi) Measurement of included angles of traverse.

v) Measurement of bearing of any one traverse leg.

vi) Booking and computation of field notes.

vii) Plotting

i) Reconnaissance

Before starting actual survey work surveyor should make the preliminary inspection of area to be survey to decide the best possible way of starting the work.

ii) Marking the stations:

Every traverse station is selected keeping in view that at least two stations is visible from there.

Traverse station are marked on the ground by the rigid objects like wooden pegs, mortar, etc.

Reference sketches should be made so that the station can be located even if the station or pegs are removed.

iii) Measurement of the traverse legs.

The distance of traverse leg between stations is measured either with chain or tape.

iv) Measurement of traverse angle

Interior angles of the traverse are measured directly by using theodolite.

v) Correction of measured angles

Total sum of all measured angles must be equal to theoretical sum of angles (i.e. Sum of measured angles = Theoretical sum of interior angles)

Theoretical sum of angles,

∑Sum_T= (2n-4)x90^o

If measured sum of angles is not equal to theoretical sum then difference is error,

Error(e) = ∑Sum_M - ∑Sum_T

This error can be distributed equally.

vi) Measurement of magnetic bearing

Forward bearing and backward bearing of any one traverse leg is measured by using compass.

vii) Field notes:

All the data is properly noted on the field book in a proper table.

viii) Plotting

Above data is analyzed and independent co-ordinates are calculated and those co-ordinates are plotted in drawing sheet at suitable scale.

# Some general terms related to traversing

1) Latitude

Latitude of a survey line is its co-ordinate length (component) along the North direction.

It is +ve when measured upward and -ve when measured downward.

2) Departure

Departure of any survey line is its co-ordinate length (component) along the east direction.

It is +ve when measured rightward and –ve when measured leftward.

3) Consecutive co-ordinate:  

Relative coordinate of a point w.r.t. to previous point is it’s consecutive co-ordinate.

For a line AB consecutive coordinate of point B is (departure of AB , latitude of AB)

This coordinate of B is taken w.r.t. to A assuming co-ordinate of A as (0,0).

4) Total coordinate of independent coordinate

Independent coordinate of a point is the coordinate of a point take with respective to global origin.

from figure,

-        Length of line, AB = l

-        Bearing of line, AB= ɵ

-        Latitude of AB = lcos ɵ

-        Departure of AB = lsin ɵ

-        Consecutive coordinate of point B = (d,l)
                                                                           = (lsin ɵ, lcos ɵ)

-        If independent coordinate of A = (x,y)

-        Then independent coordinate of B is (x+d,y+l)

-        i.e. Easting (E)= x+d ; Northing (N) = y+l

 

 

5) Closing Error:

Sum of all latitude must be zero in closed traverse.

i.e. ∑L=0

And sum of all departure must be zero in closed traverse.

i.e. ∑D=0

If above condition does not occur then the traverse will not end at the point from where it is started and this length between starting and ending point is called closing error and is given by

e =

it’s direction is given by

Ө=tan^-1(

6) Balancing the traverse

The process of adjusting the consecutive coordinate of each line by applying correction to them such a way that algebraic sum of latitude and departure of the traverse is equal to zero is called balancing of traverse.

Two method of balancing traverse are:-

i) Bowditch’s method

ii) Transit method

i) Bowditch’s Method

Bowditch’s rule is used for adjusting the traverse in which the angles and distance are measured with same precision. If ∑L and ∑D are error in latitude and departure then ,

·       correction for latitude (C_L)=  Total error in latitude x

                                              =∑L x

·       correction for departure (C_D)= Total error in departure x

                                                    =∑D x

 

ii) Transit Method

Transit method is used to balance the traverses in which angular measurements are more precise than linear measurements.

·       correction for latitude (C_L)=  Total error in latitude x

                                              =∑L x

·       correction for departure (C_D)= Total error in departure x

                                                    =∑D x

4.3 Traverse Adjustment and Computation of Total Coordinates

i) Measurement of traverse legs and angles

ii) Adjustment of angle (balancing angular misclosure)

sum of included angles = (N-2)x180^o

Angular misclosure = observed – actual sum

Permissible angular misclosure = ± ∑

iii) Measurement of bearing of first line.

iv) Calculation of bearing of all other lines

v) Calculation of consecutive coordinates of traverse line

vi) Checking for closing error

for no closing error,

 

permissible closing error

 

vii) Balancing the closing error methods

-        Graphical method

-        Bowditch method

-        Transit method

-        Axis method

viii) Calculation of independent coordinate

ix) Plotting of traverse in suitable scale.

 

 

 

4.4   Traverse Plotting

Final product of survey is plotting the observed data and creating the meaningful maps. Traverse plotting is plotting of surveyed traverse which is necessary as framework for plotting detailed observations.  Accuracy of a survey depends upon the accuracy with which its control points are plotted. The traverse stations which are also known as the control points can be plotted either by the angle and distance method or by coordinate method.

1) Angle and distance method:

In this method distance between the stations are laid off to scale and angles or bearing is plotted. Thus the traverse stations are plotted with reference to previous station. Therefore the accuracy of the location of each station on the plan depends on the accuracy with which previous points are plotted. Even if there is slight error, error gets accumulated and the position of the last station may be displaced for a considerable distance from its true position. So this method is used for plotting of small traverse or for traverse of low accuracy.

2) Coordinate method:

After completion of works in field and data collection in field book, traverse adjustment and computation of total coordinate is done. This independent coordinate are plotted by drawing series of grid lines parallel to the x and y direction. Here, x direction represents the easting and the y direction represents Northing. These grid lines are spaced at some regular uniform interval say 50, 100, 200 or as suitable for the scale of the map. Error while plotting of an independent coordinate of a station does not affect the accuracy while plotting the independent coordinate of another station.

Step for traverse plotting by coordinate method:-

i) Tabulation and collection of all the observed data from field

ii) Preparation of Gale’s table for the computation of total coordinates

iii) Selection of proper paper size for plotting

iv) Selection of proper scale for plotting

v) Preparation of Grid for plotting of major stations and minor stations. 

vi) Plotting of stations

vii) Using proper symbols to denoting major stations, traverse lines and other features.

4.5 Omitted measure measurements in traverse

Sometime due to obstacle or carelessness we forget to make measurement of traverse and  this is called omitted measurement. These omitted measurements can be calculated using geometric formula only in case of closed traverse provided that the unknown quantities are not more than two.

If l₁, l₂,….., l_n are the length of traverse legs and Ө₁, Ө₂,….., Ө_n be their bearing then

∑L = l₁cos Ө₁ + l₂cos Ө₂ + …..+ l_ncos Ө_n= 0

∑D = l₁sin Ө₁ + l₂sin Ө₂ + …..+ l_nsin Ө_n= 0

Solving these equation we get;

l =

Ө= tan^-1( )

Types of omitted measurements

There are following cases

1. a) When length of one traverse leg is omitted.

    b) When bearing of one traverse leg is omitted.

    c) When length and bearing of one traverse leg is omitted.

2. When length of one traverse leg and bearing of another adjacent leg are omitted.

3. When length of two traverse legs are omitted.

4. When bearing of two traverse legs are omitted.

Case I : Either length or bearing or both of one traverse leg is omitted.

∑D’= Total sum of departure of line AB

-        ABCDEFA is a closed traverse:

-        Either length or bearing or both of the traverse leg AF are omitted from the field measurement.

Then,

i) Calculate the algebraic sum of latitude () and departure () from A to F.

ii) Since, for closed traverse, algebraic sum of latitude and departure should be zero. Then,

 

 

Then, its length and bearing is calculated by equation (3) and (4)

 

Case II

Length of one leg and bearing of adjacent leg omitted

Here length of EF and bearing of FA legs are omitted.

ð Join EA, which is a closing line of traverse.

From ()EAF

<FEA ()

Using sine law,

 

Now, by knowing (). Bearing of AF can be calculated, i.e. bearing of AF= Bearing of EA + ()

3. Length of two adjacent leg omitted

From above figure (b), in which length of EF and FA both are omitted.

Join AF, then , from ()

4. Bearing of two adjacent legs are omitted

Here, bearing of EF and FA, both are omitted.

 

By comparing these equations, we get value of ()

Now, by knowing the bearing of EA, angles (), the nearing of legs EF and FA may be easily calculated.