### KTU B.Tech S5 Lecture Notes Geomatics

**CE307 Geomatics **

Download Module I & II LectutreNotes

**CE 307 GEOMATICS **

**MODULE I**

CLOSED TRAVERSE
A closed traverse is a series of connected lines whose lengths and bearings are measured off these lines (or sides), which enclose an area. A closed traverse can be used to show the shape of the perimeter of a fire or burn area. If you were to pace continuously along the sides of a closed traverse, the finishing point would be the same as the starting location. Note in the following sketch how the traverse is followed clockwise. If the direction was followed counterclockwise at any point, the bearing letters would change to their opposites but the numbers would not, as shown in the first sketch (1) below. The second sketch (2) is a closed traverse. Here, the series of lines completes a distance area, and the starting and ending points are the same.
Convert the bearings to magnetic readings. Adjust the magnetic readings to true north readings. Plot the closed traverse in feet using an engineer’s tenth ruler and protractor.
Repeat this step for each distance.
The NW quadrant is between 270° and 360°. 360° – 42° = 318° The resulting magnetic reading are listed in the table below.
When plotting the values that are in the southern quadrants with a semicircle protractor, rotate the protractor so the 0°/180°line is down (facing south) and read the numbers on the inner scale. Continue to complete all the points. The end result should be a closed traverse as shown.
P1 to P2 = 360° – 332.5° = N27.5°W Label the lines of the traverse with the corresponding bearings. |

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**Traverse Computations**

Field operation for traverses yields angles or directions and distance for a set of lines

connecting a series of traverse stations. Angles can be checked for error of closure and

corrected so that preliminary corrected values can be computed. And observed distances can

be reduced to equivalent horizontal distanced. The preliminary directions and reduced

distances are suitable for use in traverse computations, which are performed in a plane

rectangular coordinate system.

Computation with plane coordinates by considering the figure below.

Let the reduced horizontal distance of traverse lines ij and jk be dij and djk respectively, and

Ai and Aj be the azimuths of ij and jk. Let Xij and Yij be the departure & latitude.

Xij= dij sin Ai = departure

Yij = dij cos Ai =latitude

If the coordinates of i are xi and yi

So, the coordinates of j are:

Let the reduced horizontal distance of traverse lines ij and jk be dij and djk respectively, and

Ai and Aj be the azimuths of ij and jk. Let Xij and Yij be the departure & latitude.

Xij= dij sin Ai = departure

Yij = dij cos Ai =latitude

If the coordinates of i are xi and yi

So, the coordinates of j are:

Xj=xi+xij ; yj= yi+yij

Xk=xj+xjk ; yk=yj-yjk

=xi+xij+xik ; =yi+yij-yjk

xjk =djk sin Aj yjk=djk cos Aj

Note: the signs of azimuth functions

If the coordinates for the two ends of a traverse line are given, distance between two ends

can be determined as:

dij =[(xj-xi)2+(yj-yi)2]1/2

The azimuth of line ij from north and south is

*https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=20&cad=rja&uact=8&ved=0ahUKEwimqL_xp4TWAhWDp48KHW5LAdMQFgiNATAT&url=http%3A%2F%2Fwww.wsdot.wa.gov%2Fpublications%2Ffulltext%2Fdesign%2FWebinar%2F5_2011%2FLecture-traverse-comps.pptx&usg=AFQjCNEYNqYyiaWFjx-snZLsJgWpalIxcw*

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**Balancing the Traverse:**

The term ‘balancing’ is generally applied to the operations of applying corrections to

latitudes and departures so that ΣL = 0, ΣD=0. This applies only when the survey forms a closed

polygon.

The following are common methods of adjusting a traverse:

- Bowditch’s method
- Transit method
- Graphical method
- Axis method

**1) Bowditch’s Method: **To balance a traverse where linear and angular measurements are

required this rule is used and it is also called as compass rule. The total error in latitude

and departure is distributed in proportion to the lengths of the sides.

The Bowditch’s rule is:

Correction to latitude (or departure) of any side = Total error in latitude (or departure) * length of

that side /perimeter of traverse

Thus if, CL = Correction of latitude of any side CD= correction to departure of any side

ΣL = Total error in latitude

ΣD = total error in

departure

Σl = length of the perimeter

l = length of any side

CL = ΣL*(l/Σl) and CD=ΣD*(l/Σl)

**2) Transit Method: **It is employed when angular measurements are more precise than

linear measurements.

The Transit rule is:

Correction to latitude (or departure) of any side = [Total error in latitude (or departure) * latitude

L (or departure D) of that line Arithmetic sum of latitude LT (or departure DT)]

CL=ΣL*(L/LT) and CD=ΣD*(D/DT

**MODULE II**