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# KTU B.Tech S5 Lecture Notes Geomatics

### KTU B.Tech S5 Lecture Notes Geomatics

##### CE307 Geomatics

CE 307  GEOMATICS

MODULE I

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

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:

1. Bowditch’s method
2. Transit method
3. Graphical method
4. 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

Curve Surveying – Elements of simple and compound curves – Method of setting out– Elements of Reverse curve (Introduction only)– Transition curve – length of curve – Elements of transition curve – Vertical curve (introduction only)

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