# Islamic University of Gaza Civil Engineering Department ... Islamic University of Gaza Civil Engineering Department Surveying II ECIV 2332 By Belal Almassri Chapter 7 Coordinate geometry and traverse surveying Part 2 Resection

Traverse Surveying Definitions Types, Utilizations and advantages Computations and correction errors Examples 6. Resection As in the following figure, the horizontal position of a new point like P can be Determined

by measuring the horizontal angles to three points of known coordinates like: A & B & C A c B b R

M N P C

Procedure: Let J = + then J = 360 ( M+ N+ R ) AB AC compute & & b & c & R from AB A,ACB ,C . the known coordinates of points: (R= ) 2- compute J = 360 ( M+ N+ R ) 3- compute H = b sin M / c sin N

4- compute ( tan = sin J / (H + cos J )) 5- compute 180 - N AP =AC 6- compute = + 7- compute AP = b sin / sin N 8- compute Xp AP& Yp Xp = XA + AP sin AP Yp = YA + AP cos

1- Example 7.6: Traverse Surveying Definitions: Traverse is one of the most commonly used methods for determining the relative positions of a number of survey points. Traverse is a method in the field of surveying to establish control networks. It

is also used in geodetic work. Traverse networks involved placing the survey stations along a line or path of travel, and then using the previously surveyed points as a base for observing the next point. Utilizations: property survey to establish boundaries. Location and construction layout surveys for highways, railways and other works. Helps the surveys for

photogrammetric mapping. Types of Traverse: a- Closed Traverse Traverse b- Open Advantages: Less organization needed. Few observations needed. More accurate than other methods. Suits different types of utilizations Open Vs Closed:

Closed traverse is useful in marking the boundaries of wood or lakes . Open traverse is utilised in plotting a strip of land which can then be used to plan a route in road construction. Choice 1. 2. 3. 4.

of traverse stations: As close as possible to the survey details. Traverse shortest line should be greater than 1/3 of the longest line (preferred to be equal). Traverse stations should be selected in firm ground. From one station we can see the back sight and the foresight. Underground . . . .

Computations and correction of errors A- Determine the Azimuth of each line: 1- When ( 1 + ) > 180 2 = - ( 180 1) = + 1 - 180 2- When ( 1 + ) < 180 2 = + 180 + 1 = + 1 + 180 B- Checks and correction of errors : X last point X first point = X all lines Y last point Y first point = y all lines In order to meet the previous two conditions,

the following corrections are performed: 1- Angle correction: a- Closed loop traverse: For a closed traverse of n sides, - sum of true internal angles = (n 2 ) 180 - error = sum of measured angles ((n 2 ) 180 ) - correction per angle = - error / no of internal b- connecting traverse: If the azimuth of the last line in the traverse is known, then the error

- = c (calculated azimuth) - n (known azimuth) - correction / angle = - / n the corrected azimuth - i = i ( initially computed azimuth) i ( / n)i ( initially computed azimuth) i ( / n) 2- Position correction: IF the calculated and known coordinates of last point are: ( X c , Y c ) & ( X n , Y n )respectively, then : - Closure error in x-direction( x ) = X c X n - Closure error in y-direction( y ) = Y c Y n - Closure error in the position of the last points = x + y

Compass ( Bowditch ) Rule : used for position correction as follow: Correction to departure of side ij( x) = -(length of side ij / total length of traverse)( x ) Correction to departure of side ij( y) = -(length of side ij / total length of traverse)( y ) Correction can be done directly to coordinates: Cxi = - (Li / D) ( x ) & Cyi = - (Li / D) ( y ) Where: Li=the cumulative traverse distance up to station i &D=total length of the traverse

The corrected coordinates of station i ( x'i , y'i ) are: X'i = Xi + Cxi & Y'i = Yi + Cyi Allowable error in Traverse surveying Azimuth and bearing North to east or west / South to east or west