1. Islamic University of Gaza Civil Engineering Department Surveying II ECIV 2332 By Belal Almassri

2. Chapter 7 Coordinate geometry and traverse surveying – Part 2 - Resection - Traverse Surveying Definitions - Types, Utilizations and advantages - Computations and correction errors - Examples

3. 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 P C B N M c b Ө R Ф β

4. Let J = β + Ф then J = 360º – ( M+ N+ R ) 1- compute & & b & c & R from the known coordinates of points: A, B,C. (R= - ) 2- compute J = 360º – ( M+ N+ R ) 3- compute H = b sin M / c sin N 4- compute Ф ( tan Ф = sin J / (H + cos J )) 5- compute Ө = 180º - N – Ф 6- compute = + Ө 7- compute AP = b sin Ф / sin N 8- compute Xp & Yp Xp = XA + AP sin Yp = YA + AP cos Procedure:

5. Example 7.6:

7. 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.

8. 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 b- Open Traverse

9. 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.

10. Choice of traverse stations: 1. As close as possible to the survey details. 2. Traverse shortest line should be greater than 1/3 of the longest line (preferred to be equal). 3. Traverse stations should be selected in firm ground. 4. From one station we can see the back sight and the foresight.

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12. Computations and correction of errors A- Determine the Azimuth of each line: 1- When ( α 1 + Ө ) > 180º α 2 = Ө - ( 180º – α 1) = Ө + α 1 - 180º 2- When ( α 1 + Ө ) < 180º α 2 = Ө + 180º + α 1 = Ө + α 1 + 180º

13. 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 º - error = sum of measured angles – ((n – 2 ) × 180 º) - correction per angle = - error / no of internal angles

14. b- connecting traverse: If the azimuth of the last line in the traverse is known, then the error - εα = α c (calculated azimuth) - α n (known azimuth) - correction / angle = - εα / n the corrected azimuth - α i = α ’i ( initially computed azimuth)– i ( εα / 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( ε x ) = X c – X n - Closure error in y-direction( ε y ) = Y c – Y n - Closure error in the position of the last points = √ ε x² + ε y ²

15. Compass ( Bowditch ) Rule : used for position correction as follow: Correction to departure of side ij( ∆x) = -(length of side ij / total length of traverse)( ε x ) Correction to departure of side ij( ∆y) = -(length of side ij / total length of traverse)( ε y ) Correction can be done directly to coordinates: Cxi = - (Li / D) ( ε x ) & Cyi = - (Li / D) ( ε 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

16. Azimuth and bearing North to east or west / South to east or west