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Islamic University of Gaza Civil Engineering Department Surveying II ECIV 2332 By B elal A lmassri

Islamic University of Gaza Civil Engineering Department Surveying II ECIV 2332 By B elal A lmassri. Chapter 7 Coordinate geometry and traverse surveying – Part 2. Resection Traverse Surveying Definitions Types, Utilizations and advantages Computations and correction errors Examples. A.

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Islamic University of Gaza Civil Engineering Department Surveying II ECIV 2332 By B elal A lmassri

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  1. Islamic University of GazaCivil Engineering DepartmentSurveying IIECIV 2332ByBelalAlmassri

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

  3. A b c R Ө B C Ф β M N P 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

  4. Procedure: 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

  5. Example 7.6:

  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.

  7. 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

  8. 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.

  9. Choice 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.

  10. Underground . . . .

  11. Computations and correction of errors A- Determine the Azimuth of each line: 1- When ( α1 + Ө ) > 180º α2 = Ө - ( 180º – α1) = Ө + α1 - 180º 2- When ( α1 + Ө ) < 180º α2 = Ө + 180º + α1 = Ө + α1 + 180º

  12. 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

  13. b- connecting traverse: If the azimuth of the last line in the traverse is known, then the error - εα= αc (calculated azimuth) - αn (known azimuth) - correction / angle = - εα / n the corrected azimuth - αi = 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

  14. 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

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

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