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 P C B N M c b Ө R Ф β

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:

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 b- Open Traverse

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 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.

Underground....

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 º 2- When ( α 1 + Ө ) < 180º α 2 = Ө + 180º + α 1 = Ө + α º

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

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

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

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