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

Islamic University of GazaCivil Engineering Department

Surveying IIECIV 2332

ByBelal Almassri

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

6. ResectionAs 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 & CA

P

CB

NM

c bӨ

RФβ

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 N4- compute Ф ( tan Ф = sin J / (H + cos J ))5- compute Ө = 180º - N – Ф6- compute = + Ө 7- compute AP = b sin Ф / sin N8- compute Xp & YpXp = XA + AP sinYp = YA + AP cos

AB AC

AP AC

AP

AP

Procedure:

AB AC

Example 7.6:

Traverse SurveyingDefinitions:- 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 errorsA- 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

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 = 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

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 traverseThe 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