Islamic University of Gaza Civil Engineering Department Surveying II ECIV 2332 By B elal A lmassri
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Transcript of Islamic University of Gaza Civil Engineering Department Surveying II ECIV 2332 By B elal A lmassri
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Islamic University of GazaCivil Engineering Department
Surveying IIECIV 2332
ByBelal Almassri
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Chapter 7 Coordinate geometry and traverse surveying – Part 2 -Resection -Traverse Surveying Definitions-Types, Utilizations and advantages-Computations and correction errors-Examples
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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
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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
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Example 7.6:
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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.
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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
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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.
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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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Underground . . . .
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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
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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
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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
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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
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Azimuth and bearing
North to east or west / South to east or west