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 ID: 425805
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Islamic University of GazaCivil Engineering DepartmentSurveying IIECIV 2332ByBelal Almassri Slide2
Chapter 7 Coordinate geometry and traverse surveying – Part 2 Resection Traverse Surveying DefinitionsTypes, Utilizations and advantagesComputations and correction errorsExamplesSlide3
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
C
B
N
M
c
b
Ө
R
Ф
βSlide4
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 –
Ф
6- compute
= + Ө 7- compute AP = b sin Ф / sin N
8- compute Xp & Yp
Xp = XA + AP sinYp
= YA + AP cos
Procedure
:Slide5
Example 7.6:Slide6Slide7
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.Slide8
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 TraverseSlide9
Advantages:Less organization needed.Few observations needed.More accurate than other methods.Suits different types of utilizationsOpen 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.Slide10
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. Slide11
Underground . . . . Slide12
Computations and correction of errorsA- Determine the Azimuth of each line: 1- When ( α1 + Ө ) > 180º α2 = Ө - ( 180º –
α
1) =
Ө
+
α
1 - 180º
2- When
(
α
1 +
Ө
) < 180º
α2 = Ө + 180º + α
1 = Ө + α1 + 180ºSlide13
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
Slide14
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 -
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 ²Slide15
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 Slide16
Azimuth and bearingNorth to east or west / South to east or west