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					                              Maps and Plans
Background                    Basic Computations
                              Geometrical Concepts
                              Errors and Statistics
                              Distances               coordinates
                              Angles
Measurements                                          heights
                              Height differences

                Mid Semester examination
New Technologies           GPS

Practical Surveying           Setting Out

Analysis                      Geographical Information Systems
                                                         1
Legalities involved           Cadastral Surveying

Computer assisted surveying
The Department of Civil Engineering

CE-209 Fundamentals of Surveying

   Lecture 2 Maps and Plans in Surveying/Basic
       Computations/Geometrical Concepts

               Dr.Orhan ERCAN

                                                 2
Maps and Plans in Surveying…..
   Surveys are carried out to make maps and
   plans.

           Maps and plans are used to carry out
                                      surveys.
Survey Types
 *   Detail
 *   Control
 *   Setting Out
 *   Heighting




                   4
Surveying Terminology
 *   Survey area
 *   Coordinates
 *   Control Points
 *   Datums
 *   North


                        5
Elements of a map eg
 *   North - directions
 *   Grid
 *   Coordinates
 *   Scale - distances
 *   Heights


                          6
What is involved in conducting a survey?
 * What are the measurements made?
 * What do these measurements mean?
 * What further computations are
   required?
 * How good are our measurements?


                                       7
What are the measurements made?
 * angles (degs,mins,secs, rads)

 * distances (m, km)

 * Height differences (m)

   1000m = 1km
   100cm = 1m                      8
   10mm = 1cm
   1000mm = 1m
What do these measurements mean?
 * Angles
    * angles between points (eg)
    * bearings




                                   9
Basic Computation #1 Converting degrees,
minutes, seconds to decimal degrees and
radians
Angle measured : 28o 31' 25"

1o = 60'
1' = 60"
therefore 1o = 3600"

To convert to decimal degrees = 28 + 31/60 + 25/3600
                              = 28.5236o

p radians = 180o where p ~ 3.1416
                                                          10
To convert decimal degrees to radians = 28.5236 x p/180
                                      = 0.497831rads
Basic Computation #2 Converting radians to
decimal degrees, and degrees, minutes and
seconds
To convert radians to decimal degrees = 0.497831 x 180/p
                                      = 28.5236o

To convert decimal degrees to degs, mins, secs :

degs = 28
mins = (28.5236 - 28 ) x 60 = 31.416 = 31
secs = (31.416 - 31) * 60 = 24.96 = 25

28o 31' 25"
                                                           11
North Directions and Whole Circle Bearings
    * True, magnetic, arbitrary, grid
                                            N
N
                         B    D


        f
                                        C
    A
                                                12
                                            a
Further Computations from the
Measurements
 * Compute the distance and direction
   between two points given their
   coordinates.

 * Computing the coordinates of an unknown
   point given the coordinates of a known
   point and the direction and distance
   between them.
                                             13
Basic Computation #3 Computing the
distance between two points given their
coordinates - Chart 3.xls

distance    E2  N2




                                      14
Basic Computation #4 Computing the
bearing between two points given their
coordinates - Chart 2 .xls
        E
tan  
        N

            E 
  tan 1     
            N 



                                         15
Basic Computation #5 Computing the
coordinates of a point given the bearing and
distance from a known point Chart 4.xls

E  distance x sin 


N  distance x cos


E B  E A  E


N B  N A  N
                                       16
     Worked Example -
     Computation of Rectangular Coordinates

The coordinates of a point A are 311.617m E, 447.245m N. Calculate
the coordinates of point B where qAB = 37o 11’ 20” and sAB = 57.916m.



   EB  E A  s sin  AB                   N B  N A  s cos  AB
       311.617  57.916 sin 37 11 20
                                o               447.245  57.916 cos 37 o11 20
       311.617  35.007                        447.245  46.139
       346.624m                                493.384m




                                                                                     16
 Worked Example -
 Computation of bearing and distance
The coordinates of point A are 469.72m E, 338.46 N and point B are
268.14m E and 116.19mN. Compute the bearing and distance between
them.                      N               1  E AB 
                                        AB  tan 
                                                         
                                                          
                                                   N AB 
                            A                        E  E A  
                                            tan 1  B           
                                                     N B  N A 
                      AB       NAB                 268.14  469.72  
                                            tan 1                     
         sAB                                         116.19  338.46  
                                                      201.58 
                                            tan 1 
                                                      222.27 
                                                               
   B                                        tan 1 0.906915               18
               EAB             E                         +   180o
                                            42o1219
    Problem with quadrants!
                                           AB = 222o 12’ 19”
  Inverse Calculations
       4   E -ve                   1
                           E +ve
           N +ve
                           N +ve
           +360o
270o                                90o
           E -ve          E +ve
           N -ve          N -ve

           +180o           +180o          19
       3            180o            2
                                  s AB    E 2  N 2
                       N                  EB  E A 2   N B  N A 2
                                         E AB    N AB
                                               
                       A                sin  AB cos  AB
                                            201.58
                 AB       NAB       
    sAB                                 sin 222 o1219
                                       300.06m

B         EAB             E                                   20
                              Maps and Plans
Background                    Basic Computations
                              Geometrical Concepts
                              Errors and Statistics
                              Distances               coordinates
                              Angles
Measurements                                          heights
                              Height differences

                Mid Semester examination
New Technologies           GPS

Practical Surveying           Setting Out

Analysis                      Geographical Information Systems
                                                        21
Legalities involved           Cadastral Surveying

Computer assisted surveying
How good are our measurements?
 * precision

 * accuracy




                                 22
Precision refers to how good our observations
are with respect to each other.

  Accuracy refers to how good our results are
                            to the true value




                                                23
   When we talk about precision and
 accuracy we're talking about statistics
and more specifically standard deviation.



                                      24
Simple Statistics
30.615
              Mean  x 
                          x  306 .150  30.615
30.618                      n        10
30.614
30.615
                                            x  x 2
30.616      S tan dard Deviation                       0.002m
30.614                                          n
30.613
30.614
                  x  x  True 2

                                      0.002m
30.616
                        n                                25
30.618
The difference between x  x is how
we measure how good our observations
are with respect to each other -
precision.

If we replace X with the true value we
get a measure of accuracy.

Chart1.xls
                                         26
                   15                                                            15
                    .
                  . 10    .. .
              .                                                                   10
                  . 5 . .            .                                                5
          .                   .
              .                                                                    . ... .. .
                    . . 5 . 10 15
                                .                                                 . .. .... ... 5
                                                                                         ....            10 15
          .       .                                                                       . .
                                                                                     ... ....
                                                                                    .. ... ..
                .   . .     .   .
          .       .     .     .
            . . .         .
                    . .


                    (a)                                                               (b)
Highly dispersed observations, therfore low precision Closely grouped observations indicating high precision


                  15                                                               15

                  10                                                               10
                       . ... .. .                                            .
                      . . .... ...
                            ....                                                                         .
                    5 .... .... .
                             . .
                        .. ... .
                                                                                      5
                                                                     .            . ... .. .
                                                                                 . .. .... ...
                                                                                        ....     5           10 15
                              5          10 15                                           . .
                                                                                    ... ....
                                                                                   .. ... ..
                                                                                                             .
                                                                         .        .
                                                                                                     .



                    (c)                                                               (d)
  Very precise observations, however poor          Main distribution shows high precision, with several observations
                  accuracy                        which are signiicantly different. These observations can be considered
                                                                    outliers and subsequently rejected




                                                                                                                           27
Errors in Survey Measurements
 * Gross - chart 5.xls
 * Systematic - chart 6.xls
 * Random




                                28
   Errors in derived quantities
 We have measured two distances d1 and d2 in a straight line. What is the total distance (D) and its
 standard deviation?

 d1 = 154.26m and has a SD of 0.01m, d2 = 175.34m and has a SD of 0.05m




D = d1 + d2 = 154.26 + 175.34 = 329.60m

D = (d1 + e2) + (d2 + e2) = (154.26 +.01) +(175.34 +.05 )
                          = 154.27 + 175.39
                          = 329.66

difference = 0.06m                                                                         29
The coordinates of a point A are 311.617m E, 447.245m N. Calculate
the coordinates of point B where qAB = 37o 11’ 20” and sAB = 57.916m.

What are the coordinates of B. What effect would there be of an error
in the bearing of 1o and in the distance of 0.5m.


  EB  E A  s sin  AB                   N B  N A  s cos  AB
      311.617  57.916 sin 37 11 20
                               o               447.245  57.916 cos 37 o11 20
      311.617  35.007                        447.245  46.139
      346.624m                                493.384m


                                                                             30
                              Maps and Plans
Background                    Basic Computations
                              Geometrical Concepts
                              Errors and Statistics
                              Distances               coordinates
                              Angles
Measurements                                          heights
                              Height differences

                Mid Semester examination
New Technologies           GPS

Practical Surveying           Setting Out

Analysis                      Geographical Information Systems
                                                        31
Legalities involved           Cadastral Surveying

Computer assisted surveying