CIVL102 Surveying and Surveying Camp

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Surveying and Surveying Camp
Basic Goal of Surveying
   Obtain positions of built objects (3D)

Graphical representation of the results:
   Paper form as a contour map

   A plan at some suitable scale
   Digital format (CAD)
Two Main Categories by size
1. Geodetic Surveying:
   Large areas
   Considers curvature of the earth

   Determine figure of the earth (the “geoid”) and
    gravity field
   Provide an accurate framework for a large survey
The Geoid
   Mean sea level (M.S.L.)
    surface extended over the
    whole earth
   Equipotential surface                Polar axis

   Perpendicular to direction of                     Ellipsoid



   Variations in the earth’s        a
                                                        Equatorial plane

    mass distribution:
        Geoid has irregular shape
        Cannot be mathematically
         described in closed form.
        Best-fitting Ellipsoid Model
                                               Polar axis
   Geodesists: often use the
    ellipsoid that best fits the

    geoid                                           Geoid
                                                                    Equatorial plane
    Points on/ near earth surface:
    Given by geodetic latitude,
    longitude and height above
    ellipsoid                        Fig. 1.1 The geoid (irregularities
                                               greatly exaggerated)
Popular ellipsoid model:
   Geodetic Reference System of 1980 (GRS80)
   Equatorial semi-axis a = 6378.1370 km;
   Polar semi-axis b = 6356.7523 km

   Distortion inevitable when plotting a curved
    surface onto a flat map
   Various map projection methods
    (mathematical geodesy)
Second Main Category by size:
2. Plane Surveying
   Relatively small areas
   Surface of the earth: “infinite horizontal plane”
Direction of gravity:
   Constant over the entire site.
   Defines vertical lines ( “plumb lines”),
   Plane normal to a plumb line     horizontal plane.

    Rectangular coordinate system: most suitable for
    plane surveying
For distance measurements:
   Flat earth assumption acceptable (up to 10 km 10 km)
   10 km arc on earth surface: longer than subtended chord by < 10 mm
      percentage error in length measurements:
      < 10/10000000 = 1 ppm (parts-per-million)

   Laser instrument: typically error: 5 ppm
   Steel tape: no better than 100 ppm.

Plane surveying: suffices for all but the largest surveys
                 (for horizontal distances)

Geodetic surveys: seldom performed by engineers in private
    Types of Surveying
Also classified by purpose - common types:

Topographic surveys
   Determine locations & elevations of natural
    & constructed objects on the ground
   For map making
   Concerns all features of the landscape that
    can be shown for the particular map scale
Cadastral surveys
   Determine lawful boundaries & areas of
    properties rather than detail features of the
   Used in legal disputes, taxation, etc.
   Also called property surveys / boundary
Engineering surveys
   Surveying work for engineering projects before,
    during & after construction

   E.g. setting out of tall buildings and dams;
    deformation monitoring after completion

   Mining, hydrographic, highway, railroad, and
    tunnel surveys
     In our course:
   Mainly topographic and engineering surveying
   Implicit assumption:
         Small sites
         Theory and techniques of plane surveying will suffice
 Flat earth assumption may not hold for determination of elevations
   Tangent plane: deviates from spherical earth by
      ~ 2 m @ 5 km from point of tangency
      ~ 8 m @ 10 km (see Ex. 1.2).

Effects due to the earth’s curvature & remedies: Ch.2.
Survey results:
   Often plotted on a plan
   True-to-scale representation of the area in a horizontal plane

Measured: slope (inclined) distance

Plotted: horizontal projection

Height information conveyed on plan: use
   Contour lines, or
   Spot levels (small “+”s with heights printed alongside)
Consider Fig. 1.2
                                      A'                                 C
   Physical points A, B, and C

Essential information for plotting:                                      C'

   Projections AB’ & AC’
   In horizontal plane containing
    A (or any other horizontal        Fig. 1.2   Basic measurements in
    plane)                                       surveying
      Fundamental techniques in                  B
                                     A'                C

5 basic quantities:                                    C'

   Slope distance AB, along with     A
   Vertical angle B’AB (or zenith angle A’AB),

        Horizontal distance AB’ = AB cos(BAB’)
        Vertical distance B’B

   Similar measurements: fix C relative to A,
   Horizontal angle B’AC’ also needed to orient C
    relative to AB’ on the plot
      Other methods of measurement

   Plan distance (e.g. AB’) by taping directly
   Height difference (e.g. B’B, rise from A to B) by
    differential leveling (Ch. 2)

     Detailed techniques: subsequent chapters.

Essential characteristic about surveying:

   Before final details (such as C) can be surveyed:
    need reference points (e.g. A and B) to base the
    measurements on.
     Control survey
   Establish reference monuments
       ”Control points”
       Accuracy greatly affects final results
       Often run as first stage of survey project
    Coordinate Systems
   Coordinates to be calculated before plotting survey results
   Use of appropriate coordinate system

Plane surveying:
   Righted-handed, rectangular coordinate system
   x-y axes: on horizontal plane
   z-axis: // direction of gravity

Still need:
   Suitable origin and orientation
        Based on physical entities
        For local construction purposes:

An artificial system may suffice, e.g.
       choose convenient point “A” on site as origin
       Usually assigned +ve (large) x, y coordinates -> all
        positive horizontal coordinates in the area
       Point “B” picked relative to A
       Line AB (horizontal projection) defines “artificial north”
       AB often chosen // (or per.) to most building lines
       Height “0” (or other reference value) assigned to a
        convenient point
   All other coordinates calculated relative to these
    Surveys over extended public areas:

   Often tied to an official coordinate system
   Primary level of control: from government authority

Official rectangular coordinate system: usually:
   x- and y-axes: directions of east and north
   Coordinates values along x, y axes: eastings (E) and
    northings (N)
   Origin: usually in the country / region; assigned +ve &
    large (E, N)
       all other horizontal coordinates positive
   “0” of z-axis: often defined at mean sea level (M.S.L.)
    Measuring angles and directions

   Observe bearings
   Used in reconnaissance and hasty work

   A telescopic sight pivoted both horizontally & vertically
   Built-in graduated circles for measuring horizontal & vertical angles
   Angles: usually displayed in the /’/” system

2 radians = 360 (degrees); 1 = 60’ (minutes); 1’ = 60” (seconds)
   Theodolites sold in Europe: g/c/cc system: angles in gons (or grads)

   360 = 400g (gons); 1g = 100c; 1c = 100cc
    Note: 50g79c98cc : conveniently expressed as 50.7998g

   Theodolites used on construction sites: 20”, 6”, 5” or 3” of arc

   Geodetic theodolites: 1” or even 0.1”
Optical theodolite &   Electronic theodolite with
angle readings         EDM mounted on top
      Measuring lengths

Measuring tape                measuring tape

   Direct linear
   Cheap
   For small details
                          Steel tape
       Electronic Distance
       Measurement (EDM)

   Laser equipment for very accurate distance

   Measure up to thousands of meters with only a few
    mm’s error

   Used in all serious control work, and often in detail
    surveys as well
EDM   EDM & rechargeable battery
      Measuring height differences:

Level & staff

   Level: has telescope that can rotate about vertical
    axis, maintaining horizontal line of sight
   Staff: long rod held vertically over point of interest,
    provides height readings to be read by the level
   A pair of readings determines the change in height
Automatic Level   Staff   Readings on
                          a staff
      The tripod
   Three-legged stand with
    pointed metal shoes
   Most surveying
    instruments: mounted on
    top of tripods during use
   Tripod legs: maneuvered
    to make instrument
    roughly horizontal &
    centered over the station
    marker, followed by fine
    adjustments on the
                        Surveying equipment mounted on a wooden tripod
      More advanced instruments

Total station

   Theodolite, EDM, data
    processor & display unit
   Instant data conversion
    into 3-D coordinates
   Interface with computers

                               Total station with memory cards
Aerial camera
   Produces aerial photos for topographic, engineering, &
    cadastral surveys

   Used to view stereoscopic pairs of aerial photos;
    approximate heights of objects can be determined by
    stereoscopic viewing.

Global Positioning System (GPS)
   Satellites-based systems giving accurate 3-D coordinates of
    point on earth occupied by a GPS receiver. Also used for
    navigation purposes
 Computing tools
   Computers, plotters, spreadsheets & CAD: invaluable tools for
    the surveyor
   Saves hours of time & potential mistakes


   Automating long & routine calculations (Ch.2,4)
   Least squares adjustment (Ch.1,2,3,4)
   Graphical solutions (Ch.3,4,6)
   Plotting thousands of points with little effort (Ch.5),
   etc.
Preliminaries, Planning, & General Rules

Any survey project:
   Involves a series of measurements
   Errors accumulate

Fundamental principle of surveying:

    Work from the whole to the part
    1. Establish overall framework

   Covering the whole area
   Refined methods & instruments
   Minimal number of points
            minimize error
      2. Fill in details based on
         accurate control framework
   Cheaper & quicker methods used
         meaningless for subsequent measurements to
          be more precise than underlying framework

   Carry out all measurements (& calculations)
    so that final product meets accuracy required
    by the purpose of survey

   Suit the means to the end since accuracy is
    costly in speed & resources.

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