CIVL102
Surveying and Surveying Camp
Basic Goal of Surveying

Obtain positions of built objects (3D)
Graphical representation of the results:
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Paper form as a contour map
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A plan at some suitable scale
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Digital format (CAD)
Two Main Categories by size
1. Geodetic Surveying:
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Large areas
Considers curvature of the earth
Purposes:
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Determine figure of the earth (the “geoid”) and
gravity field
Provide an accurate framework for a large survey
The Geoid

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Mean sea level (M.S.L.)
surface extended over the
whole earth
Equipotential surface
Perpendicular to direction of
gravity
Polar axis
Ellipsoid
b

Geoid

Variations in the earth’s
mass distribution:

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Geoid has irregular shape
Cannot be mathematically
described in closed form.
a
Equatorial plane
Best-fitting Ellipsoid Model
Polar axis
Ellipsoid
Geodesists: often use the
ellipsoid that best fits the
geoid
b

Geoid
a
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:
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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

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Relatively small areas
Surface of the earth: “infinite horizontal plane”
Direction of gravity:

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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)

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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
practice
Types of Surveying
Also classified by purpose - common types:
Topographic surveys

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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
landscape

Used in legal disputes, taxation, etc.

Also called property surveys / boundary
surveys
Engineering surveys

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Surveying work for engineering projects before,
during & after construction
E.g. setting out of tall buildings and dams;
deformation monitoring after completion
Others:
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Mining, hydrographic, highway, railroad, and tunnel
surveys
In our course:
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Mainly topographic and engineering surveying
Implicit assumption:
 Small sites
 Theory and techniques of plane surveying will suffice
Note:

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:

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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

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Contour lines, or
Spot levels (small “+”s with heights printed alongside)
B
Consider Fig. 1.2
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Physical points A, B, and C
A'
B'
Essential information for plotting:
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Projections AB’ & AC’
In horizontal plane containing
A (or any other horizontal
plane)
C
A
Fig. 1.2
Basic measurements in
surveying
C'
Fundamental techniques in
surveying
B
A'
C
B'
5 basic quantities:

Slope distance AB, along with

Vertical angle B’AB (or zenith angle A’AB),
A
Horizontal distance AB’ = AB cos(BAB’)
Vertical distance B’B
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Similar measurements: fix C relative to A,
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Horizontal angle B’AC’ also needed to orient C
relative to AB’ on the plot
C'
Other methods of measurement
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Plan distance (e.g. AB’) by taping directly
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Height difference (e.g. B’B, rise from A to B) by
differential leveling (Ch. 2)
Detailed techniques: subsequent chapters.
Essential characteristic about surveying:
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Before final details (such as C) can be surveyed:
need reference points (e.g. A and B) to base the
measurements on.
Control survey
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Establish reference monuments
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”Control points”
Accuracy greatly affects final results
Often run as first stage of survey project
Coordinate Systems
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Coordinates to be calculated before plotting survey results
Use of appropriate coordinate system
Plane surveying:
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Righted-handed, rectangular coordinate system
x-y axes: on horizontal plane
z-axis: // direction of gravity
Still need:
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Suitable origin and orientation
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Based on physical entities
For local construction purposes:
An artificial system may suffice, e.g.

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Usually assigned +ve (large) x, y coordinates -> all
positive horizontal coordinates in the area
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Point “B” picked relative to A
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Line AB (horizontal projection) defines “artificial north”
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choose convenient point “A” on site as origin
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:

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Often tied to an official coordinate system
Primary level of control: from government authority
Official rectangular coordinate system: usually:
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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
Compass
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Observe bearings

Used in reconnaissance and hasty work
Theodolite
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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)
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Theodolites sold in Europe: g/c/cc system: angles in gons (or grads)
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360 = 400g (gons); 1g = 100c; 1c = 100cc
Note: 50g79c98cc : conveniently expressed as 50.7998g
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Theodolites used on construction sites: 20”, 6”, 5” or 3” of arc
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Geodetic theodolites: 1” or even 0.1”
Optical theodolite &
angle readings
Electronic theodolite with
EDM mounted on top
Measuring lengths
Measuring tape

Direct linear
measurements
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Cheap

For small details
Fiberglass
measuring tape
Steel tape
Electronic Distance
Measurement (EDM)
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Laser equipment for very accurate distance
measurement
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
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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
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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
instrument.
Surveying equipment mounted on a wooden tripod
More advanced instruments
Total station
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Theodolite, EDM, data
processor & display unit
combined
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
Stereoscope

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
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Saves hours of time & potential mistakes
Applications:
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Automating long & routine calculations (Ch.2,4)
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Least squares adjustment (Ch.1,2,3,4)
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Graphical solutions (Ch.3,4,6)
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Plotting thousands of points with little effort (Ch.5),
etc.
Preliminaries, Planning, & General Rules
Any survey project:
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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
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Cheaper & quicker methods used
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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.