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451-102 Surveying for Builders

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					CE-209 Fundamentals of
      Surveying
 Lecture 4 Angle Measurement
                              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

Legalities involved           Cadastral Surveying

Computer assisted surveying
   Why do we need to measure
           angles?
• The location of points and orientation of
  lines frequently depend on the measurement
  of angles and directions.
What do we need to measure an
           angle?

                                Direction of turning (+)
 Reference or starting line




                              Angular distance
    Units of angle measurement
• Sexagesimal system

eg 90o 20’ 35” = 90.343o = 1.577rads
        Types of angles
Z              S
                   MLN – Horizontal angle
                   SLM – Vertical angle
                   TLN – Vertical angle
                   ZLS – Zenith angle
L              M   ZLT – Zenith angle


    R
                          N


                      T
  Angles, bearings and azimuths
• The bearing, direction or azimuth of a line is the
  horizontal angle between it and an arbitrarily
  chosen reference line called a north point.
• ‘True’ north – reference line through the north and
  south poles
• Magnetic north – defined by a freely suspended
  magnetic needle
• Assumed or arbitrary north.
   How do we measure angles?
• Compass
• Theodolite
• Total Station
               The compass
• No longer used for survey work
• Consists of a magnetised steel needle mounted on
  a pivot at the centre of a graduated circle
• Points towards magnetic north unless disturbed by
  local attraction.
• 0o near the equator to 90o near the poles
              The theodolite
• Main components - sighting telescope, two
  graduated circles in mutually perpendicular
  axes and level vials.

                              Trunnion or transit axis


                                   Line of collimation
        Vertical axis
                        Axis of plate level vial
      Components of a theodolite
•   Telescope
•   Trunnion axis
•   Horizontal vernier plate
•   Vertical circle
•   Horizontal/vertical clamp
•   Horizontal/vertical slow motion screws
•   Plate bubble
•   Horizontal circle/lower plate
     Method of circle reading
• Direct
• Micrometer
• Automatic
       Setting up a theodolite
• Centring
• Levelling
• Elimination of parallax
Reading angles with a theodolite
• Clockwise angles
• Face left/right
• Rounds of angles
    Measuring horizontal angles
• Select RO
• Set reading on horizontal circle
• Swing telescope to sight other points and record
  ‘face left’ directions
• Transit telescope to ‘face right’ and read direction
  for all points including the RO
• One round of angles completed
• Change zero and repeat.
Reducing horizontal observations
• Method
• Checks
     Measuring vertical angles
• Read after horizontal angles
• Horizontal hair used for sighting targets
• Automatic compensator or index level vial
     Reducing vertical angles
• Method
• Checks
    In Figure 1, the horizontal angle was measured at B to C and A.
    Following is an extract from the field book showing the
    directions measured. Reduce the observations and compute the
    value of the angle CBA.               [4 marks]
Station at     Station to       Face left    Face Right
                            deg min sec      deg    min                sec
B              C            00    03   50    180       04              30
B              A            83    58   50    264       00              00


                                                            A




                                                                            B


                                                   C

                                                            Figure 1
            Total stations
• Three basic components – EDM, electronic
  digital theodolite, microprocessor
• No micrometer – resolves angles directly
   Errors in Angle Measurement
• Gross – reading, pointing, setting up over the
  wrong point, booking
• Random – settling of tripod, wind, temperature,
  refraction
• Systematic/instrumental
   – Horizontal axis not perpendicular to the vertical axis
   – Axis of sight not perpendicular to the horizontal axis
   – Axis of the plate bubble not perpendicular to the
     vertical axis.
   – Vertical index error

				
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