Angles and Bearings

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Angles and Bearings

• Concepts, Observation and Computation

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Concepts

• A direction
• Simply that, like over there
• A Bearing
• A direction relative to a datum
• Generally the datum is called North
• There are several to choose from!
• True North, Magnetic North, Grid North, Ogleby
  North
• An Angle
• The difference between two directions

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Bearing Datums

• True North
• The astronomical North
• The axis about which the Earth rotates
• Associated with latitude and longitude
• Magnetic North
• Very unstable, handy for navigation
• Grid North
• A mathematical construct for mapping

Although not the correct plural of datum, it is
what we use as data has a different meaning
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Bearing Datums

• Are also associated with coordinate systems
• Refer coordinates PPT
• We will be using a grid system
• UTM Zone 55S
• Based on the GDA/MGA
• For this unit, they can be treated as planar
  cartesian system (x,y)

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The Theodolite

• An instrument for measuring directions (angles)
• http//en.wikipedia.org/wiki/Theodolite
• Generally electronic, previously optical
• The graduations were on glass circles

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Angle reading with a jigger

• The instrument is set up over a mark on the
  ground
• It is then levelled in all directions
• A simple task
• The process compensates for some systematic error
  in the instrument
• The telescope is then sighted to a target
• Focus the eyepiece beforehand
• Then focus the telescope

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Angle reading with a jigger

• The target is sighted twice, once on each face
• Observe which side of your face is closest to the
  vertical circle, that is the face
• The telescope is transited and traversed to put
  the vertical circle on the other sied of your
  face
• This eliminates collimation error!

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Resection

• A method of determining position (E,N) by
  measuring angles between known points
• The angles are derived from a series of
  directions measured by a theodolite
• This weeks practical!

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Resection

• Set the instrument over a survey mark
• Sight to the left hand most target
• Set the horizontal circle on the instrument to
  zero
• Start on face-left
• Sight clockwise to the next target, record the
  reading
• Continue to the next target

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Resection

• At the last target, change face
• The vertical circle of the instrument should now
  be on the other side of your face
• Sight the targets again and record the readings
• Mean (average) the angles if the observations
  have been successful
• Difference b/n FL and FR 180 horizontal
• Sum of verticals 360

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REB
StPl
BHP
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Reduce these angles from the observations
REB
Calculate these angles
StPl
BHP
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REB
StPl
BHP
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Tienstras Formula

• For the sake of simplicity, we will reduce the
  data though Tienstras formula
• It ONLY works if we label the angles correctly
• The formula is derived from the solution of 2
  simultaneous triangles. You can do it this way
  if you like a challenge
• You could use Excel!
• Take care, the numbers are large