451200 Geomatics Science 2

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451-200 Geomatics Science 2

• Lecture 4
• Height Determination

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At the end of todays lecture students should

• Be able to define the different datums
  underpinning heights.
• Be able to determine heights through precise
  levelling techniques.
• Understand the computations involved in
  trigonometric heighting.

 
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Why do we need to measure heights accurately -
Tunnel Monitoring
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Why do we need to measure heights accurately -
Volcano Monitoring
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Why do we need to measure heights accurately -
South Pacific Climate and Sea level Monitoring
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Any others?
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Methods of geodetic height determination?
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Methods of geodetic height determination

• Precise leveling
• Trigonometric heighting
• GPS

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Height Datums
geoid-ellipsoid separation N h - H H
orthometric height h spheroidal height N
geoid height
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Precise levelling

• In principle precise levelling is similar to
  ordinary levelling but with several refinements
  to minimise errors and improve accuracy.

f (observer, instrument, method)
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Equipment
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Parallel plate micrometer
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Errors in precise levelling

• Collimation error
• Refraction
• Curvature

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Collimation error
Collimation error occurs when the collimation
axis is not truly horizontal when the instrument
is level. The effect is illustrated in the sketch
below, where the collimation axis is tilted with
respect to the horizontal by an angle a
the effect of the collimation error is eliminated
if sight lengths are kept equal.
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Two peg test
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Curvature
Due to the curvature of the Earth, the line of
sight at the instrument will deviate from a
horizontal line as one moves away from the level
As with collimation error, the effect is
eliminated by using equal sight lengths for fore-
and backsights.
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Refraction
The variable density of the Earth's atmosphere
causes a bending of the ray from the staff to the
level. The effect is illustrated in the sketch
below
The effect of refraction is almost totally
eliminated by using equal fore- and backsights
(because atmospheric conditions along the fore-
and backsights will not be completely identical,
there will be a small residual error).
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Errors and how to eliminate them

• Curvature - increase over the length of the line
• BS FS or sum BS sum FS
• Refraction - varies with line of sight, and time
• BS FS
• sight to the same staff first
• sequence of sightings to left and right of staff
• dont take reading lower than 0.6m
• carry out reverse levelling at a different time
  of day

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Errors and how to eliminate them

• Sighting errors
• minimise line of sights
• compare readings on left and right hand side of
  the staff
• Instrument errors
• maladjustment of the circular bubble
• compensator errors
• eliminated by always setting the instrument up
  facing the same staff

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Errors and how to eliminate them

• Staff errors
• datum error (leap frogging, even number of
  setups)
• graduation error
• warpage
• staff non verticality
• temperature corrections
• sinking or rising of the staff and instrument

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Precise levelling field procedure
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Example
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Trigonometric heighting
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Methods of trig heighting

• Single observations
• Simultaneous reciprocal observations
• Non simultaneous reciprocal observations

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Simultaneous reciprocal angles
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Accuracy and precision
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The practical
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Example
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At the end of todays lecture students should

• Be able to define the different datums
  underpinning heights.
• Be able to determine heights through precise
  levelling techniques.
• Understand the computations involved in
  trigonometric heighting.