Transcript Distance Reduction - Department of Geodesy and Surveying

Distance Reductions
Objectives
After this lecture you will be able to:
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Determine the spheroidal distance
between two points on Earth’s surface
from EDM measurements
Lecture Outline
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Distances
Normal Sections
Curve of Alignment
Distance Reduction
– Physical Corrections
– Geometric Corrections
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SP1
Conclusion
Geodetic Distances
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Great Circle (sphere)
Small Circle
Two Plane Sections (also called
Normal Sections).
Curve of Alignment
Geodesic (spheroid)
Plane Sections (Normal Sections)
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Instrument set at B
Rotation axis is
normal BN
Vertical plane
containing A = ABN.
Instrument set at A
Rotation axis is
normal AM
Vertical plane
containing B = BAM
Line A B 
Line B A
A
B
M
N
Curve of Alignment
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Locus of all points where Bearing to A = bearing to
B + 180 is called Curve of Alignment.
Marked on ground - A surveyor sets up between A
and B such that A and B are in same vertical plane
Horizontal angles are angles between curves of
alignment
– But can assume normal sections because start off same
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Spheroidal triangles are figures formed by 3 curves
of alignment joining the 3 points
A
Normal Section
A to B
B
Curve of Alignment
Normal Section
B to A
Heights and Distances
Measured Distance (d1)
A
Slope Distance (d2)
Mean Terrain Height
HA
Terrain
Level Terrain Distance
hM
B
hA
Geoidal (Sea Level) Distance (S’)
HB
(S”)
Geoid or
Sea Level
NA
hB
Ellipsoidal Distance (d4)
Ellipsoidal Chord Distance (d3)
Ellipsoid
NB
Distance Reduction
Distance Reduction involves:
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Physical Corrections
Geometric Corrections
Physical Corrections
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1. Atmospheric correction
• First velocity correction
• Second velocity correction.
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2. Zero correction (Prism constant).
3. Scale correction.
4. First arc-to-chord correction.
First Velocity Correction
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Covered in earlier courses
Formula available - function of the
displayed distance, velocity of light and the
refractive index.
Correction charts normally available
– to set an environmental correction (in ppm) or
– to determine the first velocity correction to be
added manually
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Some only require the input of
atmospheric readings and the calculations
Second Velocity Correction
Zero Correction
(Prism Constant)
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Obtained from calibration results
Scale Correction
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Obtained from calibration results
First Arc-to-Chord Correction
(d1-d2)
For Microwaves
3
1
-d
Correction
2
384R
 0.6 mm for d  30 km
First Arc-to-Chord Correction
(d1-d2)
For Light
3
1
-d
Correct ion
2
1176R
 0.02mmfor d  10 km
Geometric Corrections
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1. Slope correction
2. Correction for any eccentricity of
instruments
3. Sea Level correction (or AHD
correction)
4. Chord-to-arc correction (sometimes
called the second arc-to-chord)
correction)
5. Sea Level to spheroid correction
Slope Correction
To calculate level terrain distance
l  d - RL
2
2
2
Eccentrics
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Try to avoid them!
If they can’t be avoided - connect them
both vertically and horizontally
Include redundant observations
AHD (Sea Level) Correction
lR
s 
R  RLm
"
W hereR  R m   
Chord-to-Arc Correction
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d3 to d4 or S” to S’ if correct radius is
3
used
d3
Cc  a 
Correction is
2
or 
24R
S "3
24R
Geoidal (Sea Level) Distance (S’)
(S”)
Ellipsoidal Distance (d4)
Ellipsoidal Chord Distance (d3)
2
Sea Level to Spheroid
Correction
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Where N is the average height
difference between spheroid and AHD
s is required spheroidal length
R is a non-critical value for earth’s
'
radius
Rs
s 
R N
Geoidal (Sea Level) Distance (S’)
(S”)
NA
Ellipsoidal Distance (d4 or s)
Ellipsoidal Chord Distance (d3)
NB
Example from Study Book
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Follow example from study book for full
numerical example
Geoscience Australia’s Formula
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Combined and separate formula
available
Spreadsheets
– Will be used in Tutorials
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Also in Study Book
SP1 Requirements
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In Study Book
Conclusion
You can now:
 Determine the spheroidal distance
between two points on Earth’s surface
from EDM measurements
Self Study
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Read relevant module in study materials
Review Questions