MGA Concepts and Grid Calculations

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MGA Concepts andGrid Calculations

• Geodetic Surveying B

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Objectives

• Apply fundamental knowledge of MGA to grid
  calculations
• Calculate and apply grid convergence.
• Determine grid coordinates of a point given known
  coordinates of a start point and grid bearing and
  spheroidal distance from that start point.
• Determine grid bearing and spheroidal distance
  between known points

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Overview of Coordinates

• There are three aspects to Understanding and
  Using Coordinates
• Datum
• Projections
• Observations

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Datum, Projections and Observations

• A datum is the underlying basis for coordinate
  systems
• Positions on the datum can be projected to
  create grid coordinates
• Observations (bearings and distances) in the
  real world need to be corrected to conform to the
  datum and projection

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Why Coordinates?

• The use of a uniform system of coordinates allows
  spatial information from various sources to be
  integrated
• Increasing requirement for coordination in all
  types of surveys
• At the heart of Australian Spatial Data
  Infrastructure (ASDI), GIS and GPS
• Required in International Standards

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Approximation - an Important Underlying Concept

• All exact science is dominated by the idea of
  approximation Bertrand Russel
• Coordinates are simply a way to approximate the
  real world using a mathematical model
• Some models are better approximations than others

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Understanding and Using Datums
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Ellipsoids and Geoids
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AGD - The Old Datum

• Terrestrial Observations
• Systematic Errors
• Constrained by Doppler (transformed)
• Distribution
• Homogeneity
• Location of Marks

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GDA - International Basis

• International Terrestrial Reference Frame (ITRF)
  is a particular realization of an idealized
  reference system...
• observation at certain sites and with certain
  factors in the processing produces...
• set of positions and velocities of those sites at
  a certain time.
• reference ellipsoid - GRS80

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GDA and the ITRF
Link to ITRF by GPS observations at IGS sites and
the Australian National Network (500km). GDAs
link to ITRF makes it compatible with WGS84
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Queensland GDA94 Data Set
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Magnitude of Shift

• All coordinates
• apparently shift in
• excess of 200m.

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Distortions between Transformed AGD84 and GDA94
Western Qld
Central Coast
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Types of Coordinates Systems
Semi-minor axis (b)
Semi-major axis (a)
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Projection Coordinates onGDA and AGD
Map Grid Australia on GDA
NMGA
EMGA
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Terminology
Universal Transverse Mercator
Std. 6 Degree Zones, with the same Central
Meridians etc.
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Understanding and Using Projections
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UTM Projection

• 6? Degree zones
• Longitude of Zone 1 3? east longitude
• 0.9996 Scale Factor on Central Meridian

• 500 000 m false easting
• 10 000 000 m false northing
• 1/2 degree overlap

Ref Chapter 1. GDA Technical Manual ICSM Web
Site
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AMG/MGA - UTM Projection
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AMG/MGA - UTM Projection
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AMG - Redfearns Approx (See Study Book)
ER, NR Rectangular Coords Note meridian
distance (m) NR ET, NT Transverse Mercator
Coords E, N AMG Coords without false
origin E, N AMG Coordinates
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GDA94 to MGA94(Redfearns Formulae)

• Datum Parameters
• Semi-Major Axis (a)
• Inverse Flattening (f)
• Projection Parameters
• Longitude of Central Meridian (Zone)
• Scale Factor on Central Meridian
• False Easting, False Northing

• Input Data
• Latitude, Longitude Height
• Computed Parameters
• Radius of Curvature
• Meridian Distance
• Foot-Point Latitude
• Function (semi-major axis, inverse flattening and
  latitude)
• Output
• Easting, Northing, Zone, Grid Conv. , Point Scale
  Factor

Ref Chapter 5. GDA Technical Manual ICSM Web
Site
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GDA94 - MGA94 (Example)
Ref Redfearn.xls GDA Technical Manual ICSM
Web Site
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Geographic Coordinates Converted in Overlapping
Zones.
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MGA94 to GDA94(Redfearns Formulae)

• Datum Parameters
• Semi-Major Axis (a)
• Inverse Flattening (f)
• Projection Parameters
• Longitude of Central Meridian (Zone)
• Scale Factor on Central Meridian
• False Easting, False Northing

• Input Data
• Easting, Northing, Zone Height
• Computed Parameters
• Foot-Point Latitude
• Radius of Curvature
• Meridian Distance
• Function (semi-major axis, inverse flattening and
  latitude)
• Output
• Lat, Long, Grid Conv, Point SF

Ref Chapter 5. GDA Technical Manual ICSM Web
Site
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MGA94 - GDA94 (Example)
Ref Redfearn.xls GDA Technical Manual ICSM
Web Site
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Scale Convergence

• Line Scale Factor (K)
• L/s (plane / ellipsoidal)
• ? S/s (grid / ellipsoidal)
• Grid Bearing (?)
• Plane Bearing (q) Arc-to-Chord Correction
  (?)
• Azimuth (a) Grid Convergence (?)

Ref Glossary of Terms. GDA Technical Manual
ICSM Web Site
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Grid Bearing Ellipsoidal Dist from MGA94
Coordinates

• Grid Bearing function (plane bearing
  arc-to-chord correction )
• Arc-to-chord correction function ( eastings,
  northings and approx mean latitude)
• Ellipsoidal Distance function (plane distance
  line scale factor )
• Line Scale Factor function ( CM scale factor,
  eastings approx. mean latitude)

Ref Chapter 6. GDA Technical Manual ICSM Web
Site
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Grid Bearing Ellipsoidal Dist from MGA94
Coordinates (Example)
Grid North
L 54992.279
S ? L
A
s 54972.271 K 1.000 363 97
Plane Bearing (?) Plane Distance (L)
Grid Bearing (?AB )
?AB 125?17?21.18?
?A -20.67? ?AB 125?17?41.86? ?B 19.18?
?BA 306?52?05.37?
B
Grid Distance (S)
Grid Bearing (?BA )
Ref Test Data. GDA Technical Manual ICSM Web
Site
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Grid Calculations inOverlapping Zones
ZONE 54
ZONE 55

• Plane Distance
• Ellipsoid Distance
• Line Scale Factor
• Arc-to-Chord (A)
• Arc-to-Chord (B)
• Plane Bearing
• Grid Bearing (AB)
• Grid Bearing (BA)
• Grid Convergence

• 54992.279
• 54972.271
• 1.00036397
• -20.67?
• 19.47?
• 125? 17? 21.18?
• 125 ? 17? 41.86?
• 305 ? 17? 01.72?
• -1 ? 52? 43.22?

55003.307 54972.271 1.00042107 23.94? -25.19? 128
? 58? 08.37? 128? 57? 44.44? 308 ? 58? 33.56? 1
? 47? 19.36?
Ref GridCalc.xls GDA Technical Manual ICSM Web
Site
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Plane Coordinates
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Plane Coordinates
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Plane Coordinates
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Summary

• We investigated methods to
• Calculate and apply grid convergence.
• Determine grid coordinates of a point given known
  coordinates of a start point and grid bearing and
  spheroidal distance from that start point.
• Determine grid bearing and spheroidal distance
  between known points

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Self Study

• Read Module 6 (first part)

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Review Questions