1. MGA Concepts and Grid Calculations
Geodetic Surveying B

2. 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

3. Overview of Coordinates
There are three aspects to Understanding and Using Coordinates
Datum
Projections
Observations

4. 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

5. 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

6. 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

7. Understanding and Using Datums

8. Ellipsoids and Geoids Geocentric Datum (best fit globally) Local Datum
The Geoid
(Mean Sea Level)
Geocentric Datum
(best fit globally)
Local Datum
AGD84
(best fits Australia)

9. AGD - The Old Datum Terrestrial Observations Systematic Errors
Constrained by Doppler (transformed)
Distribution
Homogeneity
Location of Marks 8

10. 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

11. GDA and the ITRF Link to ITRF by GPS observations
at IGS sites and the Australian
National Network (500km).
GDA’s link to ITRF makes it
compatible with WGS84

12. Queensland GDA94 Data Set
QUT1
SUGA
TEXA
MULA
NORM
BREA
BRDV
WILF
WOLL
MUCK
BANZ
BARC
PI EB
HOWI
GREN
OLVE
BASS
EMUU
TOWA
Qld 100km
Network

13. Magnitude of Shift All coordinates apparently shift in excess of 200m.4

14. Distortions between Transformed AGD84 and GDA94
Western Qld
Central Coast

15. Types of Coordinates SystemsX Y Z
Semi-minor
axis (b)
Semi-major
axis (a) N E
Projection l f h
Geodetic
- X
+ Y
- Z
Cartesian

16. Projection Coordinates on GDA and AGD
Map Grid Australia
on GDA
NMGA
NAMG
EAMG
Australian Map Grid
on AGD
EMGA

17. the same Central Meridians etc.
Terminology
GDA94
AGD84
Latitudes &
Longitudes
Universal Transverse Mercator
Std. 6 Degree Zones, with
the same Central Meridians etc.
AMG84
MGA94
Eastings, Northings
& Zone

18. Understanding and Using Projections

19. UTM Projection 6 Degree zones Longitude of Zone 1 : 3 east longitude
Scale Factor on Central Meridian
m false easting
m false northing
1/2 degree overlap
Ref: Chapter 1. GDA Technical Manual: ICSM Web Site

20. AMG/MGA - UTM Projection
Zone Boundary 150E
Zone Boundary 144E
Central Meridian 147E
Zone
Projection Plane
Zone
Central Meridian 141E
Scale Factor 1.0
Scale Factor
Terrain
Surface
Geoid N
Ellipsoid
Scale Factor 1.0
Scale Factor
Scale Factor

21. AMG/MGA - UTM Projection

22. AMG - Redfearn’s 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

23. GDA94 to MGA94 (Redfearn’s 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

24. GDA94 - MGA94 (Example)
Ref: Redfearn.xls : GDA Technical Manual : ICSM Web Site

25. Geographic Coordinates Converted in Overlapping Zones.

26. MGA94 to GDA94 (Redfearn’s 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

27. MGA94 - GDA94 (Example)
Ref: Redfearn.xls : GDA Technical Manual : ICSM Web Site

28. 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

29. 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

30. Grid Bearing & Ellipsoidal Dist from MGA94 Coordinates (Example)
North
L =
S  L A
s =
K =
Bearing (AB )
Grid
Plane Bearing ()
Plane Distance (L)
AB = 1251721.18
A = 
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

31. Grid Calculations in Overlapping Zones
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
+23.94
-25.19
128 58 08.37
128 57 44.44
308  58 33.56
+1  47 19.36
-20.67
+19.47
125 17 21.18
125  17 41.86
305  17 01.72
-1  52 43.22
Ref: GridCalc.xls GDA Technical Manual : ICSM Web Site

32. Plane Coordinates Zone 55 Error 0.4 300 km Central Meridian
Ellipsoid
Zone Boundary
Central Meridian
Projection Plane
Zone
300 km
Error 0.4

33. Plane Coordinates Zone 55 /2 Error 0.06 100 km Central Meridian
Ellipsoid
Zone Boundary
Central Meridian
Projection Plane
Zone /2
100 km
Error 0.06

34. Plane Coordinates E,N E,N X,Y X,Y Plane Bearing Grid Bearing
Grid Distance
E,N
E,N
X,Y
Grid Bearing
Grid Distance
X,Y
Plane Bearing
Plane Distance

35. 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

36. Self Study
Read Module 6 (first part)

37. Review Questions