rsa projection & coordinate system proposal: …...vy: difference between geodetic longitude...

RSA Projection & Coordinate System Proposal: February 2019 1

OVERVIEW

➢ Why review the projection?

➢ Coordinate system comparisons

➢ Projection characteristics

➢ Projection distortions

➢ Projection distortion summary

➢ Why review the coordinate system?

➢ Proposed coordinate system

➢ Area implications

➢ Other issues to consider?


South Africa’s : Extent


16½°

12¾°

WHY REVIEW THE PROJECTION?

➢ The current projection used in South Africa is the Gauss

Conform Projection (Transverse Mercator limited to 2°

longitude zones);

➢ Geo-spatial information used on a wide range of

applications covering large geographical extents, from

provincial coverage to national coverage. For these

applications the 2° zones may be a limitation;

➢ Do other projections, which provide for greater

geographical coverage, meet the requirements to be

adopted as an alternative to the Gauss Conform

Projection?


COORDINATE SYSTEM COMPARISONS

Conformality is a requirement.

The following projections are compared:

➢ Gauss Conform (current projection);

➢ UTM (widely used);

➢ Lambert’s Conformal Conic Projection (suits areas with

greater east-west extent);

▪ Lambert’s Conformal Conic Projection with Two

Standard Parallels (4° zones);

▪ Lambert’s Conformal Conic Projection with Two

Standard Parallels (3° zones).


The number of zones used to cover South Africa’s extent are:

➢ Gauss Conform: 9;

➢ UTM: 4 (with first and last zone only partly used);

➢ Lambert’s Conformal Conic Projection with Two Standard

Parallels (4° zone): 3;

➢ Lambert’s Conformal Conic Projection with Two Standard

Parallels (3° zone): 4.


COORDINATE SYSTEM COMPARISONS


GAUSS CONFORM CS (Lo.)

Nine (9) x 2° wide E-W zones.


UTM CS (CM)

Four (4) x 6° wide E-W zones.

LAMBERT CC CS – 3 ZONES


Three (3) x 4° wide N-S zones.

LAMBERT CC CS – 4 ZONES


Four (4) x 3° wide N-S zones.

GAUSS CONFORM PROJECTION:CHARACTERISTICS


Longitude of origin )Lo.)or Central meridian (CM) where scale =1

Click on the

icon to open…

Click on the

icon to open…

LAMBERT’S CONFORMAL CONICPROJECTION: CHARACTERISTICS


Two standard parallels where scale =1

𝟏

𝟔𝒕𝒉

𝟏

𝟔𝒕𝒉

𝟒

𝟔𝒕𝒉

22°S

22½°S

24½°S

25°S

LAMBERT’S CONFORMAL CONICPROJECTION: CHARACTERISTICS


Two standard parallels where scale = 1

Two standard parallels where scale = 1

GAUSS CONFORM PROJECTION


Tissot’s Indicatrix: Represents relative scale increase. Circular due to conformality.

Scale equal in all directions around a point, preserving angles and shape.

Gauss Conform: Scale and shapes increase from the Central Meridian (Lo.)

UTM PROJECTION




UTM: Scale and shapes increase from the Central Meridian.

LAMBERT’S – 2 PAR: 3 ZONES (4°)




Lambert’s: Scale and shapes increase from the Standard parallels outwards.


3º

3º

3º

GAUSS CONFORM DISTORTION

GAUSS CONFORM DISTORTION


22°S 25½°EvY: 13.44m

vX: 759.71m

Sc: 1.000296

(296 ppm)

22°S 26°EvY: 3.98m

vX: 337.61m

Sc: 1.000132

(132 ppm)

22°S 27°EvY: 0.00m

vX: 0.00m

Sc: 1.000000

(0 ppm)

22°S 28°EvY: 3.98m

vX: 337.61m

Sc: 1.000132

(132 ppm)

22°S 28½°EvY: 13.44m

vX: 759.71m

Sc: 1.000296

(296 ppm)

28°S 25½°EvY: 10.42m

vX: 906.90m

Sc: 1.000269

(269 ppm)

28°S 26°EvY: 3.09m

vX: 403.02m

Sc: 1.000119

(119 ppm)

28°S 27°EvY: 0.00m

vX: 0.00m

Sc: 1.000000

(0 ppm)

28°S 28°EvY: 3.09m

vX: 403.02m

Sc: 1.000119

(119 ppm)

28°S 28½°EvY: 10.42m

vX: 906.90m

Sc: 1.000269

(269 ppm)

34°S 25½°EvY: 7.22m

vX: 1014.54m

Sc: 1.000237

(237 ppm)

34°S 26°EvY: 2.14m

vX: 450.86m

Sc: 1.000105

(105 ppm)

34°S 27°EvY: 0.00m

vX: 0.00m

Sc: 1.000000

(0 ppm)

34°S 28°EvY: 2.14m

vX: 450.86m

Sc: 1.000105

(105 ppm)

34°S 28½°EvY: 7.22m

vX: 1014.54m

Sc: 1.000237

(237 ppm)

+6°

-1.5° -1° +1° +1.5°

+6° +6°

+6° +6° +6°

+6° +6°

-1.5° -1° +1° +1.5°

vY: Difference between geodetic longitude distance and projected distance from Lo.27 at that latitude at that point.

vX: Difference between geodetic latitude distance and projected distance from the equator at that point.

Sc: Scale at that point (in parts per million).


UTM DISTORTION

6º

6º

6º

UTM DISTORTION


22°S 24°EvY: 16.43m

vX: 2,066.31m

Sc: 1.000786

(786 ppm)

22°S 27°EvY: 0.00m

vX: 973.52m

Sc: 0.999600

(-400 ppm)

22°S 30°EvY: 16.43m

vX: 2,066.31m

Sc: 1.000786

(786 ppm)

28°S 24°EvY: 34.68m

vX: 2,389.07m

Sc: 1.000675

(675 ppm)

28°S 27°EvY: 0.00m

vX: 1,239.38m

Sc: 0.999600

(-400 ppm)

28°S 30°EvY: 34.68m

vX: 2,389.07m

Sc: 1.000675

(675 ppm)

34°S 24°EvY: 53.16m

vX: 2,553.27m

Sc: 1.000547

(547 ppm)

34°S 27°EvY: 0.00m

vX: 1,505.46m

Sc: 0.999600

(-400 ppm)

34°S 30°EvY: 53.16m

vX: 2,553.27m

Sc: 1.000547

(547 ppm)

-3°

-3°

-3°

+3°

+3°

+3°

+6° +6°

+6° +6°

vY: Difference between geodetic longitude distance and projected distance from CM.27 at that latitude at that point.

vX: Difference between geodetic latitude distance and projected distance referenced to the equator at that point.


LAMBERT’S CC CS – 3 ZONES


4º

4º

4.8

5º

LAMBERT’S DISTORTION (3 ZONES)


22°S 27°EvY: 0.00m

vX: 15.57m

Sc: 1.000335

(335 ppm)

26°S 27°EvY: 0.00m

vX: 15.76m

Sc: 1.000335

(335 ppm)

30°S 27°EvY: 0.00m

vX: 15.93m

Sc: 1.000335

(335 ppm)

24°S 27°EvY: 0.00m

vX: 0.00m

Sc: 0.999731

(-269 ppm)

28°S 27°EvY: 0.00m

vX: 0.00m

Sc: 0.999731

(-269 ppm)

32°S 27°EvY: 0.00m

vX: 0.00m

Sc: 0.999731

(-269 ppm)

26°S 27°EvY: 0.00m

vX: 15.62m

Sc: 1.000339

(339 ppm)

30°S 27°EvY: 0.00m

vX: 15.79m

Sc: 1.000339

(339 ppm)

34°S 27°EvY: 0.00m

vX: 15.95m

Sc: 1.000340

(340 ppm)

+2°

+2°

+2°

+2°

+2°

+2°

Zone North Zone Central Zone South

vY: Difference between geodetic longitude distance and projected distance from ref long (27°E) at that latitude at that point.

vX: Difference between geodetic latitude distance and projected distance from the ref lats (24°S, 28°S & 32°S) at that point.




3º

3º

3.8

5º

3º

LAMBERT’S DISTORTION (4 ZONES)


Zone North Zone North Central Zone South Central Zone South

22°S 27°EvY: 0.00m

vX: 6.77m

Sc: 1.000189

(189 ppm)

25°S 27°EvY: 0.00m

vX: 6.87m

Sc: 1.000189

(189 ppm)

31°S 27°EvY: 0.00m

vX: 7.06m

Sc: 1.000188

(188 ppm)

23½°S 27°EvY: 0.00m

vX: 0.00m

Sc: 0.999849

(-151 ppm)

26½°S 27°EvY: 0.00m

vX: 0.00m

Sc: 0.999849

(-151 ppm)

32½°S 27°EvY: 0.00m

vX: 0.00m

Sc: 0.999848

(-152 ppm)

25°S 27°EvY: 0.00m

vX: 6.81m

Sc: 1.000190

(190 ppm)

28°S 27°EvY: 0.00m

vX: 6.90m

Sc: 1.000190

(190 ppm)

34°S 27°EvY: 0.00m

vX: 7.08m

Sc: 1.000191

(191 ppm)

28°S 27°EvY: 0.00m

vX: 6.97m

Sc: 1.000189

(189 ppm)

29½°S 27°EvY: 0.00m

vX: 0.00m

Sc: 0.999848

(-152 ppm)

31°S 27°EvY: 0.00m

vX: 7.00m

Sc: 1.000190

(190 ppm)

+1.5°

+1.5°

+1.5°

+1.5°

+1.5°

+1.5°

+1.5°

+1.5°

vY: Diff. between geodetic longitude distance and projected distance from the ref long (27°E) at that latitude at that point.

vX: Diff. between geodetic latitude distance and projected distance from ref lats (23½°S , 26½°S, 29½°S & 32½°S) at that point.


PROJECTION COMPARISON SUMMARY:


ProjectionZone

Extent

No.

of

Zones

Distortion Spread Total

Gauss Conform 2° (E-W) 9 0 ppm to 132 ppm 132 ppm

UTM 6° (E-W) 4 -400 ppm to 786 ppm 1,186 ppm

Lambert’s (4°) 4° (N-S) 3-269 ppm to 340 ppm

(Agulhas 973 ppm)609 ppm

Lambert’s (3°) 3° (N-S) 4-152 ppm to 191 ppm

(Agulhas 692 ppm)343 ppm

Lambert’s (2°)? 2° (N-S) 6 -67 ppm to 85 ppm 152 ppm

WHY REVIEW THE COORDINATE SYSTEM?

➢ The current South African projected co-ordinate system is a

cartesian system with westing and southing (y,x) axes and

directions measured clock-wise from the south.

➢ This is a ‘left-handed’ co-ordinate system.

➢ Software systems, generally, operate in a ‘right-handed’ co-

ordinate system, which may result in geo-spatial

information in the current co-ordinate system being

‘erroneously’ inverted.


COORDINATE SYSTEM REVIEW


eastward: -y

Equator: x = 0m

westward: +y

CURRENT COORDINATE SYSTEM:

southward: +x

Centra

l Merid

ian: y

= 0

m

0°

+Δy, -Δx -Δy, -Δx

+Δy, +Δx -Δy, +Δx

270°90°

180°



eastward: +x

Equator: y = 4,000,000m

westward: -x

PROPOSED COORDINATE SYSTEM:

southward: -y

Centra

l Merid

ian: x

= 0

m

180°

-Δx, +Δy +Δx, +Δy

-Δx, -Δy +Δx, -Δy

90°270°

0°


Latitude Longitude Lo. x y35 20 21 -91,290 -3,875,050

35 21 21 - -3,874,593

35 22 21 91,290 -3,875,050

36 20 21 -90,165 -3,986,005

36 21 21 - -3,985,543

36 22 21 90,165 -3,986,005

37 20 21 -89,013 -4,096,978

37 21 21 - 4,096,511

37 22 21 89,013 -4,096,978

Applying a false northing of 4,000,000m at the equator (i.e. y = 4,000,000m at 0°S).

x = 0m at 17°E, …, 33°E (positive eastwards).y = 0m at ~37°S (positive northwards).

TM (GAUSS CONFORM) CS REVIEW



eastward: +xwestward: -x

PROPOSED COORDINATE SYSTEM:

southward: -y

Refe

rence L

ongitu

de: x

= 0

m

Standard parallel: scale = 1

Standard parallel: scale = 1

northward: +y

Reference Latitude: y = 0m

180°

-Δx, +Δy +Δx, +Δy

-Δx, -Δy +Δx, -Δy

90°270°

0°



x = 0m at 25°E (positive eastwards).y = 0m at 24°S, 28°S and 24°S (positive northwards).



x = 0m at 25°E (positive eastwards).y = 0m at 23½°S, 26½°S, 29½°S and 32½°S (positive northwards).

AREA IMPLICATIONS


➢ Area’s of fixed property are an important component of

ownership (Deeds & SG records) and taxation (Local

authorities);

➢ The areas used in these records are computed using the

current projected coordinate reference system, which is the

Gauss Conform (Transverse Mercator) projection system;

➢ How will a change in projection system affect area

calculations?

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to open…

OTHER ISSUES TO CONSIDER

➢ Legal matters (Deeds, SG and other records)?

➢ Geospatial datasets locked into the projection system?

➢ Discipline specific software (i.e. Cadastral, Engineering)?

➢ Geocoding based on current projection system?

➢ Mapping and map series?

➢ Raster geo-referencing (documents, imagery)?

➢ Who may and who must comply?


THAT’S IT FOLKS!!

THANK YOU!!


rsa projection & coordinate system proposal: …...vy: difference between geodetic longitude...

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