## Defining Custom Datums

Most coordinate systems use one of MapInfo's predefined datums, listed in this appendix. If you need to use a datum that isn't in the list, and you know what the datum's mathematical parameters are, then you can define the coordinate system using a custom datum. MapInfo uses the following information to define a datum:

• An ellipsoid, also called a spheroid. This is an ellipse rotated around its minor axis to form a three-dimensional surface. The ellipsoid is described by two mathematical parameters: the length, in meters, of its semi-major axis (denoted by the letter a) and its degree of flattening (denoted by the letter f). MapInfo supports over 40 predefined ellipsoids, which are listed in the next table.
• Three shift parameters specifying the distance, in meters, to shift the ellipsoid along each of its axes. These parameters are usually denoted by dX, dY, and dZ. You may also see them denoted by DX, DY, and DZ, or by u, v, and w.
• Three rotation parameters specifying the angle, in arc-seconds, to rotate the ellipsoid around each of its axes. These parameters are usually denoted by EX, EY, and EZ. You may also see them denoted by eX, eY, and eZ, or by e, y, and w.
• A scale correction factor specifying the amount, in parts per million, to adjust the size of the ellipsoid. This parameter is denoted by the letter m, or sometimes k.
• The longitude of the prime meridian, in degrees east of Greenwich. The prime meridian specifies which location on earth is assigned longitude 0×. Most datums use Greenwich as the prime meridian, so this parameter is usually zero. However, some datums use a different location as the prime meridian. For example, the NTF datum uses Paris as its prime meridian, which is 2.33722917 degrees east of Greenwich. If you use the NTF datum in a coordinate system, all longitudes in that coordinate system are relative to Paris instead of Greenwich.

You can define a custom datum in any coordinate system definition. Appendix F describes how to define a coordinate system. To define a custom datum in a coordinate system, you use datum number 9999 followed by the datum parameters, in this order:

9999, EllipsoidNumber, dX, dY, dZ, EX, EY, EZ, m, PrimeMeridian

Some datums specify only an ellipsoid and shift parameters (dX, dY, dZ), with no rotation parameters, scale correction, or prime meridian. In those cases, you can use datum number 999 instead of 9999, to simplify the definition:

999, EllipsoidNumber, dX, dY, dZ

The ellipsoid number must be chosen from the following list. Currently, there is no way to define a custom ellipsoid. If you need to use an ellipsoid that does not appear on this list, please notify MapInfo Technical Support so that we can add your ellipsoid to a future MapInfo Professional version.

Two ellipsoids have been added. These are: Everest Pakistan #50, and ATS 77 (Average Terrestrial System) #51.

The ellipsoid names for Everest ellipsoids have been standardized according to NIMA specs to conform to the most current standards used in the GIS and mapping communities. The name changes are summarized in this table:

Ellipsoid #
Old Name
New Name/NIMA Designation

11

Everest (1830)

Everest (India 1830)

17

Everest (Kertau)

Everest (W. Malaysia and Singapore 1948)

39

Everest (Timbalai)

Everest (Brunei and East Malaysia (Sabah and Sarawak))

48

Everest (West Malaysia)

Everest (West Malaysia 1969)

40

Everest (Kalianpur)

Everest (India 1956)

The additions and the new names are reflected in this table.

Number
Ellipsoid
a
1/f

9

Airy 1930

6377563.396

299.3249646

13

Airy 1930 (modified for Ireland 1965)

6377340.189

299.3249646

51

ATS7 77

6378135.0

298.257

2

Australian

6378160.0

298.25

10

Bessel 1841

6377397.155

299.1528128

35

Bessel 1841 (modified for NGO 1948)

6377492.0176

299.15281

14

Bessel 1841 (modified for Schwarzeck)

6377483.865

299.1528128

36

Clarke 1858

6378293.639

294.26068

7

Clarke 1866

6378206.4

294.9786982

8

Clarke 1866 (modified for Michigan)

6378450.047484481

294.9786982

6

Clarke 1880

6378249.145

293.465

15

Clarke 1880 (modified for Arc 1950)

6378249.145326

293.4663076

30

Clarke 1880 (modified for IGN)

6378249.2

293.4660213

37

Clarke 1880 (modified for Jamaica)

6378249.136

293.46631

16

Clarke 1880 (modified for Merchich)

6378249.2

293.46598

38

Clarke 1880 (modified for Palestine)

6378300.79

293.46623

39

Everest (Brunei and East Malaysia (Sabah and Sarawak))

6377298.556

300.8017

11

Everest (India 1830)

6377276.345

300.8017

40

Everest (India 1956)

6377301.243

300.80174

50

Everest (Pakistan)

6377309.613

300.8017

17

Everest (W. Malaysia and Singapore 1948)

6377304.063

300.8017

48

Everest (West Malaysia 1969)

6377295.664

300.8017

18

Fischer 1960

6378166.0

298.3

19

Fischer 1960 (modified for South Asia)

6378155.0

298.3

20

Fischer 1968

6378150.0

298.3

21

GRS 67

6378160.0

298.247167427

0

GRS 80

6378137.0

298.257222101

5

Hayford

6378388.0

297.0

22

Helmert 1906

6378200.0

298.3

23

Hough

6378270.0

297.0

31

IAG 75

6378140.0

298.257222

41

Indonesian

6378160.0

298.247

4

International 1924

6378388.0

297.0

49

Irish (WOFO)

6377542.178

299.325

3

Krassovsky

6378245.0

298.3

32

MERIT 83

6378137.0

298.257

33

New International 1967

6378157.5

298.25

43

NWL 10D

6378135.0

298.26

42

NWL 9D

6378145.0

298.25

44

OSU86F

6378136.2

298.25722

45

OSU91A

6378136.3

298.25722

46

Plessis 1817

6376523.0

308.64

52

PZ90

6378136.0

298.257839303

24

South American

6378160.0

298.25

12

Sphere

6370997.0

0.0

Struve 1860

6378297.0

294.73

34

Walbeck

6376896.0

302.78

25

War Office

6378300.583

296.0

26

WGS 60

6378165.0

298.3

27

WGS 66

6378145.0

298.25

1

WGS 72

6378135.0

298.26

28

WGS 84

6378137.0

298.257223563

The shift and rotation parameters describe the ellipsoid's orientation in space, as compared to the WGS 84 datum. It's important to make sure that these parameters have the correct signs (positive or negative). Usually, a document describing a local datum will list the parameters required to convert coordinates from the local datum to WGS 84. (This is the same as saying that the parameters were derived by subtracting the local datum from WGS 84.) In that case, you can use the parameters exactly as they appear in the document. However, if you have a document that lists parameters for converting coordinates in the opposite direction - from WGS 84 to the local datum - then you must reverse the signs of the shift, rotation, and scale correction parameters.

It's also very important to list the parameters in the correct order. Some documents list the rotation parameters with EZ first, like this: EZ, EY, EX. In those cases, you must reverse the order of the rotation parameters when defining the custom datum. This is especially easy to overlook when your document uses Greek letters to denote the parameters. If the document lists the parameters in order as w, y, e, then you must reverse their order in the custom datum definition.

Here's an example of a local datum description (we'll call it LD-1) as it might appear in a technical article:

 a 6378388.0 m f 1 / 297.0

 DX 93.5 m DY 103.5 m DZ 123.3 m eX -0.25 eY 0.11 eZ 0.07 m -2.1 ppm

This datum uses the International ellipsoid, which is number 4 in the ellipsoid table above. The other parameters describe a conversion from WGS 84 to the local datum, so we must reverse their signs. No prime meridian is listed, so we can assume that Greenwich is used. The custom datum definition in MapInfo would look like this:

9999, 4, -93.5, -103.5, -123.3, 0.25, -0.11, -0.07, 2.1, 0

You can insert this string of numbers in place of the datum number in any line in the MAPINFOW.PRJ file. For example, you could define the following coordinate systems using this custom datum:

Note: Strings must be entered on a single line.

```"Longitude / Latitude (LD-1)", 1, 9999, 4, -93.5, -103.5, -123.3, 0.25, -
0.11, -0.07, 2.1, 0
"UTM Zone 30 (LD-1)", 8, 9999, 4, -93.5, -103.5, -123.3, 0.25, -0.11, -
0.07, 2.1, 0, 7, -3, 0, 0.9996, 500000, 0
```

Here's another sample local datum description, called LD-2 this time:

 a 6378245.0 m f 1 / 298.3

 u +24 m v -123 m w -94 m w +0.13 y +0.25 e -0.02 m +1.1 Þ 10-6

This datum uses the Krassovsky ellipsoid, which is number 3 in the ellipsoid table above. We do not need to reverse the signs of the parameters, since they describe a conversion from the local datum to WGS 84. However, the rotation parameters are listed with w first, so we must reverse their order in the custom datum definition:

```9999, 3, 24, -123, -94, -0.02, 0.25, 0.13, 1.1, 0
```

Here's a final example, LD-3, that provides only the ellipsoid and shift parameters:

 a 6378249.145 m f 1 / 293.465

 dX -7 m dY 36 m dZ 225 m

This datum uses the Clarke 1880 ellipsoid, which is number 6 in the ellipsoid table above. We do not need to reverse the signs of the parameters or worry about the order of the rotation parameters (since they aren't present). In this case, you can use datum number 999 instead of 9999 in the custom datum definition. These two definitions are equivalent, and you can use either one:

```999, 6, -7, 36, 225
9999, 6, -7, 36, 225, 0, 0, 0, 0, 0
```

As with the other custom datum definitions, you would insert one of these definitions in place of the datum number in a MAPINFOW.PRJ line, as follows:

```"Longitude / Latitude (LD-3)", 1, 999, 6, -7, 36, 225
"UTM Zone 30 (LD-3)", 8, 999, 6, -7, 36, 225, 7, -3, 0, 0.9996, 500000, 0
```