342 15 “Ellipsoid-of-revolution to cylinder”: transverse aspect
We compute the scale factor of the reference meridian by minimizing the Airy distortion measure in
a given strip with respect to the ellipsoid-of-revolution in a preceding section. There is an International
Agreement to use the scale factor 0.999 587.
Important!
In practice, we use relative to the reference meridian the zone number (L 0 +3
◦ )/6
◦ +30. In use
is also the reference Easting/Northing with respect to the meridians L 0 = −177
◦ = 177
◦ W,
L 0 = −171
◦ , · · · , L 0 = −3
◦ , L 0 = 3
◦ , . . . , L 0 = 171
◦ = 171
◦ E. For instance, Germany is
located between the zone 32 and the zone 33. The easterly coordinate is equipped with an
offset number 500000 m, called “false Easting”. In contrast, Northings are changed by an
offset of 10 000 000 m on the southern hemisphere (y < 0) to avoid negative coordinates, an
artifical effect, called “false Northing”. The strip overlap is chosen as 0.5
◦ .
Example 15.7 (UTM coordinates. Easting versus Northing coordinates).
The point 1 is described relative to the Geodetic Reference System 80 (GRS 80), the surface normal
cooordinates by L = 6.8
◦ and B = 51.2
◦ . Compare with Figs. 15.14–15.16.
First meridan strip (scale factor 0.999 578).
Important!
x 1 (UTM) = −153 697.036 m, y 1 (UTM) = 5 674 241.346 m.
Easting: 346 302.964 m, Northing: 5 674 241.346 m, zone 32.
Important!
The point 1 is located 153 697.036 m West of the reference meridian of the zone 32, that is
L 0 = 9
◦ and 5 674 241.346 m North of the equator.
Second meridan strip (scale factor 0.999 578).
Important!
x 2 (UTM) = 265 448.926 m, y 2 (UTM) = 5 678 805.917 m.
Easting: 765 448.926 m, Northing: 5 678 805.917 m, zone 31.
Important!
The point 1 is located 265 448.926 m East of the reference meridian of the zone 31, that is
L 0 = 3
◦ and 5 678 805.917 m North of the equator.
End of Example.
We compute the scale factor of the reference meridian by minimizing the Airy distortion measure in
a given strip with respect to the ellipsoid-of-revolution in a preceding section. There is an International
Agreement to use the scale factor 0.999 587.
Important!
In practice, we use relative to the reference meridian the zone number (L 0 +3
◦ )/6
◦ +30. In use
is also the reference Easting/Northing with respect to the meridians L 0 = −177
◦ = 177
◦ W,
L 0 = −171
◦ , · · · , L 0 = −3
◦ , L 0 = 3
◦ , . . . , L 0 = 171
◦ = 171
◦ E. For instance, Germany is
located between the zone 32 and the zone 33. The easterly coordinate is equipped with an
offset number 500000 m, called “false Easting”. In contrast, Northings are changed by an
offset of 10 000 000 m on the southern hemisphere (y < 0) to avoid negative coordinates, an
artifical effect, called “false Northing”. The strip overlap is chosen as 0.5
◦ .
Example 15.7 (UTM coordinates. Easting versus Northing coordinates).
The point 1 is described relative to the Geodetic Reference System 80 (GRS 80), the surface normal
cooordinates by L = 6.8
◦ and B = 51.2
◦ . Compare with Figs. 15.14–15.16.
First meridan strip (scale factor 0.999 578).
Important!
x 1 (UTM) = −153 697.036 m, y 1 (UTM) = 5 674 241.346 m.
Easting: 346 302.964 m, Northing: 5 674 241.346 m, zone 32.
Important!
The point 1 is located 153 697.036 m West of the reference meridian of the zone 32, that is
L 0 = 9
◦ and 5 674 241.346 m North of the equator.
Second meridan strip (scale factor 0.999 578).
Important!
x 2 (UTM) = 265 448.926 m, y 2 (UTM) = 5 678 805.917 m.
Easting: 765 448.926 m, Northing: 5 678 805.917 m, zone 31.
Important!
The point 1 is located 265 448.926 m East of the reference meridian of the zone 31, that is
L 0 = 3
◦ and 5 678 805.917 m North of the equator.
End of Example.