Geography Reference
In-Depth Information
15-5 Examples (Gauss-Krueger/UTM Coordinates)
Various interesting Examples. Mapping of the transverse Mercator projection. Gauss-
Krueger/UTM coordinates. Strip system, meridian strip system of Germany.
There has been the result that the regular transverse Mercator projection of the sphere is simple
and its mathematical version does not cause any problem. The picture changes if we move to the
transverse Mercator projection of the ellipsoid-of-revolution.
It relates to the
elliptical transverse cylinder
.Itis
confor-
mal
. Its central meridian and each meridian 90
◦
apart from
it are straight lines. Its equator is a straight line, other
meridians and parallels are
complex curves
. Scale is true
along the central meridian or along two straight lines in the
map equidistant from and parallel to the central meridian,
constant along any straight line on the map parallel to the
central meridian. Scale becomes
infinite
90
◦
from the ref-
erence meridian. It is used extensively for
quadrangle maps
at scales from 1:25000 to 1:25000
We recall the representation of Transverse Mercator coordinates for the ellipsoid-of-revolution in
the following form (Figs.
15.6
,
15.7
,
15.8
,
15.9
,and
15.10
).
x
(
l,b
)=
=
x
10
l
+
x
11
lb
+
x
30
l
3
+
x
12
lb
2
+
x
31
l
3
b
+
x
13
lb
3
+
x
50
l
5
+
x
32
l
3
b
2
+
x
14
lb
4
+
+O(6)
(15.107)
(Easting)
,
y
(
l,b
)=
=
y
01
b
+
y
20
l
2
+
y
02
b
2
+
y
21
l
2
b
+
y
03
b
3
+
y
40
l
4
+
y
22
l
2
b
2
+
y
04
b
4
+
y
41
l
4
b
+
y
23
l
2
b
3
+
+O(6)
(15.108)
(Northing)
.
West and East of the
reference meridian
, we choose a strip
of
1
.
5
◦
in longitude for a Gauss-Krueger strip system, for
instance, according to Examples
15.5
and
15.6
in the strips
6
◦
,9
◦
,and12
◦
forGermany.Incontrast,ETRS89isgiven
in UTM coordinates requiring a strip of
±
3
◦
width, a 6
◦
±
wide strip reference system.
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