Geoscience Reference
In-Depth Information
Conditions for the UTM projection are:
1. The projection is conformal
2. The central meridian is projected as a straight line
3. The central meridian and all distances have a scale factor of 0.9996 after
projection
The scale factor along the central meridian is 0.9996 rather than 1, which is a
reduction of 0.0004. For distances that are not close to the central meridian, the
UTM has an advantage over the Gauss projection in reducing the amount of
distance distortion and satisfies the needs of topographic maps.
Analogous to the Gauss projection, the UTM system divides the regions north of
84 N and south of 80 S into 60 longitudinal zones of 6 . These zones are numbered
1 through 60, starting at longitude 180 , and proceeding eastward (Beijing is in
zone 50). To avoid negative coordinates for positions located west of the central
meridian, the central meridian has been given a false y-coordinate of 500,000 m. A
false x-coordinate of 10,000,000 m is allocated to the equator in the southern
hemisphere.
6.6.2 Computational Formula for UTM Projection
UTM and Gauss projections are essentially the same. The previous two conditions
for the UTM projection correspond to those for Gauss projection. The only differ-
ence between them lies in that for the UTM projection, the central meridian has a
scale factor of 0.9996, rather than 1.0. It can be seen that UTM and Gauss pro-
jections are related by a similarity transformation, based on which, one can write
out the formula for computing the UTM projection according to relevant formulae
for the Gauss projection:
1. For the direct solution of the UTM projection, one can reckon the Gauss plane
coordinates (x Gauss , y Gauss ) using the formulae for the direct solution of the
Gauss projection and obtain the UTM plane coordinates (x UTM , y UTM ) according
to the formulae below:
x UTM
0
:
9996x Gauss
ð6:86Þ
y UTM
0
:
9996y Gauss :
2. For the inverse solution of the UTM projection, we can compute the
corresponding (x Gauss , y Gauss ) given the (x UTM , y UTM ) using the formulae below:
x Gauss
x UTM =
0
:
9996
ð
6
:
87
Þ
y Gauss
y UTM =0:9996:
Then, apply the formulae for the inverse solution of the Gauss projection to
calculate (L, B).
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