Geoscience Reference
In-Depth Information
Table 6.5 Numerical values for the scale factor (m) for different distances ( y) of the point from
the central meridian at different latitudes (B) (GRS80 Ellipsoid)
y (km)
B
ﾼ
0
B
ﾼ
10
B
ﾼ
20
B
ﾼ
30
B
ﾼ
40
50
1.000030936
1.000030923
1.000030887
1.000030832
1.000030764
100
1.000123745
1.000123695
1.000123550
1.000123328
1.000123057
200
1.000495011
1.000494810
1.000494231
1.000493344
1.000492258
300
1.001113890
1.001113437
1.001112134
1.001110139
1.001107694
350
1.001516230
1.001515613
1.001513839
-
-
50
60
70
80
90
y (km)
B
ﾼ
B
ﾼ
B
ﾼ
B
ﾼ
B
ﾼ
50
1.000030692
1.000030624
1.000030569
1.000030533
1.000030520
100
1.000122768
1.000122497
1.000122277
1.000122133
-
200
1.000491103
1.000490019
-
-
-
conformal projection). With y
1, i.e., the central meridian remains
unchanged in length after the projection (which is consistent with the conditions
for the Gauss projection). In the case of y
ﾼ
0, m
ﾼ
0, with its value being either positive or
negative, m is invariably greater than 1, which means that the differential line
segments away from the central meridian are all stretched after the projection. The
distortion of distance (m
6ﾼ
1) increases proportionally with y
2
. For any arbitrary
meridian, the distance distortion increases with distance from the standard parallels.
Again, for any arbitrary meridian except for the central meridian, the distortion of
distance is maximal at the equator, i.e., the lower the latitude, the more significant
the distortion of distance.
The distortion of distance is harmful, but it actually exists. We cannot violate
this law to eliminate the distortion. Therefore, in practical cases we can only impose
appropriate limitations on distance distortion, making its effect on mapping and
application of maps insignificant. The way to limit such a distortion is the zone-
dividing projection.
As mentioned earlier, the projection zones in China primarily consist of 6
zones
and 3
zones. The national basic maps at scales ranging from 1:25,000 to 1:100,000
use the zones 6
of longitude in width, and the topographic maps at scales of
1:10,000 or larger use the zones that are 3
of longitude wide. It is often the case that
the distortion of distance is fairly significant in lower-latitude regions, so at north
latitude 20
o
and further south in the south of China this effect in mapping and
map application should be considered. For instance, it can be seen from (
6.66
) that
y
2
2R
2
; so, in areas at the north latitude 20
o
, close to the dividing meridian of
6
zones, the distortion of distance m
m
1
ﾼ
1 can amount to
1
820
, which is quite large
and cannot be neglected for the 1:25,000 or 1:50,000 scale maps. For example, in
such a case, the side length of 10 km is subject to a distance distortion of 12.2 m. On
the 1:25,000 scale map, such distortion is approximately 0.5 mm. Generally, the
point position error on the map (i.e., mapping error) is allowed to be less than 0.2
mm. Such effects in mapping and map application must be taken into consideration.
For the 3
wide zone, in areas at latitude 20
∘
or further south, the distance
distortion of the 3
zone boundary reaches 1/3,300. Such a distortion still cannot be
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