Geography Reference
In-Depth Information
One easily overlooked source of distortions is the difference between
the datums, geoids, and ellipsoids used in creating different geographic
information or maps. Even if geographic information or a map is made by
the same agency or company using the same projection, a change in the
datum, geoid, or ellipsoid can lead to distortions when compared with other
geographic information or maps for the same area.
Describing Distortions
To describe and assess distortions, it is useful to determine the scale factor
(SF) at different places on a map. By comparing scale factors with map scale
at the standard point or standard lines you can assess the scale distortions
using this formula:
Local scale
Scale factor =
mcase sasor =
Principle scale
Where
local scale
is the scale calculated at a particular place and
principle scale
is the scale computed at the standard point or a standard line.
For example, the scale factor of a transverse Mercator projection with a
principle scale of 1:400,000,000 calculated between 20
S will indi-
cate how much distortion the projection introduces. First, calculate the local
scale by measuring along the meridian between 20
°
and 30
°
S. This gives you
the map distance, which is 3.1 cm (1.2 in.) (shown in Figure 4.9 with the
letter A). You compute the ground distance between the same portion of
the meridian by consulting a table showing the lengths of a degree of
latitude along a meridian. At 20
°
and 30
°
°
a degree of latitude is 110,704.278 m
long. Multiplying the 10
S would measure approximately
1,107,042.78 m or 1,107.04 km. Second, by substituting the 3.1 cm and
1,107.04 km into the map scale equation, you can calculate the local scale:
°
of latitude to 30
°
Map scale = earth distance/map distance
Map scale = 1,107.04 km/3.1 cm
TABLE 4.3. Table of Meridian Distances for Various Latitudes
Latitude (
°
)
Miles
Kilometers
0
68.71
110.57
10
68.73
110.61
20
68.79
110.70
30
68.88
110.85
40
68.99
111.04
50
69.12
111.23
60
69.23
111.41
70
69.32
111.56
80
69.38
111.66
90
69.40
111.69
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