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

Search WWH ::

Custom Search