Gauss and UTM Conformal Projections and the Plane Rectangular Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 321

Table 6.6 Numerical values
of the distance distortion for
different longitudes (l ) and
latitudes (B)

l ﾼ 0 l ﾼ 1 l ﾼ 2 l ﾼ 3

B

90 0.00040 0.00040 0.00040 0.00040

80

0.00040 0.00040 0.00038 0.00036

70 0.00040 0.00038 0.00033 0.00024

60

0.00040 0.00036 0.00025 0.00006

50 0.00040 0.00034 0.00015 +0.00017

40 0.00040 0.00031 0.00004 +0.00041

30

0.00040 0.00028 +0.00006 +0.00063

20 0.00040 0.00027 +0.00014 +0.00081

10

0.00040 0.00026 +0.00019 +0.00094

0 0.00040 0.00025 +0.00021 +0.00098

3. The formula for arc-to-chord correction of the UTM projection agrees with that
of Gauss projection. Conversions like ( 6.87 ) are not needed because the arc-to-
chord correction is the correction applied to compensate for distortion of straight
lines when projected, which is fundamentally independent of projection method.
4. The relationship between the scale factor m UTM of the UTM projection and
m Gauss of the Gauss projection is:

m UTM ﾼ 0 : 9996m Gauss : ð 6 : 88 Þ

5. To compute the distance correction of the UTM projection, first we transform the
coordinates according to ( 6.87 ) and calculate the Gauss plane distance D Gauss
according to the formula for distance corrections in the Gauss projection; then,
we reckon the UTM plane distance based on the formula

D UTM ﾼ 0 : 9996D Gauss : ð 6 : 89 Þ

6. The formula for meridian convergence on the UTM plane completely corre-
sponds to that on the Gauss plane.

The distance distortion of the UTM projection can be analyzed using ( 6.88 ).
Table 6.6 presents the distortion of distances given the different longitudes and
latitudes.
Table 6.6 shows that the distortion of distance along the central meridian is

0.00040, namely, the central meridian has a scale factor of 0.9996. This allows the
greatest distortion of distance at B 0 o , l 3 o to be smaller than 0.001. The two ﾼ ﾼ

secant lines (about 180 km away from the central meridian on the equator, i.e., at

1 40 0 ) have no distortion of distances. Distances become more distorted
away from these two secant lines. The distance distortion will have a negative value
inside the two secants and a positive value outside.

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