Gauss and UTM Conformal Projections and the Plane Rectangular Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 314

Fig. 6.17 Grid
convergence

Practical Formula

Equation ( 6.71 ) is the practical formula that yields an accuracy of 0.001 m:

" #

2
þ

2
þ

4

1
2

y m
R m

1
24

Δ y

R m

1
24

y m
R m

D ﾼ S 1 þ , ð 6 : 76 Þ

c

where R m ﾼ

e 02 cos 2 B m ; see (5.35).

If B m is unknown, we can put

1 þ

1
2

X and calculate B m according to the formula for computing latitude

from the meridian arc length.
For instance, given y 1 ﾼ

ﾼ ð x 1 þ x 2 Þ

269759.6 m, y 2 ﾼ 297219.7 m, B m ﾼ 31 27 0 , and

S ﾼ 34862.820 m, one obtains D ﾼ 34,897.394 m.

Alternatively, given x 1 ﾼ 3496205.1 m, y 1 ﾼ 269759.6 m, x 2 ﾼ 3474669.9 m,

y 2 ﾼ 297219.7 m, and S ﾼ 34862.820 m, one gets D ﾼ 34,897.394 m.

6.5.4 Grid Convergence

Grid convergence is needed in determining the grid azimuth. We will hereby derive
the formula for computing the grid convergence.
On the Gauss projection plane, as shown in Fig. 6.17 , the angle between the
projected meridian P 0 N 0 passing through point P 0 (the curve with l constant) and

the vertical grid line P 0 L is referred to as the Gauss plane grid convergence. Because
the Gauss projection is a conformal projection, the projected meridian and parallel

ﾼ