Gauss and UTM Conformal Projections and the Plane Rectangular Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 284

2 3 9

=

m 4

1
2 m 2

1
24

4 5

t 2

2 4

x ﾼ X þ Nt þ 5 þ 9 ʷ þ 4 ʷ

2
4

3
5

, ð 6 : 30 Þ

;

m 3 m 5

1
6

1
120

t 2

2

5 18t 2 t 4 y ﾼ Nm þ 1 þ ʷ þ þ

where the meridian arc with length X is computed also according to (5.41), (5.42),
and (5.43), respectively, according to different ellipsoidal parameters. Computa-
tions continuing to the sixth-power term will be sufficient.

Example

Relevant parameters used in the practical formulae for the Krassowski, Ellipsoid,
GRS75 Ellipsoid, and GRS80 Ellipsoid are given in Sect. 5.2.2 .
We take the computer programmed computation of ( 6.29 ) as an example;
cf. Table 6.1 .

6.4.2 Formula for Inverse Solution of the Gauss Projection

Derivations of the Formula

As Fig. 6.9 shows, the formulae for the inverse solution of the Gauss projection are
those used to compute the geodetic coordinates (L, B) or the corresponding (l, q)
with given Gauss plane coordinates (x, y) of point P.
The equation of projection from plane to ellipsoid is:

f 0 1 q ﾼ ðÞ x ; y

: ð 6 : 31 Þ

f 0 2

l ﾼ ðÞ x ; y

Analogous to the derivations of the formulae for the direct solution of the Gauss
projection, we expand the equation of projection ( 6.31 ) from the plane onto the
ellipsoid into the power series and determine the specific forms of the projection
function f 0 1 and f 0 2 using the method of undetermined coefficients according to the
three conditions for Gauss projection. Therefore, the formulae for the inverse
solution of the Gauss projection will be derived.
The value of y at point P is small compared to the radius of the ellipsoid. So, the
function in ( 6.31 ) can be expanded into the power series of y. The expansion point is
the point F (x, 0), which is the foot of the perpendicular from point P to the central
meridian, also known as the foot point. The latitude of this point is called the