Gauss and UTM Conformal Projections and the Plane Rectangular Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 285

Table 6.1 Direct solution of the Gauss projection: sample computation

Computational results (m)
6 zones

Ellipsoidal
parameters

3 zones

Given data

B ﾼ 40 58 0 32.33 00
L ﾼ 100 10 0
20.11 00

Krassowski Ellipsoid x ﾼ 4,538,610.951 x ﾼ 4,538,610.951
y ﾼ 98,666.625 y ﾼ 98,666.625
y false ﾼ 17, 598, 666.625 y false ﾼ 33, 598, 666.625

GRS75 Ellipsoid x ﾼ 4,538,532.847 x ﾼ 4,538,532.847

y ﾼ 98,665.022 y ﾼ 98,665.022

y false ﾼ 17, 598, 665.022 y false ﾼ 33, 598, 665.022

GRS80 Ellipsoid x ﾼ 4,538,530.729 x ﾼ 4,538,530.729

y ﾼ 98,664.975 y ﾼ 98,664.975

y false ﾼ 17 598 664.975 y false ﾼ 33, 598 664.975

35 26 0 40.38 00 B ﾼ Krassowski Ellipsoid x ﾼ 3,925,560.035 x ﾼ 3,924,588.054

115 08 0
51.22 00

L ﾼ

y ﾼ 168,198.578 y ﾼ 104,193.075

y false ﾼ 20, 331, 801.422 y false ﾼ 38, 604, 193.075

GRS75 Ellipsoid x ﾼ 3,925,492.277 x ﾼ 3,924,520.313

y ﾼ 168,195.836 y ﾼ 104,191.377

y false ﾼ 20, 331, 804.164 y false ﾼ 38, 604, 191.377

GRS80 Ellipsoid x ﾼ 3,925,490.447 x ﾼ 3,924,518.483

y ﾼ 168,195.757 y ﾼ 104,191.328

y false ﾼ 20, 331, 804.243 y false ﾼ 38, 604, 191.328

Fig. 6.9 Inverse solution of
Gauss projection

footprint latitude and is denoted by B f , whose corresponding isometric latitude is q f .
The meridian arc length from the equator to B f is X f ; namely, the ordinate of point
F is x X f , and the value of B f can be obtained reversely from X f according to the

formula for meridian arc length.
According to the symmetry property of the Gauss projection and the second
condition for the projection, the series can be directly written according to ( 6.23 ):

ﾼ