Geoscience Reference
In-Depth Information
Table 5.1 Transformation between geodetic (L, B, H) and Cartesian (X, Y, Z) coordinates
L, B, H
X, Y, Z
Known data
!
Ellipsoidal parameters
Computational results (m)
L
ﾼ
77
11
0
22.333
00
Krassowski Ellipsoid
X
ﾼ
1,178,143.5316
33
44
0
55.666
00
B
ﾼ
Y
ﾼ
5,181,238.3896
H
ﾼ
5,555.660 m
Z
ﾼ
3,526,461.5382
GRS75 Ellipsoid
X
ﾼ
1,178,124.3290
Y
ﾼ
5,181,153.9404
Z
ﾼ
3,526,400.6434
GRS80 Ellipsoid
X
ﾼ
1,178,123.7744
Y
ﾼ
5,181,151.5015
Z
ﾼ
3,526,399.0011
X, Y, Z
L, B, H
Known data (m)
!
Ellipsoidal parameters
Computational results
77
09
0
27.2049
00
X
ﾼ
1,177,888.777
Krassowski Ellipsoid
L
ﾼ
33
57
0
18.7484
00
Y
ﾼ
5,166,777.888
B
ﾼ
Z ﾼ 3,544,555.666
H ﾼ 3,878.5341 m
L ﾼ 77
09
0
27.2049
00
B ﾼ 33
57
0
18.8303
00
H ﾼ 3,984.3839 m
GRS75 Ellipsoid
L ﾼ 77
09
0
27.2049
00
B ﾼ 33
57
0
18.8296
00
H ﾼ 3,987.3758 m
GRS80 Ellipsoid
5.4 Normal Section and Geodesic
5.4.1 Radius of Curvature of a Normal
Section in an Arbitrary Direction
A plane containing the normal to the ellipsoid is called the normal section plane
(Fig.
5.10
). A normal section is created by intersecting the normal section plane
with the surface of the ellipsoid, such as the meridian. An oblique section, on the
other hand, is the intersection of the ellipsoid with any other plane that does not
contain the surface normal, such as the parallel.
The normal section plays a vital role in geodetic computations. Observations of
horizontal directions are usually referred to the direction of the plumb line, so if the
plumb line coincides with the normal or coincides with the normal after corrections
are applied, then the intersection of the ellipsoid with the vertical plane will be the
normal section. In order to carry out geodetic computations on the surface of the
ellipsoid, the properties of a normal section must be understood, and the radius of
curvature of the normal section is one of the important concerns. At every point on
the ellipsoid, infinitely many normal sections pass. In general, the radius of curva-
ture varies with the direction of the normal sections. We will first derive the formula
for radius of curvature of the normal section in an arbitrary direction, followed by
that in special directions.
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