442 20 Geodetic mapping
Box 20.10 (General eigenvalue problem (Λ 1 , Λ 2 ), Riemann coordinates).
Λ 1 = 1 +
1
6V
2
0
b
2 +
V
2
0 cos
2 B 0
6
l
2 −
t 0 (1 + 2η
2
0 ) cos
2 B 0
6
bl
2 +
+
η
2
0 t 0 (1 − η
2
0 (71 − 72t
2
0 ) − 72η
4
0 (1 − 4t
2
0 ))
6V
6
0
b
3 +
+
(7 − 5t
2
0 + η
2
0 (14 − 29t
2
0 ) + η
4
0 (7 − 24t
2
0 )) cos
4 B 0
360
l
4 −
−
(1 + η
2
0 (8 − 7t
2
0 ) + 13η
4
0 (1 − t
2
0 ) + 6η
6
0 (1 − t
2
0 )) cos
2 B 0
60V
4
0
b
2 l
2 +
+
b
4
360V
8
0
h
7 + 2η
2
0 (19 − 12t
2
0 ) + η
4
0 (55 + 1107t
2
0 − 1080t
4
0 )+
+η
6
0 (24 − 2109t
2
0 + 7560t
4
0 ) − 3240η
8
0 t
2
0 (1 + 4t
2
0 )
i
,
Λ 2 = 1 .
(20.139)
Box 20.11 (Maximum angular distortion (ω), Riemann coordinates).
ω =
1
6V
2
0
b
2 +
V
2
0 cos
2 B 0
6
l
2 −
t 0 (1 + 2η
2
0 ) cos
2 B 0
6
bl
2 +
+
η
2
0 t 0 (1 − η
2
0 (71 − 72t
2
0 ) − 72η
4
0 (1 + 4t
2
0 ))
6V
6
0
b
3 +
+
(2 − 5t
2
0 + η
2
0 (4 − 29t
2
0 ) + η
4
0 (2 − 24t
2
0 )) cos
4 B 0
360
l
4 −
−
(8 + η
2
0 (34 − 21t
2
0 ) + η
4
0 (44 − 39t
2
0 ) + 18η
6
0 (1 − t
2
0 )) cos
2 B 0
180V
4
0
b
2 l
2 +
+
b
4
360V
8
0
h
2 + 4η
2
0 (7 − 6t
2
0 ) + η
4
0 (50 + 1107t
2
0 − 1080t
4
0 )+
+η
6
0 (24 − 2109t
2
0 + 7560t
4
0 ) − 3240η
8
0 t
2
0 (1 + 4t
2
0 )
i
.
(20.140)
8
◦
9
◦
10
◦
0
◦
−1
◦
+1
◦
2.5 5
8
◦
9
◦
10
◦
48
◦
47
◦
49
◦
2.5
5
Fig. 20.8. Principal distortion Λ 1 [ppm], Riemann coordinates. Left: L 0 = 9
◦ , B 0 = 0
◦ (equator). Right:
L 0 = 9
◦ , B 0 = 48
◦ .