Geodetic Mapping - Map Projections: Cartographic Information Systems - page 493

First step:
determine L F ,B F ,α F0 = α 0F = π/ 2, starting point P 0 ,s = y = x c ,x = y c =0 ,α 0F = π/ 2
given. As a result, u = y cos α 0F =: u 0 =0and v = y sin α 0F =: v 0 = y lead to the general
series ( 20.112 ), just replacing B P ,L P ,α P0 ,and α 0P by B F ,L F ,α F0 ,and α 0F , respectively.
Second step:

determine B F ,L F ,α FP = γ, starting point P F ,s = x = y c ,y = x c =0 ,α FP = α F 0 +3 π/ 2

given.

L = L F +[10] F u F +[11] F u F v F + [12] F u F v F +

···

= L 0 +[10] 0 u 0 +[11] 0 u 0 v 0 + [12] 0 u 0 v 0 + ··· (20.129)

+[10] F u F +[11] F u F v F + [12] F u F v F + ,

B = B F + [01] F v F + [20] F u F + [02] F v F + [21] F u F v F +

···

···

= B 0 + [01] 0 v 0 + [20] 0 u 0 + [02] 0 v 0 + [21] 0 u 0 v 0 +

··· (20.130)

+ [01] F v F + [20] F u F + [02] F v F + [21] F u F v F + ··· ,

α PF = α FP +[10] α F u F + [11] α F u F v F + [12] α F u F v F +

···
= α F0 +[10] α F u F + [11] α F u F v F + [12] α F u F v F + ··· + 3 π (20.131)

2

= α 0F +[10] α 0 u 0 + [11] α 0 u 0 v 0 + [12] α 0 u 0 v 0 + ··· + 3 π

2

+[10] α F u F + [11] α F u F v F + [12] α F u F v F +

··· .

The coecients [ μν ] 0 and [ μν ] F , respectively, have to be computed at the point B 0 and B F ,
respectively.

A numerical example is given in Tables 20.3 and 20.4 .

Table 20.3 Fermi coordinates: input { L 0 ,B 0 ,x,y } versus output { L,B } .Partone

Reference ellipsoid, WGS84 (GRS80):
A 1 = 6 378 137 m ,E 2 =0 . 006 694 380 02 .

Fermi origin:
B 0 =48 ◦ N ,L 0 =9 ◦ E .

Fermi coordinates:
y = 234 123 . 034 m ,x = 65 356 . 124 m .

Initial azimuth α 0F :
α 0F =50 ◦ 48 13”.512 4.