Geodetic Mapping - Map Projections: Cartographic Information Systems - page 485

η 0 t 0 (4 + 17 η 0 − 9 η 0 t 0 +13 η 0 +76 η 0 t 0 )

8 V 0

(40) = −

N 0 , (20.105)

t 0 (3 − t 0 +3 η 0 )
120

N 0 cos 5 B 0 ,

(50) = −

(20.106)

(41) = N 0 cos 4 B 0
360 V 0

50 t 0 +15 t 0 +2 η 0 (7 37 t 0 )+ η 0 (7 24 t 0 )] ,

[7 − − − (20.107)

N 0 cos 3 B 0
180 V 0

40 t 0 + η 0 (16 31 t 0 − 45 t 0 )+ η 0 (8 + 9 t 0 )] ,

(32) = − [8 − − (20.108)

(23) = N 0 cos 2 B 0
180 V 0

[ − 8 − η 0 (7 + 174 t 0 − 45 t 0 )+ (20.109)

+2 η 0 (5 − 83 t 0 − 90 t 0 )+3 η 0 (3 + 2 t 0 )] ,

N 0 cos B 0
360 V 0

[8 + 4 η 0 (28 69 t 0 )+ (14) = − −− (20.110)

+ η 0 (20 507 t 0 + 405 t 0 )+3 η 0 (32 7 t 0 − 1140 t 0 )] ,

− −

(50) = N 0 η 0
40 V 10

4+4 t 0 + η 0 (3 98 t 0 +15 t 0 )+

[ − − (20.111)

0

2+ η 0 (9 179 t 0 +90 t 0 )+ η 0 (11 256 t 0 − 1320 t 0 )] . − −

For the ellipsoid-of-revolution, we present the solution of
the initial value problem given {L 0 ,B 0 ,α 0 } relating x =
r cos α 0 = SN ( B 0 )cos B 0 L 0 , y = r sin α 0 = SM ( B 0 ) B 0 .
Box 20.5 contains the coe cients [ μν ] up to order five based
upon the Lie recurrence. In contrast, we add the solution
of the boundary value problem x ( l, b )and y ( l, b )interms
of the coecients ( μν )uptoorderfiveinBox 20.6 .This
approximation is accurate to the order smaller than 0 . 0003
for l := L − L 0 , 0 . 0002 for b := B − B 0 ,and0 . 001 for

α − α 0 for distances up to 100km (Boltz approximation).