11-2 Special mapping eq uations 287
Fig. 11.2. M
apping the sphere to a cy linder: transverse aspect, eq uidistant mapping,
B 0 = 0
◦ , transverse
Plate C
arr´ ee projection.
11-22 Conformal mapping (transverse Mercator projection), compare with Fig. 11.3
x
y
= R cos B 0
A
ln cot
π
4 −
B
2
= R cos B 0
A
ln tan
π
4 +
B
2
=
= R cos B 0
A
1
2 ln
1+sin B
1−sin B
=
= R cos B 0
A
ar tanh(sin B)
,
(11.5)
Λ 1 = Λ 2 =
cos B 0
cos B
.
(11.6)
11-23 Equal area mapping (transverse Lambert projection), compare with Fig. 11.4
x
y
= R
A cos B 0
sin B
cos B 0
,
(11.7)
Λ 1 =
cos B 0
cos B
, Λ 2 =
cos B
cos B 0
.
(11.8)