Geodesics - Map Projections: Cartographic Information Systems - page 732

S 2 R , conformal coordinates generated by the universal transverse
Mercator projection, solution of the boundary value problem, departing point Frankfurt, arrival point Taipeh,
time given for constant speed movement with respect to the arrival point

Fig. E.3. Maupertuis gauged geodesic on

cos Φ =cos q 1

R 1+tan 2 q 1 R tanh 2 q 2

tanh q 2

R , sin( Λ

− Λ 0 )= −

R / cos Φ,

(E.49)

λ =cos arcsin tanh q 2
R

,

(E.50)

d s 2 =cos 2 arcsin tanh q 2
R

[(d q 1 ) 2 +(d q 2 ) 2 ] .

(E.51)

(iv) Universal Conic Projection (UC):
q 1 = r cos α, q 2 = r sin α, α = nΛ, r = c tan π

n

Φ
2 4 −

, (E.52)

r cos Φ
cn (tan( 4 −

λ =

2 )) n .

(E.53)

Φ

Variant one (UC). Equidistant map of the parallel circle Φ 0 / line-of-contact:

cot Φ 0
(tan( 4 −

n =sin Φ 0 ,c = R

2 )) n ,

(E.54)

Φ