Mercator Projection and Polycylindric Projection - Map Projections: Cartographic Information Systems - page 818

Tab l e I . 2 Airy optimal dilatation factor ρ 0 for a symmetric strip, generalized UPC, WGS 84. Symmetric strip
[ Λ W = Λ 0 −

ΔΦ, Φ 0 + ΔΦ = Φ N ], strip width 3 ◦ , ΔΦ =1 . 5 ◦

ΔΛ, Λ 0 + ΔΛ = Λ E ] × [ Φ S = Φ 0 −

Zone Φ 0 Φ S Φ N ρ 0 Zone Φ 0 Φ S Φ N ρ 0

0 0 ◦ − 1 . 5 ◦ +1 . 5 ◦ 0.999887 ± 1 ± 3 ◦ ± 1 . 5 ◦ ± 4 . 5 ◦ 0.999886

± 2 ± 6 ◦ ± 4 . 5 ◦ ± 7 . 5 ◦ 0.999884 ± 3 ± 9 ◦ ± 7 . 5 ◦ ± 10 . 5 ◦ 0.999881

12 ◦ 10 . 5 ◦ 13 . 5 ◦ 15 ◦ 13 . 5 ◦ 16 . 5 ◦

± 4 ± ± ± 0.999876 ± 5 ± ± ± 0.999870

18 ◦ 16 . 5 ◦ 19 . 5 ◦ 21 ◦ 19 . 5 ◦ 22 . 5 ◦ ± 6 ± ± ± 0.999862 ± 7 ± ± ± 0.999852

24 ◦ 22 . 5 ◦ 25 . 5 ◦ 27 ◦ 25 . 5 ◦ 28 . 5 ◦

± 8 ± ± ± 0.999840 ± 9 ± ± ± 0.999826

30 ◦ 28 . 5 ◦ 31 . 5 ◦ 33 ◦ 31 . 5 ◦ 34 . 5 ◦ ± 10 ± ± ± 0.999809 ± 11 ± ± ± 0.999789

36 ◦ 34 . 5 ◦ 37 . 5 ◦ 39 ◦ 37 . 5 ◦ 40 . 5 ◦

± 12 ± ± ± 0.999764 ± 13 ± ± ± 0.999735

42 ◦ 40 . 5 ◦ 43 . 5 ◦ 45 ◦ 43 . 5 ◦ 46 . 5 ◦

± 14 ± ± ± 0.999699 ± 15 ± ± ± 0.999656

48 ◦ 46 . 5 ◦ 49 . 5 ◦ 51 ◦ 49 . 5 ◦ 52 . 5 ◦ ± 16 ± ± ± 0.999602 ± 17 ± ± ± 0.999535

54 ◦ 52 . 5 ◦ 55 . 5 ◦ 57 ◦ 55 . 5 ◦ 58 . 5 ◦

± 18 ± ± ± 0.999450 ± 19 ± ± ± 0.999341

60 ◦ 58 . 5 ◦ 61 . 5 ◦ 63 ◦ 61 . 5 ◦ 64 . 5 ◦ ± 20 ± ± ± 0.999197 ± 21 ± ± ± 0.999002

66 ◦ 64 . 5 ◦ 67 . 5 ◦ 69 ◦ 67 . 5 ◦ 70 . 5 ◦

± 22 ± ± ± 0.998729 ± 23 ± ± ± 0.998330

72 ◦ 70 . 5 ◦ 73 . 5 ◦ 75 ◦ 73 . 5 ◦ 76 . 5 ◦

± 24 ± ± ± 0.997714 ± 25 ± ± ± 0.996691

78 ◦ 76 . 5 ◦ 79 . 5 ◦ 81 ◦ 79 . 5 ◦ 82 . 5 ◦ ± 26 ± ± ± 0.994804 ± 27 ± ± ± 0.990705

84 ◦ 82 . 5 ◦ 85 . 5 ◦ 87 ◦ 85 . 5 ◦ 88 . 5 ◦

± 28 ± ± ± 0.978842 ± 29 ± ± ± 0.910273

Tab l e I . 3 Airy optimal dilatation factor ρ 0 for a symmetric strip, generalized UPC, WGS 84. Symmetric strip
[ Λ W = Λ 0 − ΔΦ, Φ 0 + ΔΦ = Φ N ], strip width 6 ◦ , ΔΦ =3 ◦ ΔΛ, Λ 0 + ΔΛ = Λ E ] × [ Φ S = Φ 0 −

Zone Φ 0 Φ S Φ N ρ 0 Zone Φ 0 Φ S Φ N ρ 0

0 ◦ 3 ◦ +3 ◦ 6 ◦ 3 ◦ 9 ◦ 0 − 0.999546 ± 1 ± ± ± 0.999536

± ±

12 ◦

±

9 ◦

±

15 ◦

± ±

18 ◦

±

15 ◦

±

21 ◦

2 0.999504 3 0.999448

± ±

24 ◦

±

21 ◦

±

27 ◦

± ±

30 ◦

±

27 ◦

±

33 ◦

4 0.999362 5 0.999236

± 36 ◦ ± 33 ◦ ± 39 ◦ ± 42 ◦ ± 39 ◦ ± 45 ◦

± 6 0.999057 ± 7 0.998796

± 48 ◦ ± 45 ◦ ± 51 ◦ ± 54 ◦ ± 51 ◦ ± 57 ◦ ± 8 0.998407 ± 9 0.997799

± 60 ◦ ± 57 ◦ ± 63 ◦ ± 66 ◦ ± 63 ◦ ± 69 ◦

± 10 0.996782 ± 11 0.994899

72 ◦ 69 ◦ 75 ◦ 78 ◦ 75 ◦ 81 ◦

± 12 ± ± ± 0.990804 ± 13 ± ± ± 0.978942

84 ◦ 81 ◦ 87 ◦ ± 14 ± ± ± 0.910374

Example I.3 ([95 ◦ <Λ< 145 ◦ ] × [ − 12 ◦ <Φ< +8 ◦ ]).

For the Airy optimal UPC, we have chosen a strip width of 6 ◦ between Φ S = 12 ◦ and Φ N =8 ◦ of

southern and northern latitude, in particular, to match the geographic region of Indonesia. Once
we refer to WGS 84, the strip system as well as the dilatation factor ρ 0 per strip is illustrated by
Fig. I.3 , namely for the zones 0 ,

−

± , − 2.

End of Example.

Furthermore, we computed by means of ( I.34 ) the left principal stretches Λ 1 = Λ 2 = Λ S ( Φ 0 ,Φ ; ρ 0 )
of each st rip and plotted them in Figs. I.4 , I.5 ,and I.6 . Moreover, Tables I.4 and I.5 give the
latitu de Φ of each strip according to the strip width ρ 0 and Φ 0 along which the mapping is equidis-
tant. Φ is determined by solving ( I.34 ) for given strip width, ρ 0 and Φ 0 under the condition that
Λ 1 = Λ 2 = 1 holds. Obviously, the variation of the left principal stretch Λ 1 = Λ 2 = Λ S ( Φ 0 ,Φ ; ρ 0 )
is small within the chosen strip. Alternatively, we may say that the radius of the left Tissot circle
Λ 1 = Λ 2 = Λ S ( Φ 0 ,Φ : ρ 0 ) varies only for a small amount, a favourable result of the Airy optimal
UPC.