hw2 - map proj cy & ca

8/2/2019 HW2 - MAP PROJ CY & CA

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ADVANCE NAVIGATION EXERCISE 2

MAP PROJECTIONS, CONVERGENCY & CONVERSION ANGLE

HOMEWORK 2 : Q1 , Q5 , Q10 , Q15 , Q17

Question 1.

The great circle bearing of B (5000'N 1000'E) from A (4000'N 0200'W) is 060T. What is the greatcircle bearing of A from B ? (248.5 T)

(Sin 45 = .71, Cos 45 = .71, Tan 45 = 1.0)

Question 2.

The initial great circle track from C (3600N 1500'E) to D in latitude 42N is 300T and the final track at

D is 295T.

a) What is the longitude of D ? ( 7 East)

b) What would be the approximate track direction at 11E ?(297.5 T)

(Sin 39=.63, Cos39=.78, Tan 39=.81)

Question 3.

The great circle bearing of E from F is 090T and the great circle bearing of F from E is 265T. In

which hemisphere are E and F ? (Southern Hemisphere)

Question 4.

The great circle bearing of G (4500'S 17400'E) from H (4000'S 17000'W) is 250T.

What is the great circle bearing of H from G ? (081 T (080.7))

(Sin 42%2 = . 67, Cos 42 = .74, Tan 451/2 = .92)

Question 5.

a) Determine the value of convergency between J (5812'N 0400'W)and K (5812'N

0600'E). (8.5)

b) What is the rhumb line bearing of K from J ?(090 T. On same Latitude so a Rhumb Line Track)

c) What is the great circle bearing of J from K ? (274 T. (274.25))

(Cos 5812' = .53, Cot 5812' = 0.62, Sin 5812' = 0.85)

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Sin 30 = 0.5 Cos 30 = 0.87 Tan 30 = 0.58

Question 6.

The convergency of the meridians through M and N which are in the southern hemisphere is 12. If

the rhumb line track from M to N is 249T, what is the great circle bearing of:

a) N from M ? (243 T)

b) M from N ? (075 T)

Question 7.

The great circle bearing of position B in latitude 3000'S from position A (3000'S 16500'E) is

100T.

What is:

a) The great circle bearing of A from B ? (260 T)

b) The longitude of position B ? (155 West)

Question 8.

The rhumb line bearing of position C from position D (3000N 17900'W) is 090T. The great

circle bearing of D from C is 287T.

What is:

a) The great circle bearing of C from D ? (073 T)

b) The approximate latitude and longitude of position C ?(30N111 W)

Question 9.

The great circle bearing of position F in longitude 2400'E from position E at 27OON 0800'W

measured at longitude 0800'E is 084T.The great circle bearing of E from F, measured at F is 272T.

What is:

a) The great circle bearing of F from E measured at E ? (076 T)

b) The approximate latitude of F ? (Latitude 33 North)

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Question 10.

The great circle track from A to B measures 227T at A and 225T at B. What is theconvergency of the meridians through A and B and in which hemisphere are they ?. (2 of

Convergency and in Northern Hemisphere)

Question 11.

The convergency of the meridians through M and N which are in the southern hemisphere is 12.If the rhumb line track from M to N is 249T, what is the great circle bearing of:

a) N from M. (243 T)b) M from N. (075 T)

Question 12.

a) In what latitude is the convergency between two meridians on the earth equal to twicetheir convergency in latitude 20N ? (Latitude 43 North)

b) Is there a latitude where the convergency would be three times the value at 20N ?.(No, as 3 times convergency value would be greater than longitude change)

Question 13.

A and B are in the same hemisphere.The great circle bearing of A from B is 268T and the great circle bearing of B from A is

092T.

i) In which hemisphere are A and B ? (Southern Hemisphere)

ii) What is the rhumb line bearing of B from A ?.(090 T, as A and B on same latitude)

b) C and D are in the same hemisphere.The great circle bearing of D from C is 063T and the rhumb line bearing of C from D is

240T.

i) In which hemisphere are C and D ? (Southern Hemisphere)

ii) What is the approximate great circle bearing of C from D ?(237 T)

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ADVANCE NAVIGATION EXERCISE 2Question 14.

Position X 6400'S 11 50'W. Position Y 6400'S 0510'W.

Give: a) The convergency between the meridians of X and Y. (6)

b) The approximate great circle bearing of X from Y. (2677)

c) The rhumb line track from X to Y. (090T)

Question 15.

a) Calculate the convergency between positions A (5530N 0435'W) and B (6400'N2237'W). (15.5 Convergency; callit 16)

b) If the rhumb line track from A to B is 313T what is the approximate great circle

bearing of A from B ?. (125 T)

Question 16.

The great circle bearing of A from B is 245 T and the rhumb line bearing of B from A is 060T.

If the mean latitude between A and B is 53 and the longitude of B is 0215'E, what is the

longitude of A ? (010 15' W)

Question 17.

A and B are both in the southern hemisphere and the convergency of their meridians is 8. Thegreat circle bearing of B from A is 094T.

If the position of B is 2300'S 2000'W, what is the position of A ?.(Position A is at 23 00S 04028.5'W, Rhumb Line is 090T)

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18. What map projection is the most suitable for use in polar area?

ans : Polar Stereographic projection

19. What map projection is the most suitable for use in equator area?

ans : Mercator projection

20. What map projection is the most suitable for use in the mid latitude ?

ans : Lambert projection

21. What is Standard Parallel of Latitude ?

ans : In Lambert Projection , Standard Parallel is the parallel of latitude where the cone touch the

EARTH

22. What kind of line ( straight line / curve / concentric circle ) the parallel of latitude is in the

following charts:

a) Mercator Chart ______________

b) Lambert Chart _______________

c) Polar Stereographic ________________

ans : a) straight line b) concentric circle c ) concentric circle

23. What kind of line ( straight line or curve ) the great circle is in the following charts: ( note :great circle in this question is not equator nor meridians )

a) Mercator Chart : ______________

b) Lambert Chart :i. great circle not connecting two points on parallel of origin : _______________

ii. great circle connecting two points on parallel of origin : ______________ iii. For practical purposes, especially in plotting : _________________

c) Polar Stereographic ( Great Circle course not near the pole ) ________________d) Polar Stereographic ( Great Circle course near the pole ) ________________

ans : a) curve b) i. curve ii. straight line iii. Straight line

c ) curve d) straight line

24. In Lambert Chart, great circle not connecting two points on parallel of origin appear as_________ _________ to the parallel of origin.

ans : curves concave

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25. What kind of line ( straight line or curve ) the rhumb line is in the following charts:

( Assume rhumb line course is 045 degree true )a) Mercator Chart ______________

b) Lambert Chart _______________c) Polar Stereographic ________________

ans : a) straight line b) curve c ) curve

26. In Lambert projection, rhumb line is ________ to the pole.

Ans : concave

27. In Mercator projection, great circle is _________ to the Pole.

Ans : convex

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hw2 - map proj cy & ca

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