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# 2.Position on the Earth

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Earth's graticule. Distances along great circles, small circles, convergence,...

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### 2.Position on the Earth

1. 1. Do you really know where you are?
2. 2. Feb-12 Alejandro Menéndez , MA 2
3. 3. PROPERTIES: •Circle = 360º Sexagesimal system: •1º = 60’ •1’ = 60’’ Directions always refered to a datum (North, Prime Meridian or Equator) Cartesian System (x,y)Feb-12 Alejandro Menéndez , MA 3
4. 4. PROPERTIES: Always mesured in clockwise direction from the reference datum Recap trigonometry!Feb-12 Alejandro Menéndez , MA 4
5. 5. DEFINITION: Angle of the arc along the meridian joining the Eq. and the point. Also, the angle of the arc along a meridian between the Eq. and the paralel where the point is.Feb-12 Alejandro Menéndez , MA 5
6. 6. Feb-12 Alejandro Menéndez , MA 6
7. 7. PROPERTIES: • From 0º up to 90º (North/South) • 2 digits needed • Standard expressions: • 6015N or N6015 (Accuracy 0.5’ of arc or 0.5nm) • 601508N or N601508 (Accuracy 0.5’’ of arc or 15.4m) • 6015.13N or N6015.13 (Accuracy 0.5’’ of arc or 15.4m)Feb-12 Alejandro Menéndez , MA 7
8. 8. DEFINITION: Shortest angular distance between the Prime Meridian and the meridian passing through that pointFeb-12 Alejandro Menéndez , MA 8
9. 9. Feb-12 Alejandro Menéndez , MA 9
10. 10. PROPERTIES: • From 0º to 180º (East/West) (Up to Greenwich Anti- Meridian) • 3 Digits • Standard expressions: • 05530E or E05530 (Accuracy of 0.5’ of arc) • 0553020E or E0553020 (Accuracy of 0.5’’ of arc) • 05530.30E or E05530.30 (Accuracy the same)Feb-12 Alejandro Menéndez , MA 10
11. 11. DEFINITION: Shortest angular distance along a meridian between two parallels of latitude. D LAT: Minutes CH LAT: Degrees and minutes *Exercises!Feb-12 Alejandro Menéndez , MA 11
12. 12. DEFINITION: Shortest angular distance along a parallel between two meridians D LONG: Minutes CH LONG: Degrees and minutes *Exercises!Feb-12 Alejandro Menéndez , MA 12
13. 13. DEFINITION: Algebraic middle value of latitude for two positions.Feb-12 Alejandro Menéndez , MA 13
14. 14. DEFINITION: Algebraic middle value of longitude for two positions.Feb-12 Alejandro Menéndez , MA 14
15. 15. DEFINITION: Net drawn on the surface of the Earth formed by the Prime Meridian and the rest of meridians in one sense, and the Equator plus the parallels of latitude.Basis for Position Creates a CartesianReference System SystemFeb-12 Alejandro Menéndez , MA 15
16. 16. Feb-12 Alejandro Menéndez , MA 16
17. 17. DEFINITION: Longitudinal distance along a parallel of latitude between two predetermined meridiansFeb-12 Alejandro Menéndez , MA 17
18. 18. D = (2 π R/360) β r NP d d = (2 π r / 360) β D β = CHLong R 000ºFeb-12 Alejandro Menéndez , MA 18
19. 19. r α = LAT r = R Cos α = R Cos LAT RFeb-12 Alejandro Menéndez , MA 19
20. 20. d = (2 π r / 360) β β = CHLong r = R Cos LAT d = (2 π /360) R CosLAT CHLong Departure (d) = 60 CHLong CosLATFeb-12 Alejandro Menéndez , MA 20
21. 21. D = 60(nm/º) CHLong Cos(Lat) For every GC: 1nm = 1’ -> 60nm = 1ºFeb-12 Alejandro Menéndez , MA 21
22. 22. DEFINITION: Tilt angle of meridians towards one another. Angular change of direction of a GC course as it passes from one meridian to the otherFeb-12 Alejandro Menéndez , MA 22
23. 23. PROPERTIES: • All meridians meet at the poles with an angle equal to the CHLong between them • All meridians are parallel as they cross the Equator • Increases with an increasing latitude • Increases with and increasing change in longitude • Angular difference between the initial and final course along a GC passing through two definite pointsFeb-12 Alejandro Menéndez , MA 23
24. 24. Feb-12 Alejandro Menéndez , MA 24
25. 25. CALCULATION: CONVERGENCY : CHLong x Sin (LAT) CONVERGENCY: GCTTin - GCTTfin ¡ Convergency between two positions on different latitudes might be calculated using the mean latitude !Feb-12 Alejandro Menéndez , MA 25
26. 26. Feb-12 Alejandro Menéndez , MA 26
27. 27. DEFINITION: Difference in direction between the GC track and the RL track running through two positions, observed at any of the points C.A. = ½ CONVERGENCY C.A. = 0.5 CHLong Sin MLatFeb-12 Alejandro Menéndez , MA 27
28. 28. Feb-12 Alejandro Menéndez , MA 28
29. 29. Feb-12 Alejandro Menéndez , MA 29
30. 30. Feb-12 Alejandro Menéndez , MA 30
31. 31. The GC track will always be closer to the nearest pole than a RLFeb-12 Alejandro Menéndez , MA 31
32. 32. Feb-12 Alejandro Menéndez , MA 32
33. 33. What is the difference in nm and km from position A (41º25’N) to position B(79º30’N). Both on the same meridian? An aircraft is to fly from position 72ºN 002º30’E to position 72ºN 177º30’W on the shortest possible route a) Give the initial True track direction. b) Will the track direction remain the same for the whole flight? c) Give a reason for the answer given in b aboveFeb-12 Alejandro Menéndez , MA 33
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