1. Navigation NAU 102 Lesson 3

2. The Nautical Chart A graphical representation of part of the earth. Shows water depths, shoreline, prominent land features, navigation information. Used for waterborne navigation. It is not a map!

3. The Nautical Chart We have a problem! The earth is spherical. Charts are planar. The sphere must be “projected” onto the plane. This results in distortion.

4. Chart Projections Desirable Features True shape of physical features. Correct angular relationships. Equal area. Constant scale values. Great circles as straight lines. Rhumb lines as straight lines. You can’t have everything!

5. Chart Projections From wikipedia.org

6. Chart Projections For large areas, only one 1 or 2 of the desired characteristics can be achieved. Most important for navigation: True shape Correct angular relationships Known as conformal projections

7. Chart Projections Types of Chart Projections Cylindrical (Mercator) Conical/Polyconical (Lambert Conformal) Azimuthal (Gnomonic) Hundreds of others, but not used for navigation

8. Chart Projections Cylindrical Projections A cylinder is placed tangent to the earth

9. Chart Projections Cylindrical Projections Planes of meridians are extended to the cylinder

10. Cylindrical Projections Mercator Projection The cylinder is tangent to the equator. Meridians are drawn parallel. High latitudes are stretched to maintain angular relationships. Typically derived mathematically A conformal projection.

11. The Spherical Earth A perfectly circular island 90°N 75°N 60°N 45°N Meridians are not parallel.

12. Mercator Projection Meridians are drawn parallel. Size and shape of island are distorted. 90°N 75°N 60°N 45°N Parallels of latitude are stretched.

13. Mercator Projection Meridians are stretched. Size is distorted but land shape is retained. 75°N 60°N 45°N

14. Mercator Projection How much stretch do we need? It depends on the latitude. 75°N 60°N 45°N The higher the latitude, the greater the stretch. This is stated in Meridional Parts.

15. Meridional Parts (M) The length of a meridian as drawn on a Mercator chart between the equator and any given latitude. Expressed in units of 1' of longitude at the equator.

16. Meridional Parts 1800 nm 30°N 0° Meridional parts in 30° = 1876.9 0° 30°N Drawn as if 1876.9 nm long

17. Meridional Parts Calculated using the formula: M = a log e 10 log tan (45 + L/2) – a (e 2 sin 3 L + e 4 /3 sin 3 L + e 6 /5 sin 5 L + …) Or, just look them up in Bowditch Table 6.

19. Cylindrical Projections Mercator Projection From wikipedia.org

20. Cylindrical Projections Mercator Projection Maintains angular relationships. Rhumb lines are straight lines. Great circles are curved. Size is distorted but land shape is retained. Cannot include the poles – infinite expansion would be required.

21. Cylindrical Projections Mercator Projection

22. Cylindrical Projections Mercator Projection Most common projection for navigation. Distance can be measured directly from the chart. Direction can be easily measured.

23. Cylindrical Projections Transverse Mercator Oblique Mercator

24. Gnomonic Projection Features are projected from the center of the earth onto a tangent plane.

25. Gnomonic Projection Distance and direction cannot be measured directly. Meridians are drawn straight (but, not parallel). Parallels are curved. Shape, distance and size are distorted.

26. Gnomonic Projection Great Circles plot as straight lines. Rhumb lines are curved. Known as Great Circle Charts Used for voyage planning.

27. Conical Projections Uses a secant cone. Lambert Conformal Projection Great circles plot as straight lines. Used for near polar navigation.

28. Conical Projections

29. Projection Comparisons

30. Other Projections Stereographic/Orthographic Used for polar navigation and decoration Points projected from opposite side of the earth or from infinity

31. Plotting Sheets Used mid-ocean Pre-labeled latitude lines No land/ocean features Unlabeled longitude lines You can make your own!

32. Plotting Sheets Universal Plotting Sheet You label the latitude lines Can be used for any latitude/longitude You draw the longitude lines Longitude scale varies by mid-latitude

33. Introduction to Navigation Questions?