Navigation NAU 102 Lesson 3

A graphical representation of part of the earth. 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!

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.

You can’t have everything! 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!

Chart Projections From wikipedia.org

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

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

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

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

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

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

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

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

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

Expressed in units of 1’ of longitude at the equator. 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.

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

Meridional Parts Calculated using the formula: M = a loge 10 log tan (45 + L/2) – a (e2 sin3L + e4/3 sin3L + e6/5 sin5L + …) Or, just look them up in Bowditch Table 6.

Cylindrical Projections Mercator Projection From wikipedia.org

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.

Cylindrical Projections Mercator Projection

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

Cylindrical Projections Transverse Mercator Oblique Mercator

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

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

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

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

Conical Projections

Projection Comparisons

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

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

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

1 inch on chart = 80,000 inches on Earth Chart Scales Scale – the ratio of a given distance on the chart to the actual distance which it represents on Earth. e.g. 1:80,000 or 1/80,000 1 inch on chart = 80,000 inches on Earth

Chart Scales Scale can be stated by: Ratio or fraction e.g. 1:80,000 or 1/80,000 A statement e.g. “2 inches to the mile” A graphic scale

Chart Scales Small Scale = Large Area Large Scale = Small Area e.g. 1/100,000 vs. 1/10,000 The larger the scale, the greater the detail.

Introduction to Navigation Questions?