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 MAP PROJECTIONS

       The essential problem faced by a map maker or cartographer is that it is impossible to represent large areas of the near spherical earth on a flat piece of paper. Whatever method is chosen will have inaccuracies of scale to varying degrees - usually the greater the represented area the greater will be the distortions. Therefore, for the navigating mariner travelling over the surface of the earth quite slowly, there will only be very minor scale inaccuracies on the relatively large scale charts normally used.
      There are three common basic methods of projecting the earth on to a piece of paper - with many other combinations and variations designed to suit specific needs. These are Cylindrical, Conic & Azimuthal (or Planar) projections. There are also modern mathematical projections for which the mariner will not have a practical use. Each projection has within its class a range of variations to suit different needs.

 Some Definitions

Conformality
When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps.
A map cannot be both conformal and equal area.

Distance
A map is equidistant when it portrays distances from the center of the projection to any other place on the map.
 

Scale
Scale is the relationship between a distance portrayed on a map and the same distance on the Earth.

Direction
A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions.

Area
When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area map.

Rhumb Line
A line draewn on a map cutting meridians at a constant angle. A Rhumb Line drawn on the real earth would curve towards the nearer pole.

 Great Circle
An imaginary line drawn on the surface of the earth dividing it into 2 equal hemispheres. The circular disk so shaped would pass through the earth's centre. The shortest path between two points on the surface is a great circle path

Cylindrical Projection
Imagine that the surface of the map as a cylinder that encircles the globe, touching it at the equator. The parallels of latitude are extended outward from the globe, parallel to the equator, as parallel planes intersecting the cylinder. Because of the curvature of the globe, the parallels of latitude nearest the poles when projected on to the cylinder are spaced progressively further apart, and the projected meridians of longitude are represented as parallel straight lines, perpendicular to the equator and continuing to the North and South poles. When the cylinder is slit vertically and rolled out flat the resulting map represents the Earth's surface as a rectangle with equally spaced parallel lines of longitude and unequally spaced parallel lines of latitude. Although the shapes of areas on the cylindrical projection are increasingly distorted towards the poles, the size relationship of areas on the map is equivalent to the size relationship of areas on the globe.

Cylindrical Projection Properties
     Lines of latitude and longitude are parallel intersecting at 90 degrees.
     Meridians are equidistant.
     Forms a rectangular map.
     Scale along the equator or standard parallels is true.
     Rumb Lines are straight lines. Great Circles are curved lines
     Can have the properites of equidistance & conformality.

Cylindrical
Projection

   The familiar Mercator projection is basically a cylindrical projection, with certain modifications. A Mercator map is accurate in the equatorial regions but greatly distorts areas in the high latitudes. However, directions are represented faithfully. Any line cutting two or more meridians at the same angle is represented on a Mercator map as a straight line.   Such a line, called a rhumb line, represents the path of a vessel following a steady compass course. Using a Mercator map, a navigator can plot a course simply by drawing a line between two points and reading the compass direction from the map.

Mercator Projection

   Distance measurement from the map needs to be made using the latitude scale surrounding the distance to be measured - as long as each measured distance segment is no longer than about 200 NM.

Map & Chart List

Conic Projections
   
  In preparing a conic projection a cone is assumed to be placed over the top of the globe. After projection, the cone is slit and rolled out to a flat surface. The cone touches the globe at all points on a single parallel of latitude-called the Standard Parallel (SP). The resulting map is extremely accurate for all areas near that parallel, but becomes increasingly distorted for all other areas in direct proportion to the distance of the areas from the SP. Because a cone cannot be made to touch the globe in the extreme polar and equatorial regions, the various conic projections are used to map comparatively small areas in the temperate zones.

Standard Conic Projection

 

Lambert's Conformal

     To provide a greater mapped area of less distortion a special conic projection was developed - called a Lambert's Conformal. The sides of the cone intersect the earth's surface at two places instead of just touching at one place. This projection will then have two SPs where the scale will be correct. For areas between the SPs the area represented on the map will be smaller than the correct scale - and vice versa for areas outside the SPs.
     The polyconic projection is a considerably more complicated projection in which a series of cones is assumed, each cone touching the globe at a different parallel, and only the area in the immediate vicinity of each parallel is used. By compiling the results of the series of limited conic projections, a large area may be mapped with considerable accuracy. Polyconic maps offer a good compromise in the representation of area, distance, and direction over small areas.

Conic Projection Properties
     Equally Spaced Parallels. Great Circles are curved.
     Neither Conformal nor Equal Area
     Equidistant Meridians converging at a common point
     Scale correct at standard parallel(s)

Azimuthal or Planar Projections
     Azimuthal projection maps are useful for viewing the polar regions of the world, because the poles usually appear near the centre, with longitudinal lines meeting at the poles and spreading away from each other as they move away from the poles. The polar regions are relatively free of distortion, but the distortion increases as the longitudinal lines move toward equatorial areas. This group of map projections is derived by projecting the globe on to a flat plane that may be touching it at any point. The group includes the gnomonic, orthographic, and stereographic plane projections.


Azimuthal Projection

     Two other types of plane projection are known as the azimuthal equal area and the azimuthal equidistant; they cannot be projected but are developed on a tangent (touching) plane. The gnomonic projection is assumed to be formed by rays projected from the centre of the Earth. In the orthographic projection the source of projecting rays is at infinity, and the resulting map resembles the Earth as it would appear if photographed from outer space. The source of projecting rays for the stereographic projection is a point diametrically opposite the tangent point of the plane on which the projection is made.

The nature of the projection varies with the source of the projecting rays. Thus the gnomonic projection covers areas of less than a hemisphere, the orthographic covers hemispheres, the azimuthal equal area and the stereographic projections map larger areas, and the azimuthal equidistant includes the entire globe. In all these types of projection, however (except in the case of the azimuthal equidistant), the portion of the Earth that appears on the map depends on the point at which the imaginary plane touches the Earth. A plane-projection map with the plane tangent to the surface of the Earth at the equator would represent the equatorial region, but would not show the entire region in one map; with the plane tangent at either of the poles, the map would represent the polar regions.
     Because the source of the gnomonic projection is at the centre of the Earth, all great circles, that is, the equator, all meridians, and any other circles that divide the globe into two equal parts, are represented as straight lines. A great circle that connects any two points on the Earth is always the shortest distance between the two points. The gnomonic map is therefore a great aid to navigation when used in conjunction with the Mercator.

Azimuthal Projection Properties (Gnomonic)
    
 Neither conformal nor equal area     

     Great Circles are straight lines - representing the shortest distance between two points.
     Rumb lines are concave toward the nearer pole.

     
Scale is correct only at the centre - becoming increasingly distorted with increasing distance from the centre.
     Less than one hemisphere can be seen on one map.

Mathematically Based Projections
     For accurate delineation of large areas on a small scale, a number of so-called projections have been developed mathematically. Maps based on mathematical computation represent the entire Earth in circles, ovals, or other shapes. For special purposes the Earth is often drawn not within the original form of the projection but within irregular, joined parts. Maps of this type, called interrupted projections, include Goode's interrupted homolosine and Eckert's equal-area projection.
     Goode's interrupted homolosine projection was developed mathematically in 1923 by J. Paul Goode. The globelike feeling and minimal distortion of land masses in this projection have made it a favourite for portraying world-wide thematic maps.

Two views of a Goode's Projection

Sport Phillip Marine services the boating, yachting & fishing needs of the Mornington Peninsula from Frankston, Daveys Bay, Mt. Eliza, Mornington, Mt. Martha, Safety Beach, Martha Cove, Dromana, Rosebud, Rye, Blairgowrie, Sorrento and Portsea on Port Phillip Bay to Yaringa, Warneet, Somers, Hastings, and Flinders on Westernport Bay.

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