Chart projections
• Maps and charts are representations of portions of the Earth’s surface, to a
suitable scale, on a flat surface.
• Charts differ from maps in that charts show a large amount of information for
navigational usage.
• A surface is said to be developable if it can be placed flat without being
stretched or torn i.e, distorted. The curved surface of a sphere like that of the
Earth is non-developable since it cannot be placed without distortion.
Therefore distortion is inescapable in any map or chart representing the
Earth’s surface. (four types of distortion – Distance, Direction, shape and area)
• There are various projections used in map making. A projection is an
arrangement of lines representing meridians and parallels of latitude. A map
projection is therefore a representation of the meridians and parallels of
latitude, on a plane surface.
Projection
• Projection is representing surface of the earth on to a developable surface, i.e,
which can be flattened as plane without distortion.
• If points on the surface of the sphere are projected from a single point, the
projection is said to be perspective or geometric.
• If points on the surface of the sphere are mathematically calculated the
projection is said to be mathematical projection.
• Mercator projection is a conformal projection which preserves the shape and
maintains angular relationship with the objects in the neighborhood. In this
projection, the grids are mathematically calculated.
Map projection
• Map projection. Is a systematic transformation of the latitudes and longitudes
of locations from the surface of a sphere or an ellipsoid into locations on a
plane. Maps cannot be created without map projections. All map projections
necessarily distort the surface in some fashion.
• To create an ideal map, one needs a projection which preserves angles,
distances and areas. Unfortunately, there is no projection which preserves all
these measurements.
• For purposes of navigation preserving angles is the most important property.
• The Mercator projection exaggerates areas far from the Equator
Advantages and Disadvantages of Mercator projection
• Advantages • Disadvantages
• Preserves angles and therefore also • Mercator’s projection does not
shapes of small objects. preserve lengths or areas further from
• Close to the equator, the distortion of the equator.
lengths and areas is insignificant. • The smallest distance on the globe is
• A straight line on the map corresponds not realized by a straight line on the
with a constant compass direction, it is map.
possible to sail and fly using a constant • Not suitable for teaching geography and
azimuth in political maps (this projection
• Simple navigation. distorts areas and sizes of states and
continents, e.g, Africa and Greenland
• Meridians and parallels make a seem to be of the same size)
rectangular grid on the map. • Line with the shortest distance is not
• Aside from nautical and aerial use, obvious from the map.
Mercator’s projection is practical for
visual mapping of the earth’s globe
(without polar areas)
Mercator Charts
• Characteristics of a Mercator Chart
• (1) Chart is orthomorphic – Though areas appear larger at higher latitudes,
directions are correct.
• (2) The equator appears as a straight line.
• (3) All meridians are projected as equidistantly spaced (N-S) parallel straight
lines, and cross the Equator at right angles.
• (4) All parallels of latitude are projected as (E-W) parallel straight lines
perpendicular to the projected meridians.
• (5) The distance between consecutive parallels increases as latitude increases.
• (6) All Rhumb lines are projected as straight lines.
Mercator Charts
• Characteristics of a Mercator Chart…(Contd)
• (7) All arcs of great circles, with the exceptions of the arc of or any meridian,
are projected as curves which are concave to the projected equator, that is to
say the Great Circle Path (GCP) always lies on the pole ward side of the Rhumb
line.
• (8) Angles, such as course and bearing angles are easily and accurately
determined.
• (9) One minute of d’long is the same size in all parts of the chart.
• (10) One minute of d’Lat increases in size steadily as we go away from the
Equator
• (11) Polar Regions do not appear.
Mercator Projection- Disadvantages
• 1. Distortion of the Earth’s surface.
• As Mercator’s projection moves away from the equator, the representation of
the Earth’s surface is distorted. This distortion makes the shapes found at the
poles look bigger than they really are.
• Mercator’s projection shows that Greenland is the size of Africa, that Alaska is
larger than Brazil and that Antarctica is an infinite expanse of ice.
• However, in fact Greenland is the size of Mexico, the territory of Alaska is 1/5
that of Brazil and Antarctica is a little larger than Canada.
• 2. Polar zones are not represented
• Because the projection of Mercator is based on cylinder, it is difficult to
represent the polar zones of the planet Earth. For this reason, the poles are not
included in this type of cartographic projection.
Mercator Charts
• Defects/Disadvantages of a Mercator Chart
• (1) Every latitude has a different scale of distance.
• (2) Great circle arcs, except those of the Equator or meridians are projected as
curves. This makes for difficulty in the practice of Great Circle sailing.
• (3) The variation of the latitude scale causes areas to be exaggerated
proportional to their latitudes. It will be noticed that on a Mercator chart of
the world, Greenland appears larger than the continent of South America, and
yet the range of Latitude of Greenland is no more than about a quarter of that
of South America
Limitations of the Mercator projection
• The scale along a meridian on a Mercator chart is given by the Longitude scale
multiplied by the secant of the latitude. The secant of angles approaching 900
gets very large and approaches infinity. The length of one minute of latitude
therefore approaches infinity towards the poles. It is not possible for this
reason, to use the Mercator projection for polar regions. This is of no great
disadvantage to the marine navigator as very little navigation is done in these
regions. Polar charts are usually constructed on the polar gnomonic projection.
• Probable Q. Explain mathematically as to why a Mercator projection chart is
not suitable for navigation in the polar regions..?
Mercator Projection
• The Mercator projection is a cylindrical map projection presented by the
Flemish geographer and cartographer Gerardus Mercator in 1569. It became
the standard map projection for nautical purposes because of its ability to
represent lines of constant course, known as rhumb lines or loxodromes, as
straight segments that conserve the angles with the meridians. Although the
linear scale is equal in all directions around any point, thus preserving the
angles and the shapes of small objects (which makes the projection
conformal), the Mercator projection distorts the size of objects as the latitude
increases from the Equator to the poles, where the scale becomes infinite. The
Mercator projection is still used commonly for navigation.
• Cylindrical projection, orthomorphic with the cylinder tangential along the
equator.
• A projection is orthomorphic if the scale of distance at any point of the chart is
equal in all directions
Mercator Projection- Advantages 1/3
• 1. Explore the world.
• Before Mercator’s projection, there were already maps showing the full extent
of planet earth. However, this was the first that provided people with the
means to explore and navigate across the seas. Mainly, this projection is useful
for tracing routes with a steady course in a straight line.
• In addition to creating a projection, Mercator published a geometric formula
that corrected the distortion presented on its map. These calculations enabled
seafarers to transform projection measurements into degrees of latitude by
facilitating navigation.
• Like any flat rendering of the Earth, Mercator’s projection presents distortion.
The globe is the only true representation of the earth’s surface.
Mercator Projection- Advantages 2/3
• 2. Keep the scales.
• The projection of Mercator is proportional. This means that to compensate for
the North-South distortion (from pole to pole), an east-west distortion is also
introduced.
• Other projections can make a square building look rectangular, because the
distortion exists in only one direction.
• On the other hand, because it is proportional, the distortion generated by
Mercator does not make the objects appear more elongated or flattened, but
simply larger.
• This is another reason why the cartography web services use this type of
projection and not others.
Mercator Projection- Advantages 3/3
• 3. Angles are represented correctly.
• The projection of Mercator has the property of representing the angles as they
are. If in the real plane there is an angle of 900 the projection will show an angle
of the same amplitude.
• This is another reason why Google Maps and other similar applications prefer
Mercator over other projections.
• 4. Calculations of this projection are simpler than those of other projection
• The mathematics behind the Mercator projection are much simpler than other
projections today. For this reason, online mapping services prefer its use.
• The applications of Google Maps, Bing Maps and OpenStreetMaps are based on
Mercator projection.
Types of Charts
• For navigation purposes, it is required that the chart represents the shape
of the land correctly in any particular vicinity and the most common form
of sailing, rhumb line tracks, can be laid off as straight lines on the chart.
• Charts are classified on the basis of :
• (i) The type of projection used to draw the chart, e.g. Mercator, Gnomonic,
• (ii) The purpose of the chart, i.e. Nautical charts, tidal charts, pilot or
routeing charts, lattice charts
• (iii) The scale of the charts, i.e, ocean charts, coastal charts, harbour
charts, plan charts.
Mercator Charts
Advantages Disadvantages
1. Rhumb line courses are laid off as straight lines. 1. Great circle courses cannot be laid off as they would
appear curved
2. Distances are easily measured as scale of distance = 2. Polar regions cannot be represented due to
scale of latitude extremely large distortions.
3. Shapes of land masses in the neighborhood of a 3. The scale of distance which is the scale of latitude is
point are correctly shown. a varying unit.
4. Angles between rhumb lines are unaltered between 4. Areas cannot be compared due to varying distortion
the Earth and the Chart
5. Direction remain correct though distortions of areas
occur.
6. Directions and position lines can be transferred
correctly from one chart to another as parallel lines
Gnomonic Charts
Advantages Disadvantages
1. All regions of the world including 1. Rhumb line courses and bearings
polar regions can be represented on cannot be laid as they appear curved.
gnomonic charts.
2. Great circle course are easily laid off 2. Bearings and position lines cannot
as straight lines be transferred from one chart to
another as parallel lines, because the
meridians are convergent
3. Measurement of distances and
courses is difficult
