Projections
The nautical chart is an image of a part
of the earth in two dimensions. This reproduction is a two dimensional
image of a part of the earth, which is of course 3 dimensional. This
results in various distortions, but as long as two requirements are met we
can use this image for navigational purposes. Firstly, the angles between
three objects in the chart should be the same as the angles between the
real objects which they represent. Secondly, a straight course should
appear as a straight line in the chart.
To fulfil these demands our chart ought to have both parallels & meridians
which are straight and parallel. As such the meridians & parallels will be
perpendicular to each other.
A well known method to create such a chart is called the Mercator
Projection after Gerard Kremer (Mercator),
a Flemish scholar who studied in 's Hertogenbosch and Leuven. In 1569 he
invented the projection which made him famous.
His chart was designed for sailors and constructed by wrapping a cylinder
around the planet so that it touches the equator. On this cylinder the
surface of the earth is projected and finally the cylinder is cut open to
yield our chart. But where the meridians converge on the globe they run
parallel in the projection (see chart below), indicating the distortion.
Look, for example, at a high parallel. The length of such a parallel on
the globe is much smaller than the equator. Yet, on the chart they have
exactly the same length creating a distortion which gets bigger nearer to
the poles. The figure below shows us the construction of the mercator
projection. From this it is clear that only the vertical scales should be
used for measuring distances.
The vertical
scale depicted on the right demonstrates the distortion. While the two
little grey markers have the same size, the upper one measures only 0.71
degrees. So, distances (in miles or in minutes) should not only be read on
the vertical scale, but also at approximately the same height.
The horizontal scale is only valid for one
latitude in the chart and can therefore only be used for the coordinates
(a point, but not a line). If you divide the surface of the earth in eight
pieces, and lift one out and project it, you end up with the figure below.
The result is that both AA' and BB' are now as long as the bottom of the
chart and are 'too long'.
But there are of course other
projections in use by sailors. An important one is the
Stereographic projection which is constructed
by projecting on a flat plane instead of a cylinder. On this chart
parallels appear as slightly curved and also the meridians converge at
high latitudes. So, strictly speaking, a straight course will not appear
as a straight line in the chart, but the parallels remain perpendicular to
the meridians. Most often, distortions are scarcely noticed when this
projection is used to chart a small area. Like the mercator projection,
the vertical scale represents a meridian and should be used for measuring
distances.
Another projection is the Gnomeric projection
on which the meridians are again converging. But most importantly, the
parallels are arcs of a circle while great circles appear as straight
lines. On a sphere the shortest route between A and B is not a straight
line but an arc (part of a great circle). Though this is also true when
you for example cross a little bay, we use for simplification a
Loxodrome (a handy straight line on your
mercator chart which does not reflect your shortest route). On a Gnomeric
chart this same loxodrome is an arc, while your shortest route (a great
circle) ends up as a straight line. Hence, the gnomeric projection is
particularly useful when sailing great circles (like when you dabble in
circumnavigation) and is clearly beyond the scope of a coastal navigation
course.
Organization of the
Chart

