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well away from buildings, etc. set
aside for this purpose. Allowing for
deviation is called compensation.
Maps & Charts
The words map and chart are
nowadays used interchangeably but,
officially, a chart will show parallels
and meridians with minimum
topographical features, and be used
for plotting. A map will show greater
detail of the Earth's surface.
The point about them both is that
their representation of the Earth's
surface is only accurate within a
relatively small area, since you are
trying to show a 3 dimensional
object on a 2 dimensional surface.
The further from the centre of projection
you go, the more the distortion is
but, to all intents and purposes, it
can mostly be ignored. You can see
the problem if you flatten a globe:
There are many ways of
compromising for this, and each
suits a different purpose, so lines
drawn on maps based on different
projections will not cross through
the same places.
The quality of orthomorphism, that all
charts should strive for, means the
scale must be correct on all
directions within a very small area.
In addition, parallels must always
cross meridians at right angles.
Otherwise, no chart is perfect, as
you will find when you fold them:
Lambert's Conformal
Imagine the Earth with a light
shining at the centre, then place a
cone on the top. Where the cone
meets the earth, the shadows of the
land formations will be accurate, but
will be out of shape the further
North and South you go.
This is the conic projection, the basis of
the Lambert Conformal, and is what
most of the charts used today are
based on, as the meridians will be
straight, even if they converge
towards the North:
Great circles are assumed to be
straight lines (actually they are very
shallow curves), and rhumb lines will
144 JAR Private Pilot Studies
be curves concave to the nearer pole.
Johannes Lambert overcame the
problem of scale expansion in the
18th century by pushing the
imaginary cone further into the
Earth's surface, so it cuts in two
places:
This gives it two Standard Parallels, or
points where scale is correctly
shown. To be sure, there is a slight
contraction between them, but this is
considered insignificant (1% or less)
if two-thirds of the chart are
between the Parallels.
Mercator
The Mercator projection does things
differently. Instead of a cone, the
Earth is surrounded with a vertical
cylinder, touching at the Equator.
Meridians now do not converge, so
rhumb lines will be accurate, but
distance between latitude lines
increases away from the centre (not
significant below about 300 nm, but
always use the scale near the distance
to be measured):
Again, shapes will be accurate where
the cylinder touches the surface, but
the distortion will be much greater
the further away (as a point of
interest, Mercator was the first chart
to be used for maritime navigation in
the 16th century). Since rhumb lines
on this projection are straight lines, it
follows that great circles must be
curved, in this case, concave to the
Equator, that is, the rhumb line is
always nearer the Equator.
The rhumb line looks shorter than
the great circle because of scale
expansion. The relevance of this lies
with plotting radio bearings, because
radio waves take the shortest way
(e.g. great circles), so long distances
need the conversion angle to be
applied to plot them as straight
rhumb lines – in fact, an ABAC scale
on the chart will do this for you.
Complications also arise from
whether the plot is done at the
aircraft (ADF) or the station
(VOR/VDF), but we won't go into
that here.
Navigation 145
The Mercator projection is the one
mostly used for plotting charts, as
constant headings are easier to use.
Transverse Mercator
This is a horizontal cylinder
projection, and a straight line still
represents a great circle. The Central
Meridian (CM), where the cylinder
touches the sphere, coincides with
the relevant latitude, so True North
and Grid North are the same along
it. However, because rectangular grid
lines are drawn based on the CM,
moving East or West means
applying some sort of grivation (see
below). A scale factor also has to be
applied as you move around the map
to convert ground distances to
measured distances. To reduce this,
the projection uses two North-South
　
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