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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 (luckily, not in the exam) 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.
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
lines with a scale factor of 1, so in
the centre the correction is less
than 1 (0.9996 for the UTM), while
the outer parts have it greater than 1.
The WAC at 1:1,000,000 and the
VNC at 1:500,000 are based on a
two-parallel Lambert Conformal
Conic, whereas the larger scale VTA
at 1:250,000 uses Transverse
Mercator (the Vancouver VTA
covers a bit over 2° of longitude).
The Transverse Mercator's
advantages include accuracy (over
small areas, at least). Wide countries
are split into zones usually no wider
than 6° of longitude, at which point
the distortion becomes unacceptable.
Universal Transverse Mercator
UTM is a metric grid system based
on Transverse Mercator, designed by
the US military, using 60 6°
longitude zones and 20 8° latitude
bands between 80° S to 80° N,
giving 1200 areas overall. Longitude
zones are numbered 1-60 starting at
180°W. Latitude bands are lettered
from C (excepting I and O)
Northwards from 80°S. Each 6° by
8° area has its own grid, based on
100,000 m squares. Each column
and row is lettered, and when the
numbers are used, Eastings are given
first.
Polar Stereographic
These charts are used in polar
regions, because the others cannot
cope with convergence that well. To
get the details correct, the paper is
held flat over the top of the Pole and
the imaginary light projected straight
up from the centre of the Earth to it:
146 Canadian Private Pilot Studies
On these, rhumb lines are not the
shortest course, and you must use
great circles instead. Since they are
straight lines, meridians are crossed
at different angles.
The Arctic
Up there, it’s darker for longer and
there are fewer navaids. The
compass begins to get unreliable,
and there is increased deviation due
to the aircraft's own magnetic field.
Scale
Assuming a constant scale, the ratio
between distances on a map and the
Earth's surface is expressed as a scale
based on the map's size. For a scale
of 1:500,000 (commonly referred to
as a half-mil), one inch on the map is
equal to 500,000 inches on the
Earth. There are 63,360 inches to the
mile, so an inch on a half-mil map is
7.89 statute miles.
You can tell which chart has a larger
scale by looking at the representative
fractions, obtained by dividing chart
distance by Earth distance. Thus, a
chart distance of one inch divided by
its Earth equivalent of 13.7 nm
would be a 1/1000000 map, and of a
smaller scale than a 1/500000.
A "one-inch map" means one that
uses one inch for one mile. A
"quarter inch map" has 4 miles to
the inch (about the length of the
distance between the joint on your
thumb and the tip, for quick
reference). Not everything on the
map is done to this scale; if it were,
you would hardly see roads and
railways, so they are artificially
expanded to be visible. The centre of
any object is its actual position.
If you need to find out what Earth
distance is represented by a chart
distance, multiply the chart distance
by the scale. For example, if asked
　
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