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When giving position, latitude is
always given first, as in 45°N,
163°W. The distance between
parallels of latitude is 60 nautical miles,
because 1 nm is the distance
subtended by 1 minute of latitude,
but it varies slightly between the
Poles and the Equator because the
Earth bulges in the middle (6108 and
6046 feet, respectively, but 6080 is
used for calibration, and is actually
only correct at 48° latitude). One
minute of longitude, however, will
only be 1 nm at the Equator, due to
convergency (the distance between
meridians gets smaller toward the
Poles). You can find the true length
by multiplying the change of
longitude (in minutes) by the cosine
of the latitude, so at 60°, the distance
between meridians is 30 nm (this is
called the departure formula).
Great Circles & Rhumb Lines
Great Circles have planes that go
through the centre of the Earth, or,
in other words, are circles whose
radius is that of the Earth, so the
definition includes lines of longitude
and the Equator. Since meridians are
half lines of longitude, they are semigreat
circles. Although they are the
shortest distance between two
points, the angle created when they
cross meridians changes
(convergency again), so your course
is continually under review.
Rhumb Lines, on the other hand, cut
each meridian at the same angle, but
they are not straight (they are
concave toward the nearer Pole), so
are longer in distance. All lines of
latitude are rhumb lines, but the
Equator is a great circle as well (lines
of latitude are also small circles).
Navigation 311
Convergency
Convergency is the angle of inclination
between two meridians, or the
difference between great circle tracks
measured at two points (transfer one
meridian to the other and measure
the angle). In the diagram below, the
great circle lies between 60°N, 30°W
and 60°N, 30°E:
The 30°W meridian has been
transferred across from its original
position. The difference between the
measurements at the start and end
points is the earth convergency. To
calculate it, take the change of
longitude and multiply it by the sine
of the mean latitude. It's handy when
plotting radio bearings, which are
great circles, against tracks, which
use rhumb lines.
The conversion angle is the difference
between the rhumb line and great
circle between two points – it is half
the convergency. At the halfway
point, the two are parallel, which is
why you should measure your track
at the mid-point if you use a chart
where straight lines are great circles.
However, the difference between
them is not worth worrying about
below 1,000 miles, considering the
convenience of being able to steer
one track. Just split up a journey
longer than that into 1,000-mile
stage lengths.
Direction
This is always expressed with
reference to True North, that is,
ignoring any magnetic effects from
the earth itself. A bearing is the
clockwise angle between North and
any line between two points.
In the above case, B is on a bearing
of 044° from A, in relation to North.
The opposite is the reciprocal, quickly
found by adding or subtracting 180°,
that is, 224°.
Magnetic Bearings
One problem is that a compass does
not point towards True North, but
Magnetic North, since the Earth
generates its own magnetism – and
the two Norths (or Souths) do not
coincide at their respective Poles.
The next is that the magnetic force is
not constant over the globe – it may
be varied by local deposits of metals
under the ground, for example, and
bend the magnetic flux lines. The
way to Magnetic North will
therefore vary from place to place.
In addition, the lines of force will be
vertical near the poles:
312 Canadian Professional Pilot Studies
The North Magnetic Pole was
discovered by Soviet explorers to be
the rim of a magnetic circle 1000
miles in circumference:
It is approximately 600 miles from
the true Pole.
On a map, which is drawn initially
for True North, there is a dotted line
called an isogonal that represents the
local magnetic variation to be
applied to any direction you wish to
plan a flight on:
It is westerly where the variation is
to the left of the meridian, and
Easterly when to the right. It also
changes every year, since the
magnetic pole moves East, about
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