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of velocities, discussed below.
First, however, we need to get
acquainted with the Earth, which is
not actually round, but flatter at the
Poles than at the Equator. For our
purposes, though, and the
mathematical models inside the
average GPS, it is a sphere.
To help find your position, a series
of lines is drawn from Pole to Pole
through the Equator, called lines of
longitude. They may also be called
meridians, when split in half, and by
convention are drawn for every
degree you go round the Equator.
Also, by convention, they start at
Greenwich, in London, England
(with the Prime Meridian at 0°), and
are calculated to 180° East or West:
The opposite side to any meridian is
its anti-meridian.
Since the Earth takes 24 hours to
spin on its axis, 15 lines of longitude
represent 1 hour, and it is noon
when the Sun is overhead any
particular meridian. The spinning is
anticlockwise when viewed from the
top of the Earth, so the Sun will
appear to rise from the East and set
in the West.
however, is not enough, since you
could be anywhere on it, so more
imaginary horizontal lines are drawn,
parallel to each other, North and
140 JAR Private Pilot Studies
South of the Equator, up to 90° each
way, called lines of latitude. Now you
can get lost more accurately! The
latitude of any point is the arc of the
meridian between the Equator and
the parallel through the point:
Latitude lines are always parallel to
each other, whereas longitude lines
(meridians) converge. They are also
fixable by natural means - the Sun,
Moon and planets pass over the
Equator, for example, and the
tropics of Cancer and Capricorn
represent the limits of the Sun's
travel North and South as it rises
and sets every day (it sets further
South each day, until, on December
21st, it stops for three days to go
North again. On June 21st, it stops
going North to go South).
Ptolemy had plotted some sort of lat
& long system by 150 AD, but he
used the Canaries for the Prime
Meridian, which has also been at the
Azores, Cape Verdi, Rome and Paris,
to mention but a few (it wouldn't
surprise me to learn the Ancient
Egyptians used the pyramids).
Eventually, it was placed in
Greenwich, because King George
was a keen astronomer.
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 nautical mile is the
distance covered by 1 minute of
latitude, but it varies slightly between
the Poles and the Equator because
the Earth bulges in the middle (6080
feet is used, but it 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).
Since we take 24 hours to go round
the Sun, in one hour, we move
through 15°, or we take 4 minutes to
go through 1°. Similarly, in 1 minute
we transit 15 minutes, or take 4
seconds to go through 1 minute.
Just to remind you, a degree is split up
into minutes, which in turn are split
into seconds. Also, meridians diverge
in the Southern Hemisphere.
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
Navigation 141
latitude are rhumb lines, but the
Equator is a great circle as well (lines
of latitude are also small circles).
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°,
　
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