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NAVIGATION
STEERING A CRAFT IS A COMPLEX BUSINESS.
ESPECIALY WHERE THERE ARE NO MARKED ROADS OR VISIBLE
LANDMARKS
NAVIGATION
Navigation is the science of directing a craft by determining its position, course and
distance travelled. It is concerned with finding the way, avoiding collision, conserving
fuel and keeping time. In ancient times, people found their way over land and sea by
sighting the sun and stars.
A long time ago the Chinese discovered that a piece of iron ore, known as a
lodestone, when floated on water, always pointed north.
Pytheas, a Greek explorer in the 4th Century B.C. sailed far enough north to
discover the legendary Thule which inspired Virgil to create the concept of Ultima
Thule, the 'uttermost point attainable'.
'Farthest Thule', where day and night each lasted for six months, and the sea was
thick and impenetrable.
It may have been Iceland, or Norway, or the Shetlands.
There is a place marked Thule in north-west Greenland and is the name given to a
highly developed and specialized pre-historic Eskimo culture.
Pytheas pobably determined his course by throwing overboard a small log tied to a
knotted line which as it drifted astern and the line was payed out, the number of
knots, the number of knots that were payed out while an hourglass emptied gave the
speed of the vessel.
Mariners also used the log and line to determine course.
Starting from a known point, the navigator noted his direction of travel from his
compass and drew a line on his chart to represent his course.
Along the course he marked off the distance (speed times time) as determined
from the log.
The calculation of his position by this method was known as deduced reckoning,
later shortened to dead reckoning.
Navigators still check their position by the sun and stars.
The sextant enables a navigator to determine his ship's longitude
by exact measurements of the stars' positions. This requires
knowing the position that the stars reach above the Earth at
a certain time - requiring an accurate means of meassuring time.
Now precise time signals are brooadcast by radio.
Latitude is determined by taking angle sights of certain pole
stars or the angle of the Sun above the horizon.
A grid framework formed by a combination of meridions of longitude
and parallels of latitude established a means by which exact
positions on Earth can be determined.
Today a knot is fixed as one nautical mile per hour;
a nauticle mile is equal to one minute of arc of latitude,
or 6.076 feet (1.852 metres).
LATITUDE AND LONGITUDE
Laitude and longitude is a coordinate system
by means of which
the position or location
of any place on Earth's surface
can be determined and described.
Given in degrees, minutes and seconds,
geographical latitude
is the arc subtended
by an angle at the centre if the Earth
and measured poleward
in a north-south direction
from the equator.
As aids to show different latitudinal positions on maps or globes
equidistant cicles are plotted and drawn parallel to the equator and each other;
they are called parallels or parallels of latitude.
Different methods are used
to determine geographical latitude,
as by taking angle-sights
on certain polar stars
or by measuring with a sextant
the angle of the noon Sun above the hoizon.
The length of a degree of arc of latitude
is approximately 111 kilometers (69 miles)
longitude is a measurment of location east or west
of the prime meridian at Greenwich,
the specially designated imaginary north-south line
that passes through both geographic poles and Greenwich, London.
Measured also in degrees, minutes and seconds,
longitude is the amount of arc
created by drawing first
a line from the centre of the Earth
to the intersection of the Equator
and the prime meridian
and then another line
from the centre of the Earth to any point
elsewhere on the Equator.
Longitude is measured 180 degrees
both east and west of the prime meridian.
As aids to locate longitudinal positions
on a globe or a map,
meridans are plotted and drawn
from pole to pole where they meet.
The number of miles per degree of longitude
at the Equator is about 111.32 kilometers (69.17 miles)
and the poles, 0.
The combination of meridians of longitude
and parallels of latitude
establishes a framework or grid
by means of which
exact positions
can be established\determined
in referrence to the prime meridian and the Equator
(Because the lines of longitude
gradually draw closer together
towards the poles
the number of miles per degree of longitude
gradually diminishes from 69.17 at the Equator
to 0 miles at the poles.)
Gee! What an Odyssey.
In the 3rd Century B.C.
A Greek called Eratasthenes
Became the founding father
Of Geodesy
(funnily enough pronounced G-Odyssey)
When he calculated the circumference of the Earth
To within 15% accuracy.
He used a simple principle
of estimating the size of a great circle
passing through the North and South Poles.
Knowing the length of an arc (1)
and the size of the corresponding central angle(a) that it subtends,
one can obtain the radius of the spere
from the simple proportion
that length of arc to size of great circle
(or circumference, 2piR, in which R is the Earth's radius)
equals central angle to the angle subtended
by the whole circumference (360degrees) 1:2piR=a deg:360deg)
In order to determine the central angle a.
Eratasthenes selected the city of Syene
(the modern Aswan on the Nile)
because there the Sun in midsummer
shone at noon vertically into a well.
He assumed that all sunrays reaching Earth
were parallel to one another,
and he observed that the sunrays
at Alexandria at the same time
(midsummer at noontime) were not verticle
but lay at an angle 1\50
Of a complete revolution of the Earth
away from the zenith.
Possibly using the travel time of a camel caravan
between Alexandria and Syene,
he estimated the distance (1) between these two cities
to be 5,000 stadia.
From the above equation he obtained for the length of a great circle,
50 by 5,000=250,000 stadia, which,
using a plausible contemporary value for the stadium (185 metres),
is 46,250,000 metres (152,000,000 feet).
The result is about 15% too large
in comparison to modern measurement,
but his is extremely good considering the assumptions
and the equipment with which the observations were made.
The second known determination
was made by Poseidonus (1st Century BC)).
He used the distance between Alexandria and Rhodes Island,
where the star Canopus was on the horizon at the same time
that it was 1\48th of a complete revolution of the Earth
above the horizon in Alexandria.
The distance was estimated using the time it took
a sailboat to travel between these two points
He encountered many proplems,
such as those caused by refraction
but his result was only 11% too large.
CELESTIAL NAVIGATION
Is the use of observed positions
of celestial bodies
to determine a navigator's positiion.
At any moment some celestial body
is at the zenith
of any particular location
on Earth's surface.
This location is called the ground position (GP)
GP can thus be stated
in terms of celestial coordinates,
with the declination of the celestial object
equal to latitude
and the Greenwich hour angle
equal to longitude.
Almanacs such as those published by the Nautical Almanac Office
of the U.S. Naval Observatory provvide these coordinatesss for
the Sun, Moon and planets (or navigator's stars); the tabulation
are given in terms of Greenwich Civil Time.
From this information a line of position can be plotted.
In principle, the line could be drawn on a very large sphere,
but, in practice, a Mercator chart, or plotting sheet, is used.
The navigator then uses a sextant or bubbles octant
to measure the altitude of the celestial object
and records this altitude using Greenwich Civil Time.
The navigator estimates his positiion,
this being the dead-reckoning position.
The altide and the bearing
that the celestial object would have
at this position
are calculated or taken from tables.
The dead-reckoning position
is marked on a plotting sheet
and a line drawn
in the direction
of the celestial object's calculated bearing.
From this information
and from the difference between
the observed and computed altitudes
of the celestial object,
known as the intercept,
the position of the navigator
can be calculated.
CELESTIAL SPHERE
Is the apparent surface of the heavens,
on which the stars seem to be fixed.
For the purpose of establishing
coordinate systems to mark
the positions of heavenly bodies,
it can be considered a real sphere
at an infinite distance from Earth.
The Earth's axis, extended to infinity,
touches this sphere
at the north and south celestial poles,
around which the heavens seem to turn.
The plane of the Earth's Equator,
extended to infinity,
marks the celestial equator.
The position of the observer is at its centre.
As a result of Earth's rotation from west to east,
the celestial sphere seems to turn from east to west.
ASTRONOMICAL ZENITH.
The point on the celestial sphere
located directly above the observer,
at 90degrees distance from the horizon,
and amounts to the extention
of a plumb-line to the celestial sphere.
GEOCENTRIC ZENITH.
The point on the celestial sphere
marking the extention of a line
connecting the point of observation
with the centre of the Earth.
Since the Earth is a spheroid
rather than a sphere,
these two points do not coincide.
DECLINATION.
The co-ordinate in the equator system (delta
)
which is the measure of the angular distance
of a body from the celestial equator.
Declination is measured positively (plus)north
and negatively (minus) south
of the celestial equator from 0 degees to 90 degrees.
HOUR CIRCLE
A great circle
in the equator system which passes through
a specified point
on the celestial sphere
and the celestial pole.
Declination is measured along hour circles.
HOUR ANGLE
The angle between the hour circle of a star
and the celestiall meridian.
It is the arc measured westward from the meridian
from 0 hour to 24 hours