Navigation - Basic Terminologies

 Navigation - Basic Terminologies 

 In this topic you will be introduced to the elements of navigation, some of which go back many hundreds of years. Terrestrial and coastal navigation has been practiced as long as man has gone out on the water. The vessels involved did not venture far from the coast. Celestial navigation - navigation by the movement and the position of heavenly bodies - evolved gradually for navigation when out of sight of land. Modern technology has reached a level at which much navigation is automated, but the need to ensure a safe ship demands constant awareness of surroundings and looking out for risk.

 Shape of Earth

The shape of the earth was long known to be spherical as per Aristotle and Pythagoras; the reason for their suggestion was based on the observation that it caused curved shadows during the lunar eclipses.
About two thousand years later Sir Isaac Newton suggested that the earth was not a perfect sphere but flattened at its poles (axis of rotation).  He also noted that the earth’s shape is an oblate spheroid. The difference in axes is said to be about one part in three hundred. This means the earth's equatorial (the equator divides the earth in two equal parts as the northern and southern hemispheres) diameter is 7926 miles and the polar diameter is 7900 miles. This 26 miles difference is due to the oblate shape.
The oblate shape slightly complicates geographical matters concerning the calculation of heights of mountains and high structures; therefore the heights are measured with respect to sea level.
The following media explains about the Earth

Great Circle, Small Circle

GREAT CIRCLE
A great circle is a circle on the surface of a sphere whose plane passes through the centre of the sphere.
Note

• A great circle divides the sphere into two identical parts, each called a hemisphere.

• The radius of a great circle is equal to that of the sphere.

• Any number of great circles could pass through a given point on the surface of the sphere. However, all these great circles would also pass through a point diametrically opposite to the given point.

• Only one great circle can pass through any two given points on the surface of a sphere. However, if the two points are diametrically opposite to each other, any number of great circles can pass through the two points.

Pole of a Great Circle

The pole of a great circle is a point on the surface of the sphere which is equidistant and hence ninety degrees away from all parts of the circumference of the great circle. Each great circle would therefore have two poles which are situated diametrically opposite to each other. 

SMALL CIRCLE

A small circle is a circle on the surface of a sphere, whose plane does not pass through the centre of the sphere. The radius of a small circle is less than that of the sphere.

  

The following media explains about the great circle 

The following media explains about the small circle

Spherical Triangle

A spherical triangle is a figure formed on the sphere (in this case the earth sphere) by three great circular arcs, all less than 180 degrees. The sum of the angles is not fixed but will be always greater than 180 degrees, intersecting pair wise in three vertices. It is an off-shoot of planar triangle geometry. If any side of the spherical triangle is exactly 90 degrees it is termed quadrantal. The sine rule and cosine rule formulae are used to calculate the sides and angles.

SPHERICAL ANGLE 

A spherical angle is an angle on the surface of a sphere, formed by the intersection of two great circles. 

NOTE 

• In practice, a spherical angle can be measured by drawing tangents to the two great circle arcs from the point of intersection. The value of the angle between the tangents is the magnitude of the spherical angle. 
• The maximum value of a spherical angle is two right angles (180 degrees). 
• Vertically opposite angles are equal. 

SPHERICAL TRIANGLE

A spherical triangle is a triangle on the surface of a sphere, formed by the intersection of three great circles. 

PROPERTIES OF SPHERICAL TRIANGLES 

The magnitude of the side of a spherical triangle is the angle subtended by it at the centre of the sphere and is expressed in degrees and minutes of arc. 

• The maximum value of a side of a spherical triangle is 
• The maximum value of an angle of a spherical triangle is
• The sum of the three sides of a spherical triangle is less than
• The sum of the three angles of a spherical triangle is any value between two right angles and six right angles (i.e., between  and ). 
• The sum of any two sides of a spherical triangle is greater than the third. 
• The greater side has the greater angle opposite to it. 
• If two sides of a spherical triangle are equal, the angles opposite to them are also equal to each other. 
• A right angled spherical triangle is one in which one angle equals to  In a spherical triangle, it is possible for more than one angle to be equal to  
• A quadrantal spherical triangle is one in which one side equals to  In a spherical triangle, it is possible for more than one side to be equal to
• A spherical triangle which is not a right angled or a quadrantal one is called an oblique spherical triangle. 

SYMMETRICAL SPHERICAL TRIANGLES

Two spherical triangles are said to be symmetrically equal when each of the six elements (i.e. three sides and three angles) of one are equal in value to each of the six elements of the other. 

Because spherical triangles lie on the surface of a sphere, and are hence three dimensional, 'symmetrically equal' does not necessarily mean congruent. Two triangles are said to be congruent only if it is possible to superimpose one on the other. 

ABC and DEF are two spherical triangles as seen from outside the sphere. All six elements of triangle ABC are correspondingly equal to the six elements of triangle DEF. However the triangles are latterly inverted (are mirror images) and, both being convex, it is not possible to superimpose one on the other. The two triangles are, therefore, symmetrically equal but not congruent. 

Two spherical triangles are symmetrically equal if

• Three sides of one are correspondingly equal to the three sides of the other. 
• Two sides and the included angle of one are respectively equal to the two sides and included angle of the other.
• Three angles of one are respectively equal to the three angles of the other.
• Two angles and the included side of one are respectively equal to the two angles and included side of the other.

Earth's Axis

The earth rotates on its own axis and at the same time revolves around the sun in a elliptical orbit. 

The axis of rotation is not perpendicular to the plane of the orbit and instead it is inclined by an angle of 23.5° to the vertical. 

The earth’s axis maintains its orientation in space i.e. it keeps pointing in the same direction with respect to space. 

This fixed orientation and the tilt of the axis causes different seasons as the earth orbits around the sun. 

When the north end of the axis is tilted towards the sun, the northern hemisphere experiences summer and the southern hemisphere experiences winter. 

The opposite happens when the north end of the axis is tilted away from the sun.

Poles

North Pole

The north pole is located in the middle of the Arctic Ocean  and is known as the geographic (true) north pole or terrestrial north pole. It is the point in the northern hemisphere where the earth’s axis of rotation meets the surface of the earth.

South Pole

It is the opposite. The south pole is also known as the terrestrial or true south pole. It is one of two points where the earth’s axis of rotation intersects its surface.

The following media explains the poles

Magnetic Poles

The earth acts as a giant magnet with its magnetic poles close to the axis of rotation of the earth. The earth’s magnetic field has a more complicated shape than that due to a bar magnet. The north magnetic pole to which the compass needle points is located at a point on Ellesmere Island in North Canada. The difference is about 500 km between the true north and the north magnetic pole. The south magnetic pole is located in Antarctica. The magnetic poles are moving slowly.

Equator

An imaginary circumferential line on the earth’s surface equidistant from the true north and south poles, dividing the earth into the northern southern hemispheres. It is about 40,075 km long and passes though 13 countries. 78.7% of the line lies across the water and 21.3% across land. The plane of the equator passes through the center of the earth. It is also the reference for measuring latitudes and is a great circle.

Meridians

A meridian is the half of a great circle drawn on the earth's surface from the true north pole to the true south pole. A meridian is also called a line of longitude and is half of a great circle. The meridians converge at the poles. 

The following media illustrates the meridians

Latitude and Parallels of Latitude

Parallels of latitude are small circles on the surface of the earth whose planes are parallel to the plane of the equator. They used as reference to measure latitude of a vehicle, place or a person.

Latitude is one of the two co-ordinates used to indicate the position of a person, a place or a ship. It is measured from 0 to 90 degrees from equator to the pole named north or south. Hence 0 degree latitude indicates all places along the equator, 90^°S latitude denotes the geographic south pole and 90^°N denotes the geographic north pole.

Latitude of a place can also be defined as the measure of arc of the meridian contained between the equator and the parallel of latitude passing through that place. 

The above definition will hold good in all parts of the earth if it was a perfect sphere. But we already know that the earth is very slightly deformed from a perfect spherical shape and is called an oblique spheroid. The latitude of a place can be measured in two ways and the two values are close but do not exactly match. The latitude obtained by these two methods is known as geographic latitude and geocentric latitude.

The geocentric latitude is defined as the angle at the centre of the earth subtended and contained between the equator and your parallel of latitude.

The geographic latitude is defined as the angle at which a vertical line to the surface of the earth at your position meets the plane of the equator. This vertical does not always meet the plane of the equator at the centre.

The latitude co-ordinate of a position is normally expressed in the format  XX^° XX.X^’ N/S.

For example: 35^° 24.2^’N or 63^° 51.8^’S

The following media illustrates the parallels of latitude

The following media illustrates latitude

Prime Meridian

We require two co-ordinates to denote a position on the earth’s surface. One of them is latitude and the equator is taken as the zero reference for measuring latitudes. Similarly, in the case of longitude, one meridian must be assigned as zero reference for measuring longitudes. 

The prime meridian is that meridian which is assigned as the zero line of longitude. The prime meridian and it’s anti-meridian together form a great circle and this great circle divides the earth into two halves namely the eastern hemisphere and the western hemisphere.

The prime meridian is basically arbitrary and many regions had their own conventions throughout history. In 1851, the meridian based at the Royal Observatory, Greenwich was established by Sir George Airy as the prime meridian and is now accepted worldwide. It is also referred to as the Greenwich meridian.

The following media illustrates the prime meridian

Longitude

Longitude is one of the two co-ordinates of a place. It can be defined as the measure of the arc of the equator contained between the prime meridian and the meridian passing through that place. It is named east or west depending upon whether that place lies to the east or to the west of the prime meridian. A value of longitude cannot be more than 180 degrees. If a place is 190 degrees east of the prime meridian, it will be referred to as 170^°W and not as 190^°E. 

The longitude co-ordinate is normally expressed in the format XXX^° XX.X^’ E/W.

For example: 008^° 24.6^’W or 157^° 18.5^’E

The following media illustrates longitude

Difference of Latitude and Difference of Longitude

D’Lat, or difference in latitude, is the number of degrees by which two parallels of latitude are separated from each other. The D’Lat can also have a name N/S depending upon whether a vessel is changing its latitude in the northerly direction or in the southerly direction.

D’Long, or difference in longitude, is the number of degrees by which two meridians are separated from each other. The D’Long can also have a name E/W depending upon whether a vessel is changing its longitude in the easterly or in the westerly direction.

Comparison of latitude and longitude

LATITUDE	LONGITUDE
Direction is from east to west	Direction is north to south
Parallel to the Equator	Converging at the poles and widest at the Equator
Range 0 to 90° North or South	0 to 180° East or West
Denoted by Greek letter φ phi	Denoted by Greek letter lambda (λ)
All locations along a common latitude fall in same hemisphere	Locations along a common longitude may be in different hemispheres
Denotes distance from north or south of equator	Denotes distance from prime meridian east or west
Location of same latitude does not fall in same time zone	All locations on same longitude fall in same time zone
No of lines are – 180	No of lines are – 360
Classifies temperature zones	Classifies time zones
Besides the equator four other parallels are of Importance. They are Arctic Circle, Tropic of Cancer, Tropic of Capricorn, Antarctic Circle.	The important longitudes are the Prime Meridian at 0 degrees and the International Date Line at 180 or nearly 180 degrees.

Geographical, Statute and Nautical Mile

Geographical mile

A geographical mile is the linear unit of length spanned by 1 minute of arc along the earth’s equator. In SI units it is 1855.3 metres. It is 800 feet longer than the statute mile. 

Statute mile

A unit of distance measured on land equal to 1760 yards, approximately 1.609 kilometers.

Nautical mile 

A nautical mile or a sea mile is a unit of distance set by international agreements as being exactly 1852 meters (about 6076 ft); it was defined as the distance spanned by one minute of arc along a meridian of the earth (north – south) and developed from the sea mile. It is a non SI unit. It is used by navigators at sea and air. It is arrived at as follows: 

Approximate circumference of the earth = 40000 kms; hence 360 degrees = 40000 kms on equator.

1 degree = 40000/360 = 1.852kms.

     1 km = 0.54 nautical mile.

Most nautical charts use the mercator projection whose scale varies by about a factor of 6 from the equator to 80 degrees latitude. The nautical mile is nearly equal to a minute of latitude on a chart; therefore the distance measured with a chart divider can be roughly converted to nautical miles using the chart’s latitude scale. The standard symbol is nm.

Comparison with Kilometre

The reference for defining the length of one kilometer is taken from the earth. It was first defined by the French Academy of Sciences in 1791.

Measure the distance from the equator to the north pole along a great circle which also passes through Paris, then divide it by 10000. You have the length of the traditional unit of one kilometer. 

1 nautical mile = 1.852 km

1 geographical mile = 1.855 km

1 statute mile = 1.609 km

If you were to travel around the earth along the equator, the distance would work out to be 21600 nm (or) 40003 km

Cable and Knot

Knot  

The knot is a unit of speed used by navigators of one nautical mile per hour or 1.852 km/hour or 1.151 mph. The standard symbol is kn. 

Cable

The cable is a nautical unit of length, equal to one tenth of a nautical mile or 185.2 meters or also it is termed as 100 fathoms. The unit is named after the length of a ship’s anchor cable in the age of sailing ships.