Showing posts with label great circle routes. Show all posts
Showing posts with label great circle routes. Show all posts

Monday, June 3, 2013

Latitude

Latitude is the angular distance of a point on the earth's surface, measured in degrees from the centre of the earth. It is parallel to a line, the equator, which lies midway between the poles. These lines are therefore called parallels of latitude, and on a globe are actually circles becoming

Longitude

Imaginary lines running north/south at right angles to the parallels and passing through the poles are known as lines of longitude or meridians. The line of longitude passing through Greenwich (London) is 0 degrees or the prime meridian (so called because all lines of longitude are numbered east or west from it). The longitude of a place is its angular distance east or west of the Greenwich meridian, measured at the centre of the earth. There are 180 degrees of west longitude and similarly 180 degrees of east longitude. However, since there are 360 degrees in a circle. 180 degrees East and 180 degrees West must be one and the same line. Since the earth is spherical and has a circumference calculated at 40,232.5 km, in linear distance each of the 360 degrees of longitude is 40,232.5/360 or 111.757 km. As the parallels of latitude become shorter polewards, so the meridians of longitude, which coverage at the poles, enclose a narrower space. The degree of longitude therefore decreases in length. It is longest at the equator where it measures 111.318 km. At 25 degrees it is 100.95 km; at 45 degrees it is 78.856 km; at 75 degrees, 28.967 km; and at the poles 0 km. There is so much difference in the length of degrees of longitude outside the tropics, that they are not used for calculating distances as in the case of latitude. But they have one very important function, they determine local time in relation to G.M.T. or Greenwich Mean Time, which is sometimes referred to as World Time.
THE POSITION OF A PLACE
It is necessary to be precise in stating the position of a place in degrees, since there are two latitudes X degrees (X degrees North and X degrees South). Similarly, longitude Y degrees refers to either opposite meridians unless we state it as Y degrees east and Y degrees west.

Longitude and Time

LOCAL TIME. Since the earth makes one complete revolution of 360 degrees in one day or 24 hours, it passes through 15 degrees in one hour or 1 degrees in 4 minutes. The earth rotates from west to east, so every 15 degrees we go eastwards, local time is advanced 1 hour. Conversely, if we go westwards, local time is retarded by 1 hour. We may thus conclude that places east of Greenwich see the sun earlier and gain time, whereas places west of Greenwich see the sun later and lose time. If we know G.M.T., we merely have to add or subtract the difference in the number of hours from the given longitude. A simple memory aid for this will be East-Gain-Add (E.G.A.) and West-Lose-Subtract (W.L.S.). You could coin your own rhymes for the abbreaviations. The local time for Lagos (3 degrees east) will be 12 minutes ahead of London or 12.12 p.m. But the local time for New York (74 degrees west) will be 4 hours 56 minutes behind London or 7.04 a.m. We can put it in another way: when Londoners and Nigerians are having lunch, New Yorkers will have breakfast. This is difficult to believe, but it is true. The rotation of the earth round the sun means that at any point in time different places are experiencing a different time of day.
HOW TO CALCULATE LOCAL TIME
1. Work out the longitude difference.
2. Convert this to a time difference.
3. Adjust the time according to the direction of movement (east or west).
Example. What is the time in Calcutta (longitude 96 degrees east) when it is 9.00 a.m. in Munich (longitude 11 degrees east)?
1. Longitude difference = 85 degrees
2. Time difference 85/15 = 5 hours 40 minutes
3. Calcutta is east of Munich, therefore the time is ahead. Thus 9.00 a.m. plus 5 hours and 40 minutes = 2.40 p.m.
There are many ways of determining the longitude of a place. The simplest way is to compare the local time with G.M.T. by listening to B.B.C. radio. For example, the captain of a ship in the midst of the ocean wants to find out in which longitude his ship lies. If G.M.T. is 8.00 a.m. and it is noon in the local region, it means that he is four hours ahead of Greenwish, and must be east of Greenwich. His longitude is 4 x 15 degrees or 60 degrees east.

Great Circle Routes

Since the earth is spherical in shape, the shortest distance between any two points on the globe lies along its circumference. There are an infinite number of great circles of equal length running around the globe, e.g. the circle formed by the Greenwich Meridian and the 180 degrees meridian; the circle formed by the 130 degrees west and 50 degrees east meridians. Of the lines of latitude, only the equator is a great circle.
When drawn on a globe great circles appear as straight lines, but when they are drawn on flat maps of the world they may not appear so. In fact on many maps great circles appear curved and routes along a straight line joining two places. This is an illusion created by the distortion of the shape of the earth to allow it to be drawn on a flat map.
Modern aircrafts follow routes along sections of great circles for speedy long-distance flights and thus cut down flying time. But it is not always possible to follow great circle routes. Firstly, air routes must link numerous cities and thus planes proceed in short 'hops' from place to place; secondly, it may be impossible to fly along great circles for political reasons if some countries forbid the use of their air-space; thirdly, air routes tend to follow the land in case of accidend and rarely fly for long distances over the sea. However, where long distances have to be covered over uninhabited regions, great circle routes are the quickest. They are therefore used in crossing polar regions. Some of the major great circle routes over the pole include that from London to Vancouver or Los Angeles, that from Tokyo to Stockholm and that from Tokyo to Mexico City. Polar routes are not only quicker but also relieve air-traffic congestion on the very crowded conventional routes.