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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