Bearing & Earth as Sphere

Bearing & Earth as Sphere

In land navigation, a bearing is the angle between a line connecting two points and a north-south line, or meridian. A magnetic bearing is measured in relation to magnetic north, that is, using the direction toward the magnetic north pole (in northeastern Canada) as a reference.Bearings can be measured in two systems, Mils and Degrees.Oxford Dictionary, bearing is the direction or position of something relative to a fixed point, normally measured in degrees and with the magnetic north as zero.

Bearing

4 major cardinal directions points : north, south, east, and west (N, S, E, W)intermediate (intercardinal, or ordinal) directions: north-east (NE), north-west (NW), south-west (SW), and south-east (SE).Direction corresponds to degree of a compass Cardinal /compass Direction

Before the compass rose, maps included a wind rose to help orient the reader. North is traditionally indicated with a "fleur de lis" symbol, while East (with its religious and cosmological significance, the direction of Jerusalem) is often marked with a Maltese cross.

Wind rose & Classical winds

In the classical world, no distinction was made between the directions and the named winds emanating from them. Wind names were not standardized. Not every region in the classical world experienced the same wind coming from the same directionNames , and number and colours of direction may vary from place to place and time to time.Some other cultures make greater use of other referents, such as towards the sea or towards the mountains (Hawaii, Bali), or upstream and downstream Ex, Lingo (Guadalcanal, Solomon Islands) has four non-compass directions: landward, seaward, upcoast, and downcoast.

Non-compass Directional Systems

used to find a direction or bearinginvented in ancient China around 247 B.C., and was used for navigation by the 11th century. Dry compass was invented in medieval Europe around 1300. early 20th century, liquid-filled magnetic compassWith GPS,magnetic compasses remain popular, especially in remote areas, as they are relatively inexpensive, durable, and require no electrical power supply

Compass

Before compass, destination and direction are determined by the sighting of landmarks & observation of position of celestial bodies.earliest Chinese compasses were probably designed for harmonize environments and buildings, in accordance with geomantic principles of feng shui, use for navigational 1st recorded in 1119Chinese dry suspension compass is a wooden frame crafted in the shape of a turtle hung upside down by a board, the needle at the tail would always point in the north direction. the design is used until 18th century.Compass

In Arab the earliest reference use comes in Cairo about 1282, compass is used on a ship tripIn Medieval Europe, 1269 Petrus Peregrinus described a floating compass for astronomical purposes as well as a dry compass for seafaringIn the Mediterranean, the introduction of the compass, improvements in dead reckoning methods, and the development of Portolan charts, leading to more navigation in second half of the 13th century.Compass

an iron fishlike compass in the Islamic world occurs in a Persian talebook from 1232. The Yemeni sultan and astronomer Al-Ashraf in 1282 was the first to make use of the compass for astronomical purposes. In 1300, a dry compass is used use as a Qibla indicator" to find the direction to Mecca. In the 14th century, Ibn al-Shatir invented a timekeeping device incorporating both a universal sundial and a magnetic compass, for the purpose of finding the times of Salah prayers. Arab navigators also introduced the 32-point compass rose during this time.In India, compass was used for navigational & known as the matsya yantra, because of the placement of a metallic fish in a cup of oil

Compass

The dry mariner's compass was invented in Europe around 1300, fitted into a gimbal mounting to reduce grounding of the needle or card when used on the pitching and rolling deck of a ship

bearing compass that allows the taking of bearings of objects by aligning them with the lubber line of the bearing compass, were commonly use by the early 18th century. Steadily reduced in size and weight to increase portability, it could be carried & operated in one hand.

liquid compass, the magnetized needle or card is damped by fluid to protect against excessive swing & improving readability while reducing wear. It was introduced by Sir Edmund Halley at a meeting of the Royal Society in 1690.Compass

Besides navigational use, compass is used in building orientation, mining and astronomy.Modern compasses usually use a magnetized needle or dial inside a capsule completely filled with fluid (oil, kerosene, or alcohol) to dampens and stabilize the movement of the needle Many modern recreational and military compasses integrate a protractor with the compass, using a separate magnetized needle. Other modern compass include thumb compass, gyrocompass, solid-state compass, Qibla compass and so on.

Compass

early GreCartography or mapmaking, has start 8,000 years ago. From cave paintings to ancient maps of Babylon, Greece, and Asia, through the Age of Exploration, and on into the 21st century, people have created and used maps to help them define, explain, and navigate their way through the world.Greeks, Homer thought earth as a circular flat disk surrounded by a constantly moving stream of Ocean, suggested by the appearance of the horizon as it is seen from a mountaintop or from a seacoast500 B.C., Hacataeus create a map based on Anaximander belief, earth was a cylindrical form, like a stone pillar and suspended in space. The inhabited part of his world was circular, disk-shaped, and presumably located on the upper surface of the cylinder

Cartography

Aristotle (384322 BCE) proved that Earth is sphere:-The lunar eclipse is always circular Ships seem to sink as they move away from view and pass the horizon Some stars can be seen only from certain parts of the Earth. Eratosthenes (275195 BCE) scientifically estimated of the circumference of the earth within 0.5 percent accuracy by calculating the heights of shadows on different parts of the Egypt at a given time. He also started to chart with meridians, his imaginary northsouth lines, and parallels, his imaginary westeast lines.

Ptolemy (90-168 CE) improved the depiction of the spherical earth on a map by using perspective projection, and suggested precise methods for fixing the position of geographic features on its surface using a coordinate system with parallels of latitude and meridians of longitude. The Greenwich prime meridian became the international standard reference for cartographers in 1884.During the 1900s, improvements in printing and photography with airplanes that made production cheaper and easier.

The largest possiblecirclethat can be drawn on aspherehas the samediameteras the sphere it was drawn onThere are an infinite number of great circles that can be drawn on any perfect sphere.Thelatitudelines on aglobeall form great circles that pass through the same two points (theNorth Poleand theSouth Pole). TheEquatoris another great circle.Great Circles can be used to determine the shortest surface distance between two points on a sphere (or on the earth).

Great Circle

Ameridian(orline of longitude) is an imaginary arc on the Earth's surface from theNorth Poleto theSouth Polethat connects all locations running along it with a givenlongitude. The position of a point on the meridian is given by thelatitude. ThePrime Meridianis themeridianwith longitude 0. The Prime Meridian and its opposite the180th meridian(at 180 longitude), which theInternational Date Lineform agreat circlethat divides theEarthinto theEastern(0 and 180 of East longitude) andWesternHemispheres (0 and 180 of West longitude ).By international convention, the modern Prime Meridian passes through theRoyal Observatory, Greenwich, London known as theInternational MeridianorGreenwich Meridian, although the Prime. The term "meridian" comes from the Latinmeridies, meaning "midday"; the sun crosses a given meridian midway between the times of sunrise and sunset on that meridian.Meridian

Lines of latitude appear horizontal with varying curvature on globe; but are actually circular with different radii. Latitude is usually expressed in degrees (marked with ) ranging from 0 at the Equator to 90 at the North and South poles. The latitude of the North Pole is 90 N, and the latitude of the South Pole is 90 S. The equator divides the planet into a Northern Hemisphere, a Southern Hemisphere.Latitude can be calculated using Pole Star and noontime sun. Latitude ()

Lines of longitude appear vertical with varying curvature on globe, but are actually with identical radii at a given latitude. Longitude is usually expressed in degrees (marked with ) ranging from 0 at the Greenwich meridian to 180 east and west. Longitude can be calculated if the precise time of a sighting is known. All one needs is an accurate clock, set to Greenwich time. When the Sun "passes the meridian" at noon, we only need to check the clock: if Greenwich time is 3 p.m., we know that 3 hours ago it was noon at Greenwich and we are therefore at longitude 15 x 3 = 45 degrees west.

Longitude ()

A Greek geographer at 4th century BC1st person on record to describe Midnight Sun, polar Sun and polar ice.tide is caused by moonFind latitude by:-altitude of the Sun, elevation of north pole longest day and shortest solar elevationPhytheas of Massalia

Nicknamed beta, second best in the world in almost all field, after Archimedes.Invent the method to find prime numbers1st to measure circumference of earth, within 0.5 percent accuracy without leaving Egypt.first person to use the word "geography" and invented the discipline of geography invented a system of latitudeandlongitude, used of a new technique of charting with meridians, his imaginary northsouth lines, and parallels, his imaginary westeast linesEratosthenes of Cyrene (276-194BC)

a Portuguese mathematician, cosmographer, and professorfirst to propose the idea of a loxodromeand was also the inventor of several measuring devicesunderstand why a ship maintaining a steady course would not travel along a great circle, the shortest path between two points on Earth, but would instead follow a spiral course, called a loxodromePedro Nunes (1502-1578)

a curve that crosses each meridian at the same angle. Although a great circle is a shortest path, it is difficult to navigate because the bearing continuously changes as proceed. Following a rhumb line covers more distance than following a geodesic, but it is easier to navigate.All parallels, including the equator, are rhumb lines, since they cross all meridians at 90. Additionally, all meridians are rhumb lines, in addition to being great circles. A rhumb line always spirals toward one of the poles, unless its bearing is true east, west, north, or south, in which case the rhumb line closes on itself to form a parallel of latitude or a pair of antipodal meridians.Its use in navigation is directly linked to the style, or projection of certain navigational maps. A rhumb line appears as a straight line on a Mercator projection map.Loxodrome or Rhumb line

A rhumb line is a curve that crosses each meridian at the same angle. This curve is also referred to as a loxodrome (from the Greek loxos, slanted, and drome, path). Although a great circle is a shortest path, it is difficult to navigate because your bearing (or azimuth) continuously changes as you proceed. Following a rhumb line covers more distance than following a geodesic, but it is easier to navigate.All parallels, including the equator, are rhumb lines, since they cross all meridians at 90. Additionally, all meridians are rhumb lines, in addition to being great circles. A rhumb line always spirals toward one of the poles, unless its azimuth is true east, west, north, or south, in which case the rhumb line closes on itself to form a parallel of latitude (small circle) or a pair of antipodal meridians.The following figure depicts a great circle and one possible rhumb line connecting two distant locations. Descriptions and examples of how to calculate points along great circles and rhumb lines appear below.

22A Roman cartographerdevised a technique to produceglobes, celestial as well as terrestrial by techniques of relative mass production. Mercator projection, a cylindrical map projectionchartwith parallel lines of longitude to aid navigation by sea, as compass courses could be marked as straight lines.It became the standard map projection for nautical purposes because of its ability to represent lines of constantcourse, known asrhumb linesorloxodromes, as straight segments. Gerardus Mercator (1512-1594)

An English mathematician and cartographerexplained the mathematical basis of theMercator projectionset out a reference table giving the linear scale multiplication factor as a function oflatitude, calculated for eachminute of arcup to a latitude of 75. invented the "sea-ring" that enabled mariners to determine themagnetic variationof thecompass, the sun's altitude and the time of day in any place if the latitude was known; and a device for finding latitude when one was not on themeridianusing the height of thepole star.

Edward Wright (1561-1615)

Find the latitude of a point given the latitude of another point and distance between the two points along the same meridianFind the longitude of a point given the longitude of another point and distance between the two points along the equator or on a parallel of latitudeFind the shortest distance between two points on the earth surfaceSolve problem involving distance between two points or travelling on the surface of the earth9.4 Distances on the Surface of the Earth

Hangman Gamespecific terms, common term such as North, South, Equator and some new terms such as Great Circle, Meridian, Nautical MileInnovative Activities

Students put into groups of 4, each group is given a magnetic compass, strings and some chalk.Students A hold the compass, students B, C and D stand in pattern of triangle.Using compass, students A determine North, and then bearing one students to another.Repeat the activity with students B, C and D as the compass holder.Indoor Bearing Activity

Inside school, map can be drawn by pupilsoutside of school, example, KL lake garden, FRIM, palm oil estate, with forest ranger or guide accompaniment for safety purposeInstill cooperation, navigation skills and train physical abilityAfter the activity, have a sharing session: handling compass, reading map, planning route, moving toward destination

Treasure Hunt

Students work in pairs, with a pair of compassMark two points, A and B, construct 3 arc ended with A and B with different radiusCompare the arc length with the radiusThe greater the radius of the arc, the shorter the arc lengthThe shortest distance between two points on earth surface is along the Great Circle that passes through both points Greater the radius, shorter the Arc Length

In form 2 Geography, pupils learnt about position, Greenwich Time Meridian, longitude and latitude as well as determine time zoneCan use this as class opener or as a reflection activity, help students to link between conceptsInterconnection with Geography

Develop students creativity and innovativityEncourage students to explore other field of mathematics, other than the number and formulasHandling of Compass, type, component, applicationsReading a Map: scalar, distance, directionHistory of Mapping and NavigationWhere I wanna go, How far it is, Which direction is it inScrap book

Link: http://www.freemaptools.com/range-finder.htmShow destination from a staring point, given the bearing and the distance in betweenUseful sites

A Webquest for students that can learn independentlyLink: http://geographyworldonline.com/tutorial/instructions.html

Link: http://www.cockpitgps.com/class/index.htm

Link: http://www.apl.com/boomerangbox/d082701.htm

Besides helps to calculate distance and bearing, this site also have some awesome feature, such as finding the midpoint, destination point given distance and bearing from start point, intersection of 2 paths given star point and bearing and so onLink: http://www.movable-type.co.uk/scripts/latlong.html

help pupils test whether they can calculate correctly, enter latitude or longitude in correct format and read globeLink: http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/longlatquiz1.html

Link: http://www.softschools.com/quizzes/geography/latitude_and_longitude/quiz1050.html

Questions on longitude and latitude

Link: http://www.magnet.fsu.edu/education/tutorials/slideshows/compass/index.html

Though compass made might not as accurate as the compass manufactured in factory, pupils are now learning new skills and reasons why it might not be as accurate as compass manufactured

Useful for learning of bearingGoogle Map

Google Earth

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