General Navigation 1 PDF

6ENT1169 General Navigation 1 GENERAL NAVIGATION ONE Today’s Lecture Content ❑ The Form of the Earth EASA Part-FCL / eRules ❑ Position on the Earth Dec 2021 (Subpart C)...

6ENT1169 General Navigation 1 GENERAL NAVIGATION ONE Today’s Lecture Content ❑ The Form of the Earth EASA Part-FCL / eRules ❑ Position on the Earth Dec 2021 (Subpart C) ❑ Distances ❑ Directions ❑ Time GENERAL NAVIGATION ONE The Form of the Earth COMPRESSION Polar Diameter Polar ∅ < Equatorial ∅ ❖ 27 statue miles. ❖ 23 nautical miles. ❖ 43 kilometres. Equatorial Diameter ❖ 0.3%. ❖ 1/300th. Oblate Spheroid or Ellipsoid or Geoid GENERAL NAVIGATION ONE The Form of the Earth Earth’s Orbit around the SUN GENERAL NAVIGATION ONE The Form of the Earth Tilt of the Earth: 66.5˚. Orbital Plane GENERAL NAVIGATION ONE The Form of the Earth POLES OF THE EARTH North Pole South Pole GENERAL NAVIGATION ONE The Form of the Earth Basic Direction Earth’s Rotation as shown in ‘Elevation’ Cardinal and Quadrantal Points GENERAL NAVIGATION ONE The Form of the Earth Sexagesimal System The Sexagestimal System defines the direction in degrees from 0 to 360. ❖ North is 360°/000°. ❖ East is 090°. ❖ South is 180°. ❖ West is 270°. ❖ Always use 3 figure when expressing a direction. ▪ E.g. 20° is referred 020. 99° is referred to as 099. ❖ The term reciprocal is used to referred to an opposite direction. ▪ E.g. Reciprocal of 040 is 220. Reciprocal of 300 is 120. GENERAL NAVIGATION ONE The Form of the Earth Cartesian co-ordinate System GENERAL NAVIGATION ONE The Form of the Earth Great Circle A circle on the surface of the earth whose centre and radius are those of earth itself is called a Great Circle. A great circle can connect any two points on the Earth’s surface. Normally, only one great circle can be drawn through any two points, as shown on the diagram. The exception to this rule is that if the two points are diametrically opposed - the North Pole and the South Pole, for example - an infinite number of great circles may be drawn. The great circle joining two points has a long and a short path. The short path is always the shortest possible distance on the Earth’s surface between the two points. GENERAL NAVIGATION ONE The Form of the Earth Small Circle ❖ A circle on the surface of the earth whose centre and radius are not those of the earth is called a Small Circle. ❖ The main small circles of relevance to position are the Parallels of Latitude. GENERAL NAVIGATION ONE The Form of the Earth The Equator POLAR AXIS ❖ The Great Circle whose plane is at 90° to the axis of rotation of the earth (the polar axis) is called the Equator. ❖ It lies in an East-West direction and divides the earth equally into two hemispheres. i.e. northern and southern. ❖ For the definition of position on the Earth, the Equator is the datum for defining Latitude and is the equivalent of the X-axis of the Cartesian system. GENERAL NAVIGATION ONE The Form of the Earth Meridians ❖ The Meridians are Semi-Great circles joining the North and South poles. ❖ All meridians indicate True North- South direction. ❖ Every Great Circle passing through the poles forms a meridian and its Anti- meridian. ❖ The meridians cross the Equator at 90°. ❖ They lie in an North-South direction. Their function is to indicate position East or West of the Prime Meridian. GENERAL NAVIGATION ONE The Form of the Earth Prime (or Greenwich) Meridian ❖The Prime (Or Greenwich) Meridian: The meridian passing through Greenwich is known the Prime Meridian. ❖The Prime Meridian is the datum for defining Longitude and is the equivalent of the Y-axis of the Cartesian system. GENERAL NAVIGATION ONE The Form of the Earth Parallel of Latitude ❖The parallels of latitude are small circles on the surface of the earth whose planes are parallel to the Equator. ❖They lie in an East-West direction. Their function is to indicate position North or South of the Equator. GENERAL NAVIGATION ONE The Form of the Earth Rhumb Line ❖A Rhumb line is a regularly curved line on the surface of the Earth that cuts all meridians at the same angle. ▪ Only one Rhumb line can be drawn through two points on the Earth’s surface. ▪ A Rhumb line is not a great circle with the exception of the meridians and the Equator. ▪ All parallels of latitude are Rhumb lines. ▪ The distance along a Rhumb line is not the shortest distance between two points unless the Rhumb line is a meridian or a great circle. ▪ Normally, flights of less than 1000 nm are flown along a Rhumb Line. GENERAL NAVIGATION ONE The Form of the Earth Graticule ❖ The network formed on a map or the surface of a globe by the prime meridian, the meridians, the equator and the parallels of latitude is called the Graticule. ❖ The graticule is an analogy on the Earth's surface of the X,Y grid on graph paper. GENERAL NAVIGATION ONE Position on the Earth Angular Measurement ❖ The Sexagesimal system of measuring angles is used in navigation. ❖ Angles are expressed in terms of degrees, minutes, and seconds. ❖ A degree (symbolised by °) is the angle subtended by an arc equal to 1/360 part of the circumference of a circle. ▪ Each degree is split into 60 minutes (symbolised by ‘) ▪ Each minute is split into 60 seconds (symbolised by “) ▪ E.g. 030°42’54” GENERAL NAVIGATION ONE Position on the Earth Latitude and Longitude ❖ On the Earth, position is described using latitude and longitude. ▪ The X-axis is the Equator and is defined as 0° N/S Latitude. ▪ The Y-axis is aligned to the Greenwich Meridian (the Prime Meridian) and is 0° E/W longitude. GENERAL NAVIGATION ONE Position on the Earth Latitude ❖ The latitude of any point is the arc (angular distance) measured along the meridian through the point from the Equator to the point. ❖ It is expressed in degrees, minutes, and seconds of arc and is annotated North or South according to whether the point lies North or South of the Equator. ❖ The range of latitude values covers the Equator (0°N/S) to the geographic poles , i.e., the North Pole is 90°N and the South Pole is 90°S. GENERAL NAVIGATION ONE Position on the Earth Special Latitudes GENERAL NAVIGATION ONE Position on the Earth Longitude ❖ The longitude of any point is the shorter distance in the arc along the Equator between the Prime Meridian and the meridian through the point. ❖ Longitude is measured in degrees, minutes and seconds of arc and is annotated East (E) or West (W) depending whether the point lies East or West of the Prime Meridian (Greenwich). ❖ Longitude can be measured up to 180°E or 180°W of the Prime Meridian. These 2 meridians are coincident and are known as the Anti-Prime Meridian (APM), commonly labelled 180°E/W. GENERAL NAVIGATION ONE Position on the Earth Longitude Views of Longitude from Prime Meridian (Greenwich Meridian) and Anti-Prime Meridian GENERAL NAVIGATION ONE Position on the Earth Summary 6ENT1169 General Navigation 2 GENERAL NAVIGATION ONE Position on the Earth Summary GENERAL NAVIGATION ONE Position on the Earth Position using Lat and Long ❖ Position on the Earth is always expressed as latitude first and then longitude. ▪ Position of A is 53°N 0°E/W. ▪ Position of B is 51°30’N 001°30’W. ▪ Position of C is 53°30’N 001°30’E GENERAL NAVIGATION ONE Position on the Earth Change of Latitude (CH LAT) ❖ Ch Lat is the shortest arc along a meridian between two parallels of latitude. It is expressed in degrees and minutes. GENERAL NAVIGATION ONE Position on the Earth Calculation of Change of Latitude (CH LAT) ❖ Where two points are in the same hemisphere, the Ch Lat is the difference between the two points. ❖ E.g. Point A is 20°30’N and point B is 41°30’N. If an aircraft is travelling from A to B, what is the Ch Lat? Sol: First calculate the difference between the two points in degrees and minutes. Simply subtract the smallest from the largest: 41°30’ – 20°30’ = 21°. Note the direction of the change. In this case, the aircraft is travelling north so the Ch Lat is: 21° N. ❖ The term D Lat can also be used. Where Ch Lat is given in degrees and minutes, D Lat is given in minutes alone. For Example above, the answer would change to: 21 X 60 = 1260’N. GENERAL NAVIGATION ONE Position on the Earth Calculation of Change of Latitude (CH LAT) ❖ Where the two points are in different hemispheres, the solution is the sum of the two latitudes. ❖ E.g. Point A is 20°30’N and point B is 41°30’S. If an aircraft is travelling from A to B, what is the Ch Lat? Sol: First calculate the difference between the two points in degrees and minutes. Simply add the two together: 41°30’ + 20°30’ = 62°. Note the direction of the change. In this case, the aircraft is travelling south so the Ch Lat is: 62° S. GENERAL NAVIGATION ONE Position on the Earth Change of Longitude (CH LONG) ❖ To express the difference between two meridians, Ch Long, the smaller arc, is used. ❖ Values are expressed in exactly the same manner as Ch Lat. ❖ Remember that the value of Ch Long can never exceed 180°. ❖ The suffixes E and W are used in regard to the direction of travel. GENERAL NAVIGATION ONE Position on the Earth Calculation of Change of Longitude (CH LONG) ❖ Calculate the Ch Long between position A 165°W and position B 103°W. Assume that the aircraft is flying from A to B. Find the numerical difference between A and B. Sol: The two points are in the same hemisphere, so subtract the smaller from the larger: 165 – 103 = 62°E. Remember that anti clockwise measurement is EAST GENERAL NAVIGATION ONE Position on the Earth Calculation of Change of Longitude (CH LONG) ❖ Calculate the Ch Long between position A 165°W and position B 170°E. Assume that the aircraft is flying from A to B. Sol: It is obvious the shortest distance between the two points is by crossing the 180° meridian. The difference between 165° and 180° is 15°. The difference between 170° and 180° is 10°. The Ch Long is therefore 25°W because the movement is clockwise. GENERAL NAVIGATION ONE Distances Definitions ❖ Kilometre: The Kilometre is 1/10,000th of the average distance on the Earth between the Equator and either Pole. ❖ Thus, there are 10,000 km between the Equator and either Pole and the circumference of the Earth is 40,000 km. ❖ For conversions between Kilometres and Imperial units: ▪ 1 Kilometre (km) = 3280 feet (ft) ▪ 1 metre (m) = 3.28 feet (ft) ❖ The Statute Mile (sm): The Statute Mile is defined in a Royal Statue of Queen Elizabeth the First (of England) and is 5280 ft. ▪ Its most common use is to inform passengers in UK or US aircraft how fast the aircraft is travelling in terms of the same units they use in their cars ,i.e., statute miles per hour (mph). GENERAL NAVIGATION ONE Distances Definitions ❖ The Nautical Mile (nm): The Nautical Mile is the length of arc which subtends an angle of one minute of latitude along any meridian or one minute of longitude along the equator. ❖ The standard Nautical Mile (nm) is 6080 ft. GENERAL NAVIGATION ONE Distances Conversion Factors 1 nm = 6080 ft = 1.15 sm = 1.85 km Other useful conversion factors 1 meter 100 centimetres 3.28 feet 1 centimetre 10 millimetres 1 foot 12 inches 30.5 centimetres 1 inch 2.54 centimetres 25.4 millimetres 1 yard 3 feet GENERAL NAVIGATION ONE Distances Great Circle Distances ❖ Where two points are on the same meridian or on the Equator. ❖ E.g. Both positions in the same hemisphere. ▪ What is the shortest distance between A (64°35’N 010°00’W) and B (53°15’N 010°00’W)? Sol: If the points are on the same meridian, calculate: D Lat: 64°35’ – 53°15’ = 11°20’ = 680’. Using the definition of the nautical mile, 1 minute of arc is equivalent to 1 nm: 680’ is equal to 680 nm. ❖ E.g. Both positions in different hemispheres. ▪ What is the shortest distance between A (64°35’N 010°00’W) and B (53°15’S 010°00’W)? Sol: If the points are on the same meridian, calculate: D Lat: 64°35’ + 53°15’ = 117°50’ = 7070’ Using the definition of the nautical mile, 1’ is equivalent to 1 nm: 7070’ is equal to 7070 nm. GENERAL NAVIGATION ONE Distances Great Circle Distances ❖ E.g. Both positions on the meridian and anti-meridian in the same hemisphere. ▪ What is the shortest distance between A (64°35’N 010°00’W) and B (53°15’N 170°00’E)? ✓ If both positions are in the same hemisphere, the shortest distance of travel is over the North Pole. Sol: Find the distance to travel from A to the North Pole and from B to the North Pole. A: 90° – 64°35’ = 25°25’= 1525’ = 1525 nm. B: 90° – 53° 15’ = 36°45’ = 2205’ = 2205 nm. Therefore, the shortest distance between A and B id 1525 + 2205 = 3730 nm. GENERAL NAVIGATION ONE Distances Great Circle Distances ❖ E.g. Both positions on the meridian and anti-meridian in different hemisphere. ▪ What is the shortest distance between A (64°35’N 010°00’W) and B (53°15’S 170°00’E)? ✓ It does not matter whether the calculation uses the South Pole or the North Pole. Sol: If travel was by the North Pole, the approximate distance would be: 90° – 64°35’ = 25°25’ = 1525 nm. ▪ The answer is more than 180°, 90° + 53°15’ = 143°15’ = 8595 nm. Total 10,120 nm which is the longer distance of the two, and therefore not of If the calculation had been done using the South Pole: commercial use. ▪ 90° + 64°35’ = 154°35’ ▪ Subtract the answer found from 90° - 53°15’ = 36°45’ 360°. Total = 191°20’ ▪ 360° - 191°20’ = 168°40’ = 10 120’ Total 10,120 nm. GENERAL NAVIGATION ONE Distances Great Circle Distances ❖ Two points on the Equator. ▪ What is the great circle distance between A (00°00’N/S 012°00’W) and B (00°00’N/S 012°00’E)? ✓ The calculation is the same as for two points on the same meridian. Sol: Calculate D Long between A and B. A to the Prime Meridian is 12°. B to the Prime Meridian is 12°. Total 24° = 1440’ = 1440 nm. GENERAL NAVIGATION ONE Distances DEPARTURE: EAST – WEST Distances ❖ Departure is the distance between two meridians along a specified parallel of latitude, usually in nautical miles. ❖ Departure is maximum at the equator where 1° Change of Longitude (Ch Long) equals 60’ of arc of a Great Circle. ❖ Change of Longitude can sometimes be referred to as Difference in Longitude (D Long). ❖ Departure is zero at both poles because the meridians converge and meet at these two points. ❖ Departure varies as the cosine of the latitude, it can be found by applying the formula;- ▪ Departure (nm) = D Long x cos of Lat GENERAL NAVIGATION ONE Distances DEPARTURE: EAST – WEST Distances ❖ E.g. Calculate the distance between two meridians that are 10° apart at latitude 60°N. Sol: D Long = 10° x 60 = 600’. Therefore, Departure = D Long cos Lat 60 = 600 x cos60 = 600 x 0.5 = 300 nm. GENERAL NAVIGATION ONE Directions ❖ True Direction: True Direction is defined as being related to the geographic North and South poles - i.e. the two ends if the axis of the Earth's rotation. ❖ The Earth has two 'magnetic poles' which are not co-located with the geographic poles and have a very small annual movement within the Earth. GENERAL NAVIGATION ONE Directions ❖ Magnetic Pole: Is the (horizontal) direction indicated by a freely suspended magnet influenced only by the Earth's magnetic field; this direction is also referred to as the 'magnetic meridian' at that point. ❖ Magnetic Direction: Is measured from magnetic North clockwise through 360° and is suffixed by the letter (M), e.g. 043(M) and 270(M) etc. ❖ Variation: The angular difference between True and Magnetic North directions at any point is called the angle of variation. ▪ Variation is the angle between True North and Magnetic North and is measured in degrees East or West from True North. ❖ Heading: The direction in which the fore and aft axis of the aircraft is pointing is known as the aircraft's heading. GENERAL NAVIGATION ONE Directions VARIATION ❖ E.g. When Magnetic direction is the same as True direction the variation is nil; otherwise Magnetic North direction may lie either to the West or East of the True North Direction. See figure below. Westerly Variation ❖ The direction of the aircraft relative to True North is 105°. ❖ The direction of the aircraft relative to Magnetic North is 122°. ❖ Magnetic North is to the West of True North. ❖ Hence, the variation is 17° W or -17 °. GENERAL NAVIGATION ONE Directions VARIATION ❖ E.g. When Magnetic direction is the same as True direction the variation is nil; otherwise Magnetic North direction may lie either to the West or East of the True North Direction. See figure below. Easterly Variation ❖ The direction of the aircraft relative to True North is 105°. ❖ The direction of the aircraft relative to Magnetic North is 088°. ❖ Magnetic North is to the East of True North. ❖ Hence, the variation is 17°E or +17°. GENERAL NAVIGATION ONE Directions VARIATION The following rule has been deduce from the examples shown in previous slides which must be remembered: VARIATION EAST ➔ MAGNETIC LEAST VARIATION WEST ➔ MAGNETIC BEST GENERAL NAVIGATION ONE Directions Lines on Aeronautical Charts ❖ Isogonal Lines: A “pecked” or “dashed” blue line on the aeronautical chart connecting places of equal magnetic variation. ❖ Agonal Lines: A line on aeronautical chart connecting places of no or zero magnetic variation. GENERAL NAVIGATION ONE Directions Deviation ❖ Any ferromagnetic material (iron or steel) or electrical circuits in an aircraft may well have a magnetic field which will affect the compass, so that the direction indicated by the compass needle will not be Magnetic North. ❖ Non-ferromagnetic material, e.g. brass, aluminium, will not have a magnetic field and so will not affect the compass. ❖ The angle between Magnetic North and the direction indicated by a compass needle is called the angle of deviation. ❖ Deviation is the angle between Magnetic North and Compass North measured in degrees East or West from Magnetic North. GENERAL NAVIGATION ONE Directions Deviation Westerly Deviation ❖ The direction of the aircraft relative to True North is 100°. ❖ The direction of the aircraft relative to Magnetic North is 125°. ❖ The direction of the aircraft indicated by the Compass is 135°. ❖ Hence, the deviation is 10°W or -10°. GENERAL NAVIGATION ONE Directions Deviation Easterly Deviation ❖ The direction of the aircraft relative to True North is 100°. ❖ The direction of the aircraft relative to Magnetic North is 125°. ❖ The direction of the aircraft indicated by the Compass is 115°. ❖ Hence, the deviation is 10°E or +10°. GENERAL NAVIGATION ONE Directions DEVIATION The following rule has been deduce from the examples shown in previous slides which must be remembered: DEVIATION EAST ➔ COMPASS LEAST DEVIATION WEST ➔ COMPASS BEST GENERAL NAVIGATION ONE TIME Solar System – Planetary Orbit – Kepler’s Law ❖ The Solar System consists of the sun and nine major planets (of which the Earth is one). {One would argue that there are only Eight now}. ❖ Planetary orbits (and therefore the Earth's orbit) are governed by Kepler's laws of planetary motion which are: 1. The orbit of each planet is an ellipse with the sun at one of the foci. 2. The line joining the planet to the sun, known as the radius vector, sweeps out equal areas in equal time. 3. The square of the sidereal period of a planet is proportional to the cube of its mean distance from the sun. GENERAL NAVIGATION ONE TIME Kepler’s Second Law GENERAL NAVIGATION ONE TIME Perihelion: is where the sun is closest to the Earth: ❖ The sun is approximately 91.4 million miles from the Earth. ❖ It occurs on 4 January. ❖ The Earth’s orbital speed is at its greatest. Aphelion: is at its farthest point from the sun: ❖ The sun is approximately 94.6 million miles from the Earth. ❖ It occurs on 3 July. ❖ The Earth’s orbital speed is at its lowest. GENERAL NAVIGATION ONE TIME ❖ The earth rotates about its geographic N/S axis in an anti-clockwise direction when viewed from the North Celestial Point. This rotation determines our measurement of a ‘day’. ❖ The Earth orbits the Sun in an anti-clockwise direction when viewed from the North Celestial Point. The orbital period determines our measurement of a 'year’. ❖ The changing orbital speed affects our measurements of a day. GENERAL NAVIGATION ONE TIME SEASON OF THE YEAR GENERAL NAVIGATION ONE TIME MEASUREMENT OF DAY ❖ A 'day' may be defined as the length of time taken for the Earth to rotate once about its axis measured against a celestial body, e.g., the Sun or a star. OR ✓ A day is defined as the interval that elapses between two successive transits of a heavenly body across the same meridian. ❖ Measurements against a star are called 'sidereal' and against the Sun are called 'solar’. CIVIL DAY: The civil day is the day that suffices for human affairs. It begins at midnight when the mean sun is on the observer’s anti-meridian, and it ends at the next midnight. THE APPARENT SOLAR DAY: The interval that elapses between two successive transits of the actual sun across the same meridian is an apparent solar day. GENERAL NAVIGATION ONE TIME MEASUREMENT OF DAY MEAN SUN: The mean sun is assumed to move along the celestial equator at a uniform speed around the Earth and to complete one revolution in the time it takes for the true sun to complete one revolution in the ecliptic. MEAN SOLAR DAY: ❖ The time interval between two successive transits of the mean sun across the same meridian is called a mean solar day. ❖ In one mean solar day, the mean sun moves westward from the meridian and completes one circuit of 360° longitude in the 24 mean solar hours into which the day is divided. ❖ The rate of travel is 15° of longitude per mean solar hour. The mean solar hour (called an hour for short) is further divided into 60 minutes. These are then divided into 60 seconds. GENERAL NAVIGATION ONE TIME MEASUREMENT OF DAY LOCAL MEAN TIME (LMT): ❖ Local mean time is the time according to the mean sun. ❖ When the mean sun transits (crosses) a particular meridian, the Local Mean Time (LMT) at all places on that meridian is 1200 hrs (midday, noon). ❖ Similarly, when the mean sun transits the anti-meridian of a point, the LMT at the point is 0000 hrs (2400hrs) or midnight. ❖ Conventionally, midnight of a particular night, say the night of the 6th/7th, is regarded as 2400hrs LMT on the 6th or 0000hrs on the 7th. GENERAL NAVIGATION ONE TIME Conversion of Arc (Angle) to Time Because the earth rotates 360° in 24 hrs, we can convert angular arc to time as follows: ❖ 360° = 24 hrs. ❖ 15° = 1 hour. ❖ 1° = 4 minutes. ❖ 15' of a degree of arc = 1 minute of time. ❖ 15"(seconds of arc) = 1 second of time. ❖ Example: Convert 127° of arc into time. ▪ Sol: Divide 127° by 15 = 8.4667 hours. ▪ The answer is now in hours but the hours must be converted to minutes. ▪ Convert the decimals of hours (.4667) to minutes by multiplying by 60,i.e. 0.4667 X 60 = 28 ▪ Answer: 8hrs 28 minutes GENERAL NAVIGATION ONE TIME Conversion of Arc (Angle) to Time Because the earth rotates 360° in 24 hrs, we can convert angular arc to time as follows: ❖ 360° = 24 hrs. ❖ 15° = 1 hour. ❖ 1° = 4 minutes. ❖ 15' of a degree of arc = 1 minute of time. ❖ 15"(seconds of arc) = 1 second of time. ❖ Example: Convert 096°17' of arc into time. ▪ Express the arc in decimal form by dividing the minutes by 60. i.e. 17’ ÷ 60 = 0.283. ▪ Arc = 096.283°. ▪ Divide arc by 15 to give decimal time 096.283° ÷ 15 = 6.4189 hrs. ▪ Convert decimal hours back to minutes.4189 x 60 = 25 minutes (to the nearest minute) ▪ Answer: 6 hours 25 minutes GENERAL NAVIGATION ONE TIME Universal Co-ordinated Time (UTC) ❖ UTC is the LMT at the Greenwich Meridian. ❖ It is more accurate than Greenwich Mean Time, as it is calculated against International Atomic Time. ❖ UTC is used by aviation as the reference time. ❖ For all practical navigation purposes, UTC equals GMT. ❖ UTC is the datum for world time. CONVERSION OF LMT TO UTC ❖ It is often necessary to convert LMT into UTC or vice versa. ❖ Based on the fact that the sun appears to travel across the earth from east to west, the following rule applies: Longitude east, UTC least (less advanced) Longitude west, UTC best (more advanced) GENERAL NAVIGATION ONE TIME Universal Co-ordinated Time (UTC) CONVERSION OF LMT TO UTC ❖ It is often necessary to convert LMT into UTC or vice versa. ❖ Based on the fact that the sun appears to travel across the earth from east to west, the following rule applies: Longitude east, UTC least (less advanced) Longitude west, UTC best (more advanced) For example: Find the UTC if the LMT in Cairo (longitude 30°E) is 0900 hours. GENERAL NAVIGATION ONE TIME GENERAL NAVIGATION ONE TIME Standard Time ❖ It is clearly impractical for each and every place to keep the LMT applicable to its own meridian. ❖ For convenience, all places in the same territory, or part of the same territory, maintain a standard of time as mandated by the government responsible for that territory. ❖ Some countries such as Canada, Australia, and the United States are spread across a large change in longitude. ❖ One Standard Time is not sufficient, and it is necessary to enter the list with the area rather than the country. ❖ The Standard Time for UK is UTC (GMT) at all times of the year. GENERAL NAVIGATION ONE TIME International Date Line ❖ An anomaly occurs at meridian 180°W/E. ❖ Places East of Greenwich are ahead of UTC, places West behind UTC. ❖ The LMT at 180° is, therefore, 12 hours ahead or behind UTC, and there is a 24-hour time difference between two places separated by the Greenwich anti-meridian. ❖ The local date must change when crossing 180°; this is called the International Date Line. ❖ The change of date depends upon whether the aircraft is travelling west or east. ▪ For an aircraft on a westerly track, a day must be added to the calendar. The 14th becomes the 15th ▪ For an aircraft on an easterly track, a day must be subtracted from the calendar. The 14th becomes the 13th GENERAL NAVIGATION ONE TIME International Date Line ❖ The International Date Line follows the 180° meridian, except where there are inhabited areas. A deviation may occur in these places. GENERAL NAVIGATION ONE TIME International Date Line GENERAL NAVIGATION ONE Bibliography ▪ EASA Part-FCL/eRules, Dec 2021, Subpart C. ❖ General Navigation, CAE Oxford ATPL Series Books. (Including pictures) ❖ General Navigation, Atlantic Flight Training ATPL Series Books. (Including pictures) ❖ FAA Pilot’s Handbook of Aeronautical Knowledge. ❖ Air Navigation, Volume 3, Air Pilot’s Manual, Pooley’s Ninth Revised Edition 2010. 6ENT1169 General Navigation 3 GENERAL NAVIGATION TWO Today’s Lecture Content ❑ Terrestrial and Aircraft Magnetism EASA Part-FCL / eRules Dec 2021 (Subpart C) ❑ Charts ❑ Triangle of Velocities ❑ 1 in 60 Rule GENERAL NAVIGATION TWO Basic Magnetism ❖ Magnetism: Is a force of nature or power which is apparent in the earth and also in the atmosphere surrounding the earth. ❖ Magnetic Field: The field of a magnet is the space around it in which its magnetic influence is felt. Lines of Force ❖ Poles of the Magnet: As seen above, the ‘lines of force’ traced by iron fillings converge towards small areas near the ends of the magnet. These two areas are called ‘poles’ of the magnet. GENERAL NAVIGATION TWO Basic Magnetism Red and Blue Poles ❖ A freely suspended bar magnet (or compass needle) in the earth’s magnetic field will align itself roughly North-South. (Left figure below) ❖ The end which points North is known as a North-seeking or red pole. The other end is a South- seeking or blue pole. ❖ By convention, magnetic lines of force are directed out from the red pole and back in to the blue pole as shown in right figure below. ❖ For convenience the magnet has been divided into two halves, one half containing the red pole, the other half containing the blue pole. GENERAL NAVIGATION TWO Basic Magnetism Magnetic and Non-Magnetic Materials ❖ Magnetic materials are ‘ferrous’ metals iron and steel, steel being iron alloyed with substances such as carbon, cobalt, nickel, chromium, and tungsten. ❖ These metals are called ‘ferromagnetic’ and in an aircraft they may be magnetised and produce deviation in the aircraft’s compasses. ❖ Many materials used in aircraft construction are non-magnetic and do not affect the compass. Examples of such non-ferrous substances are aluminium, duralumin, brass, copper, plastic, and paint. Aluminium Brass Copper Duralumin GENERAL NAVIGATION TWO Basic Magnetism Hard and Soft Iron ❖ Ferromagnetic material can be broadly divided into two classes, hard iron and soft iron. The words hard and soft do not refer to the physical properties of the material but to their magnetic characteristics. ❖ Hard iron magnetism is said to be ‘permanent’, meaning that the material, typically steel containing cobalt or chromium, remains magnetised for an indefinite period after it has been removed from the magnetising field. ❖ Soft iron magnetism is called ‘temporary’ (or ‘transient’ or ‘induced’) the substance being easy to saturate magnetically with only a weak magnetising field but retaining little or no magnetism when the field is removed. ❖ Some materials exhibit magnetic characteristics which lie somewhere between those of hard iron and soft iron. These substances can be magnetised but this ‘sub-permanent’ magnetism is lost partly or wholly over a period of time. GENERAL NAVIGATION TWO Terrestrial Magnetism ❖ The earth behaves as though a huge permanent magnet were situated near the centre producing a magnetic field over the surface. ❖ Figure below, shows that the poles of this hypothetical earth-magnet do not lie on the earth’s spin axis, this lack of symmetry giving rise to magnetic variation. ❖ An imaginary line called a Magnetic Meridian joins the poles together. ❖ If a freely suspended magnetised needle is positioned at various locations within the Earth's magnetic field, it lines itself up with its red pole pointing towards the Earth’s magnetic North pole. Earth’s Magnetism GENERAL NAVIGATION TWO Terrestrial Magnetism Magnetic Dip ❖ The lines of force initially emerge vertically from the South magnetic pole, and then bend over to become parallel with the Earth's surface, before descending vertically at the North magnetic pole. ❖ If a magnetic needle is transported along a meridian from North to South, it initially has its red end pointing down towards the Earth. ❖ Near the magnetic equator, the needle is horizontal; and at the southern end of its travel the blue end points toward the Earth. GENERAL NAVIGATION TWO Terrestrial Magnetism Magnetic Dip ❖ The angle that the lines of force make with the Earth's surface at any given place is called the Angle of Dip. ❖ Angle of Dip varies from 0° at the magnetic equator, to virtually 90° at the magnetic poles. ❖ Lines drawn on the Earth’s surface joining places of equal dip are known as Isoclinals (BB and CC), ❖ A line joining places having zero dip are an Aclinic lines (AA). The Aclinic Line is also the magnetic equator, which is close to the geographical equator, but is not the same line. GENERAL NAVIGATION TWO Terrestrial Magnetism Field Strength ❖ The total force T exerted at a point by the earth’s field acts in the direction taken up by a freely-suspended magnet influenced only by the earth’s field. ❖ The total force, angle of dip, and magnetic variation at a point are sometimes known as the ‘magnetic elements’ for that place. ❖ It is convenient to resolve this total force T into its horizontal and vertical components H and Z respectively. GENERAL NAVIGATION TWO Aircraft Magnetism ❖ Aircraft contains within its structure large quantities of material which are either magnetic or capable of being magnetised. ❖ The other magnetic properties arise as a result of the complex electric and electronic devices carried on board. ❖ The combine effect is to produce a local magnetic field surrounding the compass which may cause deviation of the directive elements of the compass system way from the local magnetic meridian. ❖ Aeroplane magnetism is classified in a similar manner to that of hard iron and soft iron. ❖ The cause of the compass deviation can be grouped as follows: ▪ Permanent Magnetism. (Hard Iron) ▪ Sub-permanent Magnetism. (Both Iron) ▪ Transient Induced Magnetism. (Soft Iron) GENERAL NAVIGATION TWO Aircraft Magnetism Analysis of Aircraft Magnetism ❖ The various factors which contribute to cause the compass deviation are termed as ‘PARAMETERS’, and are indicated by letters. ❖ Those for ‘the permanent’ (or hard iron) magnetism being capital letters and those for ‘induced’ (or soft iron) magnetism being small letters. Hard Iron Parameters: ❖ The hard iron magnetism is resolved into three parameters, coinciding with the axis of the aircraft and its right angle to each other. They are called parameter P, Q and R. ❖ These parameters are considered to be positive when the blue poles of the magnet (aircraft magnetism) are forward, to starboard and beneath the compass and when in opposite directions, they are said to be negative. GENERAL NAVIGATION TWO Aircraft Magnetism Analysis of Aircraft Magnetism Soft Iron Parameters: ❖ There are nine soft iron parameters and are called a,b,c,d,e,f,g,h,and k respectively. ❖ They are assumed to represent the effect of iron rods lying in horizontal or vertical direction. ❖ The parameters which represents magnetism in horizontal are a,b,c,d,e,g, & h. ❖ The parameters which represents magnetism in vertical are c, f & k. They are marked by small letter “z”. The cz acts along the fore and aft axis and fz acts along the lateral axis. GENERAL NAVIGATION TWO Aircraft Magnetism Compass Reading Errors There are two types of compass reading errors. 1) Accelerations and Decelerations Errors. 2) Turning Errors. Acceleration and Deceleration Errors Due to the construction mechanism of the magnetic compass and earth’s & aircraft magnetic field effects on the compass, the compass gives us erroneous readings. The summary is as below. Accelerations and Decelerations Errors: ❖ Occurs only when flying on Easterly or Westerly headings. ❖ Acceleration causes apparent turns towards nearer pole. (i.e. apparent turn north in northern hemisphere and apparent turn south in southern hemisphere). ❖ Deceleration causes apparent turns towards further pole. (i.e. apparent turn south in northern hemisphere and apparent turn north in southern hemisphere). ❖ It does not occur on Northerly or Southerly headings. GENERAL NAVIGATION TWO Aircraft Magnetism Compass Reading Errors Turning Errors: ❖ Occurs only when flying on Northerly or Southerly headings. ❖ It does not occur on Easterly or Westerly headings. ❖ The error is Maximum when passing through magnetic North or South headings, decreasing to zero when passing through East or West heading. ❖ The error increases with increase in magnetic latitude. When heading and hemisphere are same, to come out on correct heading, ‘stop-short’. When heading and hemisphere are opposite, to come out on correct heading, ‘over shoot’. Turning Errors GENERAL NAVIGATION TWO Charts Chart ❖ A chart is a representation of the part of the Earth’s surface. ❖ A map is normally a representation of an area of land, giving details that are not required by the aviator, such as a street map or road atlas. ❖ A chart usually represents an area in less detail and has features which are identifiable from the air. Representation of Earth on Flat Paper ❖ To represent the spherical Earth on a flat sheet is difficult. ❖ It is important to understand how different areas are displayed. ❖ A chart projection is the method the cartographer uses to display a certain portion of the Earth’s surface. GENERAL NAVIGATION TWO Charts Properties of an Ideal Chart ❖ Constant scale over the whole chart. ❖ Areas of the Earth correctly represented (Conformal). ❖ Great circles should be straight lines. ❖ Rhumb lines should be straight lines. ❖ Position should be easy to plot. ❖ Charts of adjacent areas should fit exactly. ❖ Each cardinal direction should point in the same direction on all parts of the chart. ❖ Areas should be represented by their true shape. GENERAL NAVIGATION TWO Charts The ideal chart is an impossibility. For navigation it is important that: ❖ Bearing and distance are correctly represented. ❖ Both bearing and distance are easily measured. ❖ The course that is flown is a straight line. ❖ Plotting of bearings is simple. CHART CONSTRUCTION: Before the chart can be constructed, three processes must be completed: ❖ The Earth needs to be reduced in size to the required scale. This is known as the reduced earth (RE). ❖ A graticule needs to be constructed to represent latitude and longitude. ❖ The land area is then drawn on the chart. GENERAL NAVIGATION TWO Charts ORTHOMORPHISM ❖ Orthomorphism is a Greek word meaning correct shape. ❖ Only on small areas of charts is this possible. ❖ The term is rarely used in context with maps and charts today. CONFORMALITY: The word conformal is a more modern term used to describe the property of orthomorphism. ❖ Where charts are concerned, the terms orthomorphism and conformality mean that bearings are correctly represented. ❖ For a chart to be conformal and to have bearings correctly represented: ▪ Meridians of longitude and parallels of latitude must cut at right angles. ▪ The scale must be correct in all directions. GENERAL NAVIGATION TWO Charts Types of Projections ❖ There are 3 general types of projection surfaces; 1. Azimuthal/Plane. 2. Cylindrical. 3. Conical. ❖ Charts produced directly from a projection are called perspective or geometric projections. ❖ Charts produced by mathematical methods are called non-perspective charts. GENERAL NAVIGATION TWO Charts Azimuthal/Plane Projection An azimuthal (or 'plane') projection is produced by placing a flat sheet of paper against a point on the earth. A common use is to provide charts of the North/South polar regions. Azimuthal Projection Azimuthal Graticule GENERAL NAVIGATION TWO Charts Cylindrical Projection The earliest chart projections were produced in the 16th century by a Flemish navigator called Gerhard Kremer who used the Latin alias 'Mercator'. His projections used cylinders of paper wrapped around the "reduced earth" and touching the RE at the Equator. Cylindrical Projection Cylindrical Graticule GENERAL NAVIGATION TWO Charts Conical Projection Conical projections involve placing a cone of paper over the Reduced Earth and projecting the graticule onto the cone. Subsequently the cone is slit along one side and the cone can then be opened to produce a flat sheet of paper. Conical Projection Slit along meridian ‘0’ Conical Graticule GENERAL NAVIGATION TWO Charts Mercator Projection ❖ Often called as Normal or Direct Mercator. ❖ Is a cylindrical projection type chart where the projection surface touches the reduced earth at Equator. ❖ The geographical poles cannot be projected as they become axis of the cylinder. ❖ It is non-perspective projection as the orthomorphism/conformality is achieved through mathematical construction. GENERAL NAVIGATION TWO Charts Mercator Graticule GENERAL NAVIGATION TWO Charts Properties of Mercator Chart ❖ Meridians: Straight parallels lines. ❖ Latitude: Straight parallel lines with spacing increasing toward the poles. ❖ Orthomorphic: Yes (after mathematical modelling). ❖ Rhumb Line: Straight lines. ❖ Great Circle: A curve concave toward the Equator, except for the meridians and the Equator, which are straight lines. ❖ Scale: Expands away from the Equator by the secant of the latitude. ❖ Limitations: 70°N/S. GENERAL NAVIGATION TWO Charts Lambert’s Conformal Conical Projection ❖ It is possible to project the graticule of the earth on to the inside surface of a cone. This process gives the conical family of projections from which Lambert's is derived. ❖ A cone is placed over a reduced earth, in such a way that the cone is tangential with the reduced earth along a parallel of latitude. The apex of the cone will lie on the extended line of the earth's axis as shown in Figure. ❖ A light source at the centre of the reduced earth casts shadows of the graticule on the inside surface of the cone. ❖ These shadows could be marked in, the cone removed, cut down its slant side and rolled out flat to give a simple conical projection as illustrated in Principle of Simple Conical Projection Figure. GENERAL NAVIGATION TWO Charts Lambert’s Conformal Conical Projection ❖ On the simple conical projection, scale is correct on the parallel of tangency, in the example shown, 45°N. This parallel, on which scale is correct, is called the 'Standard Parallel'. Scale expands on either side of the Standard Parallel. ❖ Figure below illustrates quite clearly that when the cone is flattened 360° of longitude are represented in a segment of a circle of 250 degrees, in this case. The size of the segment is controlled by the parallel of latitude chosen to be the parallel of tangency - the higher the latitude chosen the larger will be the segment. A simple Conical Projection - Graticule GENERAL NAVIGATION TWO Charts Lambert’s Conformal Conical Projection ❖ The Lambert’s Conformal Chart does not use one The Scale is: Standard Parallel, but two. ❖ Is correct at the Standard Parallels ❖ Expands away from the Standard ❖ The Standard Parallels are split by a mean parallel - the Parallels ❖ Contracts toward the Parallel of Origin Parallel of Origin. ❖ Is least at the Parallel of Origin Lambert’s Conformal Conical Projection Lambert’s Conformal Conical Projection – Part Graticule GENERAL NAVIGATION TWO Charts Properties of Lambert’s Conformal Conical Chart ❖ Meridians: Straight lines converging toward the pole. ❖ Latitude: Concentric arcs concave towards the pole with nearly constant spacing. ❖ Orthomorphic: Yes. ❖ Rhumb Line: Curves concave to the pole. ❖ Great Circle: are curve concave to the parallel of origin. Near the parallel of origin, they may be interpreted as straight line. ❖ Scale: Constant at the Standard Parallels. GENERAL NAVIGATION TWO Triangle of Velocities Basic Definitions ❖ Air Speed: The speed with which an aircraft passes through air is called the air speed and is measured by means of an Airspeed Indicator. ❖ Indicated Air Speed (IAS): It is the direct reading of the air speed on the dial of the Air Speed Indicator (ASI). ▪ IAS is independent of wind and is same regardless of whether aircraft is flying upwind, downwind or at any angle to the wind. GENERAL NAVIGATION TWO Triangle of Velocities Basic Definitions ❖ Rectified or Calibrated Air Speed (RAS or CAS): It is the Indicated Air Speed corrected or Instrument and Position Errors. ❖ True Air Speed (TAS): It is the RAS or CAS corrected for Density Error. (i.e. for temperature and height). ❖ Ground Speed: It is the speed of the aircraft relative to the ground. Or it is TAS corrected for wind velocity. ▪ TAS + Tail Wind = Ground Speed. ▪ TAS – Head Wind = Ground Speed. ▪ It can also be measured by noting the time interval between two observations of the aircraft actual position over the ground. ❖ Wind Speed: It is the speed at which the wind is blowing. Usually combined with direction. GENERAL NAVIGATION TWO Triangle of Velocities Basic Definitions ❖ Heading (Hdg): It is the direction in which the longitudinal axis (fore and aft axis) of an aircraft is pointing. It can be TRUE, MAGNETIC or COMPASS depending on the reference north from which it is measured. The Aircraft Heading is 000˚ (C) The Aircraft Heading is 090˚ (C) GENERAL NAVIGATION TWO Triangle of Velocities Basic Definitions ❖ Track (TRK): It is the direction of the path of an aircraft intended to be followed over the ground. It can be TRUE, MAGNETIC or COMPASS depending on the reference north from which it is measured. ❖ Track Made Good (TMG): It is the direction of the aircraft actually traced by an aircraft over the ground. ❖ Track Error: It is an angular difference between the required track and the TMG. It is measures from required track port or starboard. ❖ Drift: It is the angle between the heading and track. GENERAL NAVIGATION TWO Triangle of Velocities Basic Definitions GENERAL NAVIGATION TWO Triangle of Velocities The Triangle of Velocities ❖ The Air Vector: The Air Vector consists of Heading and True Air Speed (TAS). The Air Vector is always drawn with one direction arrow. ❖ The Wind Vector: The Wind Vector consists of Wind Direction and Wind Speed. Wind direction is always given in terms of the direction that the wind has come from, not where it is blowing to. GENERAL NAVIGATION TWO Triangle of Velocities The Triangle of Velocities ❖ The Ground Vector: The Ground Vector is drawn by joining up the Air Vector and the Wind Vector. The resultant vector is Track and Ground Speed. The Ground Vector is always drawn with 2 direction arrows. GENERAL NAVIGATION TWO Triangle of Velocities The Triangle of Velocities ❖ Figure below is a diagram of the Triangle of Velocities. ❖ In practice, pilots do not normally draw it out to scale on graph paper, but solve it using an analogue navigation computer. GENERAL NAVIGATION TWO Triangle of Velocities Practical Example You are in a Cessna 172. TAS is 100 knots. Heading of 000°T. The forecast W/V is 240/30. What will be your track and groundspeed? Sol: On graph paper provided, draw in the Air Vector. It will have a direction of 000°T and a vector length equivalent to 100 knots (say, 100 mm). Scale – 1mm = 1 knot. The Air Vector GENERAL NAVIGATION TWO Triangle of Velocities Practical Example ❖ Now draw in the Wind Vector. It was 240°/30 kt. ❖ Remember, it’s from 240°. It will actually point in the direction 060°T. ❖ Whatever units you used in proportion to 100 knots TAS (100 mm), draw the length of the wind vector in the same units (30 mm). The Air Vector and the Wind Vector GENERAL NAVIGATION TWO Triangle of Velocities Practical Example ❖ Now join the start of the Air Vector to the end of the Wind Vector to establish the resultant – the Ground Vector:- The complete Triangle of Velocities GENERAL NAVIGATION TWO Triangle of Velocities Practical Example ❖ Now measure the track with a protractor and you will find that it is 012°. ❖ Measure the length of the ground vector you will find a vector length equivalent to 118 knots. ❖ What this is telling you is that if you fly a heading of 000°T at a TAS of 100 knots in a wind of 240°/30kt, your path over the ground will actually be a track of 012°T at a groundspeed of 118 knots. ❖ It would be a bit long-winded if every time you wanted to fly, you had to start doing little scale drawings on graph paper. There has to be a quicker way. It’s called the Navigation Computer - using the Wind Face Side. GENERAL NAVIGATION TWO 1 in 60 Rule 1 in 60 Rule ❖ Over the years, pilots have had to find ways to calculate angles quickly and easily. One of these is called the “1 in 60 rule”. ❖ The 1 in 60 rule is based on the fact that the error in the track of one degree will result in the aircraft being one nautical mile off-track in a distance of sixty miles. ❖ This rule is valid about a maximum off track of 20˚, above that the theory starts to break down. GENERAL NAVIGATION TWO 1 in 60 Rule ❖ Imagine that you have a line on a piece of paper exactly 60 cm long: ❖ Now raise a perpendicular at one end, exactly 10 cm high, and join them with a hypotenuse: ❖ This will create an angle, Z, in the above diagram. ❖ If the adjacent is 60 cm long and the opposite is 10 cm long, then the angle Z will be 10°. ❖ Similarly, if the adjacent is 60 cm long and the opposite is 5 cm high, Z will be 5°. ❖ If the opposite is 8 cm high, z will be 8°, and so on - up to a maximum of about 20 degrees, when the theory starts to break down. GENERAL NAVIGATION TWO 1 in 60 Rule Some formulae for 1 in 60 Rule. To find Track Error 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇𝒇 𝑻𝒓𝒂𝒄𝒌 ❖ Track Error (in degrees) = x 60. 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒇𝒍𝒐𝒘𝒏 ❖ Example, you find yourself 6 miles right of track after 40 miles along track. In the above formula: 6 Track Error = x 60 40 Track Error = 9˚. GENERAL NAVIGATION TWO 1 in 60 Rule To calculate the Heading Alteration to reach Destination ❖ There are 3 basics techniques for getting back on track: ▪ Double Track Angle Error. ▪ Track Error Angle and Closing Angle. ▪ Combined Track Error Angle and Closing Angle Single Calculation. GENERAL NAVIGATION TWO 1 in 60 Rule Double Track Angle Error ❖ Consider the following situation: You are planning to fly a particular track (say 090°T) and you have done your flight plan and calculated a heading to fly. You fly that heading (accurately, I assume) but after 30 miles along track you get a pinpoint (a visual fix) which puts you 4 miles left of track. ❖ The track error is 8˚. If we do nothing about it, we will continue to diverge from track at the same rate. The following situation will develop:- GENERAL NAVIGATION TWO 1 in 60 Rule Double Track Angle Error ❖ The first thing is to stop this trend. We have drifted 8˚ to the left, so turn 8˚ right. ❖ Just turning 8° right has not solved the navigation problem, though. It has merely prevented it from getting any worse. We are now paralleling track, 4 nm to the left of it, but not getting back to it. ❖ In order to get back to track we need to double the correction i.e. 16° to the right. GENERAL NAVIGATION TWO 1 in 60 Rule Track Error Angle and Closing Angle ❖ Consider the following situation. Your total track distance is 78 nm. As before, after 30 nm along track, you get a pinpoint 4 nm left of track. As before, your track error angle is 8° to the left. ❖ As before, turning 8° to the right will only parallel track. We now need to calculate the closing angle on order to proceed to the turning point. GENERAL NAVIGATION TWO 1 in 60 Rule Track Error Angle and Closing Angle ❖ This is not too difficult. If we have gone 30 nm along a 78 nm track, there must still be a further 48 nm remaining. ❖ We are 4 nm off track in 48 to go, so that is 1 in 12 - which is 5 in 60. Therefore our closing angle is 5°. ❖ So, we turn 8° right to parallel track and a further 5° right to converge, making a total turn of 13° required. ❖ Therefore, to summarise, the required amount of turn is the sum of Track Error Angle and Closing Angle. Heading Alteration = Track Error + [ 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇𝒇 𝑻𝒓𝒂𝒄𝒌 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒐 𝒈𝒐 x 60]. GENERAL NAVIGATION TWO Bibliography ▪ EASA Part-FCL/eRules, Dec 2021, Subpart C. ❖ General Navigation, CAE Oxford ATPL Series Books. (Including pictures) ❖ General Navigation, Atlantic Flight Training ATPL Series Books. (Including pictures) ❖ FAA Pilot’s Handbook of Aeronautical Knowledge. ❖ Air Navigation, Volume 3, Air Pilot’s Manual, Pooley’s Ninth Revised Edition 2010.  , 0 L\ 1 o N - 9-c f 3, o' /-J - --- x 6t) e;, I. 0 uJJ- 2.J- oo 'h-JlL - :i 2 6 o, ;Jo I l I r,.,_I 20 30 0 2 0 3o'rJ ° + LI o" 3:,0.S..__,v f - - Go' 60' vi t i - 1Av,_ :::: 6L Oo _so;,tq j o OD\ !}.ocJ1 "' ' 0'\. 6 {J)J: 0 I vA,,/) , I , 6i DD y:b o::: 36 60 s[j Lu"- 6ENT1169 Tutorial 1 General Navigation Sample Questions Change of Latitude 1. Position A. 29˚ 55’ N to B. 88˚ 20’ N. Answer: 58˚ 25’ N. 2. Position A. 33˚ 35’ S to B. 42˚ 15’ S. Answer: 08˚ 40’ S. 3. Position A. 62˚ 25’ N to B. 73˚ 55’ S. Answer: 136˚ 20’ S. 4. Position A. 15˚ 57’ S to B. 22˚ 27’ N. Answer: 38˚ 24’ N. 5. Position A. 72˚ 10’ N to B. 57˚ 20’ N. Answer: 14˚ 50’ S. 6. Position A. 59˚ 10’ S to B. 22˚ 55’ S. Answer: 36˚ 15’ N. Change of Longitude 1. Position A. 67˚ 30’ E to B. 145˚ 20’ E. Answer: 77˚ 50’ E. 2. Position A. 72˚ 55’ E to B. 22˚ 37’ E. Answer: 50˚ 18’ W. 3. Position A. 72˚ 30’ W to B. 82˚ 50’ E. Answer: 155˚ 20’ E. 4. Position A. 172˚ 30’ E to B. 170˚ 50’ W. Answer: 16˚ 40’ E. 5. Position A. 92˚ 30’ W to B. 155˚ 25’ W. Answer: 62˚ 55’ W. 6. Position A. 23˚ 30’ E to B. 45˚ 50’ W. Answer: 69˚ 20’ W. Distances 1. Calculate the distance between A. 65 30N 150 00E and B. 23 50N 150 00E. Answer: 2500 nm. 2. Calculate the distance between A. 00 00N 155 30W and B. 00 00N 167 30E. Answer: 2220 nm 3. Calculate the distance between A. 60 00N 172 50E and B. 60 00N 150 30W. Answer: 1100 nm. 4. At what latitude a distance of 900 nm will involve a D long of 30 degrees? Answer: 60˚. 5. How many hours will it take to go round the earth at 60 deg. Lat. at a G/S of 600 kts? Answer: 18 hrs. 6. An Aircraft flies due south from place X 40˚00’ N 179˚ 00’E at a ground speed of 120 knots for 2 hours. Find its position at the end of the flight. Answer: 36˚ 00’ N/S 179˚ 00’E. 7. An Aircraft flies due east from place X 30˚00’ N 04˚ 00’W at a ground speed of 220 knots for 5 hours. Find its position at the end of the flight. Answer: 30˚ 00’ N. N 17˚ 10’E. Time 1. Convert this Arcs in to time a. 172 30 E. Answer: 11 hrs 30 min. b. 169 20 W. Answer: 11 hrs 17 min 20 sec. c. 20 10 W. Answer: 1 hr 20 min 40 sec. d. 07 30 E. 0 hrs 30 min. 2. LMT at position A. 48 30 N 103 15 E is 1045 hrs on 17th June. What is the LMT at position B. 48 30S 007 1E? Answer: 0420 hrs 17 June. 3. At 30 00N 46 30E the time is 0300 LMT. What is the time at 60 00N 016 15W? Answer: 2249 previous day. 4. LMT at position A. 40 40 N 169 45 E is 0610 hrs on 14th March. What is the LMT at position B. 30 30N 170 30W? Answer: 0729 hrs 13 March. Created by Sagar Patel January 2021 6ENT1169 Navigation, Human Factors, and Meteorology 2022-23 General Navigation Sample Questions Direction Conversion ˚ TRUE VARN ˚MAG DEVN ˚COMP 260 291 3E 10W 1E 070 354 7W 2E 10E 296 1W 076 071 +1 022 -3 035 -3 +2 119 Triangle of Velocities TRACK MADE HDG ˚(T) W/V TAS GS GOOD ˚(T) 273 230/40 286 150 124 181 150/30 194 90 66 054 350/28 073 88 80 141 280/35 135 190 217 029 090/40 016 170 155 310 045/45 302 320 327 187 270/60 157 110 119 1 in 60 Rule 1. You are flying from A to B. You find that your position is 60 nm outbound from A and 7 nm left of the required track. What is your track error angle? Answer: 7˚L. 2. You are flying from C to D. You find that your position is 120 nm outbound from C and 8 nm right of the required track. What is your track error angle? Answer: 4˚R. 3. You are flying from E to F. You find that your position is 90 nm outbound from E and 6 nm right of the required track. What is your track error angle? Answer: 4˚R. 4. You are flying from G to H. You find that your position is 30 nm outbound from G and 4 nm left of the required track. What is your track error angle? Answer: 8˚L. 5. You are flying from J to K, which is a required track of 045oT. You find that your position is 80 nm outbound from J and 4 nm left of the required track. What is your track made good? Answer: 042˚T. 6. You are flying from L to M, which is a required track of 220oT. You find that your position is 45 nm outbound from L and 3 nm right of the required track. What is your track made good? Answer: 224˚T. 7. You are flying from N to P, which is a required track of 315oT. You find that your position is 40 nm outbound from N and 6 nm left of the required track. What is your track made good? Answer: 306˚T. 8. An aircraft leaves A to fly to B, 95 nm distance. Having flown 35 nm, the aircraft position is found from a ‘pinpoint’ (a geographical point over which the aircraft has flown); the pinpoint is 7 nm right of track. a. What is the track error? Answer: 12˚ right. b. What alteration of heading is required to fly direct to B? Answer: 19˚ left. Created by Sagar Patel October 2022  ·.c e.. Jiu, c.tC-Ao Vlf l,vf , O I... rnA-C? 08);0 0 p Vc aJJur1 t, l) P- u e 0 c_0 fYl. c) ·, V A- V,11,ucJfU'() w- , { '.2.60 1- w P-N 29.:L 3E.2. 7> i ()6.i. ::LovJ 0·1 :i. :i-8 CJ::f-C> I) ev cJy:'lr, I ) [of' f­ wf.J,f, u1.1,f be 1. 35 -=,-w 0 0 :1. 2. 359 ui '30G.102 2.9b.:Lw.:2...'-1 -:.;- " +" (plus) is East 0'1-b +5 o-=l-- ::L +.1- 010 " --- " (minus) is West () ?--2 t G 006 '2> Q 09 -:1. '2.0 3 +2 :i21 1 23 I 1N cl),,- I/ e..1o ei_,1-f a }