GNAV 1 Exam Review: Lessons 5-9

GNAV 1 Review

• The exam includes questions from lessons 5, 6, 7, 8 and 9
• Lesson 5 (Directions and Coordinates) has 3 theory questions
• Lesson 6 (Coordinates and Distance) has 3 calculation questions
• Lesson 7 (Lines on the Earth) has 4 calculation and 2 theory questions
• Lesson 8 (Magnetism and Compasses) has 5 theory and 2 TVMDC/CVMDC with drift questions
• Lesson 9 (Conic Projections) has 2 scale, 4 Lambert calculation, and 5 theory questions

Key Concepts to Review

• Oblate Spheroid or Ellipsoid definition
• Geoid definition
• Parallels of Latitude / Meridians
• Latitude / Longitude (change calculations)
• Coordinates calculations
• Finding position on the opposite Side of Earth
• Ratio of Ellipticity
• Geocentric and Geodetic Latitudes definitions
• Distance Conversions
• 1° on a great circle equals 60 NM
• 1’ on a great circle equals 1 NM
• Departure formula and calculations
• Calculation of circumference, radius and diameter of Earth
• Distance over the poles formula applies when the sum of the longitude of 2 points equals 180°
• Rhumb Line track / small circles (Definition and properties)
• Great circles (Definition and properties)
• Convergency formula (general)
• Conversion angles
• Soft and Hard Iron
• The north pole on a magnet is red, and the south pole is blue
• Earth’s Magnetism (North pole vs True pole; is the Earth's North pole actually a North or South magnetic pole?)
• Isogonals, Agonic, Isoclinic, Aclinic (magnetic equator)
• TVMDC or CDMVT calculations WITH DRIFT (L or R) or WITH CORRECTION ANGLE (L or R)

Definitions and Procedures

• DIP definition explains where it is the strongest
• Compass Swing (procedure on when to reswing a compass)
• General Aviation Chart Requirements
• Graticule is a conformal or orthomorphic chart definition
• Scale definition and calculations
• Convergency formula for a projection
• Constant of the cone helps determine the parallel of Origin with the constant of the cone

Lambert Charts

• Covergency formula
• Great circles, Rhumb lines, Strait line
• Concave or Convex relation
• Normal maximum Spread of the scale
• Scale variation in size, where is the smallest? Biggest? Contracts? Expands?
• Constant of the Cone
• Parallel of origin, standard parallels
• Where is the convergency correct?
• Where is the scale correct?

Earth Shape

• An oblate or ellipsoid spheroid is a 3D shape similar to a sphere, but flattened at the poles and wider at the equator
• The Earth is an oblate spheroid, slightly flattened at the poles and wider at the equator

Geoid Definition

• The geoid is the shape that the ocean surface would take under the influence of gravity and the rotation of the Earth alone
• Considers other influences such as winds and tides were absent

Parallels and Meridians

• Meridians run north/south, parallels of latitude east/west

Calculating Latitude and Longitude Changes

• Different hemispheres: Add angles
• Same hemisphere: Subtract smaller angle from larger
• Consider the shortest route around Earth when calculating longitude changes

Coordinate Calculations

• Latitude Change for different hemispheres: ADD latitudes
• Latitude Change for same hemisphere: SUBTRACT latitudes

Finding Position on Opposite Sides of the Earth

• Given initial position: e.g. 88°22’S, 07°45’N
• To solve: 88°22’S + 07°45’N= 95°67
• To express correctly convert 60 of those mins to 1° then obtaining a different latitude of 96°07’

Latitudes

• Geocentric is relating or measured from the Earth's center
• Geodetic is a coordinate system and a set of reference points used for locating places on earth

Latitude Distance Calculation

• 1 degree equals 60 nautical miles (NM)
• Calculated by multiplying latitude change by 60 NM per degree

Departure (East/West Distance) Calculation

• Uses the formula: Departure (NM) = Change of Longitude (minutes) × Cosine of Latitude
• Distance decreases as latitude increases from equator to poles
• Xavi method: Departure =change of longitude x cos°(lat) x 60

Distance Over Poles Calculation

• Angle = 180° - (Latitude 1 + Latitude 2)
• Converts angle to nautical miles (1 minute = 1 NM)
• Formula applicable only when longitudes are 180° apart
• Add latitudes, subtract total from 180°

Rhumb Lines

• Lines of constant direction that cross all meridians at the same angle

Key Properties of Rhumb Lines

• Always have a constant track direction
• Always longer than great circle routes
• Always lie on the equatorial side of great circles
• Useful for short distances or low latitudes

Small Circles

• Circles that do not pass through the center of the sphere

Key Characteristics of Small Circles

• Radius is less than the sphere's radius
• An unlimited number can be drawn between any two points on a sphere
• Parallels of latitude are examples of small circles

Relationship of Circles and Rhumb lines

• Rhumb lines never follow the same path as great circles, except for meridians and the equator

Great Circles

• The shortest distance between two points on the Earth's surface

Key Properties of Great Circles

• Passes through the center of the sphere
• Track direction changes continuously (except along meridians and equator)
• Only one great circle connects two points (except at opposite poles)

Geometric Characteristics of Great Circles

• Formed by the intersection of a plane passing through the center of the sphere and the sphere's surface
• Largest circle that can be drawn on a sphere's surface

Navigation Implications of Great Circles

• Preferred for long-distance travel
• Requires advanced navigation systems like GPS or Flight Management Systems
• Track direction changes based on convergency (calculated by change of longitude × sine of mean latitude)

Convergency Formula (for great circles)

• Convergency = change of longitude × sin(mean latitude)

Calculation Steps

• Find mean latitude by averaging the two point latitudes
• Multiply change in longitude by sine of mean latitude
• Best used for positions within 30° longitude difference

Conversion Angle Formula

• Conversion Angle = ½ Convergency

Note

• Helps determine the angle between great circle and rhumb line tracks

Soft Iron

• Easily magnetized and demagnetized
• Quickly attains maximum magnetism
• Loses magnetism easily when the magnetic field is removed

Hard Iron

• Difficult to magnetize
• Retains magnetism for a longer period
• More resistant to losing its magnetic properties

Molecular Explanation

• In soft iron, molecular magnets align quickly and disperse easily
• Hard iron's molecular magnets are more resistant to realignment

Magnet Pole Colors

• North pole is traditionally colored red
• South pole is traditionally colored blue

Important Nuance

• For the Earth's magnetic poles, this color convention can be confusing
• The Earth's north magnetic pole is actually a blue (south) pole
• The Earth's south magnetic pole is actually a red (north) pole

Earth's Magnetic Poles vs Geographic Poles

• The Earth's magnetic poles do not coincide with the geographic poles
• The magnetic pole is not at the end of the, but some distance inside
• Long thin magnets have poles near the ends
• Short fat magnets (like Earth) have poles further in
• The area referred to as the 'north magnetic pole' is physically a south magnetic pole
• The magnetic pole is not aligned with the Earth's rotational axis

Variation

• The angle between true meridian and magnetic meridian is called variation
• Variation can range from 0° to 180° across the Earth

Magnetic Navigation Terms

• Isogonal's: Lines on a map that connect points with equal magnetic variation between true and magnetic north
• Agonic Line: A special line where magnetic variation is zero (true north and magnetic north align perfectly)
• Isoclinic Lines: Lines connecting points with the same magnetic dip angle
• Aclinic Line: The magnetic equator where the magnetic dip angle is zero degrees, meaning the compass needle remains perfectly horizontal

Note on Magnetic Lines

• These lines help navigators understand how magnetic fields vary across the Earth's surface

Dip Definition

• The magnetic compass reads most accurately at headings of 0º (North) or 180º (South) during a level 360-degree turn with a 15-degree bank minimises errors
• At these headings, the compass can better align with the Earth's magnetic field, leading to more accurate readings