Notes Flashcards

Question 1

Q

Earth - Shape, Dimensions, and Convergence

Shape of Earth:
• Oblate Spheroid: The Earth is flattened at the poles and bulging at the equator due to rotation.
• Compression Ratio:
Formula: Compression Ratio = (Major Axis - Minor Axis) ÷ Major Axis
Value: 0.3%

Dimensions:
• Equatorial Diameter = 6888 NM (~40,075 km)
• Polar Diameter = 6863 NM (~39,931 km)
• Difference = 23 NM (~43 km)

Convergence:
• Definition: Angle of inclination between meridians at a given latitude.
• Maximum: At poles.
• Zero: At equator.
• Formula:
Convergence = (Δ Longitude) × sin(mean latitude)
• Convergence Angle (CA):
CA = Convergence ÷ 2

Navigation - Great Circle vs. Rhumb Line

Great Circle (GC):
• Shortest path between two points.
• Track constantly changes.
• Crosses the equator and poles.

Rhumb Line (RL):
• Maintains constant compass direction.
• Appears straight on a Mercator map.
• Longer at higher latitudes.

Key Differences:
• At Poles: Maximum deviation between GC and RL.

Wind and Drift

Wind Components:
• Tailwind (TW) = Wind Speed × cos(Angle)
• Crosswind (CW) = Wind Speed × sin(Angle)

Drift:
• Drift Angle: Difference between actual track and intended heading due to wind.
• Adjustments:
• Left drift → Add to heading.
• Right drift → Subtract from heading.

Optimal Runway Use:
• Maximize headwind.
• Minimize crosswind.

Fuel, Endurance, and Distance

Endurance:
• Definition: Total time an aircraft can fly with available fuel.
• Formula: Endurance = Fuel on Board (FOB) ÷ Fuel Consumption Rate

Distance Calculation:
1. Latitude-based:
Distance (NM) = Change in Latitude (chlat) × 60
2. Longitude-based (adjust for latitude):
Distance (NM) = Change in Longitude (chlong) × 60 × cos(chlat)

Descent and Rate of Descent (ROD)

Gradient Formula:

Gradient (%) = (Vertical Distance ÷ Horizontal Distance) × 100

ROD Formula:

ROD = (101.3 × Ground Speed × Gradient) ÷ 60

Factors Affecting ROD:
• Decrease in Ground Speed (GS) → Decrease in ROD.
• Decrease in Headwind (HW) → Decrease in GS.

Problem-Solving for Coordinates
1. Case 1: Check if coordinates are antipodal.
  • If Yes → Distance = 10,800 NM.
  • If No → Move to Case 2.
2. Case 2: Check if sum of latitudes and longitudes = 180°.
  • If Yes → Travel via poles.
  • If No → Move to Case 3.
3. Case 3: Use formulas:
  • Destination Distance (NM) = Change in Latitude (chlat) × 60
  • Departure Distance (NM) = Change in Longitude (chlong) × 60 × cos(chlat)
Earth Models and Geoid
• Geoid: Irregular, actual shape of Earth based on gravitational field.
• Ellipsoid: Simplified model used for navigation and calculations.
• Geodetic Models:
• WGS-84 (adopted globally) defines the Earth’s size and shape for navigation.
Additional Notes and Conversions

Latitude and Longitude:
• 1° Latitude = 60 NM
• 1 NM = 1.852 km = 6080 ft

Semi-Axis Calculations:
• Semi-major axis = Equatorial Radius.
• Semi-minor axis = Polar Radius.

Miscellaneous Conversions:
• 1 US Gallon = 3.785 liters
• 1 Imperial Gallon = 4.546 liters

Great Circle Backtrack:
• Average Great Circle Backtrack = (RL) Track

Compass deviation changes with both time and place due to varying magnetic fields and local influences.

Wind is blowing towards the South at 40 knots.
• Direction is given from where the wind originates.

With a Westerly Variation, True North is east of Compass North.

Deviation is 4°W and True north is east of Compass north

All meridians are rhumb line and not semi GC

Highest Value of Longitude

Longitude is measured from 0° to 180° (East or West). The maximum value is along the Greenwich Anti-Meridian (180°).

Magnetic Variation Changes

Magnetic variation changes with time and place due to shifts in Earth’s magnetic field.

Distance to PNR (Point of No Return)
• The PNR is the farthest point an aircraft can fly and return safely to the departure point with the available fuel.
• If there is no wind, the PNR distance is maximum, as headwind/tailwind reduces effective range.

Maximum in nil wind conditions

With a tailwind, the CP shifts closer to the destination, as the ground speed increases.

Departure: 40°N 20°E
• Destination: 80°N 160°W.

For shortest route (great circle), the initial track is northward.

A kilometre is defined as:
• 1/10,000th of the distance from the Equator to the poles along a meridian.

The Earth’s polar diameter is slightly less than the equatorial diameter due to flattening at the poles.
Less by 40 km

A 10-knot decrease in headwind reduces the ground speed, increasing the time to descend. To maintain the glide slope, the rate of descent must decrease.

A rhumb line maintains a constant angle to all meridians. It is not a great circle or a line of variation.

Length of a Nautical Mile

The length of a nautical mile is constant regardless of location. It is defined based on the Earth’s meridian.

Feet in a Kilometer

1 kilometer is approximately 3280 feet.

Negative Magnetic Variation

A negative magnetic variation indicates that the true north lies east of magnetic north.
True North is East of Magnetic North

Rhumb Line Path

A rhumb line crosses all meridians at the same angle, forming a spiral path that approaches the pole but never reaches it.

A spiral path leading towards the North Pole

Question 2

Q

Convergence Formula

Convergence = (Δ Longitude) × sin(mean latitude)

Convergence Angle (CA) = Convergence ÷ 2

Endurance Formula

Endurance = Fuel on Board (FOB) ÷ Fuel Consumption Rate

Distance Calculation Formulas
1. Latitude-based distance:
  Distance (NM) = Change in Latitude (chlat) × 60
2. Longitude-based distance:
  Distance (NM) = Change in Longitude (chlong) × 60 × cos(chlat)
Gradient and Rate of Descent (ROD)
1. Gradient (%) = (Vertical Distance ÷ Horizontal Distance) × 100
2. ROD = (101.3 × Ground Speed × Gradient) ÷ 60
Wind Component Formulas
1. Tailwind (TW) = Wind Speed × cos(Angle)
2. Crosswind (CW) = Wind Speed × sin(Angle)
Semi-Axis Difference (Earth Dimensions)

Compression Ratio = (Major Axis - Minor Axis) ÷ Major Axis

Problem-Solving for Coordinates
1. Destination Distance (NM) = Change in Latitude (chlat) × 60
2. Departure Distance (NM) = Change in Longitude (chlong) × 60 × cos(chlat)
Miscellaneous Conversions
1. 1 Nautical Mile (NM) = 1.852 km = 6080 ft
2. 1 US Gallon = 3.785 liters
3. 1 Imperial Gallon = 4.546 liters

Question 3

Q

Shape of Earth:
• Commonly known as Oblate Spheroid, Ellipsoid, or Geoid.
• Flattened at the poles due to Earth’s rotation.
• Compression (flattening at poles) caused by higher centrifugal force at the equator.
• Compression Ratio (Ratio of Ellipticity):
Compression Ratio = (Major Axis - Minor Axis) / Major Axis

Earth Dimensions:
• Equatorial Diameter (Major Axis): 6888 nautical miles
• Polar Diameter (Minor Axis): 6865 nautical miles
• Difference: 23 nautical miles (or 43 km, 275 m)

Measurements:
• 1 Nautical Mile:
• 1 NM = 1.852 km
• 1 NM = 6080 ft
• Circumference of Earth: 21600 NM or 40000 km

Earth Models:
• WGS84 (World Geodetic System 1984):
• Used by the USA.
• Adopted as the ICAO world standard.

Key Circles:
• Prime Meridian: Datum for measuring longitudes; passes through Greenwich.
• Parallels of Latitude: Small circles parallel to the equator.
Examples:
• Arctic Circle: 66.5° N
• Tropic of Cancer: 23.5° N
• Tropic of Capricorn: 23.5° S
• Antarctic Circle: 66.5° S

Great Circle:

•	Cuts Earth into two equal halves.
•	Shortest distance between two points on Earth.
•	Plane passes through Earth’s center.

Rhumb Line (RL):

•	Line of constant course; cuts all meridians at an equal angle.
•	RL track:
•	90° or 270°: Circles latitude.
•	360°: Ends at the North Pole.
•	180°: Ends at the South Pole.

Rotation of Earth:
• Viewed from North Pole: Anti-clockwise
• Viewed from South Pole: Clockwise
• Viewed laterally (front): West to east

Latitude and Longitude:
• Latitude:
• Distance north or south of the equator.
• Circles run east-west; values up to 90°.
• Annotated as North or South depending on hemisphere.
• Longitude:
• Distance east or west of the prime meridian.
• Lines run north-south; values up to 180°.
• Annotated as East or West depending on location.

Formulae:
1. Compression Ratio:
Compression Ratio = (Major Axis - Minor Axis) / Major Axis
2. Departure:
Departure = Chlong × 60 × cos(Latitude)
3. Distance:
Distance = Chlat × 60
4. Position Change:
• Same Sign: Subtract
• Opposite Sign: Add

Finding Position B (Given Position A and Chlong/chlat):
• Same Sign: Add.
• Opposite Sign: Subtract.

Conversions:
• 1 Degree = 60 Minutes
• 1 Minute = 60 Seconds
• 1 Minute = 1 Nautical Mile

Homing vs. Tracking:
• Homing: Giving correction after getting drifted.
• Tracking to Station: Giving correction before getting drifted.

Greatest Difference Between Initial GC Track and Mean GC Track:
• Found in areas with more mean latitude or maximum mean latitude.
• The closer you are to the poles (higher latitude), the greater the curvature of Earth, leading to a greater difference.

Average of Tracks:
• Average of GC Track = RL Track

Great Circle (GC) vs. Rhumb Line (RL):
• Great Circle:
• Concave to Earth.
• Cuts Earth into two equal halves.
• Diameter of GC = Diameter of Earth.
• Shortest distance on Earth between two points.
• Plane of cut always passes through the center of the Earth.
• Largest circle that can be drawn on Earth’s surface.
• On charts: Curved line.
• Rhumb Line (RL):
• Line of constant course; cuts all meridians at equal angles.
• Always concave to corresponding pole.
• RL Track:
• 90° or 270°: Circles latitude.
• 360°: Ends at North Pole.
• 180°: Ends at South Pole.
• 270° to 89°: Spirals to North Pole.
• 91° to 269°: Spirals to South Pole.
• On charts: Straight line.

Key Relationships Between GC and RL:
• Meridian: Not a great circle; it is a rhumb line.
• Longitude: Not a great circle; it is a rhumb line.
• Latitude: Not a great circle; it is a rhumb line.
• Equator: Both a GC and RL.
• Meridian + Anti-Meridian: Great Circle, but not a rhumb line.

Directions:
• True North: Geographical north.
• Magnetic North: Where a suspended magnetic needle aligns due to Earth’s magnetic field.
• Compass North: Alignment of a compass in an aircraft, influenced by electrical/magnetic components of the aircraft.

Variation and Deviation:
Variation:
• Angle between true north and magnetic north.
• Changes with location and time.
• Maximum value: 180° East or West.
• Represented by blue dashed lines on VFR charts.

Deviation:
•	Angular difference between magnetic north and compass north.
•	Varies from aircraft to aircraft and heading.
•	Every aircraft has its own compass deviation card.

Track, Heading, and Drift:
• Track: Path of aircraft described on the ground.
• Heading: Direction in which the aircraft’s nose points.
• Both track and heading can be true, magnetic, or compass.
• Drift: Angular difference between track and heading:
• Track > Heading: Right drift, left wind.
• Track < Heading: Left drift, right wind.
• Track Made Good (TMG): Path of aircraft followed on the ground.

Nautical Mile:
• Definition: Arc from the Earth’s center to its surface.
• At poles: 6107 feet.
• At equator: 6036 feet.
• Average: 6076 feet.
• Standard Calculation: 6080 feet (used from 45°N to 45°S, unless otherwise specified).
• ICAO Recommendation: 1 Nautical Mile = 1852 meters.

Kilometer:
• One ten-thousandth of the distance from the equator to the pole.
• Conversion relationship:
• 1 Degree Latitude = 60 Minutes.
• 1 Minute = 1 Nautical Mile.
• Therefore, 1 Degree Latitude = 60 Nautical Miles.
• Longitude:
• 1 Degree Longitude = 60 Nautical Miles (only at the equator).

Directional Notations:
• West:
• Next West, Left, Port, Minus (-).
• East:
• Next least, Right, Starboard, Plus (+).

Antipodal Definition:
• Two points are antipodal if they are directly opposite to each other on the Earth’s surface.
• Example: The North Pole and South Pole are antipodal points.

Solving Distance Questions:

Case 1:
• Are the coordinates antipodal?
• If Yes: Distance = 10800 nautical miles.
• If No: Check Case 2.

Case 2:
• Is the sum of the longitudes of both coordinates = 180°?
• If Yes: Fly via poles.
• If No: Check Case 3.

Case 3:
• Distance = Change in Latitude × 60.
• Departure = Change in Longitude × 60 × cos(Change in Latitude).

Track vs. Heading:
• Track: Planned path of the aircraft on the ground.
• Heading: Direction in which the aircraft’s nose is pointing.
• Track Made Good (TMG): Actual path followed by the aircraft.
• Required Track: Path the aircraft should follow after deviation.

1 in 60 Rule:
• Definition: One nautical mile off-track from the planned track subtends an angle of 1° at a distance of 60 nautical miles.
• Examples:
• 8 nautical miles = 3° at 60 NM.

Departure:
• Definition: Distance along parallels of latitude in the east-west direction.
• Formula:
Departure = Change in Longitude × 60 × cos(Latitude)
• Maximum at equator, zero at poles.

Distance Formula:
• Formula:
Distance = Change in Latitude × 60

Track Error (TE) and Closing Angle (CA):
• Track Error Formula:
Track Error = (60 × Off Track) / Distance Covered
• Closing Angle Formula:
Closing Angle = (60 × Off Track) / Distance to Go

Required Track Calculations:
1. Track Made Good (TMG):
TMG = Planned Track + Track Error
2. Total Correction Angle (TCA):
TCA = Track Error + Closing Angle
3. Required Track:
Required Track = TMG ± TCA

TAS (True Airspeed) vs. GS (Ground Speed):

True Airspeed (TAS): Aircraft speed in air; constant unless throttle settings change.

Ground Speed (GS): Speed at which aircraft covers ground.
• Nil Wind: TAS = GS
• Headwind: TAS > GS
• Tailwind: TAS < GS

Endurance:
1. Total Endurance Formula:
Total Endurance = Fuel on Board (FOB) / Fuel Consumption per Hour
2. Safe Endurance Formula:
Safe Endurance = (FOB - Reserve Fuel) / Fuel Consumption

•	Note: Endurance is always expressed in time.

Conversion Factors:
• 1 US Gallon: 3.785 Litres
• 1 UK (Imperial) Gallon: 4.546 Litres
• Specific Gravity: Measures the thickness of a liquid.
• Formula:
Mass (kg) = Volume (Litres) × Specific Gravity

Key Pointer Notes:

Scale:
• Definition: Relationship between the line drawn on a chart and the actual distance on Earth between the same points.
• Formula 1:
Scale = Chart Length (CL) / Earth Distance (ED)
• Formula 2:
EDA / EDB = cos(A) / cos(B)

Earth Convergence:
• Definition: Angle of inclination between two meridians at a given latitude.
• Maximum at poles, zero at equator.
• Increases with latitude and Dlong (difference in longitude).
• Formulas:
Convergence = Dlong × sin(Mean Latitude)
Convergence = Angular Difference between two GC Tracks
• Key Note:
• GC is straight and RL is curved on Earth.
• On charts: GC is curved, RL is straight.
• Radio signals follow GC paths.
• RL is always on the equatorial side of Earth.

Conversion Angle (CA):
• Definition: Angular difference between GC and RL.
• Formula:
CA = Convergence / 2

Rhumb Line (RL) and Great Circle (GC):
• If points A and B are on the same latitude:
• RL = 90° or 270°.
• In the Northern Hemisphere:
• Opposite RL can be taken for returning from B to A.
• Opposite GC cannot be taken as the track always changes in GC.
• Smiling face for Northern Hemisphere (we live here).
• In the Southern Hemisphere:
• Opposite applies.

Wind Components:
• Formulas:
• Tailwind: -V × cos(θ)
• Headwind: V × cos(θ)
• Crosswind: V × sin(θ)
• θ: Angle between runway and wind direction (aircraft track magnetic).
• V: Wind speed.
• Best Runway for Takeoff/Landing:
• Maximum headwind.
• Minimum crosswind component.

Descent (ROD - Rate of Descent):
• Key Concepts:
• VSI (Vertical Speed Indicator).
• GSA/GPA Component: 3°.
• Formulas:
• GSA = 6 × Height in Feet / (R in Nautical Miles × 6080)
• Gradient (%) = Vertical Distance / Horizontal Distance × 100
• Gradient = VD / HD
• ROD = Change in Altitude in Feet / Time in Minutes
• ROD = 101.3 × GS / 60
• ROD = 101.3 × Gradient × GS
• Key Notes:
• ROD is directly proportional to GS.
• Wind Effects:
• Decrease in tailwind = Decrease in GS.
• Increase in headwind = Decrease in GS.
• Decrease in headwind = Increase in GS.

Answer

A

Earth’s Magnetism Notes

Basics of Earth’s Magnetism
• Earth behaves like a giant magnet.
• Magnetic needle aligns itself to Earth’s magnetic field, pointing towards magnetic north and south.
• Magnetic compasses work based on Earth’s magnetic field.

Components of Earth’s Magnetic Field
1. Horizontal Component (H):
• Responsible for providing direction in aircraft.
• Also known as directive force.
• Formula: H = T cos θ (T = Tesla, θ = Latitude).
• Key Points:
• H is maximum at the equator.
• H is minimum at the poles.
• Magnetic needle is most effective at the equator.
2. Vertical Component (Z):
• Responsible for magnetic dip.
• Magnetic Dip: The angle between a freely suspended magnet and the horizontal plane.
• Formula: Z = T sin θ (T = Tesla, θ = Latitude).
• Key Points:
• Z is maximum at the poles (90°).
• Z is zero at the equator.
• Magnetic needle stands vertical at poles, causing false readings.

Compass Requirements
1. Horizontality:
• Compass should remain horizontal for correct functioning. It should not dip
Or tilt.
• Achieved using pendulous suspension system.
• Center of gravity is kept below the pivot point to reduce the effect of Z.
2. Sensitivity:
• Compass should detect small heading changes.
• Achieved by:
• Using lightweight magnets.
• Increasing polar strength of the magnet.
• Reducing pivot friction using jeweled (metallic) pivots.
3. Aperiodicity:
• Compass should prevent oscillation or vibration.
• Achieved using liquid and damping wires, which break oscillations and keep the compass steady.
• these damp wires, break the oscillation and bring the magnet dead beat.

Properties of Liquid Used in Compass
• Colorless and transparent.
• High boiling point and low freezing point.
• Low coefficient of expansion.
• Low viscosity (thin consistency).
• Non-corrosive.

Common Liquids Used:
• Alcohol + Water
• Kerosene

Errors in Magnetic Compass

Turning Error
• Cause: Due to magnetic dip.
• Location Impact:
• No turning error at the equator.
• Maximum error at poles (30°).
• Zero on east-west heading.
• Maximum on north-south heading.

• Northern Hemisphere (UNOS):
• U: Undershoot North.
• Turning through North (360°) towards East or West: Compass lags (under-reads).
• Pilot Action: Undershoot the heading.
• O: Overshoot South.
• Turning through South (180°) towards East or West: Compass leads (over-reads).
• Pilot Action: Overshoot the heading.

• Southern Hemisphere (SUNO):
• S: Overshoot North.
• Turning through North (360°) towards East or West: Compass leads (over-reads).
• Pilot Action: Overshoot the heading.
• U: Undershoot South.
• Turning through South (180°) towards East or West: Compass lags (under-reads).
• Pilot Action: Undershoot the heading.

•	Summary:
•	If heading and hemisphere name are the same, compass will under-read.
•	If heading and hemisphere name are different/opposite, compass will over-read.

Acceleration Error
• Cause: Acceleration on easterly or westerly heading.
• Effect: Compass needle shows an apparent turn towards the nearer pole.
• Location Impact:
• Maximum error on east-west heading.
• Zero error on north-south heading.
• Compass Behavior:
• Compass card moves opposite to the compass needle.

De acceleration Error
• Cause: Deacceleration on easterly or westerly heading.
• Effect: Compass needle shows an apparent turn towards the farther pole or equator.
• Location Impact:
• Maximum error on east-west heading.
• Zero error on north-south heading.
• Compass Behavior:
• Compass card moves opposite to the compass needle.

Key Pointer Notes:

Magnetic Compass Components:
• Magnetic Needle: Aligns with Earth’s magnetic field.
• Compass Card: Displays headings; marked with cardinal directions.
• Damping Fluid: Mixture of alcohol and water or kerosene; reduces oscillations.
• Housing: Encloses the compass system.

•	Movement of damping fluid causes liquid swirl, which can affect compass readings.
•	Overheating decreases liquid swirl, while underheating increases it.

Liquid Swirl:
• Caused by damping fluid movement due to rapid altitude, direction, or speed changes.
• Overheating = Decreased liquid swirl.
• Underheating = Increased liquid swirl.

•	Proper temperature regulation is crucial for accurate compass functionality.

Standard Rate of Turn (SRT):
• Rate 1 Turn: 3°/second.
• Rate 2 Turn: 6°/second.
• Rate 3 Turn: 9°/second.

•	Used for calculating smooth turns in aviation.

Compass Card Behavior:
• If the needle shows clockwise, the compass card moves anti-clockwise.
• If the needle shows anti-clockwise, the compass card moves clockwise.

•	This is due to relative motion between the needle and the compass card.

DMRC (Direct Remote Magnetic Compass) vs. RIC (Remote Indicating Compass):

Components:
• DMRC: Magnetic needle, compass card, damping fluid, housing.
• RIC: Flux gate sensor, electronic display, processor.

•	Each compass type has distinct components suited to its function.

Working Principles:
• DMRC: Magnetized needle aligns with Earth’s magnetic field.
• RIC: Flux gate sensors detect Earth’s magnetic field electronically.

•	RIC is technologically advanced compared to DMRC.

Display:
• DMRC: Direct reading on compass card.
• RIC: Displayed electronically, often on HSI (Horizontal Situation Indicator).

•	Electronic displays provide better integration with modern avionics.

Placement:
• DMRC: Components inside the cockpit.
• RIC: Flux gate sensors on wingtips.

•	RIC’s placement minimizes magnetic interference from the aircraft.

Advantages and Disadvantages:

DMRC:
• Advantages: Simple design, no external power needed.
• Disadvantages: Affected by magnetic interference, turning, acceleration, and deceleration errors.

RIC:
• Advantages: Integrated with autopilot and systems like FMS/FMC.
• Disadvantages: Requires electrical power, susceptible to power loss.

•	DMRC is basic and mechanical; RIC is advanced but power-dependent.

Here are the revised Key Pointer Notes for easy copy-pasting to other apps:

Key Pointer Notes:

Variation vs. Deviation:
• Variation:
• Changes with location and over time.
• Different at various geographic locations.
• Deviation:
• Changes from aircraft to aircraft.
• Affected by the magnetic properties of the aircraft.

Compass Swing Requirements:
• Conducted after:
• Heavy landing.
• Changing magnetic latitude.
• Permanent change of aircraft base.
• Major overhaul.
• Engine change.
• Crossing magnetic/electrical storms (e.g., northern lights).
• Hammering incidents.

Lines of Magnetic Influence:
• Agonic Lines: Join places of zero variation.
• Isogonic Lines: Join places of the same variation.
• Aclinal Lines: Join places of zero magnetic dip (e.g., magnetic equator).
• Isoclinal Lines: Join places of the same magnetic dip.
• Isogonal Lines: Converge at both true north and magnetic north.

Aircraft Magnetism:
• Two Components:
1. Hard Iron: Permanent magnetism.
2. Soft Iron: Temporary magnetism.

Hard Iron:
• Permanent magnetism; difficult to magnetize but retains magnetism once magnetized.
• Examples: Nickel, cobalt, iron alloyed with aluminum.
• Components:
• P: Longitudinal axis.
• Q: Lateral axis.
• R: Vertical axis.
• Does not change with latitude or aircraft heading.

Soft Iron:
• Temporary magnetism; easily magnetized but loses magnetism when the force is removed.
• Induced by Earth’s magnetic field.
• Changes with latitude and heading.
• Components:
• Coefficient of A: Constant across headings; results from compass misalignment.
• Coefficient of B: Maximum on east or west.
• Coefficient of C: Maximum at north or south poles.

Coefficient Formulas:
1. Coefficient A:
Coefficient A = (Deviation at N + S + E + W + NE + SE + SW + NW) / 8
2. Coefficient B:
Coefficient B = (Deviation at E - Deviation at W) / 2
Deviation = B × sin(Heading)
3. Coefficient C:
Coefficient C = (Deviation at N - Deviation at S) / 2
Deviation = C × cos(Heading)
4. Total Deviation:
Total Deviation = A + (B × sin(Heading)) + (C × cos(Heading))

Compensation Methods:
• Coefficient A: Compensated by lubber line.
• Coefficients B & C: Compensated by micro-adjusters.

Time and Related Concepts

General Notes
• Time, GMT (Greenwich Mean Time), UTC (Coordinated Universal Time), and Zulu Time are the same in calculation.
• GMT becomes UTC when corrected by the atomic clock.
• UTC is the reference time used in aviation and remains consistent globally at a given moment.

Q: What is UTC?
A: Coordinated Universal Time, the globally consistent time used in aviation as a reference.

Local Mean Time (LMT)
• Definition: LMT refers to the time based on the mean sun at a specific meridian.
• At midday (1200 hours), the mean sun crosses the meridian.
• At midnight (0000 hours or 2400 hours), the mean sun crosses the anti-meridian.
• All locations on the same meridian have the same LMT.
• LMT varies with longitude and is based on the observer’s anti-meridian and mean sun.

Formula:
Change in Time = Change in Longitude ÷ 15

•	Earth rotates 15 degrees per hour (360 degrees ÷ 24 hours).

Q: How is LMT calculated?
A: By dividing the change in longitude by 15 degrees per hour.

Q: Why does LMT vary?
A: Because it changes with the observer’s meridian and the position of the mean sun.

Standard Time (ST)
• Standard time is used instead of LMT for practical purposes within a country.
• It is decided by the governing authorities of a country to ensure uniformity.
• Example: India’s Standard Time (IST) is based on LMT at 82°30’ E (Mirzapur).
• IST = GMT + 5 hours 30 minutes

Q: Why is Standard Time used instead of LMT?
A: Because LMT differs for each longitude, which is impractical for a country.

Q: What is IST?
A: Indian Standard Time, equal to GMT + 5 hours 30 minutes, based on the meridian at 82°30’ E.

Greenwich Mean Time (GMT)
• GMT can also be defined as the LMT at the Greenwich Meridian (0° longitude).
• Longitude Rule:
• Longitude East: GMT decreases.
• Longitude West: GMT increases.

Q: What is GMT?
A: The LMT at the Greenwich Meridian.

Q: How does longitude affect GMT?
A:
• Moving east: GMT decreases.
• Moving west: GMT increases.

International Date Line (IDL)
• The IDL is a zigzag line near the 180° meridian, adjusted to pass through unpopulated areas.
• Crossing IDL rules:
• Easterly track: Subtract one day (gain a day).
• Westerly track: Add one day (lose a day).

Q: What happens when crossing the IDL?
A:
• Crossing eastward: Subtract a day.
• Crossing westward: Add a day.

Q: Why is the IDL zigzag?
A: To avoid populated areas.

Critical Point (CP) / Point of No Return (PNR) / Point of Equal Time (PET)

Definition
• Critical Point (CP): The decision point on your route where, in case of an emergency, you can either continue to your destination or return to your departure point.
• Known as Point of No Return (PNR), Point of Equal Time (PET), or Equal Time Point (ETP), all referring to the same concept.
• It is calculated before the flight to ensure quick decision-making in emergencies.

Key Facts About CP
1. Purpose:
• Identifies the point where the flight time to the destination equals the flight time back to the departure point.
• Essential for emergency landings, ensuring the quickest option is known.
2. Midway in Time, Not Distance:
• CP is midway in time but not necessarily in distance unless:
• Outbound Ground Speed (GS) = Homebound Ground Speed (GS) (No wind condition).
3. Wind Effects on CP:
• Headwind: CP shifts towards the destination.
• Tailwind: CP shifts towards the departure point.
• Beam Winds (90° to track): CP remains at the midpoint in time but may vary in distance.
4. CP and Wind Dependence:
• CP always shifts into the wind (headwind or tailwind).
• Stronger beam winds increase time-to-CP but do not change departure.
5. Independence from Fuel/Endurance:
• CP is calculated purely based on time and wind conditions, not fuel availability.

Formulas and Concepts
• CP Time Rule:
CP = Halfway in Time (not distance, except when outbound GS = homebound GS).
• Wind Dependence:
• CP moves into the wind, adjusting for headwind or tailwind.
• Beam Winds:
• When beam winds increase, departure remains constant, but time-to-CP (TCP) increases.

Practical Usage
• CP is calculated before the flight to:
• Ensure immediate decision-making in case of emergencies.
• Identify the optimal point for diversion to the nearest airfield.

Q: Why is CP important in aviation?
A: It ensures pilots can make an informed decision to either return or proceed in case of an emergency.

Q: How does wind affect CP?
A:
• Headwind: CP shifts towards the destination.
• Tailwind: CP shifts towards the departure point.
• Beam Winds: CP remains midway in time but varies in distance.

Q: Is CP dependent on fuel or endurance?
A: No, CP is calculated based on time and wind conditions, independent of fuel or endurance.

Q: When is CP midway in distance?
A: Only when the outbound ground speed equals the homebound ground speed (no wind).

Critical Point (CP) and Point of No Return (PNR)

Critical Point (CP)

Definition:
The decision point on a route where, in case of an emergency, the aircraft can either proceed to the destination or return to the departure point.

Formulas:
1. Distance to CP (DCP):

DCP = DH / (O + H)

Where:
• DCP: Distance to CP
• DH: Total distance between departure and destination
• O: Outbound ground speed
• H: Homebound ground speed

2.	Time to CP (TCP):

TCP = DCP / O

Where:
• TCP: Time to CP

Special Cases:
• One-Engine Failure: For calculating DCP, use the outbound (O) and homebound (H) speeds for one-engine failure.
• Normal Task: For normal task calculations, use normal O and H.

Facts to Remember:
• CP is midway in time, not necessarily in distance.
• CP always moves into the wind:
• Headwind moves CP closer to the destination.
• Tailwind moves CP closer to the departure point.
• CP is independent of fuel or endurance.

Point of No Return (PNR)

Definition:
Also known as Point of Safe Return (PSR) or Radius of Action, it is the furthest point on the route where the aircraft can fly out and still return to the base within safe endurance limits.

Formulas:
1. Distance to PNR (DPNR):

DPNR = (E × O × H) / (O + H)

Where:
• DPNR: Distance to PNR
• E: Endurance (fuel available minus reserve fuel)
• O: Outbound speed
• H: Homebound speed

2.	Time to PNR (TPNR):

TPNR = DPNR / O

Facts to Remember:
• Dependence on Fuel:
• DPNR increases with fuel or endurance.
• DPNR decreases with higher fuel consumption.
• Wind Effect:
• Nil winds result in the maximum DPNR.
• Any wind component reduces DPNR.
• DPNR is usually ahead of DCP.
• In one-engine failure, use normal TAS and fuel consumption for outbound calculations.

Mass and Balance (CG - Center of Gravity)

Center of Gravity (CG)

Definition:
The point through which the force of gravity acts upon a mass, affecting stability.

Key Points:
• The CG is the point of balance of the aircraft.
• It is parallel to the gravity vector and perpendicular to the longitudinal axis.

Key Subpoints
1. Datum:
• The reference point on the longitudinal axis of the aircraft from which all CG locations are measured.
2. Arm:
• The fore-and-aft distance from the datum to any specific point in the aircraft.
3. Moment:
• The product of the mass of an object and its arm.

Moment = Mass × Arm

Aircraft Mass Terminology
1. Basic Empty Mass (BEM):
• The mass of the aircraft as delivered from the manufacturer, including:
• Standard items such as unusable fuel, lubricating oil, fire extinguishers, emergency oxygen, and auxiliary units.
2. Dry Operating Mass (DOM):
• The aircraft mass ready for service, excluding usable fuel and payload.
• Includes:
• Crew and crew baggage
• Catering equipment
• Portable water, lavatory chemicals, food, and beverages

Note: BEM, DOM, and Aircraft Prepared for Service (APS) are often used interchangeably.

Holding

Definition:
• A racetrack-shaped pattern flown by aircraft for maintaining position while waiting for further instructions.

Aircraft Weight and Fuel Terminology

Payload or Traffic Load
• Payload: Revenue-generating load, including the total mass of passengers, baggage, and cargo.
• Traffic Load: Payload plus certain non-revenue-generating load.
Note:
• Payload = Revenue-Generating Load.
• Traffic Load = Payload + Non-Revenue Load.

Fuel Types
1. Ramp Fuel (Block Fuel):
• Total fuel on board plus startup and taxi fuel.
• Formula:

Ramp Fuel = Fuel on Board + Startup and Taxi Fuel

2.	Trip Fuel:
•	Fuel required for the trip from departure to destination.
3.	Contingency Fuel:
•	5% of Trip Fuel.
4.	Alternate Fuel:
•	Fuel required to reach an alternate aerodrome if needed.
5.	Reserve Fuel:
•	Fuel required for holding:
•	Jet/Turbine Engines: 30 minutes at 1500 feet.
•	Tower Prep/Reciprocating Engines: 45 minutes at 1500 feet.
6.	Ballast Fuel/Weight:
•	Removable or permanently installed weight to bring CG within allowable range.
•	Can be in the form of fuel or other weights.

Mass Terminology
1. Operating Mass (OM):
• Total mass of the aircraft ready for takeoff, excluding traffic load.
• Formula:

OM = DOM + Takeoff Fuel

2.	Zero Fuel Mass (ZFM):
•	Total mass of the aircraft, including dry operating mass (DOM) and payload, but excluding usable fuel.
•	Formula:

ZFM = DOM + Payload

3.	Takeoff Mass (TOM):
•	Total mass of the aircraft at the time of takeoff, including all components.
4.	Landing Mass (LM):
•	Mass of the aircraft upon landing.
•	Formula:

LM = TOM - Trip Fuel

5.	Ramp or Taxi Mass (RM):
•	Mass of the aircraft at the start of taxiing.
•	Formula:

RM = TOM + Taxi and Startup Fuel

•	Note: Ramp Mass is the heaviest among all.

Structural and Regulated Takeoff Masses

1.	Structural Takeoff Mass (STOM):
•	Maximum permissible takeoff mass at the start of the takeoff roll, as provided by the manufacturer.
2.	Performance-Limited Takeoff Mass (PLTOM):
•	Maximum permissible takeoff mass based on departure aerodrome limitations and prevailing conditions.
3.	Regulated Takeoff Mass (RTOM) / Maximum Takeoff Mass (MTOM):
•	The lower value of STOM and PLTOM.
•	Used for all calculations as the safest limit.

Steps to Calculate Payload or Traffic Load

1.	Create a Table:
•	Include given values such as RTOM, DOM, ZFM, TOM, and LM.

2.	Find RTOM/MTOM:
•	Identify the regulated or maximum takeoff mass based on given structural and performance limits.

3.	Calculate Mass Components:
•	Determine traffic load, ramp fuel, trip fuel, and reserve fuel as per provided formulas.

Question 4

Q

True North vs. Magnetic North:
• True North: Refers to the geographic North Pole.
• Magnetic North: Refers to the direction where a magnetic compass points, influenced by Earth’s magnetic field.
• Variation:
• The angle between True North and Magnetic North.
• Changes depending on the position of the aircraft.

Questions and Answers:
1. What is True North?
• True North refers to the geographic North Pole, a fixed point on Earth’s surface.
2. What is Magnetic North?
• Magnetic North is the direction a magnetic compass points, influenced by Earth’s magnetic field.
3. Define Variation and explain its significance in navigation.
• Variation is the angular difference between True North and Magnetic North. It is crucial for correcting navigational headings to ensure accurate travel paths.

Variation:
• Definition: Angular difference between True North and Magnetic North.
• Representation: Variation lines are marked on navigation charts.

Questions and Answers:
1. How is Variation represented on navigation charts?
• Variation is represented as dashed lines on charts, indicating the degree and direction of deviation (e.g., 5°E or 10°W).
2. Why does Variation change with location?
• Variation changes because Earth’s magnetic field is irregular and shifts geographically over time.

Headings:
• True Heading: Direction of the aircraft relative to True North.
• Magnetic Heading: Direction of the aircraft relative to Magnetic North.

Questions and Answers:
1. What is the difference between True Heading and Magnetic Heading?
• True Heading is measured relative to True North, while Magnetic Heading is measured relative to Magnetic North.
2. How does Variation affect the calculation of True and Magnetic Headings?
• Variation is added or subtracted to convert between True Heading and Magnetic Heading:
• True Heading = Magnetic Heading ± Variation
• Add Variation if it is west, subtract if it is east.

Key Notes:
1. Magnetic North is constantly moving and varies by location.
2. Variation must be accounted for when navigating using charts.
3. Navigation charts typically display variation lines for different regions.

Questions and Answers:
1. Why is it important to account for Variation during navigation?
• Failing to account for Variation can result in navigational errors, leading to deviations from the planned route.
2. What tools or references are used to measure and adjust for Variation?
• Navigation charts, compass deviation cards, and onboard instruments like gyroscopic compasses are used to measure and adjust for Variation.

Reference to North and Direction

Key Notes:
• Reference Point: Navigation is always referenced to North.
• Measuring Directions:
• Directions are measured as angles from North.
• Example: A direction of 045° implies movement in the Northeast direction.

Questions and Answers:
1. What is the reference point for navigation?
• Navigation is always referenced to North.
2. How is direction measured?
• Directions are measured as angles from North (e.g., 045° for Northeast).

Great Circle (GC) Navigation

Key Notes:
• Scenario: An aircraft flying between coordinates 60^\circ S, 60^\circ E and 60^\circ S, 60^\circ W.
• Concept: The shortest path between two points is along a Great Circle (GC).

Questions and Answers:
1. What is the shortest path between two points on Earth?
• The shortest path is along a Great Circle (GC).
2. How is a Great Circle path calculated?
• It is calculated based on spherical trigonometry considering Earth’s curvature.

Descent Calculations

Key Notes:
• Topic: Formulas related to descent.
• Rate of Descent (ROD):
• ROD depends on ground speed (GS) and the gradient.
• Formula:
ROD = 101.3 × GS × Gradient

Questions and Answers:
1. What factors influence Rate of Descent (ROD)?
• Ground Speed (GS) and Gradient.
2. What is the formula for ROD?
• ROD = 101.3 × GS × Gradient

Flight Levels and Descent

Key Notes:
• Flight Levels:
• Defined as altitude in hundreds of feet above sea level, expressed as a level (e.g., FL300 = 30,000 ft).
• Descent Example:
• An aircraft descends from FL300 to FL080.
• Calculations include Rate of Descent and required distance/time to achieve the descent.

Questions and Answers:
1. What is a Flight Level?
• A Flight Level is the aircraft’s altitude in hundreds of feet above sea level.
2. If an aircraft descends from FL300 to FL080, what is calculated?
• The Rate of Descent and the distance/time required to achieve the descent.

Earth’s Tilt and Rotation
• Earth’s axis is tilted, referred to as the spin axis, which influences time and seasons.
• The true north and true south poles are determined by this axis.
• The equator divides Earth into two hemispheres and serves as a reference point.

Q: What is Earth’s spin axis?
A: It’s the tilted line around which Earth rotates.

Q: Why is Earth’s axis tilt important?
A: It causes variations in sunlight, leading to seasons and day-night cycles.

Q: What are the true north and south poles?
A: They are the points aligned with Earth’s spin axis.

Q: Why is the Earth’s axis tilted?
A: The tilt likely occurred due to collisions during Earth’s formation, affecting its rotation and seasons.

Spin Axis vs Normal Axis
• The spin axis is the line around which Earth rotates, while the normal axis is a vertical reference line.
• The angle between these axes is called the tilt.

Q: What is the difference between the spin axis and normal axis?
A: The spin axis is the line around which Earth rotates, while the normal axis is a vertical reference line.

Q: What is the tilt?
A: It is the angle between the spin axis and the normal axis.

Key Observations on Rotation
• Earth completes one rotation around its spin axis approximately every 24 hours, creating the day-night cycle.
• The combination of tilt and rotation affects the length of days and nights throughout the year.

Q: How long does it take for Earth to complete one rotation?
A: Approximately 24 hours.

Q: What causes the day-night cycle?
A: Earth’s rotation around its spin axis.

Q: How does the tilt affect day length?
A: It changes the amount of sunlight received at different times of the year.

Earth’s Revolution and Seasons
• Earth’s revolution around the Sun takes approximately 365.25 days and creates the seasons.
• The tilt of Earth’s axis causes variations in sunlight received, leading to different seasons.

Q: What is the difference between Earth’s rotation and revolution?
A: Rotation is Earth spinning on its axis (causing day and night), while revolution is Earth’s orbit around the Sun (causing seasons).

Q: How long does one revolution of Earth take?
A: Approximately 365.25 days, or one year.

Q: Why do seasons occur?
A: Seasons occur because of Earth’s axial tilt and its revolution around the Sun.

Q: Why are days longer in summer and shorter in winter?
A: The tilt of Earth’s axis causes certain hemispheres to receive more direct sunlight during summer and less during winter.

Solstices and Equinoxes
• Solstices:
• Summer solstice (June 21): Longest day in the Northern Hemisphere.
• Winter solstice (December 21): Shortest day in the Northern Hemisphere.
• Equinoxes:
• Spring equinox (March 21): Equal day and night globally.
• Autumn equinox (September 21): Equal day and night globally.

Q: What are solstices?
A: Times when one hemisphere receives the most or least sunlight, marking the longest or shortest days.

Q: What are equinoxes?
A: Times when the equator receives equal sunlight, leading to nearly equal day and night durations.

Q: When do the solstices occur?
A: Around June 21 (summer solstice) and December 21 (winter solstice).

Q: When do the equinoxes occur?
A: Around March 21 (spring equinox) and September 21 (autumn equinox).

Q: What happens at the poles during solstices?
A: During the summer solstice, one pole experiences 24 hours of daylight, while the other experiences 24 hours of darkness.

Time Zones and Global Implications
• The tilt and rotation of Earth impact time zones and daylight variations across regions.

Q: How does Earth’s tilt affect time zones?
A: The tilt influences the duration of daylight across different regions, which is reflected in time zones.

Q: Why do different places on Earth have different times?
A: This is due to Earth’s rotation, which causes the Sun to appear at different positions in the sky at various locations.

Astronomical Phenomena
• The Tropic of Cancer and Tropic of Capricorn mark the farthest points north and south where the Sun appears directly overhead.

Q: What is the significance of the Tropic of Cancer and Tropic of Capricorn?
A: These latitudes mark the furthest points north and south where the Sun appears directly overhead at solstices.

Q: How do solstices and equinoxes relate to Earth’s orbit?
A: Solstices occur when Earth’s tilt is most inclined toward or away from the Sun, while equinoxes occur when the tilt is neutral.

Solar System Context
• Earth’s tilt and rotation are influenced by its position in the solar system.
• Understanding these dynamics helps calculate time differences across regions.

Q: How is Earth’s rotation connected to the solar system?
A: It’s influenced by Earth’s orbit and position in the solar system.

Q: Why is understanding tilt important for time calculations?
A: It determines how sunlight is distributed, affecting time zones and seasonal changes.

• Plane of Equinoctial/Plane of Equator: Refers to the plane of Earth’s equator extended into space.
• Plane of Ecliptic: Orbital plane of Earth around the Sun.
• Inclination:
• Earth’s axis is tilted at 23.5° from perpendicular to the orbital plane.
• This tilt is responsible for the seasons.
• Earth’s axis makes an angle of 66.5° with the orbital plane.
• Declination:
• The angle between the Sun and the Equator.
• Changes annually between 23.5° North and 23.5° South.
• Maximum declination:
• 23.5° from the equator.
• 66.5° from the poles.
• Celestial Sphere:
• Imaginary sphere around Earth with a large radius.
• Concentric to Earth.
• All celestial bodies with unknown distances are assumed to lie on its surface.
• Solar System:
• Kepler’s First Law:
• Planets move in elliptical orbits with the Sun as one focal point (focale).
• Kepler’s Second Law:
• Radius vector (line joining planet and Sun) sweeps out equal areas in equal times.
• Planets move faster at perihelion (closest to Sun) and slower at aphelion (farthest from Sun).
• Definitions:
• Perihelion: Closest point of a planet to the Sun.
• Aphelion: Farthest point of a planet from the Sun.
• Tropics and Overhead Sun:
• Between 23.5° North (Tropic of Cancer) and 23.5° South (Tropic of Capricorn):
• Sun is overhead twice a year.
• Beyond these latitudes:
• Sun is never overhead.
• At the equator:
• Sun is overhead twice a year.
• Arctic and Antarctic Circles:
• Between 66.5° North (Arctic Circle) and 66.5° South (Antarctic Circle):
• Day and night occur daily.
• Beyond these latitudes:
• Day and night are not daily.
• Earth’s Motions:
• Rotation: Causes day and night.
• Revolution: Causes one year.
• Tilt/Inclination: Causes seasons.
• Angles:
• Angle between the plane of equator (equinoctial) and the plane of orbit (ecliptic): 23.5°.
• Angle between spin axis and plane of orbit: 66.5°.
• Angle between normal axis and plane of orbit: 90°.

•	Sidereal Day:
•	Time taken for Earth to complete a 360° rotation with respect to a distant star.
•	Measured using a reference meridian and successive transit of the same star.
•	Duration: 23 hours 56 minutes 4 seconds.
•	Apparent Solar Day:
•	Measured using the real Sun (apparent Sun).
•	Duration varies due to Earth’s elliptical orbit and Kepler’s Second Law:
•	23 hours 44 minutes in November.
•	24 hours 14 minutes in February.
•	Apparent Solar Day is not of constant length.
•	Mean Solar Day (Civil Day):
•	Measured using the mean Sun, an imaginary Sun moving in a circular orbit.
•	Duration: 24 hours exact.
•	Maximum difference between apparent and mean solar day:
•	16 minutes in November.
•	14 minutes in February.
•	Local Mean Time (LMT):
•	Measured using the mean Sun, which is assumed to be at the equator.
•	Sidereal Year:
•	Time taken for Earth to complete one revolution around the Sun relative to a distant star.
•	Duration: 365 days 6 hours 9 minutes.
•	Tropical Year (Apparent Solar Year):
•	Time taken for Earth to complete one revolution around the Sun relative to the same orientation (e.g., equinox or solstice).
•	Duration: 365 days 5 hours 49 minutes.
•	Tropical Year is 20 minutes shorter than the Sidereal Year.
•	Calendar Year:
•	Fixed at 365 days based on the Tropical Year.
•	Leap Year: One extra day added every four years to compensate for the real Tropical Year.
•	Key Dates and Seasons:
•	21st June:
•	Declination: 23.5°N (Tropic of Cancer).
•	Northern Hemisphere:
•	Summer season.
•	Longest daylight.
•	Summer solstice.
•	Southern Hemisphere:
•	Winter solstice.
•	21st December:
•	Declination: 23.5°S (Tropic of Capricorn).
•	Southern Hemisphere:
•	Summer season.
•	Longest daylight.
•	Summer solstice.
•	Northern Hemisphere:
•	Winter solstice.


•	21st March or 21st September:
•	Declination: 0° (at Equator).
•	Spring or Autumn:
•	Day and night are of equal length.
•	In the Northern Hemisphere:
•	March: Vernal (Spring) Equinox.
•	September: Autumnal Equinox.
•	In the Southern Hemisphere:
•	March: Autumnal Equinox.
•	September: Vernal (Spring) Equinox.
•	Types of Horizon:
1.	Celestial Horizon:
•	Plane passing through Earth’s center.
•	Perpendicular to zenith-nadir axis.
2.	Sensible Horizon:
•	Plane passing through observer’s eye level.
•	Parallel to the celestial horizon.
3.	Visible Horizon:
•	Circle bounding the observer’s view of Earth’s surface in clear atmosphere.
•	Appears as the line where Earth’s surface and sky meet (due to Earth’s curvature).


•	Visible Horizon:
•	Located below the sensible horizon.
•	Twilight:
•	Period of light in the atmosphere before sunrise and after sunset.
•	Sun is below the horizon, but its rays are refracted through the atmosphere, extending the light period.
•	Also defined as the time between sunset and night.
•	Types of Twilight:
1.	Civil Twilight:
•	Sun’s center is 0° to 6° below the sensible horizon.
2.	Nautical Twilight:
•	Sun’s center is 6° to 12° below the sensible horizon.
3.	Astronomical Twilight:
•	Sun’s center is 12° to 18° below the sensible horizon.
•	Factors Affecting Twilight:
•	Observer’s latitude.
•	Declination of the Sun.

Answer

A

Chart Theory

Maps
• Contain more geographical details depending on the scale.
• Include features like hills, rivers, roads, railways, and ground features.

Charts
• Contain fewer details, specific to their purpose.
• A projection containing only the graticule of latitude and longitude with very few geographical features is called a chart.

Projection
• Definition: The process of making maps or charts on a flat surface to represent the spherical Earth (or part of it).

Reduced Earth
• A smaller-scale representation of Earth.
• A scale model of Earth on which the projection of a chart is based.
• Example: To make a chart with a scale of 1:100,000, a reduced flat surface is used based on the spherical Earth.

Graticule
• The network of lines representing meridians (longitude) and parallels (latitude).

Ideal Projection Features
1. Scale:
• Should be correct and constant, but not always achieved.
2. Shape:
• Should be correct, and this is achieved.
3. Area:
• Should be shown correctly, but this is not achieved.
4. Bearing:
• Measurement should match Earth’s measurements (orthomorphic).
• This is achieved.
5. RL (Rhumb Line) and GC (Great Circle):
• Should be straight lines, but this is not achieved.
6. Meridians and Parallels:
• Should intersect at 90 degrees. This is achieved.
7. Worldwide Coverage:
• Not achieved.
8. Adjacent Sheets:
• Should fit perfectly together.

Orthomorphism (Conformal Property)
• Bearings are shown correctly, which can be achieved.
• Key Features:
• Meridians and parallels of latitude intersect at 90 degrees.
• Scale is constant, but not necessarily correct.
• Correct in all directions, at any point.
• Note: If a chart is orthomorphic, it will automatically have the correct shape.

Classification of Projection

Perspective Projection
• Charts produced by true or natural projection.
• No mathematical alterations are made.
Non-Perspective Projection
• Charts produced using mathematical methods.
• Most of the charts studied are non-perspective or perspective projections modified mathematically.

Three Types of Projection

1.	Cylindrical Projection
•	Examples:
•	Direct Mercator Chart
•	Transverse Mercator Chart
•	Oblique Mercator Chart
2.	Conical Projection
•	Example:
•	Lambert Chart
3.	Zenithal, Plane, or Azimuthal Projection
•	Example:
•	Polar Stereographic Projection

Projection Types and Their Characteristics

Direct Mercator Chart

Projection Type: Cylindrical Projection
Production: Perspective Projection modified mathematically → Non-Perspective
Point of Projection: Center of Earth
Line of Tangency: Equator

Properties:
1. Scale:
• Correct at the equator, expands as secant of latitude from equator to poles.
2. Shape:
• Correct at the equator, distorted in higher latitudes due to scale expansion.
3. Orthomorphism:
• Bearings are correctly shown.
4. Rhumb Line (RL):
• Straight line, unique to this projection.
5. Great Circle (GC):
• Curves concave to the equator and convex to the nearer pole.
• Exceptions: Equator and meridians are straight lines (GC).
6. Graticule:
• Meridians: Straight, parallel, equally spaced.
• Parallels: Straight, parallel, spacing increases toward poles.
7. Convergence:
• Zero, as meridians are parallel to each other. Correct only at the equator.

Usage and Limitations:
• Suitable for RL tracks, especially for countries near the equator (8°–11°N).
• Meteorological charts in India use Mercator charts.
• Cannot be used above 70–75°N or S due to large scale expansion.

Lambert’s Conformal Chart

Projection Type: Conical Projection
Production: Non-Perspective Chart
Point of Projection: Center of Earth (bulb)
Line of Tangency: Standard parallels

Properties:
1. Scale:
• Correct at standard parallels.
• Contracts within and expands outside standard parallels.
• Smallest scale is at the parallel of origin (approximately midway between standard parallels).
2. Shape:
• Correct within standard parallels, distorted outside.
3. Orthomorphism:
• Bearings are correctly shown.
• Definition: Meridians and parallels intersect at 90°, and scale is constant in all directions.
4. Rhumb Line (RL):
• Curve concave to the pole of projection, except meridians (straight lines).
5. Great Circle (GC):
• Curve concave to the parallel of origin, straight line at the parallel of origin.
6. Graticule:
• Meridians: Straight lines radiating from the pole.
• Parallels: Arcs of circles centered at the pole.
7. Convergence:
• Correct at the parallel of origin.
• Formula: Convergence = Change in Longitude × Constant of Cone
• Constant of Cone = Sine (Mean Latitude).

Usage and Limitations:
• Best for mid-latitude areas (10°–70°N/S).
• Commonly used for tropical maps, topographical maps, gypsum charts, and meteorological charts.
• Greater differences between standard parallels result in more distortion.

Polar Stereographic Chart

Projection Type: Plane or Zenithal Projection
Production: Perspective Projection
Point of Projection: South Pole (light source)
Point of Tangency: North Pole

Properties:
1. Scale:
• Correct at the poles, expands with sec² (half of cone latitude).
2. Shape:
• Correct at poles, distorted away from poles.
3. Orthomorphism:
• Bearings are correctly shown.
4. Rhumb Line (RL):
• Curve concave towards the nearer pole, except meridians (straight lines).
5. Great Circle (GC):
• Curve concave towards the nearer pole, less curved than RL.
• Near the poles, GC may be considered straight.
6. Graticule:
• Meridians: Straight lines radiating from poles.
• Parallels: Concentric circles with spacing increasing away from poles.
7. Convergence:
• Correct at poles, equal to Change in Longitude (Chlong), and reduces away from poles.

Usage and Limitations:
• Suitable for polar regions (70°–90°N/S).
• Ideal usage:
• Mercator: 10°N–10°S.
• Lambert: 10°–70°N/S.
• Polar Stereographic: 70°–90°N/S.

Transverse Mercator Chart

Projection Type: Cylindrical Projection
Production: Non-Perspective
Point of Projection: Center of Earth
Line of Tangency: Central Meridian (Datum or Contact Meridian)

Properties:
1. Scale:
• Correct at datum meridian and its anti-meridian.
• Expands as secant of great circle distance from datum meridian (east to west).
2. Shape:
• Correct at datum meridian but distorted away from it.
3. Rhumb Line (RL):
• Curve concave to the nearest pole, except meridians at 90° to datum meridian (straight lines).
4. Great Circle (GC):
• Straight line where it cuts the datum meridian at 90°.
• Elsewhere, GC becomes complex curves.
5. Graticule:
• Meridians: Datum meridian, equator, and meridians at 90° to datum meridian are straight lines.
• Elsewhere, meridians are complex curves.
• Parallels: Ellipses, nearly circular near poles.
6. Convergence:
• Correct at equator and poles.

Usage and Limitations:
• Best for countries with large latitude coverage and small longitude coverage.
• Accuracy: Best within 5° of the datum meridian.

Oblique Mercator Chart

Projection Type: Cylindrical Projection
Production: Non-Perspective
Point of Projection: Center of Earth
Line of Tangency: Datum Great Circle (Datum GC)

Properties:
1. Scale:
• Correct at datum GC.
2. Shape:
• Correct at datum GC but distorted away from it.
3. Orthomorphism:
• Bearings are correctly shown.
4. Rhumb Line (RL):
• Concave curve to the pole.
5. Great Circle (GC):
• Straight line near datum GC, complex curves elsewhere.
6. Graticule:
• Meridians: Curves concave to datum GC, straight at poles passing through datum GC.
• Parallels: Complex curves cutting meridians at 90°.
7. Convergence:
• Correct along GC of tangency (datum GC).

Usage and Limitations:
• Suitable for routes lying on a GC.
• Best accuracy within 5° of datum GC.

Question 5

Q

Aircraft Performance Notes

Definition of Performance
• Performance refers to the ability of an aircraft at any stage of flight, influenced by factors such as altitude, speed, weight, distance, temperature, winds, humidity, and gradient.

Types of Performance
1. Mandatory Performance:
• Required for the certification of an aircraft.
2. Gross Performance:
• Average performance achieved by a fleet of aircraft.
3. Net Performance:
• Actual performance of an aircraft considering factors like aging, runway conditions, and maintenance.
• Net Performance < Gross Performance.

Runway Terminology
1. Runway:
• A defined rectangular area used for takeoff and landing.
2. Stopway:
• A rectangular area at the end of the takeoff run (TORA) for stopping the aircraft during aborted takeoffs.
• Width: Same as the runway.
• Strength: May or may not match the runway.
3. Clearway:
• A rectangular area on ground or water for initial climb to a screen height of 35 feet.
• Length: Not more than half the runway length.
• Width: 75 meters (250 feet total).
• Slope: 1.25% upward from the runway end.

Declared Distances
1. TORA (Takeoff Run Available):
• Declared runway length available for takeoff.
2. ASDA (Accelerated Stop Distance Available):
• ASDA = TORA + Stopway
3. TODA (Takeoff Distance Available):
• TODA = TORA + Clearway
4. LDA (Landing Distance Available):
• Available runway length for landing, including ground roll.
• LDA = Runway Length

Runway Conditions
1. Dry Runway:
• Best for takeoff and landing, no moisture on the runway.
2. Damp Runway:
• Covered with moisture but without a shiny surface.
3. Wet Runway:
• Runway surface covered with water or sufficient moisture to appear reflective but without significant standing water.
4. Contaminated Runway:
• Standing water greater than 3mm, slush, snow, or ice covering more than 25% of the runway.
5. Hydroplaning Speed:
• Formula: Hydroplaning Speed = 9 × √(Tire Pressure in PSI)

V-Speeds
1. VMCG (Minimum Controllable Speed on Ground):
• The minimum CAS during takeoff where directional control is maintained using rudder only.
• Condition:
• V1 > VMCG .
2. VEF (Engine Failure Speed):
• Speed at which engine failure is assumed (critical engine).
3. V1 (Decision Speed):
• Speed by which a decision to abort or continue takeoff must be made.
• Limits:
• V1 > VMCG
• V1 < VR
• V1 < VMBE
4. VMU (Minimum Unstick Speed):
• Minimum CAS for the aircraft to leave the ground during takeoff.
5. VLOF (Liftoff Speed):
• CAS at which the aircraft lifts off the runway.
6. VMCA (Minimum Controllable Speed in Air):
• Minimum CAS to maintain directional control in case of engine failure.
7. VMBE (Maximum Brake Energy Speed):
• Maximum CAS where braking will not damage the system.
8. VR (Rotation Speed):
• CAS at which the pilot rotates the aircraft nose for takeoff.
• Limits:
• VR \geq 1.05 \times VMCA
• VR \geq 1.10 \times VS
9. V2 (Takeoff Safety Speed):
• CAS to be achieved within TODA at 35 feet.
• Ensures a 15° bank angle and a safe margin to stall.
• Limit: V2 = 1.2 \times VS
10. Stall Speeds:
• VS: Stalling speed.
• VS0: Stalling speed in landing configuration (dirty configuration).
• VS1: Stalling speed in takeoff configuration (clean configuration).

Takeoff Segments
1. Segment 1:
• Altitude: 35 feet to the start of landing gear retraction.
• Thrust: Full thrust on live engine.
• Speed: V2.
• Climb Gradient: Positive.
• Configuration: Flaps and slats extended, landing gear retracting.
2. Segment 2:
• Altitude: Landing gear retracted to 400 feet.
• Purpose: Maximum Takeoff Mass (M-TOM) is determined here.
• Thrust: Full thrust on live engine.
• Speed: V2.
• Climb Gradient: 2.4%.
• Configuration: Flaps and slats extended, landing gear retracted.
3. Segment 3:
• Purpose: Maintain a climb gradient of 1.2%.
• Thrust: Full thrust on live engine.
• Configuration: Flaps and slats being retracted.
4. Segment 4:
• Altitude: Up to 1500 feet.
• Thrust: Maximum continuous thrust on live engine.
• Configuration: Clean configuration (flaps and slats retracted).

Effects on Takeoff Performance
1. Runway Slope:
• Downslope: ASDA increases, V1 decreases.
• Upslope: ASDA decreases, V1 increases.
2. Wind Conditions:
• Tailwind: Increases V1, V2, and VR.
• Headwind: Decreases V1, V2, and VR.
3. Flaps:
• Increasing Flaps:
• Increases field-limited takeoff mass.
• Decreases climb-limited takeoff mass.
4. Balance Field Length:
• Occurs when Takeoff Distance Required (TODR) equals Accelerated Stop Distance Required (ASDR).

Ceiling Definitions
1. Service Ceiling:
• Aircraft’s Rate of Climb (ROC) equals 100 feet per minute (FPM).
2. Absolute Ceiling:
• Aircraft’s Rate of Climb (ROC) equals 0 FPM.

Formula Recap
1. Hydroplaning Speed: Hydroplaning Speed = 9 × √(Tire Pressure in PSI)
2. ASDA: ASDA = TORA + Stopway
3. TODA: TODA = TORA + Clearway
4. V2 Limit: V2 = 1.2 × VS
5. VR Limit: VR ≥ 1.05 × VMCA and VR ≥ 1.10 × VS

Answer

A

Basic Radio Theory

Radio Waves (Electromagnetic Waves)
• Components:
• Electric (E) and Magnetic (H) components.
• These components are perpendicular to each other.

Polarization of Radio Waves
• Definition: The direction of the electrical component (E) determines the polarization.
• Types of Polarization:
1. Vertically Polarized Wave:
• Electric component (E) is in the vertical plane.
• Magnetic component (H) is in the horizontal plane.
2. Horizontally Polarized Wave:
• Electric component (E) is in the horizontal plane.
• Magnetic component (H) is in the vertical plane.
• Receiving Antenna Placement:
• A horizontally polarized wave requires a horizontally placed antenna.
• A vertically polarized wave requires a vertically placed antenna.
• The antenna must be parallel to the electrical component (E).

Key Terms
1. Frequency:
• The number of cycles passing through a point per second.
• Unit: Hertz (Hz).
2. Wavelength (lambda):
• The distance between two crests, troughs, adjacent points, or one complete cycle.
• Unit: Meter.
3. Phase:
• The position of a radio wave in a cycle.
• Unit: Degrees.
4. Amplitude:
• The maximum displacement from the mean position.
5. Frequency-Wavelength Relationship:
• As frequency increases, wavelength decreases.
• Formula:
Frequency (Hz) = Speed of Light ÷ Wavelength

Modulation
• Definition: The process of superimposing an audio frequency or information onto a carrier wave.

Properties of Radio Waves
1. Speed:
• Travel at the speed of light: 3 × 10^8 \, \text{m/s} .
2. Medium Changes:
• Denser to rarer (e.g., land to water): Accelerates, bends away from the normal.
• Rarer to denser: Decelerates, bends toward the normal.
3. Propagation Behaviors:
• Refraction: Bending of waves due to a change in medium.
• Reflection: Bouncing back of waves from a surface.
• Diffraction: Bending of waves around obstacles.
• Attenuation: Absorption or weakening of waves by a medium.
4. Path: Follow the Great Circle Path (GC Path) for the shortest distance.

Propagation of Radio Waves
1. Ground Wave Propagation:
• Includes surface wave, space wave, direct wave, and ground-reflected wave.
• Ground Wave: All waves other than sky waves.
• Surface Wave: Travels along the surface.
• Range depends on transmitter power:
• Surface Range (Sea) = 3 × √Power
• Surface Range (Land) = 2 × √Power
• Range is proportional to wavelength (lambda).
• Range is inversely proportional to frequency.
2. Sky Wave Propagation:
• Waves are received after refraction from the ionosphere.

Line of Sight Propagation
• Followed by: Space wave, direct wave, and ground-reflected wave.
• Space Wave: Travels directly from the transmitter to the receiver.
• Range Formula:
Range (NM) = 1.25 × (√Height of Receiver + √Height of Transmitter)

Skywave Propagation

Definition
• Skywave: A radio wave with a frequency range of 3–30 MHz, refracted from the ionosphere.

Ionosphere and Layers
1. Ionosphere Layers:
• D Layer:
• Altitude: 50–100 km.
• Disappears at night, increasing the height of the ionosphere.
• E Layer:
• Altitude: 100–150 km.
• Maximum ionization at noon and in summer.
• Height increases at night as D layer vanishes.
• F Layer:
• Altitude: 150–350 km.
• Plays a crucial role in long-distance communication.
2. Ionosphere Composition:
• Consists of charged atoms (ions).
• Density depends on the number of charged ions, which are formed due to UV rays.
• More UV rays → More ionization.
• Maximum ionization: 12 noon, summer, and when the sun is overhead.

Formulas
1. Range (R) in km:
143 √height of reflecting layer in km

Features of Skywave
1. Ionization Layers:
• Affected by density, frequency, and height of the ionization layer.
2. D Layer:
• Disappears at night (sundown), causing ions to break down into atoms.
3. E Layer:
• Maximum ionization at noon and summer.
• Shifts upward at night, increasing the height of the ionosphere but making it weaker.
4. UV Rays:
• More UV Rays → More ions.
• UV rays are highest at noon and in summer.

Key Terms
1. Skip Distance:
• Distance between the transmitter and the point where the first skywave return is received.
2. Dead Space (Skip Zone):
• Distance between the end of the ground wave and the point where the first skywave return is received.
3. Critical Ray:
• The first skywave return.
4. Critical Frequency:
• Frequency at which the critical ray is received.
5. Critical Angle:
• Angle of incidence at which the critical ray is received.

Radio Signal Behaviors
1. Refraction:
• Bending of radio signals when passing through a different medium.
2. Fading: is maximum at night due to interference of sky waves with ground waves
• Variation in radio signal strength, including sudden increases or decreases.
• Overcoming Fading:
• AVC: Automatic Volume Control.
• AGC: Automatic Gain Control.
3. Attenuation:
• Weakening or absorption of signals by the propagation medium.
• Types of Attenuation:
• Ground Attenuation:
• Higher over land than sea.
• Frequency: Directly proportional to ground attenuation, inversely proportional to range.
• Atmospheric Attenuation:
• Significant at higher frequencies.
• Caused by water vapor in the atmosphere.
• Frequency: Directly proportional to atmospheric attenuation, inversely proportional to range.
• Ionospheric Attenuation:
• Caused by ions in the ionosphere.
• Frequency: Inversely proportional to ionospheric attenuation.

Frequency Relationships
1. Frequency vs. Critical Angle:
• Higher Frequency → Higher Critical Angle.
2. Frequency vs. Skip Distance:
• Higher Frequency → Higher Skip Distance.
3. Frequency vs. Dead Space:
• Higher Frequency → Larger Dead Space (on both sides).

Corrected Radio Wave Characteristics and Frequency Behavior

Frequency and Attenuation Relationships
1. Frequency vs. Atmospheric or Ground Attenuation:
• Higher Frequency → Higher Atmospheric or Ground Attenuation.
2. Frequency vs. Ionospheric Attenuation:
• Higher Frequency → Lower Ionospheric Attenuation.
3. Frequency Ranges and Behavior:
• VLF (Very Low Frequency) and LF (Low Frequency):
• Completely absorbed by the ionosphere.
• MF (Medium Frequency):
• Partially reflected back as skywave, especially at night.
• HF (High Frequency):
• Reflects back as skywave only, suitable for long-distance communication.
• VHF (Very High Frequency) and Above:
• Cross the ionosphere and become space waves, suitable for line-of-sight communication.

Wavelength Ranges and Usage
1. 1–10 cm (Centimetric):
• Used by Primary Radars (e.g., weather and surveillance radars).
2. 10–99 cm (Decimetric):
• Used by Secondary Radars (e.g., Mode C and Mode S transponders).
3. 1–9 m (Metric):
• Includes:
• VHF Aids: VDF (VHF Direction Finder), VOR (VHF Omnidirectional Range), Localizers.
• VHF Communications (air-to-ground communications).
4. 10–999 m (Hectometric):
• Includes:
• NDBs (Non-Directional Beacons).
• ADFs (Automatic Direction Finders).

Emission Designators for Navigation Aids
1. NDB (Non-Directional Beacon):
• Emission Type: Non-A1A (Continuous Carrier Without Modulation) or Non-A2A (Modulated Carrier).
2. VDF (VHF Direction Finder):
• Emission Type: A3E (Amplitude Modulated, Double Sideband, Voice).
3. VOR (VHF Omnidirectional Range):
• Emission Type: A9W (Amplitude Modulated, Double Sideband, Carrier with Subcarrier).
4. ILS (Instrument Landing System):
• Emission Type: A8W (Amplitude Modulated, Carrier with Subcarrier, Wideband).
5. VHF Communication:
• Emission Type: J3E (Single Sideband Suppressed Carrier for Voice Communication).
6. DME (Distance Measuring Equipment):
• Emission Type: P0N (Pulse Modulation with No Carrier).

Question 6

Q

What is the conversion from nautical miles to kilometers?

What is the conversion from nautical miles to feet?

What is the conversion from nautical miles to meters?

Answer

A

1 NM = 1.852 KM

1 NM = 6080 feet

1 NM = 1852 m

Question 7

Q

What is the conversion from statute miles to feet?

Answer

A

1 SM = 5280 feet

Question 8

Q

What is the conversion from nautical miles to statute miles?

Answer

A

1 NM = 1.151 SM

Question 9

Q

What is the conversion from statute miles to nautical miles?

Answer

A

1 SM = 0.865 NM

Question 10

Q

What is the conversion from kilograms to pounds?

Answer

A

1 Kg = 2.205 lbs

Question 11

Q

What is the conversion from US gallons to liters?

Answer

A

1 uSh = 3.785 l

Question 12

Q

What is the conversion from Imperial gallons to liters?

Answer

A

1 Imp.G = 4.546 l

Question 13

Q

What is the formula for Rate of Descent (ROD)?

Answer

A

ROD = change in Altitude (feet) / Time (mins)

Question 14

Q

What is the formula for ROD in terms of groundspeed?

Answer

A

ROD = 101.3 x GSA x GS

Question 15

Q

What is the formula for ROD in terms of gradient?

Answer

A

ROD = 101.3 x GS x gradient

Question 16

Q

What is the formula for the headwind component?

Answer

A

H/w Component = V * cos(θ)

Question 17

Q

What is the formula for the crosswind component?

Answer

A

X/w Component = V * sin(θ)

Question 18

Q

What does θ represent in wind velocity calculations?

Answer

A

θ = True heading - wind direction

Question 19

Q

What is the conversion from meters to feet?

Answer

A

1 m = 328 feet

Question 20

Q

What is the conversion from inches to centimeters?

Answer

A

1 inch = 2.54 cm

Question 21

Q

What is the conversion from feet to inches?

Answer

A

1 foot = 12 inches

Question 22

Q

What is the conversion from minutes to nautical miles?

Answer

A

1 min = 1 NM

Question 23

Q

What is the formula for calculating departure ?

Answer

A

Departure = Chlong x 60 x Cos(lat)

Question 24

Q

What is the formula for calculating distance in nautical miles?

Answer

A

Distance = chlat x 60

Question 25

Q

What is the tangent function in terms of sides of a triangle?

Answer

A

tan(θ) = P/b

Question 26

Q

What is the sine function in terms of sides of a triangle?

Answer

A

sin(θ) = P/A

Question 27

Q

What is the cosine function in terms of sides of a triangle?

Answer

A

cos(θ) = B/h

Question 28

Q

What is the formula for the gradient?

Answer

A

Gradient = Vertical distance / Horizontal distance

Question 29

Q

What is the formula for the Total Ground Speed Adjustment (GSA)?

Answer

A

GSA = (60 x H(feet) ) / (R(nm) x 6080)

Question 30

Q

What is the formula for magnetism H?

Answer

A

H = T * cos(θ)

Question 31

Q

What is the formula for magnetism Z(vertical component)?

Answer

A

Z = T * sin(θ)

Question 32