Notes Flashcards
- 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
- Case 1: Check if coordinates are antipodal.
• If Yes → Distance = 10,800 NM.
• If No → Move to Case 2. - Case 2: Check if sum of latitudes and longitudes = 180°.
• If Yes → Travel via poles.
• If No → Move to Case 3. - Case 3: Use formulas:
• Destination Distance (NM) = Change in Latitude (chlat) × 60
• Departure Distance (NM) = Change in Longitude (chlong) × 60 × cos(chlat)
- Case 1: Check if coordinates are antipodal.
- 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
- 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
- Latitude-based distance:
Distance (NM) = Change in Latitude (chlat) × 60 - Longitude-based distance:
Distance (NM) = Change in Longitude (chlong) × 60 × cos(chlat)
- Latitude-based distance:
- Gradient and Rate of Descent (ROD)
- Gradient (%) = (Vertical Distance ÷ Horizontal Distance) × 100
- ROD = (101.3 × Ground Speed × Gradient) ÷ 60
- Wind Component Formulas
- Tailwind (TW) = Wind Speed × cos(Angle)
- Crosswind (CW) = Wind Speed × sin(Angle)
- Semi-Axis Difference (Earth Dimensions)
Compression Ratio = (Major Axis - Minor Axis) ÷ Major Axis
- Problem-Solving for Coordinates
- Destination Distance (NM) = Change in Latitude (chlat) × 60
- Departure Distance (NM) = Change in Longitude (chlong) × 60 × cos(chlat)
- Miscellaneous Conversions
- 1 Nautical Mile (NM) = 1.852 km = 6080 ft
- 1 US Gallon = 3.785 liters
- 1 Imperial Gallon = 4.546 liters
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.
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.
What is the conversion from nautical miles to feet?
1 NM = 6080 feet
What is the conversion from nautical miles to kilometers?
1 NM = 1.852 KM
What is the conversion from nautical miles to meters?
1 NM = 1852 m
What is the conversion from statute miles to feet?
1 SM = 5280 feet
What is the conversion from nautical miles to statute miles?
1 NM = 1.151 SM
What is the conversion from statute miles to nautical miles?
1 SM = 0.865 NM
What is the conversion from kilograms to pounds?
1 Kg = 2.205 lbs
What is the conversion from US gallons to liters?
1 uSh = 3.785 l
What is the conversion from Imperial gallons to liters?
1 Imp.G = 4.546 l
What is the formula for Rate of Descent (ROD)?
ROD = change in Altitude (feet) / Time (mins)
What is the formula for ROD in terms of groundspeed?
ROD = 101.8 x GSA x GS
What is the formula for ROD in terms of gradient?
ROD = (Climb - 3) x GS x gradient
What is the formula for the headwind component?
H/u Component = V * cos(θ)
What is the formula for the crosswind component?
X/N Component = V * sin(θ)
What does θ represent in wind velocity calculations?
θ = True heading - wind direction
What is the conversion from meters to feet?
1 m = 328 feet
What is the conversion from inches to centimeters?
1 inch = 2.54 cm
What is the conversion from feet to inches?
1 foot = 12 inches
What is the conversion from minutes to nautical miles?
1 min = 1 NM
