ATPL General Navigation Key Concepts and Calculations
ATPL General Navigation Fundamentals
1. Earth Geometry and Basic Navigation Formulas
Departure (East/West)
Departure (NM) = ΔLongitude (minutes) × cos(Latitude)
Convergency (Earth)
Convergency = ΔLongitude × sin(Mean Latitude)
Conversion Angle
Conversion Angle = ½ × Convergency
| Hemisphere | Rhumb Line | Great Circle |
|---|---|---|
| Northern | Rhumb line curves toward the equator | Great circle curves toward the pole |
| Southern | Rhumb line curves toward the pole | Great circle curves toward the equator |
2. Chart Projections and Properties
Mercator Projection
- Type: Cylindrical (tangent to equator)
- Scale = True scale / cos(Latitude)
- Multiply (×) moving from the equator
- Divide (÷) moving toward the equator
- Rhumb lines are straight
- Great circles are concave to the equator
- Usable up to 70° N/S
- Shapes and angles are correct over small areas
- Radio bearings cannot be plotted directly
Simple Conic / Lambert’s Conformal Conic
- Convergency (chart) = ΔLongitude × sin(latitude of the parallel of origin)
- Parallel of origin = Reference latitude
- “Constant of the cone (n)” = sin(parallel of origin)
- Lambert’s Projection:
- 2 standard parallels (scale correct)
- 1 parallel of origin (convergency correct)
- Great Circles (GC) are nearly straight (slightly concave to parallel of origin)
- Rhumb Lines (RL) slightly concave to the pole
- Scale constant within 1%
- Coverage ≈ 80°N to 80°S
Transverse Mercator
- Tangent along a central meridian
- Convergency correct along central meridian and equator
- Useful within 350 NM of central meridian
Oblique Mercator
- Great Circle (GC) of tangency is neither the equator nor a meridian
- Used for specific routes (“one-off” charts)
Polar Stereographic
- Tangent at the pole
- Convergency and scale are correct at the pole
- Scale expands away from the pole
- Great circles appear as straight lines
- Rhumb lines are concave to the pole
Grid Navigation
- Used with polar or high-latitude charts
- Datum meridian: Where True North = Grid North
- Grid convergence: Difference between Grid North and True North
- Grivation: Variation + Convergence
3. Descent, Glidepath, and Speed Relationships
Altitude Change on a 3° Glidepath
Altitude Change (ft) ≈ 300 × Distance (NM)
Rate of Descent (ROD)
ROD (ft/min) ≈ GS (kt) × 5
(Applicable at 3° glide slope)
Glide Path Angle Calculation
Angle (°) = (100 × Height (ft)) / (Distance (ft) × 60)
4. Airspeed and Mach Relationships
IAS → RAS/CAS → EAS → TAS
(Through corrections for instrument, position, compressibility, and density)
Equivalent Airspeed (EAS)
EAS = TAS × √Relative Density
(Example: at 40,000 ft, relative density ≈ ¼)
Mach Number (M)
M = TAS / LSS
Where LSS (Local Speed of Sound) = 38.94 × √T(K)
Typical Speeds:
- Sea level (288 K) → 661 kt
- Tropopause (216.5 K) → 573 kt
5. Time, Distance, and Endurance Formulas
Point of Equal Time (PET / ETP)
Distance to PET = (D × GSHome) / (GSOut + GSHome)
Point of Safe Return (PSR / PNR)
Distance to PSR = (E × GSOut × GSHome) / (GSOut + GSHome)
Where E = Safe Endurance
6. International Standard Atmosphere (ISA)
| Parameter | Value |
|---|---|
| Temperature (SL) | +15°C |
| Pressure (SL) | 1013.25 hPa |
| Density (SL) | 1.225 kg/m³ |
| Lapse rate | 1.98°C per 1000 ft up to 36,000 ft |
| Tropopause | -56.5°C (constant to 66,000 ft) |
| Above 66,000 ft | Temp increases 0.3°C per 1000 ft |
7. Bearings, Variation, and Compass Relationships
| Formula | Meaning |
|---|---|
| QDR + Var = QTE | Magnetic from → True from |
| QDM ± 180° = QDR | Magnetic to/from relationship |
| True Bearing = Relative Bearing + True Heading | Bearing conversion |
| C + Dev = M + Var = T | Compass → True sequence |
- VOR’s variation is applied at the station.
- NDB’s variation is applied at the aircraft.
Concave = hol
Convex = bol
8. Altimetry and Atmospheric Pressure
| Pressure Setting | Definition |
|---|---|
| QFE | Zero reading at airfield datum |
| QNH | Airfield elevation reading on the airfield |
| QFF | Pressure at airfield reduced to MSL using actual temperature |
| QNE | Height indicated when 1013.25 hPa (standard setting) is selected. |
Density Altitude: Altitude in ISA that corresponds to the actual air density.
9. Celestial and Time Navigation
Solar Geometry
- Plane of the ecliptic tilted 23.5° to the equator
- Solstices:
- Summer: Sun highest (21 June, Tropic of Cancer 23.5°N)
- Winter: Sun lowest (21 Dec, Tropic of Capricorn 23.5°S)
- Equinoxes: Day and night equal (March & September)
- Aphelion: Earth farthest from Sun
- Perihelion: Earth closest to Sun
Time Definitions
| Term | Meaning |
|---|---|
| Solar Day | Time between two successive solar transits |
| Mean Solar Day | Average solar day (basis of civil time) |
| Equation of Time | Difference between apparent and mean solar time |
| Civil Year | 365.24 days |
| Leap Year | Every 4 years (except century years not divisible by 400) |
| Sidereal Time | Time measured relative to the stars |
| Mean Sun | Fictitious reference body used for mean solar time |
Longitude and Time Conversion
Longitude West: Greenwich Best (Add Time)
Longitude East: Greenwich Least (Subtract Time)
Celestial Terms
- Sub-point: Point on Earth directly below a celestial body
- Declination: Equivalent of latitude
- Hour Angle: Measured westward 0°–360° (GHA, LHA, SHA)
- Equinoctial: Celestial equator
- First Point of Aries: Fixed reference in space (0h RA)
Twilight Definitions
| Twilight | Definition |
|---|---|
| Morning Civil Twilight | Begins when Sun is 6° below horizon, ends at sunrise |
| Evening Civil Twilight | Begins at sunset, ends when Sun is 6° below horizon |
- 66.6° N/S: Sun does not rise in winter.
- 64.5° N/S: Sun does not set in summer.
- 60.5° N/S: Continuous twilight in summer.