Navigation

061 General NavigationChapter 4

Dead reckoning, the triangle of velocities, and the 1-in-60 rule form the core of pilot navigation calculations.

Schematic

Triangle of velocities — drift is from heading toward track; apply WCA opposite to drift.

Distances & conversions

Key fact

1 NM = 1.852 km = 6080 ft. 1 SM = 5280 ft. 1 km = 3280 ft. Circumference ≈ 21 600 NM or 40 000 km. 1′ of arc along a meridian = 1 NM (at 45° for oblate spheroid reference).

Formula — Departure (rhumb line distance along parallel)

Departure = change in longitude × cos(latitude)
            = change in longitude (′) × cos(lat)   [NM if Δlong in minutes]

Key fact

Distance from change in latitude on the same meridian — subtract latitudes (include 60 min per degree). If longitudes sum to 180°, route may pass via pole — add segments to pole.

Triangle of velocities

Key fact

Drift angle — angle between heading and track. Drift is FROM heading TO track. WCA is applied opposite to drift.

Key fact

Course = planned track. TMG = actual track over ground. Radials are magnetic tracks.

Formula — Wind components

Crosswind (XWC) = sin(wind angle) × wind speed
Headwind (HWC)  = cos(wind angle) × wind speed
Drift ≈ XWC × 60 / TAS
Heading = Track ± drift
GS = effective TAS ± HWC

Use effective TAS = TAS × cos(WCA) when WCA > 10°.

Key fact

VOLMET wind is true. ATC / ATIS / tower wind is magnetic. QDM = QFU = runway heading for wind component on E6-B.

Exam trap

Average TAS planning: climb use 2/3 altitude gained + initial; descent/cruise approx use ½ cruising altitude (in thousands of ft). Wind for climb at 2/3 altitude, descent at ½ altitude.

1-in-60 & track correction

Schematic

1-in-60 rule — for small angles only (when question says approximate).

Formula — Track error (1-in-60)

Track error = (distance off track × 60) / distance gone

To regain track in the same distance taken to go off — double the track error.

Formula — Track correction example

Off 2 NM after 15 NM → TE = (2/15) × 60 = 8°
Correction to intercept at B in 30 NM → (2/30) × 60 = 4°
Total alteration ≈ 8° + 4° = 12°

Key fact

Max drift ≈ wind speed / (TAS/60) — apply clock code for WCA from max drift.

DR, fixes & position lines

Key fact

DR position — on the desired track, using estimated TAS and wind. Line from last fix to DR = estimated track. Air position — where aircraft would be without wind.

Formula — Actual distance (wind triangle)

GD = (AD × GS) / TAS

Formula — Point of no return

PNR time = (GS out × GS home) / (GS out + GS home) × safe endurance

Key fact

ETA — estimated time of arrival at destination. Position lines transferred at ground speed along track.

Altitude, temperature & fuel

Key fact

Min ISA temp −56.5°C above tropopause. Density altitude ≈ PA + 120 ft per °C ISA deviation.

Formula — True altitude (approx)

TA = PA + [(QNH − 1013) × 30] + [ISA dev × 0.4% × (PA + pressure corr − station elev)]

Formula — Specific gravity

SG = mass fuel / mass water
Weight (kg) = SG × volume (litres)
Weight (lbs) = 8 × SG × volume (Imp gal)   [≈ 10 SG × Imp gal in some notes]

Glidepath & ROD

Formula — Rate of descent

ROD = glide slope (°) × range (NM) × 100
3° glideslope: ROD ≈ GS × 5
Gradient (%) = altitude diff (ft) × 100 / ground diff (ft)

NAM vs NGM

Formula — Time equivalence

NAM / TAS = NGM / GS

Same time in air and over ground — equate nautical air miles to ground miles.

Quick formula reference

Name	Formula
Departure	Δlong × cos lat
Track error	(off × 60) / gone
PNR time	(GS out × GS home) / (GS out + GS home) × T
Convergence	Δlong × sin lat
Conversion angle	½ Δlong × sin lat