What is Dead Reckoning?

Dead reckoning (DR) is the process of estimating a current position based on a known starting point, then projecting forward using a known heading, true airspeed, and elapsed time — corrected for wind effect.

Origin of the term: "Dead reckoning" likely derives from "deduced reckoning" (abbreviated "ded. reckoning"), though maritime historians debate this. The principle is the same: deduce where you must be based on where you started and how you have moved.

Key Terms and Definitions

TermAbbreviationDefinition
True CourseTCDirection from departure to destination measured on a chart relative to True North
True HeadingTHDirection the aircraft nose points, relative to True North; TC ± Wind Correction Angle
Magnetic HeadingMHTrue Heading corrected for magnetic variation; what the compass/DI reads
True AirspeedTASSpeed of the aircraft through the airmass (IAS corrected for altitude and temperature)
GroundspeedGSActual speed over the ground — TAS modified by the wind component along the track
Wind Correction AngleWCAAngle between the True Course and the True Heading required to maintain that course
TrackTRActual path of the aircraft over the ground; should equal TC if WCA is correct
Track Angle ErrorTAEAngular difference between planned track and actual track observed at a position fix
Estimated Time of ArrivalETACalculated arrival time = departure time + (distance ÷ groundspeed)

The Wind Triangle

The wind triangle is a vector diagram representing three forces that determine an aircraft's movement over the ground. Understanding it is the conceptual foundation of all DR navigation.

TH + TAS (Heading vector) Wind Track + GS (Ground vector) Departure

Vector 1 (blue): aircraft heading + TAS through the airmass. Vector 2 (amber dashed): wind moves the airmass over the ground. Vector 3 (green): resultant track and groundspeed over the ground.

Mental Model

Imagine walking across a moving walkway at an angle. You point your body (heading) in one direction, the walkway (wind) pushes you sideways, and your actual path across the floor (track) is the combined result. You must angle into the walkway to walk in a straight line — that angle is your wind correction.

Calculating Wind Correction Angle

The WCA can be calculated precisely using vector trigonometry or approximately using the formula below. The E6B flight computer (or equivalent digital tool) solves the triangle graphically.

Approximate WCA Formula WCA (°) ≈ (Wind Speed × sin(Wind Angle)) ÷ TAS

Wind Angle = angle between wind direction and desired track
Result in degrees; positive = angle from track into wind

Approximate formula limitations: The sine formula gives good results when WCA is small (<20°). For large WCA values or precise flight planning, use the E6B flight computer, CRP-5, or navigation software which solves the vector triangle exactly. Always verify against reasonable expectations.

Worked Examples

Example 1 — Pure Crosswind

Given
Track: 090° Wind: 360°/20 kt TAS: 100 kt
Wind angle to track: 360° − 090° = 90° (wind from north, track east = pure crosswind)
Crosswind component: 20 × sin(90°) = 20 kt
WCA = arcsin(20 ÷ 100) = arcsin(0.2) ≈ 11.5°
Wind from north (left of track) → correct right: steer 090 − 11.5 ≈ 078°T
Headwind component: 20 × cos(90°) = 0 → GS ≈ √(100² − 20²) = ≈ 98 kt
Heading: ~078°T  |  Groundspeed: ~98 kt

Example 2 — Mixed Head and Crosswind

Given
Track: 180° Wind: 240°/30 kt TAS: 120 kt
Wind angle to track: 240° − 180° = 60° (wind from SW, track S)
Crosswind component: 30 × sin(60°) = 30 × 0.866 = 26 kt (from right)
Headwind component: 30 × cos(60°) = 30 × 0.5 = 15 kt
WCA ≈ arcsin(26 ÷ 120) ≈ 12.5° → ~13°R (wind from right → steer right)
Heading: 180 + 13 = 193°T
Groundspeed: TAS − headwind component = 120 − 15 = ~105 kt
Heading: ~193°T  |  Groundspeed: ~105 kt

Track Angle Error (TAE) and Correction

When a position fix reveals that the aircraft is off its planned track, the Track Angle Error (TAE) is the angle between the planned track and the actual track from departure.

Regain Track and Parallel

Steer a correction heading to intercept the planned track, then turn back to the planned heading.

Correction: steer (TAE × 2) toward track
→ reaches track at midpoint of remaining distance

Aim Directly at Destination

Calculate the closing angle from current position directly to the destination and steer that heading.

Closing angle = TAE + additional angle
to destination from current position

Double TAE Rule (Practical Shortcut)

The double TAE rule is a quick mental calculation for regaining track in half the remaining distance:

  1. Determine TAE from current position fix (angle between planned and actual track from departure)
  2. Estimate the angle from current position to destination (closing angle)
  3. Total correction heading change = TAE + closing angle
  4. Steer this heading until back on track, then resume planned heading

Simplified rule: If halfway to destination and off track by 5°, steer 10° toward track (double the TAE). This will put you back on track at the destination if the track error was consistent. In practice, recalculate WCA and apply a revised heading once back on track.

ETA Calculation and Revision

Estimated Time of Arrival is the fundamental output of DR navigation planning:

ETA Formula Time (hours) = Distance (nm) ÷ Groundspeed (kt)
Time (minutes) = (Distance ÷ GS) × 60

ETA Calculation Example

Distance: 150 nm  |  Planned GS: 120 kt
Time = 150 ÷ 120 = 1.25 hours = 1 hr 15 min
Depart 09:00 UTC → ETA: 10:15 UTC
ETA: 10:15 UTC

En-Route ETA Revision

After 30 min, fix shows 50 nm covered (planned: 60 nm)
Actual GS = 50 ÷ 0.5 hr = 100 kt (planned was 120 kt)
Remaining distance: 150 − 50 = 100 nm
Revised time remaining: 100 ÷ 100 = 1.0 hr = 60 min
Revised ETA: 09:30 + 60 min = 10:30 UTC (15 min later than planned)
Revised ETA: 10:30 UTC

ETA Revision Triggers