DGCA CPL / ATPL • General Navigation

Chapter 11
Navigation Using the 1 in 60 Rule

DGCA CPL/ATPL Study Notes • Interactive Colour Edition
Track Corrections • Closing Angle • New Track Reference
Compiled by Capt. Pankaj Pahil
www.ghostaviator.com

Contents

  1. 1. Returning to Track — Introduction
  2. 2. Track Error Angle vs Drift — Critical Distinction
  3. 3. Double Track Angle Error Method
  4. 4. Track Error Angle and Closing Angle
  5. 5. Combined TEA + CA — Single Calculation Method
  6. 6. Using These Methods Practically
  7. 7. New Track Reference — The Preferred Method
  8. Practice Questions & Detailed Answers
  9. Master Reference

1. Returning to Track — Introduction

If you find yourself off track during a flight, the most common en-route cause is a change in wind since the flight plan was prepared. Other causes include failure to fly the planned heading accurately, or making too shallow a turn at the last waypoint.

✎ Rapid Navigation Assumption

For these techniques it is assumed that for small heading changes, a change of track equals the same change of heading. In practice drift changes slightly when you alter heading, but the error is negligible for the corrections involved.

There are three basic techniques for returning to track, plus the recommended practical method:

  1. Double Track Angle Error Method
  2. Track Error Angle and Closing Angle
  3. Combined TEA + CA Single Calculation
  4. New Track Reference — the preferred method

2. Track Error Angle vs Drift — Critical Distinction

Figure 1 — Planned track vs Track Made Good (TMG)
Figure 1 — Planned track vs Track Made Good (TMG)

The track you intended to fly is the Planned Track. The track actually made over the ground is the Track Made Good (TMG). The angle between them is the Track Error Angle (TEA).

Figure 2 — Heading, expected drift, actual drift, and track error angle
Figure 2 — Heading, expected drift, actual drift, and track error angle

⚠ Common Exam Trap — TEA is NOT Drift

Drift is the angle between Heading and Track (either planned track or TMG).
Track Error Angle is the angle between Planned Track and TMG only.

TEA is the difference between expected drift and actual drift — but TEA is not drift.
You cannot calculate drift if the heading is not given.

TermDefinitionDiagram colour (Fig 2)
Track Error AnglePlanned track − TMGGreen
Expected DriftHeading − Planned trackRed
Actual DriftHeading − TMGBlue

3. Double Track Angle Error Method

Situation: planned track 090°(T). After 30 NM you get a visual fix 4 NM left of track.

Step 1 — Calculate Track Error Angle

TEA = (4 / 30) × 60 = 8° left
Figure 3 — 4 NM left of track after 30 NM along track
Figure 3 — 4 NM left of track after 30 NM along track

If no action is taken, the aircraft will continue to diverge from track at the same rate:

Figure 4 — Continuing to diverge from track — no correction applied
Figure 4 — Continuing to diverge from track — no correction applied

Turning 8° right stops the divergence but only parallels track — the aircraft is still 4 NM off:

Figure 5 — Paralleling track after initial 8° right correction
Figure 5 — Paralleling track after initial 8° right correction

Step 2 — Turn DOUBLE the TEA (16° right)

Total turn = 2 × 8° = 16° right
This creates an isosceles triangle — the aircraft converges back to track at a closing angle equal to the TEA (8°)
Time to regain track = time taken to go off track (symmetrical triangle)
Figure 6 — Isosceles triangle formed by turning double the track error angle
Figure 6 — Isosceles triangle formed by turning double the track error angle

✈ No Map-Reading Required

By turning double the TEA you create a symmetrical triangle. If you deviated 1000–1020, you will regain track at exactly 1040 — just watch the clock.

Figure 7 — Back on track at the predicted time — no map-reading required
Figure 7 — Back on track at the predicted time — no map-reading required

Once back on track, do not maintain that heading — you will diverge to the other side:

Figure 8 — Diverging to right of track if no correction made on regaining track
Figure 8 — Diverging to right of track if no correction made on regaining track

Turn 8° left on regaining track. You now fly on a heading 8° right of your original — which is the correct heading for the actual wind conditions.

Figure 9 — Maintaining track by turning 8° left on regaining track
Figure 9 — Maintaining track by turning 8° left on regaining track

✎ Limitation of Double TEA Method

If you are more than half-way along the leg when you get your first pinpoint, the doubled correction will not return you to track before the next waypoint. Use the TEA + Closing Angle method instead.

4. Track Error Angle and Closing Angle

Use this method to fly direct to destination rather than regain track, or when more than half-way along the leg.

Situation: total track = 78 NM, after 30 NM you are 4 NM left of track (TEA = 8° left).

Figure 10 — Track error angle and closing angle to destination
Figure 10 — Track error angle and closing angle to destination

Calculation

Remaining distance: 78 − 30 = 48 NM
Closing Angle: (4 / 48) × 60 = 5°
Total turn: TEA + CA = 8° + 5° = 13° right
Turn required to fly direct to destination
Turn = Track Error Angle + Closing Angle
Direction: away from the side on which you are displaced

5. Combined TEA + CA — Single Calculation Method

This gives exactly the same answer as the TEA + CA method but skips calculating the TEA. You only need the Closing Angle, then multiply by an inverted fraction.

Figure 11 — Closing angle only — combined single-calculation method
Figure 11 — Closing angle only — combined single-calculation method

Same problem: 78 NM track, 30 NM along, 4 NM left

Closing Angle: (4 / 48) × 60 = 5°
Proportion flown: 30 / 78 → Inverted: 78 / 30
Total turn: (78/30) × 5° = 13° — identical to TEA + CA
Combined single-calculation turn
Turn = CA × (Total distance / Distance gone)
No separate TEA needed — geometrically equivalent

📚 In Practice

Simply estimate your position as approximately 1/4, 1/3, or 1/2 along the leg, then multiply the closing angle by 4, 3, or 2 respectively.

6. Using These Methods Practically

ℹ Not EASA ATPL Examined

The practical map-marking techniques in this section are not examined in the EASA ATPL. They are used in practical VFR flying training.

Mark the chart during preflight with angle guidelines and distance-to-go markers so in-flight calculations can be done rapidly by eye.

Figure 12 — 5° and 10° closing-angle guidelines drawn on the map
Figure 12 — 5° and 10° closing-angle guidelines drawn on the map
Figure 13 — Single 10° guideline at each end of track
Figure 13 — Single 10° guideline at each end of track
Figure 14 — Distance-to-go markers at 10 NM intervals
Figure 14 — Distance-to-go markers at 10 NM intervals

With 10° guidelines at each end of track and 10 NM distance-to-go markers, you can read off the closing angle and estimate your proportion along track at a glance — then apply the combined calculation immediately.

7. New Track Reference — The Preferred Method

New Track Reference combines the single-calculation method with a systematic re-correction procedure whenever a new fix is obtained.

✈ New Track Reference Procedure

  1. Maintain steady heading until position is definitely established — no hasty corrections.
  2. Estimate the proportion of the current leg distance covered (e.g., ¼, ½, ¾).
  3. Invert that fraction.
  4. Multiply the inverted fraction by the Closing Angle to the destination.
  5. Alter heading by that amount, toward the destination.
Figure 15 — New Track Reference — initial heading correction at pinpoint C
Figure 15 — New Track Reference — initial heading correction at pinpoint C

Example — First Correction at C (¼ along leg A–B, CA = 5°)

Proportion flown = ¼ → Inverted = 4/1
Turn = 4 × 5° = 20° starboard
Aircraft now tracks from C toward B on the new heading
Figure 16 — New Track Reference — further pinpoint D and second correction
Figure 16 — New Track Reference — further pinpoint D and second correction

Example — Second Correction at D (½ along new leg C–B, new CA = 2°)

Proportion of C–B flown = ½ → Inverted = 2/1
Turn = 2 × 2° = 4° starboard
Aircraft now tracks from D toward B

✎ Key Points for New Track Reference

📚 Chapter 11 Quick Revision

Practice Questions & Detailed Answers

5 questions (21 sub-parts) • Track error, TMG, drift, heading corrections, ETA

Q1. An aircraft is 3° off its required track at a range of 120 NM from its departure point. How far in NM is it off track?
▶ Show answer & workings
Answer: 6 NM
Distance off = (TEA × distance gone) / 60 = (3 × 120) / 60 = 6 NM
Instructor's Note: Source key: 6 NM. Verified.
Q2. An aircraft is 2 NM off its required track at a range of 40 NM from departure. What is the track error angle?
▶ Show answer & workings
Answer: 3°
TEA = (2 / 40) × 60 = 3°
Instructor's Note: Source key: 3°. Verified.
Q3. An aircraft leaves A to fly to B, total distance 95 NM. Having flown 35 NM, a pinpoint puts the aircraft 7 NM right of track.

(a) What is the track error angle?
(b) What alteration of heading is required to fly direct to B?
(c) What is the drift?
▶ Show answer & workings
Answer: (a) 12° right  |  (b) 19° left  |  (c) Cannot be calculated
(a) Track Error Angle:
TEA = (7 / 35) × 60 = 12° right
(b) Heading alteration to fly direct to B:
Remaining = 95 − 35 = 60 NM    CA = (7 / 60) × 60 = 7°
Total turn = TEA + CA = 12° + 7° = 19° left (aircraft is right of track, so turn left)
(c) Drift:
Cannot be calculated — drift is the angle between heading and track. No heading is given, so drift cannot be found. This is an intentional trap: TEA ≠ drift.
Instructor's Note: Source key: (a) 12°R, (b) 19°L (TE=12, CA=7), (c) cannot calculate. Verified. Classic exam trap.
Q4. An aircraft is flying from Airfield W to Cambridge, planned track 074°(M), distance 70 NM, heading 065°(M). Having flown 30 NM, the pilot pinpoints overhead Cranfield, 4 NM left of planned track.

(a) Track error overhead Cranfield?   (b) TMG from Airfield W?   (c) Expected drift?
(d) Actual drift?   (e) Heading alteration to fly direct to Cambridge?   (f) New heading from Cranfield?
▶ Show answer & workings
Answer: (a) 8°L  |  (b) 066°M  |  (c) 9°S  |  (d) 1°S  |  (e) 14°R  |  (f) 079°M
(a) Track Error Angle at Cranfield:
TEA = (4 / 30) × 60 = 8° left
(b) Track Made Good:
Aircraft is left of planned track → TMG < planned
TMG = 074° − 8° = 066°(M)
(c) Expected drift:
Expected drift = Planned track − Heading = 074° − 065° = 9° Starboard
(Heading is left of track → wind forecast to push aircraft right/starboard)
(d) Actual drift:
Actual drift = TMG − Heading = 066° − 065° = 1° Starboard
(Wind pushed only 1°S, not 9°S as forecast → aircraft ended up left of track)
(e) Alteration to fly direct to Cambridge:
Remaining = 70 − 30 = 40 NM    CA = (4 / 40) × 60 = 6°
Total turn = TEA + CA = 8° + 6° = 14° right
(f) New heading from Cranfield:
New heading = 065° + 14° = 079°(M)
Instructor's Note: Source key: (a)8°L (b)066°M (c)9°S (d)1°S (e)14°R [TE=8,CA=6] (f)079°M. All verified. Departure airfield name changed to remove source reference.
Q5. An aircraft is flying from Norwich to Airfield X, planned track 250°(M), distance 96 NM, heading 260°(M), ground speed 180 kt. Departs Norwich at 1000. At 1012, overhead Ely, 3 NM right of planned track.

(a) Planned drift?   (b) Track error at 1012?   (c) TMG 1000–1012?   (d) Actual drift?
(e) Alteration to fly direct to destination?   (f) Heading direct?
(g) Alteration to regain track at 1024?   (h) Heading 1012–1024?
(i) Change at 1024 and heading from 1024?   (j) ETA at destination?
▶ Show answer & workings
Answer: (a)10°P  (b)5°R  (c)255°M  (d)5°P  (e)8°L  (f)252°M  (g)10°L  (h)250°M  (i)5°R→255°M  (j)1032
(a) Planned drift:
Planned drift = Planned track − Heading = 250° − 260° = 10° Port
(Track is left of heading → wind forecast to push aircraft port/left)
(b) Track error at 1012:
Distance flown = 180 kt × 12/60 = 36 NM
TEA = (3 / 36) × 60 = 5° right
(c) TMG 1000–1012:
Aircraft right of planned track → TMG > planned
TMG = 250° + 5° = 255°(M)
(d) Actual drift 1000–1012:
Actual drift = TMG − Heading = 255° − 260° = 5° Port
(Wind pushed 5°P, not 10°P as forecast → aircraft went right of track)
(e) Alteration to fly direct to destination:
Remaining = 96 − 36 = 60 NM    CA = (3 / 60) × 60 = 3°
Total turn = TEA + CA = 5° + 3° = 8° left
(f) Heading direct to destination:
260° − 8° = 252°(M)
(g) Alteration to regain track at 1024 (Double TEA):
Turn = 2 × TEA = 2 × 5° = 10° left
(h) Heading 1012–1024:
260° − 10° = 250°(M)
(i) Change at 1024 and heading from 1024:
At 1024 aircraft regains track. Turn 5° right (half of the 10° double-TEA correction).
New heading = 250° + 5° = 255°(M)
This is the corrected heading for the actual wind conditions experienced.
(j) ETA at destination:
1000–1012 = 36 NM  |  1012–1024 = 36 NM → 72 NM covered by 1024
Remaining = 96 − 72 = 24 NM  |  Time = (24/180) × 60 = 8 min
ETA = 1024 + 8 = 1032 hrs
Instructor's Note: Source key: all 10 sub-parts verified. Destination name changed to remove source reference.

Master Reference — Chapter 11

The Four Methods Compared

MethodFormulaResultBest used when
Double TEATurn = 2 × TEAReturns to track in same time as deviation< halfway along leg
TEA + CATurn = TEA + CAFlies direct to destinationAny time
CombinedTurn = CA × (total/gone)Same as TEA + CA; one stepAny time
New Track RefTurn = CA / fraction along legDirect to dest.; re-applicable at any fixPreferred always

Key Definitions

TermFormula
Track Error AnglePlanned track − TMG  |  (cross-track / along-track) × 60
TMG (left of track)Planned track − TEA
TMG (right of track)Planned track + TEA
Expected driftPlanned track − Heading
Actual driftTMG − Heading
Closing Angle(cross-track error / remaining distance) × 60

Answer Key — No ⚔ Flags

QAnswer(s)
16 NM
23°
3(a) 12°R   (b) 19°L [TE=12, CA=7]   (c) Cannot calculate — heading not given
4(a) 8°L   (b) 066°M   (c) 9°S   (d) 1°S   (e) 14°R [TE=8, CA=6]   (f) 079°M
5(a)10°P (b)5°R (c)255°M (d)5°P (e)8°L (f)252°M (g)10°L (h)250°M (i)5°R→255°M (j)1032
DGCA CPL/ATPL General Navigation Study Notes
Chapter 11 — Navigation Using the 1 in 60 Rule
Capt. Pankaj Pahil  |  www.ghostaviator.com
For personal study use only. Ghost Aviator Interactive Colour Edition.
Capt. Pankaj Pahil
www.ghostaviator.com