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DGCA Air Navigation · 139 questions

Earth, Convergence & Departure: DGCA Air Navigation Questions and Answers

139 practice questions on Earth, Convergence & Departure with answers and explanations, plus the key concepts and formulas, from the TrueHeading question bank.

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About this topic

Use this page to revise Earth, Convergence & Departure for the DGCA Air Navigation paper. Below are the key ideas first, then 12 practice questions with answers and explanations, picked from the 139 questions in the TrueHeading bank for this topic.

In short: An oblate spheroid, slightly flattened at the poles. For most calculations treat it as a sphere.

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Key concepts: Earth, Convergence & Departure

7 ideas to know cold.

What shape is the Earth, and what numbers do you need for navigation?

An oblate spheroid, slightly flattened at the poles. For most calculations treat it as a sphere.

  • 1 minute of latitude = 1 NM (1852 m)
  • Circumference ≈ 360 × 60 = 21 600 NM
  • The polar diameter is about 43 km (23 NM) shorter than the equatorial one

What is a great circle, and why do pilots care?

A circle on the surface whose plane passes through the centre of the Earth. The shortest distance between two points lies along it.

  • The equator and every meridian (with its opposite) are great circles
  • Every other parallel is a small circle
  • A great circle crosses successive meridians at different angles, so the track keeps changing
ABGreat circle: shortest, track keeps changingRhumb line: constant trackMercator chart: rhumb line is straight, great circle curves to the poleN ↑

Rhumb line or great circle: how do they differ?

A rhumb line cuts every meridian at the same angle (constant true track). A great circle is the shortest route.

  • A rhumb line is longer, except along a meridian or the equator
  • In the northern hemisphere the great circle lies poleward of the rhumb line
  • On a Mercator chart the rhumb line is straight and the great circle is a curve

Tip: Constant track = rhumb. Shortest distance = great circle.

Define convergence and give the formula.

The angle between two meridians at a given latitude: how much a great-circle track changes direction relative to the meridians.

Convergence=Δλ×sin⁡(mean latitude)\text{Convergence}=\Delta\lambda\times\sin(\text{mean latitude})
  • Zero at the equator, equal to the change of longitude at the pole
  • Example: Δλ = 20° at 45°N gives 20 × sin 45° ≈ 14°
ΔλparallelPole (90°)meridians convergeconvergence = change of long. × sin(mean lat)

What is departure, and how do you work it out?

The distance in nautical miles along a parallel between two meridians.

Departure=Δλ (minutes of arc)×cos⁡(latitude)\text{Departure}=\Delta\lambda\ (\text{minutes of arc})\times\cos(\text{latitude})
  • 1° of longitude is 60 NM at the equator, shrinking to 0 at the poles
  • Example: 2° at 60°N is 120′ × cos 60° = 60 NM

What is the conversion angle?

The angle between the rhumb-line track and the great-circle track at the start or end of a leg. It is half the convergence.

Conversion angle=12 Δλ sin⁡(mean latitude)\text{Conversion angle}=\tfrac12\,\Delta\lambda\,\sin(\text{mean latitude})

Tip: Use it to convert a great-circle bearing into a rhumb-line bearing for plotting on a Mercator chart.

How long is one degree of longitude at 40°N?

About 46 NM.

60 NM×cos⁡40∘≈46 NM60\ \text{NM}\times\cos 40^\circ\approx 46\ \text{NM}
  • Cosine of latitude shrinks east–west distance as you go north

Practice questions: Earth, Convergence & Departure

Tap “Show answer” after you have tried each one.

Q1What is the distance along the parallel of latitude 35° between two points that differ in longitude by 10°?

  1. 541 NM
  2. 491 NM
  3. 614 NM
  4. 565 NM
Show answer

Answer: B. 491 NM

Departure = d'long × 60 × cos lat = 10×60×cos 35° = 491 NM.

Q2What is the distance along the parallel of latitude 20° between two points that differ in longitude by 2°?

  1. 113 NM
  2. 158 NM
  3. 85 NM
  4. 180 NM
Show answer

Answer: A. 113 NM

Departure = d'long × 60 × cos lat = 2×60×cos 20° = 113 NM.

Q3What is the distance along the parallel of latitude 55° between two points that differ in longitude by 3°?

  1. 119 NM
  2. 129 NM
  3. 103 NM
  4. 165 NM
Show answer

Answer: C. 103 NM

Departure = d'long × 60 × cos lat = 3×60×cos 55° = 103 NM.

Q4An aircraft flies 690 NM due east along the 45° parallel. The change of longitude is approximately:

  1. 12.2°
  2. 22.8°
  3. 16.3°
  4. 26.0°
Show answer

Answer: C. 16.3°

d'long = departure ÷ (60 × cos lat) = 690 ÷ (60 × cos 45°) = 16.3°.

Q5An aircraft flies 450 NM due east along the 65° parallel. The change of longitude is approximately:

  1. 22.2°
  2. 17.7°
  3. 15.1°
  4. 13.3°
Show answer

Answer: B. 17.7°

d'long = departure ÷ (60 × cos lat) = 450 ÷ (60 × cos 65°) = 17.7°.

Q6The earth convergency between two meridians 12° apart at a mean latitude of 65° is approximately:

  1. 9.8°
  2. 15.2°
  3. 10.9°
  4. 8.2°
Show answer

Answer: C. 10.9°

Convergency = d'long × sin lat = 12 × sin 65° = 10.9°.

Q7The earth convergency between two meridians 20° apart at a mean latitude of 60° is approximately:

  1. 27.7°
  2. 19.9°
  3. 15.6°
  4. 17.3°
Show answer

Answer: D. 17.3°

Convergency = d'long × sin lat = 20 × sin 60° = 17.3°.

Q8What is the distance between 40°N and 45°N along the same meridian?

  1. 270 NM
  2. 300 NM
  3. 345 NM
  4. 375 NM
Show answer

Answer: B. 300 NM

5° × 60 = 300 NM.

Q9What is the distance between 25°N and 28°N along the same meridian?

  1. 108 NM
  2. 288 NM
  3. 180 NM
  4. 162 NM
Show answer

Answer: C. 180 NM

3° × 60 = 180 NM.

Q10The departure between two points on latitude 20° whose longitudes differ by 4° is approximately:

  1. 240 nm
  2. 82 nm
  3. 226 nm
  4. 282 nm
Show answer

Answer: C. 226 nm

Departure = d.long (in minutes) × cos lat = 240 × cos 20° = 226 nm.

Q11The convergence between two meridians 12° apart at latitude 30° is approximately:

  1. 6.0°
  2. 12.0°
  3. 10.4°
  4. 3.0°
Show answer

Answer: A. 6.0°

Convergence = d.long × sin(lat) = 12 × sin 30° = 6.0°.

Q12The distance along a meridian between latitudes differing by 15° is:

  1. 900 nm
  2. 1665 nm
  3. 450 nm
  4. 675 nm
Show answer

Answer: A. 900 nm

One degree of latitude = 60 nm. 15 × 60 = 900 nm.

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