Convergence and Conversion Angle

Wing Commander Rajagopal

Convergence and Conversion Angle

Convergence is the angle between two meridians of longitude as they move closer together toward the poles. It affects the difference between true north directions at different positions on Earth. Conversion angle is used to calculate Great circle and Rhumb line directions.

Convergency or Earth Convergence

  • Meridians converge toward the poles and diverge toward the Equator.
  • At the Equator, meridians are parallel to each other.
  • Therefore, the angular difference between meridians at the Equator is zero.
  • At the poles, meridians meet at an angle (maximum convergence).
  • The angular difference between meridians is equal to their difference in longitude.

Earth Convergence

  • Consider meridians 000° and 045°E, which are 45° apart in longitude.
  • The angle between them on a latitude is less than 45° but greater than 0°.
  • Earth convergence is also called meridional convergence.
  • It is the angular difference between meridians at a given latitude.

Convergence at Equator and Poles

  • Convergence is the angular difference between meridians at a given latitude.
  • It is minimum at 0° latitude (Equator).
  • It is maximum at 90° latitude (Poles).

Calculation of Convergence

  • The angular difference between meridians follows a sine relationship.
  • At the Equator (0°), sin 0 = 0, so convergence is zero.
  • At the Poles (90°), sin 90 = 1, so convergence equals change in longitude.
  • Formula: Convergence = Change in Longitude × sin(latitude)

Significance of Convergence

  • Convergence is the angle between two selected meridians.
  • It represents the change in great circle track direction.
  • As an aircraft moves between meridians, great circle direction changes accordingly.
  • The amount of change in great circle track equals convergence.
  • If points are not on the same latitude, the mean latitude is used.

Conversion Angle

  • Conversion angle is the difference between Great Circle and Rhumb Line tracks.
  • It is equal to half of the convergence.
  • A rhumb line crosses all meridians at a constant angle.

Significance of Conversion Angle

  • Great circle track changes direction relative to a rhumb line.
  • The difference in track is given by the conversion angle.
  • Formula: Conversion Angle = ½ × Change in Longitude × sin(mean latitude)