Great Circle and Rhumb Line

Wg Cdr Rajagopal

Great Circle and Rhumb Line Tracks

Index

Vertex of a Great Circle

  • Vertices are the northern and southern most points of a great circle
  • Northern vertex is the point on the great circle that is closest to the north pole
  • Southern vertex is the point on the great circle that is closest to the south pole
  • The northern and southern vertices are antipodal or diametrically opposite points
  • The distance between the vertices along the great circle track would be half the earth circumference
  • Flight along a great circle would result in continuous change in direction
  • However, great circle direction at either vertices would be due east or west
  • Numerical value of Latitudes of the vertices would be same, but on the opposite hemisphere
  • Longitudes of the vertices are placed in a meridian and its anti-meridian

Equator Crossing of Great Circles

  • Great circles would intersect the equator while crossing from south to north and north to south hemispheres
  • Latitude of these points would obviously be 00 degrees
  • Longitude of these intersections would be 90 degrees away from its vertex
  • Intersection angle between the plane of equator and that of a great circle would be same as the latitude of its vertex
  • Therefore, we would be able to calculate the great circle track at the equator crossing

Great Circle Track angle at Equator Crossings on an Easterly Track

  • Great circle track at the equator crossing on an easterly track
  • North to south equator crossing will be 90 + Vertex latitude
  • South to north equator crossing will be 90 – Vertex latitude

Equator Crossing on a Westerly Track

  • Great Circle Track angle at Equator Crossings on a westerly track
  • North to south equator crossing will be 270 – Vertex Latitude
  • South to north equator crossing will be 270 + Vertex Latitude

Properties of Rhumb Line

  • Rhumb lines are uniformly curved imaginary lines drawn between two points on earth surface
  • Rhumb line intersects all en-route meridians at same angle
  • Meridians are oriented towards True North and converge at poles
  • Rhumb lines are lines of constant track direction with respect to True North
  • Track angle made between the true north and rhumb lines remain constant
  • Only one rhumb line can be drawn between two points that are not diametrically opposite
  • Infinite rhumb lines can be drawn between diametrically opposite points

Equator is a Special Line

  • Equator can be considered as a rhumb lines as well as great circle
  • Equator is a great circles hence signify the shortest distance
  • Equator being a rhumb-line has constant direction
  • Equator is a great circle with vertices at zero deg latitude
  • Equator has infinite vertices pointing due east or west
  • All points on the equator have a constant direction of 090 or 270

Meridians are Special Lines

  • Meridians are rhumb lines as well as great circles
  • Meridians are great circles hence signify the shortest distance
  • Meridians are rhumb lines and hence have constant direction
  • Meridians are great circles with vertices at 90 deg North and South latitude
  • Flight along the meridians would always be in a northerly or southerly direction
  • All points on meridians would have a constant direction of 000 or 180

Rhumb Line and Great Circle

  • Rhumb lines have a constant track direction while Great circles do not have a constant track direction
  • Flight along a great circle would be the shortest distance while Rhumb lines track distances are greater than great circle
  • Great circles tracks appear to be convex to the nearest pole or concave to the equator
  • Rhumb lines appear to be convex to the equator or concave to the nearer pole

Track of Great Circle vs Rhumb Line

  • Rhumb line is a regularly curved constant direction line while Great circle track direction changes continuously
  • Till the mid-point great circle track moves towards the nearer pole
  • At the mid-point great circle track would be equal to the rhumb line track
  • After the mid-point great circle track moves towards the equator

Value of Great Circle Track in Northern Hemisphere

  • Numerical value of great circle track depends on hemisphere as well as track direction
  • Increases on easterly track by moving towards north pole and changing clockwise
  • Decrease on westerly track by moving towards north pole and changing anti-clockwise

Value of Great Circle Track in Southern Hemisphere

  • Numerical value of great circle track depends on hemisphere as well as track direction
  • Decrease on easterly track by moving towards south pole and changing anti-clockwise
  • Increase on westerly track by moving towards south pole and changing clockwise

Best of luck