Polar Steriographic Projection

Wg Cdr Rajagopal

Polar Stereographic Projection

Index

Azimuthal Projections

  • Azimuthal projections are obtained by projection on a horizontal or flat sheet of paper
  • Since the paper is kept flat the projection forms a circular chart
  • The reduced earth touches the paper at the pole called point of tangency
  • Scale is correct only at the pole and expands away from the poles

Scale Expansion of Azimuthal Projections

  • Scale expansion is constant in all directions making the projection orthomorphic
  • Latitudes are concentric circles and longitudes are radial straight lines from the poles
  • Meridians and parallels intersect at right angles making them easy to plot

Polar Stereographic Projection

  • Polar stereographic is a Perspective Orthomorphic Projection
  • PSP is an Azimuthal projection as the paper is flat
  • Unlike other projections, light source is placed on the opposite pole
  • PSP is orthomorphic since the scale expansion is constant in all directions
  • Meridians are radial straight lines and parallels are concentric circles
  • Meridians and parallels cut at right angles

Scale Expansion in Polar Stereographic Projection

  • Scale is correct at the pole of the projection as it is the point of origin
  • Scale expands at all other latitudes as a factor of the co-latitude
  • Co-latitude is angle measured from pole (90 – latitude)
  • Scale expansion of Polar Stereographic is given by a formula
  • Scale Expansion = Sec² ( ½ Co-latitude)

Uses of Polar Stereographic

  • Polar stereographic is used for flying polar routes as grid charts and as a planning chart for a hemisphere
  • Scale expansion is within 1% from 90 to 78 degrees North or South
  • Scale expansion is within 3 % from 78 to 70 degrees North or South
  • Therefore, the projection can be considered as constant scale plotting chart above 78 degrees North and South
  • PSP can be used as planning charts from poles to 78 degrees
  • Shapes are correct at the pole and gets distorted at other latitudes

Chart Convergence

  • Chart convergence or cone constant is 1 or maximum which is correct only at the poles
  • Chart convergence is more than earth convergence at all other latitudes
  • Track angle of a great circle changes by amount of chart convergence
  • Change in great circle track on this projection would be equal to the change of longitude

Great Circles and Rhumb Lines

  • Great circles are concave to the pole which is the point of origin and Rhumb lines are concave to the pole
  • Meridians are straight lines although they are also rhumb lines
  • Above 70 degree North and South latitudes, a straight line can be considered to be great circle

Best of luck