Lamberts Conical Projection

Wing Commander Rajagopal

Lambert’s Projection

Lambert Conformal Conic Projection is a conical projection used widely in aviation charts. It preserves angles and shapes, providing accurate direction and distance over large areas. It is especially useful for flight planning in mid-latitude regions.

Lambert’s Modification

  • Lambert’s projection is a non-perspective, orthomorphic (conformal), modified conical projection.
  • In this projection, the cone is mathematically adjusted to pass inside the Reduced Earth.
  • The parallel of origin therefore lies inside the Reduced Earth.
  • The cone touches the Reduced Earth at two standard parallels.

Advantages of Lambert’s Modification

  • The simple conical projection is modified to provide accurate mapping over a wider range of latitudes.
  • Scale distortion is reduced to less than 1% over a much larger latitude coverage.

Lambert’s Standard Parallels

  • Lambert’s projection has two standard parallels.
  • The standard parallels are the latitudes where the cone touches the Reduced Earth.
  • Scale is correct along both standard parallels.
  • The two standard parallels and the parallel of origin divide the projection into four zones.
  • The spacing of these zones is in the ratio 1 : 2 : 2 : 1.

Scale Variation in Lambert’s Projection

  • Scale contracts between the two standard parallels.
  • The minimum scale occurs at the parallel of origin.
  • Scale expands outside the standard parallels.
  • The greatest scale expansion occurs near the edges of the projection.

Constant Scale Chart

  • Lambert’s projection is considered a constant scale chart under the following conditions:
    • The two standard parallels are within 16° of each other.
    • The chart limits extend no more than 24° beyond the standard parallels.
  • Under these conditions, scale error remains within 1%.
  • Distance calculations normally do not require local scale corrections.

Orthomorphism

  • Lambert’s projection is orthomorphic (conformal).
  • Meridians are straight lines converging toward the poles.
  • Parallels of latitude are arcs of circles centered on the poles.
  • Meridians and parallels intersect at 90°.

Parallels and Meridians in Lambert’s Projection

  • Scale expansion or contraction is the same in every direction around a point.
  • North-south and east-west scales change at the same rate.
  • Rhumb lines appear as curves concave toward the nearer pole.
  • Parallels of latitude follow the same curvature as rhumb lines.
  • Meridians are straight lines converging at the poles.

Earth Convergence

  • Earth convergence is the angle between two meridians at a specified latitude.
  • It represents the change in great-circle track caused by converging meridians.
  • Earth Convergence = Change in Longitude × sin(Latitude)
  • Earth convergence and chart convergence are equal at the parallel of origin.

Chart Convergence

  • Chart convergence is the angle between two meridians on the projection.
  • It represents the change in direction of a straight line drawn on the chart.
  • The straight line is neither a true great circle nor a rhumb line.
  • Chart Convergence = Change in Longitude × Cone Constant
  • Chart Convergence = Change in Longitude × sin(Latitude of Origin)

Earth and Chart Convergence

  • Earth convergence and chart convergence are equal at the parallel of origin.
  • Near the poles, chart convergence is less than Earth convergence.
  • Near the equator, chart convergence is greater than Earth convergence.

Half Chart Convergence

  • Half chart convergence is the angular difference between a rhumb line and a straight line on the chart.
  • It remains constant throughout the Lambert projection.
  • Half Chart Convergence = ½ × Change in Longitude × Cone Constant

Conversion Angle vs. Half Chart Convergence

  • The conversion angle is the angular difference between a rhumb line and a great-circle track.
  • Unlike half chart convergence, the conversion angle varies with latitude.
  • Conversion Angle = ½ × Change in Longitude × sin(Latitude)
  • On a Lambert chart, great circles are concave toward the parallel of origin.
  • At the parallel of origin, the conversion angle is equal to half chart convergence.
  • Near the equator, the conversion angle is less than half chart convergence.
  • Near the poles, the conversion angle is greater than half chart convergence.