Lamberts Conical Projection

Wg Cdr Rajagopal

Lamberts Projection

Index

Lamberts Modification

  • Lamberts is a non-perspective, orthomorphic, modified conical projection
  • Lamberts modified the simple conic mathematically to make the cone go inside the reduced earth
  • The parallel of origin is hence inside the reduced earth
  • The parallels where the cone touches reduced earth are called its standard parallels
  • Lambert modified the simple conic projection to make it usable for more latitudes
  • Scale distortion was to limited to less than 1% for more greater latitude coverage

Lambert’s Standard Parallels

  • Standard parallels are latitudes where cone touches reduced earth
  • Lamberts projection has two standard parallels where the scale is correct
  • Standard parallels and parallel of origin divide the Lamberts Projection into four parts
  • The division is in the ratio of 1 : 2 : 2 : 1

Scale Variation in Lambert’s Projection

  • Scale contracts within standard parallels and expands outside the standard parallels
  • Scale is minimum at the parallel of origin and is maximum at the edges of the projection
  • Scale is within one percent of the correct scale if the standard parallels are within 16 degrees apart
  • Lamberts is considered to be a constant scale chart if the extremities of chart are within 24 degrees apart
  • Scale calculations are not required in lamberts chart since the scale is considered correct throughout the chart

Properties of Lambert Conical Projection

  • Lamberts is an orthomorphic or conformal projection since the scale variation is constant and parallels cut meridians at right angles
  • Meridians in lamberts are straight lines originating from poles and Parallels of latitudes are arc of circles centred at pole
  • Scale expansion or contraction is same the East-West as well as North-South directions
  • Rhumb lines appear to be are concave to the nearer pole and Parallels of latitude follow the same rules as rhumb lines
  • Meridians are straight lines converging at the poles

Earth Convergence in lamberts

  • Earth convergence is the angle between meridians at a specified latitude
  • Earth convergence signifies the change in great circle track
  • Earth Convergence = Chlong x Sin Latitude
  • Earth and Chart convergence are equal at the latitude of origin

Chart Convergence in Lamberts

  • Chart convergence is the angle between two meridians in the projection
  • Chart convergence signifies change in direction of a straight line
  • Straight line is neither a Great circle or a Rhumb line in a lamberts Projection
  • Chart Convergence = Change of Longitude x Constant of Cone
  • Chart Convergence = Change of Longitude x Sin of Latitude of Origin

Comparison between Earth and Chart Convergence

  • Earth and Chart convergence are equal at the latitude of origin
  • Chart convergence less than earth convergence nearer the poles
  • Near equator, chart convergence is more than earth convergence

Half Chart Convergence

  • Half chart convergence is the difference between rhumb line and straight line
  • Half Chart convergence is constant throughout the chart
  • Half Chart convergence = ½ change of longitude x constant of cone

Comparison between Conversion Angle vs Half Chart Convergence in Lamberts Projection

  • Conversion angle is the angular difference between rhumb line and great circle
  • Conversion angle would vary at different latitudes
  • Conversion Angle = ½ Chlong X Sine Lat

Relation between Great Circle, Rhumb Line and a Straight Line in Lamberts Chart

  • Great circle is concave to parallel of origin in a Lambert chart
  • Conversion angle is same as half convergency at parallel of origin
  • Conversion angle is less than half convergency nearer the equator
  • Conversion angle is more than half convergency nearer the pole

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