Cylindrical Equal Area Projection

                        Cylindrical Equal Area Projection is a non-perspective projection developed by Lambert (1772).  In this projection, a simple circular cylinder is supposed to touch the generating globe along a selected parallel, called the standard parallel. Parallels are projected as concentric arcs of circles with varying radii. Meridians are projected as straight lines radiating from the vertex of the cone and truly spaced on the standard parallel. The principle is that the area of a segment on projection is made exactly identical to the corresponding area on the generating globe to retain the property of equal area.

THEORY:

  1. Radius of the generating globe, R = Actual radius of the earth ÷ Denominator of the R.F.
  2. Radius of the standard parallel (ø0), r0 = Rcotø0.

PROPERTIES:

  1. It is a non-perspective projection.
  2. The pole is represented by an arc of circle.
  3. The tangential scale is true only along the standard parallel.
  4. The tangential scale increase gradually away from the standard parallel toward the pole.
  5. The radial scale decreases gradually away from the standard parallel toward the pole.
  6. Inter parallel distance gradually decrease toward pole.
  7. It is an equal area projection.
  8. It is suitable for showing the distribution of any element in the mid-latitude countries or region.

EXAMPLE:1

Draw the graticules of cylindrical equal area projection for the extension of 20oW-60oW & 40oN-40oS at an interval of 10o on a scale of 1:75,000,000

Solve: Calculation Part

  STEP-1:  Radius of the reduced earth:

R= 640,000,000/75,000,000cm

   =8.53cm

STEP-2:   Division along the equator for spacing the meridians:

d= (2πR × interval) ÷ 360⁰

   =1.49cm

STEP-3:  Distance of the parallel from the equator=R sinϴ

                  ϴ (N/S)             R(cm)          R sinϴ(in cm)
                  10                  8.53               1.48
                  20                8.53               2.92
                  30                8.53               4.27
                  40                 8.53               5.48

Exercise: 1

Draw the graticules of cylindrical equal-area projection for the extension of 4oN-52oN and 24oW -40oE at an interval of 8; R.F.-1:50×106.

Exercise: 2

Draw the graticules of cylindrical equal-area projection for the extension of 16oS-52oN and 140oW -140oE at an interval of 8; Where the length of the meridian for the extension is 14cm. Calculate the R.F. also.

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