Mercator’s projection – Detailed Discussion

Introduction

The Mercator’s Projection is a cylindrical orthomorphic projection designed by Flemish, Mercator, and Wright. In this, a simple circular cylinder touches the globe along the equator. All the parallels are of the same length equal to that of the equator and the meridians are equally spaced on the parallels. Therefore, the tangential scale increases infinitely toward the pole. To maintain the property of automorphism, the radial scale is made equal to the tangential scale at any point. Hence, parallels are variably spaced on the meridians and the poles can never be represented. The parallels and meridians are represented by sets of straight lines intersecting at right angles.

THEORY:

  1. Radius of the generating globe, R= actual radius of the earth / Denominator of R.F.
  2. The height of any parallel (Ø) above the equator, yØ= 2.3026 R log tan (90⁰+Ø)/2
  3. Division on the equator for spacing the meridians at i⁰ interval, d=(2πR/360⁰) ×i⁰

PROPERTIES:

  • Parallels are represented by a set of parallel straight lines.
  • All parallels are of the same length as the equator.
  • Parallels are variably spaced on a meridian; inter-parallel distance increases away from the equator.
  • The poles cannot be represented in this projection.
  • Meridians are represented by a set of parallel straight lines truly spaced on the equator only.
  • Meridians are equally spaced on all the parallels and they are of equal dimension as well
  • Parallels and meridians intersect each other at right angles.
  • On the map, the radial and the tangential scales are identical at all points.
  • It is an orthomorphic projection.

Check out Simple Conical Projection with one standard parallel

EXAMPLE:1

Draw the graticules of Mercator’s projection from the extension of 20⁰N-80⁰N & 10⁰E-40⁰W at an interval of 10⁰ on a scale of R.F.-1:80,000,000.

STEP-1:  Radius of the reduced earth:

R=640,000,000/80,000,000cm

=8cm

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

(2πR×interval)÷360⁰

=1.39cm

STEP-3:  Distance of the parallels from the equator:

R×2.3026 log tan [(90⁰+Ø)/2]cm

Ø(N)R (in cm)(90⁰+Ø)/2(in degree)R×2.3026 log tan [(90⁰+Ø)/2] (in cm)
20⁰855⁰2.85
30⁰860⁰4.39
40⁰865⁰6.10
50⁰870⁰8.09
60⁰875⁰10.54
70⁰880⁰13.88
80⁰885⁰19.49

EXERCISE:1

  Draw the graticules of Mercator’s projection for the map of the whole world at an interval of 20⁰ on a scale of 1: 240,000,000.

     EXERCISE:2

         Draw the graticules on Mercator’s projection for an extension for 80⁰N-80⁰S & 180⁰W-180⁰E at 10⁰ intervals, where the length of the equator in the projection is 15cm. Calculate the R.F. also.

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