Bonne’s projection – In Details

Introduction

In Bonne’s projection, a simple right circular cone is supposed to touch the generating globe along the standard parallel. The radial scale is truly preserved along the central meridian and the tangential scale is preserved along all the parallels. Consequently, the parallels are represented as concentric arcs of circles but the meridians appear as smooth curves. This is the modification designed by R Bonne (a French cartographer) to the original simple conical projection with one standard parallel.

Theory

The radius of the generating globe, R=Actual radius of the earth /Denominator of R.F.

The division on the central meridian for spacing the parallels at i⁰ interval,

d= (πR÷180⁰)×I⁰

The radius of the standard parallel (Ø), r=RcotØ

The division on the parallels for spacing the meridians at i⁰ interval,

d= [(2πR cosØ × i⁰)/360⁰]

Properties

  • Parallels are concentric arcs of circles, truly spaced on the central meridian.
  • Radial scale is true only along the central meridian.
  • The tangential scale is true along all the meridians.
  • Excepting the central meridian, all are regular curves concave towards the center.
  • At any point the product of the two principal scales is unity.
  • It is an equal-area projection.
  • It is used for countries like France, Netherlands, Switzerland, Belgium, India, etc.

EXAMPLE:1

Draw graticules of Bonne’s projection at an interval of 10⁰ on a scale of 1:75,000,000 for an area extending from 5⁰S – 85⁰S & 155⁰W across the international deadline

STEP-1:  Radius of the reduced earth:

R=640000000cm/75,000,000

=8.53333cm

STEP-2:  Determination of standard parallel and the central meridian:

STANDARD PARALLEL:  5⁰S, 15⁰S, 25⁰S, 35⁰S, 45⁰S, 55⁰S, 65⁰S, 75⁰S, 85⁰S

Standard parallel=45⁰S

CENTRAL MERIDIAN:  155⁰E, 165⁰E, 175⁰E, 175⁰W, 165⁰W, 155⁰W

Central meridian=180⁰

STEP-3:  Radius of the standard parallel:

RcotØ

=8.5cm

STEP-4:  Distance along the central meridian for spacing the parallel:

(πR × interval)/180⁰

=1.489

STEP-5:  Distance along the meridian=(2πRCOSØ×Interval)/360⁰

ØR(in cm)(2πRcosØ× interval)/360⁰ (in cm)
5⁰8.51.47787
15⁰8.51.43297
25⁰8.51.34452
35⁰8.51.21523
45⁰8.51.04900
55⁰8.50.85090
65⁰8.50.62695
75⁰8.50.38395
85⁰8.50.12929

EXERCISE:1

             Draw graticules of Bonne’s Projection at an interval of 10⁰ on a scale of R.F.= 1:85,000,000 for an area extending from 20⁰N-70⁰N & 40⁰W-140⁰W.

EXERCISE:2

             Draw graticules of Bonne’s Projection at an interval of 10⁰ for the extension of 30⁰N-70⁰N & 140⁰W-140⁰E where the length of central meridian is 12 Cm. Also, calculate the R.F.

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