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
| Ø | R(in cm) | (2πRcosØ× interval)/360⁰ (in cm) |
| 5⁰ | 8.5 | 1.47787 |
| 15⁰ | 8.5 | 1.43297 |
| 25⁰ | 8.5 | 1.34452 |
| 35⁰ | 8.5 | 1.21523 |
| 45⁰ | 8.5 | 1.04900 |
| 55⁰ | 8.5 | 0.85090 |
| 65⁰ | 8.5 | 0.62695 |
| 75⁰ | 8.5 | 0.38395 |
| 85⁰ | 8.5 | 0.12929 |
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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