Table of Contents

## Introduction:

A simple circular cone touches the generating globe along a particular parallel on which parallel any kind of distortions is null. This is known as the standard parallel. Simple Conical Projection with one standard parallel is a perspective projection in which the parallels and meridians are projected directly on the inner surface of the cone with respect to a light source at the center of the generating globe.

**Theory:**

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

The division of the central meridian for spacing the parallel at i⁰ interval,

**d _{1}=(πR/180⁰) ×i⁰**

The radius of the standard parallel (ø_{0)},** r _{0 =}Rcotø_{0}**

The division on the standard parallel for spacing the meridians at i⁰ interval, d_{2}= (2π R cosϴ÷360⁰) ×i⁰

## Properties**:**

- Genetically it is a perspective projection. The parallels are concentric arcs of circles truly spaced on the central meridian.
- Poles are also represented by arcs in this projection.
- Radial scale is true along all the meridians.
- Meridians are straight lines truly spaced on the standard parallel and converging at the vertex of the cone.
- Tangential scale is true along the standard parallel only.
- Deformation is positive towards the equator and negative deformation towards the pole.
- It is an aphylactic projection, i.e., one that maintains neither area nor shape
- It is suitable for smaller countries of mid-latitude or temperate regions.

**Derivations:**

There are three main formulae are used in this projection. The derivation of the formulae is as below.

__EXAMPLE:1__

__EXAMPLE:1__

Draw graticules on simple conical projection with one standard parallel for an area between 140⁰to 150⁰W latitudes & 20⁰S to 70⁰S longitudes at an interval of 10⁰; R.F.-1:80,000,000.

__STEP-1:__** Radius of the reduced earth (R) :**

Earth’s actual radius/Denominator of the R.F.

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

=8cm.

__STEP-2:__** Determination of central meridian and standard parallel:**

__CENTRAL MERIDIAN__

140⁰ E, 150⁰E, 160⁰E, 170⁰E, I 180⁰E, 170⁰W, 160⁰W, 150⁰W

Central Meridian = 175⁰E

__STANDARD PARALLEL__

20⁰S, 30⁰S, 40⁰S, I 50⁰S, 60⁰S, 70⁰S

Standard Parallel= 45⁰S

__STEP-3:__**Radius of the standard parallel:**

Rcotø

=8cot45⁰

__STEP-4: Distance along the central meridian for placing the parallel:__

(πR× Interval)÷180⁰

=(π×8×10⁰)÷180⁰

=1.396cm

** STEP -5**:

**Distance along the standard parallel for spacing the meridians:**

(2π R cosø× Interval) ÷360⁰

=(2π8cos45⁰×10⁰)÷360⁰

=0.987cm

** Exercise:1. **Draw graticules on simple conical projection with one standard parallel for an area between 15

^{0}N -75

^{0}N longitudes & 125

^{0}E-145

^{0}W latitudes at an interval of 15 degrees with the R.F.-1: 85,000,000.

** Example:2. **Draw graticules on simple conical projection with one standard parallel for an area between 40

^{0}N-70

^{0}N longitudes & 10

^{0}W-20

^{0}E latitudes at an interval of 5 degrees with the R.F.-1: 56,000,000.

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