ZENITHAL GNOMONIC EQUATORIAL PROJECTION FOR THE CONTIENT SOUTH AMERICA AND AFRICA

EXERCISE :Prepare a graticule on the Gnomonic Equatorial Projection for the continent  of South America at scale 1:150,000,000 and interval 10˚.

INTRODUCTION: In gnomonic projection source of light is always in centre of the globe. The equatorial case of the projection is used to represent a hemisphere. The polar case is used to show the northern and southern hemispheres whereas the equatorial case is used to show the eastern and western hemispheres.

CONSTRUCTION: 

Radious of the reduce earth is 250×10⁶ /150× 10⁶ = 1.66^//

In the diagram -

NESQ = the reduced globe

EQ = The Equator

NAES = The central meridian

NOS = The axis of the Earth

OE = The radious of the reduced globe.

A = Any point on the Earth’s surface at ɸ˚ latitude along the central meridian

B = Any point on the Earth’s surface at at θ latitude and θ longitude (Zero).

C = Any point on the Earth’s surface at at ɸ˚  latitude and θ longitude

TEP = Tangent plane at the equator. 

The main problem in drawing the graticules on the projection are-

a]     To find out the distance of any parallel (ɸ˚) from the equator along the central meridian = A^/ E

b]    To find out the distance of any meridian (θ˚) from the central meridian along the equator = EB^/

c]     To find out the distance of any parallel  ɸ˚ from the equator along any meridian (θ˚) =B^/C^/

To find out the distance A^/ E, considering the right triangle OEA^/

AE/OE= tan ɸ˚

AE/OE= tan ɸ˚= R tan ɸ˚

To find out the distance A^/ E, considering the right angle triangle    OEB^/

EB^/ /OE= tan θ

EB^/ = OE tan θ˚

EB^/ = OE tan θ˚= R tan θ

OB^//OE=sec θ˚

OB^/=OE sec θ˚ R sec θ˚

Now considering the right angled triangle ∆ OBC

B^/C^//OB^/= tan ɸ˚ or BC=OB tan ɸ˚=R sec θ˚ tan ɸ˚

B^/C^//OB^/= tan ɸ˚=R sec θ˚ tan ɸ˚

Spacing between meridian along equator and between parallel along central meridian is-

R	ɸ˚	tan ɸ	R tan ɸ˚
	10˚	.17	2. 92
	20˚	.36	.60
1.66	30˚	.57	.95
	40˚	.83	1.39
	50˚

Spacing Between Parallel/Meridian from Equator is-

R	R	sec θ	ɸ	tan θ	R sec θ tan θ
			10˚	.17	.28
			20˚	.36	.60
	10˚	1.01	30˚	.57	.95
			40˚	.83	1.38
			50˚	1.19	1.98
			10˚	.17	.29
			20˚	.36	.63
	20˚	1.06	30˚	.57	.99
			40˚	.83	1.45
			50˚	1.19	2.08
			10˚	.17	.32
1.66//			20˚	.36	.68
	30˚	1.15	30˚	.57	1.08
			40˚	.83	1.57
			50˚	1.19	2.26
			10˚	.17	.36
			20˚	.36	.77
	40˚	1.30	30˚	.57	1.22
			40˚	.83	1.78
			50˚	1.19	2.55
			10˚	.17	.43
			20˚	.36	.92
	50˚	1.55	30˚	.57	1.46
			40˚	.83	2.13
			50˚	1.19	3.05

 

   

PROERTIES:

1.     The equator and all the meridians are being projected as straight line.

2.     The other parallels are projected as curve.

3.     The scale of the meridian and parallels are not true.

4.     The amount of exaggeration is increasing away from the centre of the projection.

USES:  This projection can be used mainly for drawing maps of small areas along any part of the equator.