Stereographic Polar Zenithal Projection

The Stereographic Polar Zenithal Projection is a type of azimuthal projection that maps the surface of a sphere (such as the Earth) onto a flat plane. In this projection, a light source is placed at the periphery (opposite pole) from the one being mapped. For example, if mapping the North Pole, the projection is created as if the light source were at the South Pole. This unique perspective allows lines of latitude to appear as concentric circles and meridians (lines of longitude) to radiate outward as straight lines from the central point—the pole.

This projection is known for preserving angles and local shapes accurately, making it a conformal projection. However, it introduces increasing distortion in area and distance as one moves farther from the centre (pole) toward the equator.

Construction

Question: Construct a Stereographic Polar Zenithal Projection for the North Pole at a scale of 1:300,000,000 with meridian intervals of 30° and parallels at 0°, 30°, 60°and 90°.

Solution:

1. Calculate the Radius of the Globe on the Given Scale: $$\text{Radius of the Globe} = \frac{6400 \times 1,00,000}{300,000,000} = 2.1 \, \text{cm}$$Thus, the radius of the globe on the scale of 1:300,000,000 is 2.1 cm.
2. Draw the Globe Circle:
   • Draw a circle with a radius of 2.1 cm. This circle represents the Earth on the given scale.
3. Draw the Polar and Equatorial Diameters:
   • Draw two perpendicular diameters passing through the centre O of the circle:
   • NS for the polar diameter.
   • WE for the equatorial diameter (perpendicular to NS).
4. Set Up the Projection Plane:
   • Place the projection plane (XY) at the North Pole (N), perpendicular to the polar diameter (NS).
5. Draw Radii Corresponding to Parallels (0°, 30°, 60°and 90°):
   • From the centre O, draw lines making 0°, 30°, 60°and 90° angles with the equatorial diameter OE using a protractor.
   • These lines meet the circle NWSE at points E, a’, b’, and N, respectively.
6. Draw lines from the periphery
   • From point S, extend lines such that they intersect from points E, a’, b’, and N and fall on line XY at points E’, a, b, and N, respectively.
7. Draw the Parallels:
   • Use the North Pole (N) as the centre of the projection plane.
   • Draw concentric circles with radii corresponding to the intersections of the projection plane:
     • N=90°N
     • Nb = 60°N
     • Nc = 30°N
     • NE’ = 0°N
8. Draw Meridians at 30° Intervals:
   • From the centre N, draw straight lines at 30° intervals using a protractor:
   • 0° meridian, 180° meridian opposite to it.
   • 90°E and 90°W at right angles.
9. Final Diagram:
   • The resulting projection will show the North Pole at the centre.
   • Meridians at 30° intervals radiate outward.
   • Parallels at 0°, 30°and 60° are represented as concentric circles around the pole.
   • North pole (90° ) is a Dot.

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