Constructing Some Selected Projections

Conical Projection with one Standard Parallel

• A conical projection is created by projecting the graticule of a globe onto a developable cone, touching the globe along a standard parallel.
• The standard parallel is chosen, such as 40º N, and parallels above and below it are distorted in length.
• To construct this projection for a given area, such as 10º N to 70º N latitude and 10º E to 130º E longitudes, with a scale of 1:250,000,000 and 10º intervals:
  1. Draw a circle or quadrant representing the cone’s base with the appropriate standard parallel marked.
  2. Extend tangents from points on the circle to form the cone touching the globe at the standard parallel.
  3. Use the arc distance between parallels to draw semicircles on the cone’s surface.
  4. Draw perpendiculars from the apex of the cone to the base to establish the central meridian and mark the standard parallel.
  5. Draw other parallels and meridians based on distances and intervals.
• This projection preserves certain properties:
  • All parallels are arcs of concentric circles and equally spaced.
  • Meridians are straight lines converging at the pole and intersecting parallels at right angles.
  • Scale is true along meridians but exaggerated away from the standard parallel.
  • Meridians become closer towards the pole.
• However, it has limitations such as extreme distortion in the hemisphere opposite the standard parallel.

Cylindrical Equal Area Projection

• This projection, also known as Lambert’s projection, is derived by projecting the globe’s surface with parallel rays onto a cylinder touching it at the equator.
• Parallels and meridians are projected as straight lines intersecting at right angles, with the pole represented as a parallel equal to the equator.
• To construct this projection for a world map with a scale of 1:300,000,000 and 15º intervals:
  1. Draw a circle representing the cylinder’s base.
  2. Divide the equator’s length into equal parts, then extend these divisions as parallels.
  3. Draw perpendiculars from the equator to represent meridians.
• This projection preserves:
  • Straight lines intersecting at right angles.
  • Equal length of parallels and meridians.
• However, it has limitations such as increased distortion towards the poles.

Mercator’s Projection

• Developed by Gerardus Mercator in 1569, this orthomorphic projection maintains correct shape but distorts size.
• Parallels and meridians are straight lines intersecting at right angles, with spacing increasing towards the pole.
• To construct this projection for a world map with a scale of 1:250,000,000 and 15º intervals:
  1. Draw a line representing the equator and divide it into equal parts.
  2. Calculate distances for each latitude based on intervals and draw parallels and meridians accordingly.
• Properties include straight parallels and meridians, with correct shape but increased distortion towards the poles.
• Limitations include exaggerated scale in high latitudes and infinite representation of the poles.
• Uses include world maps and navigation purposes due to its suitability for showing sea and air routes.

The Earth is a 3D sphere, but maps need to be 2D. Map projections are mathematical transformations that convert the curved Earth’s surface to a flat map, though this inevitably involves some distortion.

In this article, we will look into the topic of Map Projections in detail.