Simple conical projection

Simple conical projection with one standard parallel. A cone is wrapped around the globe so that it touches along one parallel, the standard parallel. Parallels farther from it are distorted.

The book's construction (10° N to 70° N, 10° E to 130° E, scale 1 : 250,000,000, interval 10°):

• Radius of the reduced earth = 640,000,000 ÷ 250,000,000 = 2.56 cm.
• Standard parallel: 40° N (the middle of 10°-70°); central meridian: 70° E (the middle of 10°-130°).
• Draw a quadrant of radius 2.56 cm; draw tangents from the 40° points to meet the axis extended, forming the sides of the cone. The tangent length gives the radius of the standard parallel; the arc for 10° gives the spacing of the parallels; a perpendicular from the cone's side gives the spacing of the meridians along the standard parallel.
• Draw the central meridian, the standard parallel as an arc, the other parallels at equal spacing, and the meridians as straight lines to the pole.

Properties:

• Parallels are arcs of concentric circles, equally spaced.
• Meridians are straight lines meeting at the pole and crossing the parallels at right angles; they get closer towards the pole.
• Scale is true along all meridians and along the standard parallel, but exaggerated away from it.
• The pole is shown as an arc.
• It is neither equal-area nor orthomorphic.

Limits: not suitable for a world map (extreme distortion in the opposite hemisphere), nor for large areas even within one hemisphere.

Uses: mid-latitude areas with small north-south and large east-west extent; long, narrow east-west strips such as railways, roads, narrow river valleys and boundaries: the Canadian Pacific and Trans-Siberian railways, the USA-Canada border, and the Narmada Valley.

Example (new): for a map of an area from 20° N to 60° N, the standard parallel would be 40° N; at 1 : 160,000,000 the reduced earth's radius would be 640,000,000 ÷ 160,000,000 = 4 cm.