Multiple conical projection

Polychronic Projection of the World

Polychronic Projection of the World

The multiple conic projection or polyconic projection is a cartographic projection that consists of using several overlapping cones as projection bases. The result is a map divided into stripes. The only meridian that will have the same scale is the central one, which appears as a straight line. The other meridians are curved, and the scale increases with distance. Also the line of Ecuador is a straight line, perpendicular to the central meridian. The other parallels are concentric arcs.

This projection is neither conformal nor does it preserve areas, but in the central area the scale variations are minimal.

The projection was in common use by many mapping agencies in the United States from the time of its proposal by Ferdinand Rudolph Hassler in 1825 until the middle of the century XX.

The projection is defined by:

${displaystyle x=cot(varphi)sin(lambda -lambda _{0})sin(varphi),}$

${displaystyle y=varphi -varphi _{0}+cot(varphi)(1-cos(lambda -lambda _{0})sin(varphi))}),}$

where:

• ${displaystyle lambda }$ is the length of the point to be projected;
• ${displaystyle varphi }$ is the latitude of the point;
• ${displaystyle lambda _{0}}$ is the length of the central meridian, and
• ${displaystyle varphi _{0}}$ is the latitude chosen to be the origin ${displaystyle lambda _{0}}$.

To avoid division by zero, the previous formulas spread so that if ${displaystyle varphi =0}$ then. ${displaystyle x=lambda }$ and ${displaystyle and=0}$.