What is "polyconic projection"

Polyconic \Pol`y*con"ic\, a. [Poly- + conic.] Pertaining to, or based upon, many cones.

Polyconic projection (Map Making), a projection of the earth's surface, or any portion thereof, by which each narrow zone is projected upon a conical surface that touches the sphere along this zone, the conical surface being then unrolled. This projection differs from conic projection in that latter assumes but one cone for the whole map. Polyconic projection is that in use in the United States coast and geodetic survey.

n. a conic projection of a map having distances between meridians equal to those distance on a globe

Polyconic can refer either to a class of map projections or to a specific projection known less ambiguously as the American Polyconic. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. This description applies to projections in equatorial aspect.

As a specific projection, the American polyconic projection is conceptualized as "rolling" a cone tangent to the Earth at all parallels of latitude, instead of a single cone as in a normal conic projection. Each parallel is a circular arc of true scale. The scale is also true on the central meridian of the projection. The projection was in common use by many map-making agencies of the United States from the time of its proposal by Ferdinand Rudolph Hassler in 1825 until the middle of the 20th century.

The projection is defined by:

x = cotφsin((λ − λ)sinφ) 

y = φ − φ + cotφ(1 − cos[(λ − λ)sinφ]) 

where λ is the longitude of the point to be projected; φ is the latitude of the point to be projected; λ is the longitude of the central meridian, and φ is the latitude chosen to be the origin at λ. To avoid division by zero, the formulas above are extended so that if φ = 0 then x = λ − λ and y = 0.