Conic Projections with Three or More Standard Parallels

Miljenko Lapaine

doi:10.5194/ica-proc-4-64-2021

Abstract

Abstract. The basic property of all map projections is the distribution of inevitable distortions. Conic projections with one or two standard parallels are mentioned in the literature. These are parallels with the property that the distortion of length, area and angles equals zero at each of their points. It turns out that there are conic projections with no standard parallels, as well as those with more than two standard parallels. Such projections exist not only in theory, but examples of such projections can also be constructed.

Highlights

The term "conic projection" refers to any projection in which meridians are mapped to spaced lines radiating out from the apex and circles of latitude are mapped to circular arcs centred on the apex (Wikipedia 2021)
When making a conic map, the map maker arbitrarily picks two standard parallels. Those standard parallels may be visualized as secant lines where the cone intersects the globe - or, if the map maker chooses the same parallel twice, as the tangent line where the cone is tangent to the globe
In the third section we deal with conic projections and give formulas by which we investigate standard parallels for such projections

Summary

Introduction

The term "conic projection" refers to any projection in which meridians are mapped to spaced lines radiating out from the apex and circles of latitude (parallels) are mapped to circular arcs centred on the apex (Wikipedia 2021). It has been explained several times that this is not the case (Lapaine 2017, Lapaine and Menezes 2020) Another claim is that in conic projections there are (at most) two standard parallels. This is not true either since conic projections can have more than two standard parallels This will be discussed in more detail in the paper. Only Kavrayskiy (Каврайский 1959) discussed the distribution of distortions in conic projections in general, i.e. not in special cases such as conformal, equivalent or equidistant projections.

Map scale

Conic projections

Conic projection equidistant along meridians

Conic projection with 3 standard parallels

Conic projection with several standard parallels