Original scientific paper
https://doi.org/10.32909/kg.23.42.2
Loxodrome in Conic and Azimuthal Projections
Miljenko Lapaine
orcid.org/0000-0002-9463-2329
; University of Zagreb, Faculty of Geodesy, Kačićeva 26, 10000 Zagreb, Croatia
*
* Corresponding author.
Abstract
In the introductory part of the article, we recall the important role of the loxodrome in navigation and derive a formula for the length of the arc of this curve on the sphere between two points. The loxodrome is usually associated with the Mercator projection, because in this projection its image is a straight line. In this paper, we deal with the loxodrome in conic and azimuthal projections. The image of the loxodrome in such projections is not a straight line but a spiral curve. The determination of the distance measured along the loxodrome between two points in a normal aspect conic or azimuthal projection is presented. Formulas for the length of the arc of the loxodrome in each of these projections are derived using examples of conformal, equivalent and equidistant conic projections. Azimuthal projections are special cases of conic ones, so they do not require special derivations of formulas.
Keywords
conic projections; azimuthal projections; sphere; loxodrome; arc length
Hrčak ID:
329372
URI
Publication date:
31.12.2024.
Visits: 563 *