Geodetski list, Vol. 78 (101) No. 4, 2024.
Preliminary communication
New Derivation of the Formula for the Length of a Loxodrome Arc on a Rotational Ellipsoid
Miljenko Lapaine
orcid.org/0000-0002-9463-2329
; Faculty of Geodesy, University of Zagreb, Zagreb, Croatia
*
* Corresponding author.
Abstract
If we take a distance from a map without taking into account the distortion, we will not get the correct value. We will get the correct value if we take the distortion into account, that is, if we apply an expression for distance that does not contain distortion. The article presents the problem of determining the distance between two points on a rotational ellipsoid, measured along a loxodrome or a rhumb line. First, a formula for this distance was derived in the usual way. Then, this same formula was derived using the theory of map projections. This was intended to achieve two goals. The first was that when calculating the distance between two places shown on a map, the distortion that is immanent to the map due to the applied map projection should be taken into account. The second goal was to show how, using the theory of map projections, a formula for the length of a loxodrome arc on an ellipsoid can be derived that does not depend on the applied map projection.
Keywords
map projections; ellipsoid; loxodrome; rhumb line; arc length
Hrčak ID:
330546
URI
Publication date:
31.12.2024.
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