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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Universal Plotting Sheet at High Latitudes
From: Bob Goethe
Date: 2018 Apr 5, 04:36 -0700

VP-OS Universal Plotting Sheet at High Latitudes

Unless you are at the equator, lines of longitude are always slightly converging.  But we can use a universal plotting sheet because over the space of 2° of latitude, the degree of convergence is not navigationally significant.

However, I presume that if you go far enough north, the convergence WILL become navigationally significant.

Through what latitude range is a VP-OS plotting sheet useable?

I am specifically thinking of a hypothetical voyage through Davis Strait, N 68.75°, W 62.10°, and wondering if a universal plotting sheet can be used for plotting accurate-enough DR positions.

Using Traverse Table to Directly Calculate a DR

In looking at the traverse table in Bowditch, it captures a solution to plane right triangles.  Coming up with the difference in latitude seems straightforward.  Assuming I am on a course of 45°, then:

ΔLat = DistanceSailed x cos(45°)

If I want to use that to get a difference in longitude rather than simply a nautical-miles-travelled-from-east-to-west, it appears to me that I could do this with an equation.  This is unfamiliar territory for me and I would appreciate you checking me on my concept.

Assuming that I am sailing on a course of 45°, and if the departure in nautical miles = DistanceSailed times sine of my course c, then here is my equation:

departure = DistanceSailed x sin(45°)

If the width of a degree of longitude in nautical miles = cos(latitude) x 60, then if I am at a latitude of 68° north, it would seem that:

ΔLong = [DistanceSailed x sin(45°)] / cos(68°)

Have I got this right?

Thank you very much.

Bob

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