# NavList:

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

**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