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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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Re: 360 degree slide rule trig
From: Paul Hirose
Date: 2017 Feb 10, 12:30 -0800

```On 2017-02-09 4:18, I wrote:
> The opposite problem is the determination of course and distance when
> easting and northing are known. For this conversion from rectangular to
> polar coordinates:
> 1. set C index to longitude difference on D
> 2. set cursor to cos latitude (red numbers) on S
> 3. set C index to northing on D
> 4. read course on black T
> 5. set course on black S to cursor
> 6. read distance at C index on D

In steps 4 and 5, don't round off course to the nearest degree. That can
cause large distance errors near a cardinal direction. For example, from
latitude 34° the destination is 66 minutes north and 9 minutes east.
Multiply the latter by cos 34 (red 34 on S) to get 7.47 miles easting.
Set left C index to 66 minutes on D. Read true course 6.45° on T at the
cursor. Set 6.45 on S to hairline. Read 66.5 miles at C index.

A calculator confirms the solution is accurate. But if you round course
to 6°, distance increases from 66.5 to 71 miles. The closer to a
cardinal direction, the more an error in course is magnified.
Fortunately, trig scale accuracy increases in the same proportion.
the cardinal directions if you set and read all values with ordinary
care and don't round them.

That precaution is not unique to a slide rule solution. The plane
sailing distance formula

distance = DLat / cos TC

becomes progressively less accurate near 90 or 270 if true course is
rounded to the nearest degree.

```
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