NavList:

   

Reply

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.
(Graduations are every .05° in my example.) Accuracy won't degrade near
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.

   

Reply