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Finally! A (mostly) sensible response.

George says:

> As I have explained, a meridian-parts table will not cope with courses
> of, or near, 90 or 270 deg. But it's just in that situation that plane
> sailing becomes precise. So, taking a simple spherical-Earth model, I
> would divide the distance by cos (11 deg 33.8'), convert to degrees,
> subtract from 153d 14.7', and end up with a long of E 106 d 26.7'.
>
> But we can do a bit better, knowing that because of the Earth's
> ellipsoidal shape, the length of a degree at the Equator is not 60
> miles, but approx 60.07 miles. And at a lat of S 11 d 33.8', that
> length won't have reduced much from its equatorial value. In which
> case, a closer result will be 106 d 30.0'. Peter's result, at 106 d
> 31.2', is a reasonably good answer.

Well I'm certainly relieved that my answer is at least 'reasonably' good. It
seems that the method using Meridional Parts and Distances WILL " cope with
courses of, or near, 90 or 270 deg." How about that.
>
> "Q4) We start from a nice round set of numbers: N/S 0d  E/W 0d. We go
> east for 21638.9nm. Where do we arrive?"

> Back on the equator, having gone right round-and a bit. For a
> spherical Earth, we would end up at 38' E, but more accurately, with
> an ellipsoidal model, I would put it at 12.8'E.
> All that's been needed is a bit of simple trig and some knowledge of
> the Earth's shape as a fine-correction. No call for any tables in
> those simple cases.

Sure. But again, those tables (or rather the method as a whole) has coped
perfectly well with due east and west courses, it seems.

By way of a check, I calculated the Great Circle traverse (as of course the
equator is the only line of latitude that is also a Great Circle). The
discrepancy was E00d 00.1'. If the distance of 21638.9nm is correct (?) then
I may even be so presumptuous as to speculate that my method may be more
accurate than yours.
>
> However, if that "Meridional Parts and Distances" table handles such
> examples seamlessly, where the ordinary Meridian Parts table will not,
> I am interested in finding out more about it. So far, Peter has been
> coy about supplying any information.

Firstly; tables. Plural. Parts and Distances. I thought I made that clear.

Secondly; I don't think I have been coy at all. Quite the opposite. Not only
have I volunteered the little I know, including examples, but have gone
online in search of more info. Have you gone down that path, or initiated
your own research beyond your bookshelf, if the topic is of interest?

> I didn't ask him to scan the tables, or explain them; just to tell us
> where to find them, and how to use them. Until he does so, we are left

I don't know where you can find them, and you certainly need them to use
them. Here is the provenance of the two sets of tables I have:
1. Bennett G, 1995. "Tables for the solution of problems associated with
rhumb line courses and distances using the World Geodetic System Spheroid
1984" CN SYSTEMS.
2. Following a (much) earlier discussion of the topic here, Sam (Chinese
sounding name?) kindly sent me "Table of Latitude Parts (Meridian
Distance)". Sam was a list contributor in early days. Although they have WGS
84 on them, as does the Bennett tables, they differ somewhat, as mentioned
earlier (while I was being coy). Eg; For 10d, B: 597.11, S: 596.04.
Bennett's require interpolation between whole degrees, Sam's have factors
for minutes of arc.

> I have found no references to "meridional
> distance tables" on my bookshelf. Perhaps others can help, if Peter
> will not. But he can hardly complain about being misunderstood, if he
> doesn't give us some clue to what he is on about.

Not sure I have complained about being misunderstood. I may have expressed
mild outrage about the cart coming before the horse. But am only too willing
to groom and feed that nag. In part, because my main objective is not to
score points, but rather to find out more about these Meridional Distances:
whether the combined Parts and Distances method really does produce more
accurate rhumb line traverses than alternative methods, and if so how.

   

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