Re: Loxodromic Distance Formula?

Nomen Nescio wrote:
> Using R = 6371, these are the |results| I get for table 1 (including
> theta (in radians), in parenthesis).
>
> 5567.817 5809.135 (1.3626575822)
> 4031.637 4031.637 ( .0029212129)
> 10996.670 16215.879 (1.5650755933)
> 16254.490 24544.476 (1.2175972203)
>
> Since D_gc distances are way off, I have no idea if the D_rh
> distances are right or not!

I presume this is the data from the table in question, presented in
similar manner (without theta, which was not explicitly shown in the
original table):

5564 5802
4024 4030
11019 14380
16230 16408

The D_gc distances appear to be the same to within 0.2%, which hardly
seems "way off". Two of your loxodromic distances do appear to differ
significantly. Looking at the largest discrepancy, for Canberra:

New York: +0.71122 radians north, -1.29096 radians east
Canberra: -0.61988 radians north, +2.60345 radians east

Using equation (6) from the article, the values of Sigma are
New York: Sigma = +0.78009
Canberra: Sigma = -0.66388

>From equation (5), D_rh = 16393 if I choose the shortest loxodrome,
which heads west, or D_rh = 24393 if I choose the shortest eastward
loxodrome. My first figure agrees very closely with the article, my
second agrees quite closely with yours.

Hence I suspect that you calculated for the eastward path, rather than
the shorter westward one.


- Tim
.

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