NavList:

Congratulations again to the article – and thanks for the many interesting discussions on that topic around the past few months, they’ve kept my brain busy!

And wondering: couldn’t we also remove the last multiplication? Well, it turns out that the formula can be rewritten as (use signed values):

hav(ZD) = ½ hav(L-d) - ½ hav(L+d) + ¼ hav(L+d+LHA) + ¼ hav(L+d-LHA) + ¼ hav(L-d+LHA) + ¼ hav(L-d-LHA)

This is actually very easy to compute with a table of ¼ haversines (“eighth-versine”?? I‘ll call it “qhav” for now). See attached 2-page table and form. No multiplication anymore, a few sums, one substraction, one division by 4 (can be done "visually"): the computation takes me approx. 5 mins, and slightly less if the AP is such that L-D (or L+d) and LHA are whole numbers of degrees.

Regarding precision, with the table rounded to 5 decimals the error on ZD is below 1nm (it does go up to a few nm for 2 points opposite each other near the poles).

Thanks to everyone in the group – I’m learning a lot and enjoying it.

Christophe

File:

  

File: