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Francis Upchurch wrote (in http://fer3.com/arc/m2.aspx/Graphically-solving-haversine-calculation-Upchurch-nov-2015-g33535 ):

yes I now understand the Cosine method from Erik de Man's site. i shall try A3 graph paper + accurate drawing board and vernias to try to increase accuracy. Early experimetns with an enlarged Brown-Nassau graphical slide rule + magnifier+ vernia suggests a possible accuracy to 1-2' ( under the best indoors conditions, not thrown around in a seaway!). Yes, John karl's book says it all really in terms of theory.

On equestion you may help with, but only if you find it interesting, i have done lunar clearance with th BN using John Karls page 89.

essentially we use dec =hsd, lat=Hsd,Hc = LDsd and we want to find diff in AZ (RBA) so that is same as unknown LHA.

Are you able to figure out how to use the Erik de Man cosine method to do that? I think it should be possible  if it works wth the BN, I think the formula would be cos RBA=(cosHC-sinlatxsin dec)/coslatxcosdec

Francis,

I don't think Erik de Man's graphical method is the way to go here, because of the division.

You could use either the form designed by Hanno Ix or the diagram I proposed here though (for my diagram look at the second part in the explanation I posted yesterday). RBA is indeed the equivalent of the LHA you are looking for in the first step of clearing LD. Not the difference in RBA though. When the altitude is corrected for parallax and refraction, the bearing doesn't change, so the relative bearing angle (RBA) won't change either.

The second part of clearing LD is mathematically the same as determining ZD in the longhand haversine method. So you can use the haversine table designed for that, or when precision isn't of much interest use the haversine diagram.

Regards,

Jaap