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Re: Traditional navigation by slide rule
From: Gary LaPook
Date: 2016 Oct 28, 01:03 -0700

Looking at some more usefullness for you slide rule, if you could squeeze in one more scale on the slider then you could use the rule for doing rhumb line calculations too. You need a Ln scale, natural logarithm scale, Log base e, since that is required for finding the rhumb line course. see

https://navlist.net/m2.aspx/Computing-great-circle-rhumb-lline-courses-LaPook-feb-2010-g11800

The formula looks complicated but it is really easy to do on a slide rule with an Ln scale.

pi x diference of longitude = ----------------------

destination latitude /2 + 45 = ------------------------------

tan of above = -------------------------------

Ln of above = ------------------------------------

initial latitude /2 + 45 = ------------------------------

tan of above = -------------------------------

----

Ln of above = subtract ------------------------------------

------------------------------------* 180 = --------------------------------------dvide line above by this value

arctan------------------------------- = RL course angle -----------------

plus or minus 0 or 180 or 360= Rl course----------------

With an Ln scale mounted on the slide you read out LnTAN in one step

================================================================================================================

So the form simplifies to:

pi x difference of longitude = ----------------------

destination latitude /2 + 45 = ------------------------------

Ln TAN of above = ------------------------------------

initial latitude /2 + 45 = ------------------------------

----

Ln TAN of above = subtract ------------------------------------

------------------------------------* 180 = --------------------------------------divide line above by this value

arctan------------------------------- = RL course angle -----------------

plus or minus 0 or 180 or 360= Rl course----------------

===============================================

RL dist = 60 (lat2 - lat 1) / COS RL course angle

lat2 -----------------------------------

- lat 1 ---------------------------------

----------------------------------- * 60 = -----------------------------

divide by COS course angle = ------------------------------RL distance.

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