A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: David Fleming
Date: 2015 May 15, 17:27 -0700
Solution by slide rule requires the equations used, to depend primarily on multiplication ( or division ) for their solution.
eg. Bygrave uses 1) tan(x)=tan(D)/cos(t) ; 2) y=90-x ; 3) tan(Z)=tan(t)cos(x)/cos(y) & 4) tan(Hc) = cos(Z)tan(y)
Only second step is non multiplication and can be done in your head.
For a time sight should use hav(t) = sec(L) csc(p) cos(S) sin(s-h) which Bowditch 1984 pg 586 says is the most common formula for time sight.
p=90-D or 90+D LD same/contrary respectively. S=1/2(h+L+p)
You would need a slide rule with log sin, log cos, and log haversine scales to implement. Either the sin or cosine scale could be eliminated by using identity cos(x)=sin(90-x) and some additional rules to take care of negative values for those functions. Two scales could then be accomodated with a double sided circular slide rule that has a cursor locked together on both sides.