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Here is something to think about.
The accuracy will be suspect.It will give you an idea of your noon time or
at least an idea to think of the problem an other way.
2 things must be known to do this: S.R. and S.S. Lat and the Sun's dec at
these times.There are ways to calculate the expected sun's dec but I'm not
going there now.
The accuracy of this will largely depend on how well you keep your
dr(compensating for leeway,set/drift etc).
After your noon pos is plotted and you have an idea of its time get up on
deck and 30 min before and after calculated time follow the procedure to
take the noon sight.
When at sea you can estimate the time of sun rise or sunset after a few days
of observation.
Here it is:
Plot the dr pos at the estimated time of S.R.Take the Lat.
Extend the trackline for the daily run to the time of calc. S.S. and plot
the dr. Take that Lat.
Find LMT of S.R. and S.S.
LMT = ((180 + - t)/15)
+t = sunrise
-t = sunset
+d sn
-d cn
t = cos-1((sin - 0.84 - (sin L x sin d)/(cos L x cos d))
Now you know the LMT of sr and ss
Find the lenght of daylight
ex; ss at 1850,sr at 0635. add them to find daylight = 12 h 15 min
divide that by 2 to estimate LMT of noon.
calculate and plot the LMT noon pos.
Find the center long of the ZD closest to the dr long.
Convert LMT to ZT:
subtract the smaller long from the larger long to find delta long.(remember
where your dr long is in relation to the center long of ZD)
Convert delta long to delta time: delta long/15 = delta time
ZT of Noon = LMT +  - delta time
c. long ZD W of dr long: - delta time
c. long ZD E of dr long: + delta time
Plot the ZT noon pos on the trackline and find the Lat and Long.
You now have an idea of the ZT of LAN and and the dr long.You can use the
noon sight procedure or use the dr long to calculate GMT.
Try it out.Refine it if you wish.

   

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