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Greg - 

Hey, great going. Never in my life did I think of trying a moon time sight. Exotic, man.

This afternoon I looked in Vol. i of my green Bowditch and it gives Martelli' formula as:

havt = cos(L~d) – cosz / 2cosL cosd

Since havt = (1– cost ) and  z =  (90* – h)  I rewrote the formula to:

cost = 1 – (cos(L~d) – sinh / 2cosL cosd)

With the formula now in sines and cosines, I plugged Martelli's example into a 
basic scientific calculator, but got an answer that was way off.

So, I went through and wrote down the results from each operation. At which 
point I noticed the final number was half the cosine of the angle I was 
looking for. So, I took the 2 out of the divisor and did it again. The result 
agreed with Martelli to 0.1'.

So, I think the formula is  cost = 1 – (cos(L~d) – sinh / cosL cosd)

Greg, when you can spare the time, could you check me out on this? It's been a 
long time since I messed around with equations.

Thanks, 

Hewitt
         

Sent from my iPad

On Dec 23, 2012, at 5:59 PM, "Greg Rudzinski"  wrote:

> Hewitt,
> 
> Using Frank's Martelli PDF I was able to do a Moon time sight this evening 
to near perfection.  The tables are easy to use but I do not like working in 
hours, minutes, and seconds when LHA could be given directly saving several 
steps.
> 
> Here is how the formula may compare to the tables:
> 
> ArcCos[ (SinHo ~ SinLSind)     /      (CosLCosd)
> Tab#V    Tab#III   Tab#II    Tab#IV  Tab#I
> 
> 
> Greg Rudzinski
> 
> 
> [NavList] Martelli's Time-Sight Tables
> From: Hewitt Schlereth
> Date: 22 Dec 2012 19:12
> I ordered this book from Amazon and it came yesterday. Full title is "Short, 
> easy, and improved method of finding the apparent time at the ship."
> 
> It's a trade paperback, and I have to say Hewlet-Packard made a nice job of 
> it. The signatures are stitched, so they shouldn't come loose. The only 
> shortcoming with my copy is the print on page 42 and pages 44 thru 47 of 
> Table V is light (but still quite legible).
> 
> The tables are I thru VI and the method takes them in that order. What you end 
> up with is LHA expressed in time units, so you have to convert to the angular 
> units we are used to- 1 hour = 15*, 4 mins = 1* ...
> 
> After working through his English example (the same data is used for 
> directions in French, German, Italian and Spanish), I ran the example through 
> my HP 35s using the sine/cosine formula and it gave an answer 1.0' less than 
> Martelli.
> 
> Then I tried M's table with Greg's 12-17 time sight and again the difference was 1.0'. 
> 
> My 1972 Bowditch noted that Martelli's method was still popular. Having been 
> an active navigator then having tried it now, I can see why. There are 6 
> tables, but they are short and logical. In neither of the cases I tried did I 
> have to do an interpolation.
> 
> My one cavil is to wish M had set out the formulas he used. I have the same 
> gripe about the Concise SR table in the NA. 
> 
> Net of everything, though, Martelli's book is an agreeable stocking stuffer for myself.
> 
> Hewitt
> 
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