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Hanno,

See attached your reduction method for Hc done on one side of an index card. It is a tight fit.

A few changes were made in the procedure. Degrees and minutes were used instead of minutes. Negative numbers were eliminated by subtracting the smaller from the larger.

I noticed a direct correlation between the standard Sin Cosine formula reduction method and your summing reduction method. See side by side example attachment.

It does appear that you have managed to convert a difficult multiplication process into a manageable summing process without the use of logs.

Bravo !

Greg Rudzinski

Re: Classic Trig Log Sight Reduction Revisited
From: Hanno Ix
Date: 2014 May 28, 21:38 -0700
Greg,

Your difficulties stunned me.

First, I don't know if you spotted the errata in the narrative. The correct original reduction formula is of course: sin(Hc)=sin(D)sin(L)+cos(D)cos(L)cos(t).
Secondly, if one works through any method the first time then it will take some patience to find one's way through it. The good news is that few mistakes are made after several dozen trials, as you observed when revisiting Chichester's predicament May, 27.
Did you perhaps also go through the example before attacking your problem? It may have helped if you did.
Also, I wonder why you ignored the worksheet that I also included in the memo. As a help, it reiterates the sign rules as we learned them when we first learned trigonometry. They are universal and not mysterious to you. However, I am sure the format of the worksheet could be improved. As it is, it is as much a description of the method as it is the execution of a particular CelNav case.
I tested the worksheet by submitting a CelNav problem to my wife. Actually, I gave her just values for D,L and t, the worksheet and the table. The problem was chosen to need calculations with some negative numbers. She had no prior knowledge of CelNav sight reduction, however she had algebra and trig in high school. She also taught these subjects herself in high school - 30 years ago. I thought if she could handle this calculation anyone currently in CelNav could. Well, it took her 20 minutes by progressing step by step through the worksheet without any help from me. She came up with the correct result at the first trial.
I do not think this method is a panacea for sight reduction by hand. However, as a novelty might see unexpected applications in the future.
I have attached my personal worksheet of your problem as per 05-27-14 – not quite an index card but manageable I think. The additions/subtractions etc. were done on a separate scratchpad. (The result was verified by a calculator. ) Note the slight difference to your result.

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