# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Easy Lunars**

**From:**George Huxtable

**Date:**2004 Apr 30, 13:33 +0100

Among other comments, Doug reacted to my statement- >>Of course, to work this on a calculator, all the degrees-and-minutes >>quantities have first to be converted to decimal degrees. as follows- >Some scientific calculators have the * ' " base60 function that can >accomplish all the algebraic steps in base60 thus reducing further another >step.Certain models of Casio and T.I. scientific calculators of this ability >cost around $25-30.00.Bouc-coup computing power for very little dinero.Easy >to use also. Reply from George- Yes, but be careful. Test all such routines thoroughly to make sure they do what you expect. For example, take the Casio family of programmable calculators, FX700, 730, and 795. Getting on a bit now, they are, but I have got accustomed to the way those machines work over twenty-odd years. These aren't operating in base 60, as are the ones Doug is discussing, but they offer conversion functions to translate from degrees, minutes, and seconds to decimal degrees, and vice versa. Take the function DMS$(), which converts an angle in decimal degrees, within the brackets, into a character string of whole-degrees, whole-minutes, and decimal seconds, separated by the appropriate symbols. It works fine, for both positive and negative angles. Trouble with that one is that few modern navigators wish to be troubled with arc-seconds, and prefer to express their angles as degrees and minutes (with decimal minutes). And there's no way to specify that preferred format. Of course, you can always invent a little routine to do that job just the way you want it, and ignore the DMS$() function.. A more-insidious problem occurs with the converse function DEG(d,m,s), which converts quantities d, m, and s, separated by commas, into decimal degrees. The seconds, or minutes-and-seconds, terms can be omitted with their preceding commas, and a, b, and c can be expressed as decimal numbers if preferred, so it becomes easy to convert, say 15deg 27.1' into decimal minutes. All that is fine. The problem arises when you wish to convert negative angles, as often is necessary in astronav. For example, Southern declinations are often expressed as negative. If you precede the degrees term with a negative sign, then that's fine, it becomes a negative angle when translated. The trouble is that even though the d term was negative, that doesn't ensure that m and s are also negative. So converting -1deg 15' by using DEG(-1, 15) converts to (-1degree + 15/60 degrees), or 0.75 degrees: not what was wanted, at all. To get it right, for negative angles, you must precede each term d, m and s with a - sign (such as DEG(-1, -15)) or else treat all angles as positive but then multiply the end result by (-1). I can see why they do it that way, because each term, d, m, and s is allowed to be the result of a separate mathematical expression, and so their signs may legitimately differ. This property can be handy when summing or subtracting sets of hexadecimal angles to get a result in decimal-degrees.. The above problem presents no real difficulties once you become aware of it, but discovering it for the first time can be a real pain. George. ================================================================ contact George Huxtable by email at george@huxtable.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================