NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Tables of Trig Functions and Logs of Trig Functions
From: George Huxtable
Date: 2007 May 2, 21:44 +0100
From: George Huxtable
Date: 2007 May 2, 21:44 +0100
Robert Eno wrote- | Essentially, for the same reason why I persist in using a sextant: the | challenge of doing it the hard way. Oddly enough, I find it rather | therapeutic to perform the odd sight reduction the old way using the trig | and log tables. It also hones my basic understanding of the mathematics | behind the calculations. It also gives me another level of independence of | electronic gadgetry should the latter fail me absolutely some day. Don't | misunderstand me: I still use a scientific calculator (and if I am | particularly impatient, my Celesticomp V) but for every round of sights that | I take, I reduce at least one or two using the tables: the hard way. Comment from George- I agree with that, in every respect but one, where Robert writes "It also hones my basic understanding of the mathematics behind the calculations." And for this reason: because the basic simple spherical trig expressions have been bent, twisted, and manipulated, quite beyond recognition, in order to avoid additions and subtractions, once the navigator has "gone into logs". This results in him going blindly through the set procedures "by rote", without much chance of understanding the steps involved, and simply accepting the result that comes out of that process. And so (in my view) doing all that trig manipulation by a pocket calculator provides a breath of fresh air. Now that logs are no longer called for, the basic trig expressions can be worked through, bit by bit, just as they come out of the textbook. It's easy to see what contributions the individual terms in the expressions are making. It's easy to try out simplifications and short-cuts, such as taking the sine of an angle near 90 to be exactly 1; that sort of thing, when you can see what you're actually doing. As I see it, having to use logs and lookup tables (and in their time, there was really no alternative) set back the understanding of what navigators were actually doing. Now we can enjoy the privilege of doing the mathematical manipulations absolutely straight, and far more accurately than we will ever need. How our navigational forbears, as recently as thirty-odd years ago, would have relished that opportunity! George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---