# NavList:

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

**Re: Emergency Navigation**

**From:**Alexandre Eremenko

**Date:**2012 Jul 14, 04:09 -0400

> > > Brad and Lu, > > I also think that these simple methods are not as simple if you try to > implement them in real life. > > a) Taking the altitude of Polaris. > For this you need to divide a circle, say to 1 degree accuracy. > Can you do this without instruments? I cannot. I need at least a divider, > and even then this is a highly non-trivial task. > Alternatively, you can make an instrument of straight sticks (kind of > cross staff). Then the same problem arises: to measure the length > of these sticks. Dividing a ruler is no simpler task than dividing > a circle. > All this is BEFORE you "use trigonometry". But how exactly you use > trigonometry without a calculator/tables? You compute a table of sines > and or tangents? With Ptolemy method, or using a Taylor series? > > It is true, you will need the tangent of only one angle when measuring > Polaris altitude with a cross staff, but the problem of making a ruler > remains. > > I already mentioned on this list a Russian captain Golovnin who spent 10 > years in captivity in Japan in the early XIX century. He taught the > Japanese > some modern navigation, and > his mate computed tables of trig functions for the Japanese. > I wonder how many modern captains or mates are capable of doing this:-) > > b) Using Sun. Certainly the method is not practical on a ship. > To find the noon altitude of the Sun with a gnomon (vertical tick), > you need a flat horizontal ground, a plumb line to install your stick, > then you probably have to observe for several days to find the noon > altitude on a certain day. > Declination does not seem to be such a big problem in principle: > you can compute it approximately from the dates of the solstices > and the angle between the equator end ecliptic. > (Assuming that Sun rotates on a circle not an ellipse, as the ancients > did). If you can make trigonometric tables, then you probably can > do this as well. > > With any of these methods, determination of latitude, say to 1-2 degrees > will take many days and only possible from land. > > By the way, all this is described with some details in Jules Verne novel > Mysterious Island. According to Jules Verne, Cyrus Smith used his height > (which he knew precisely) as a unit of length. But the details how he > divided this unit into smaller units are omitted:-) > Jules Verne apparently did not understand that to measure an angle > you can use arbitrary unit of length, and its relation to feet or > inches is irrelevant. The main difficulty is in dividing this unit > with sufficient accuracy. > > Alex. > > >> Brad: >> >> I must respectfully disagree.Â Â If I plant a stick in the ground >> and are >> willing to measure its shadow for a full year (or at least from one >> solstice to the other), I can indeed deduce my latitude.Â Â If I >> want to >> do it in less time (say in just a day or in a week) I must have a >> declination tableÂ and an idea of what date it is.Â Â While the >> latter >> was not necessarily forbidden by the statement of the problem, the >> former >> certainly is. >> >> I had originally wondered if I could have applied the Rule of Twelfths >> to >> approximating the sun's declination for any particular date, but it >> turns >> out that the curve of the sun's declination is NOT a sine wave (nice >> explanation in Wikipedi > > > > > > View and reply to this message: http://fer3.com/arc/m2.aspx?i=119938 > > >