NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Clarification of Question regarding LAN
From: Chuck Taylor
Date: 2004 Aug 4, 21:04 -0700
From: Chuck Taylor
Date: 2004 Aug 4, 21:04 -0700
Robert Gainer asked about how a time sight works, and how compass corrections fit in. Robert, The basic formula for a time sight, given in Bowditch (1984 and other editions), is cos(t) = ( sin(h) - sin(L)*sin(d)) / cos(L)*cos(d) where you are finding t = meridian angle as a function of h = observed altitude (corrected) L = latitude, assumed or obtained by other means d = declination A time sight can be taken at any time you can see the sun. The above formula is a derivative of the Law of Cosines for a spherical triangle. You solve for meridian angle (and hence longitude) by assuming that the latitude is known. Notice that if your assumed latitude is off a bit, then your solution for the meridian angle (and hence for longitude) will also be off by some amount. It so happens that this error is minimized if you take the sight at the time at which the sun crosses the prime vertical circle (PVC). That is one reason why time sights were traditionally taken at the time of PVC crossing. The time of PVC crossing is usually computed, either by tables (such as Table 25 of Bowditch 1981 Vol 2), or by formula. You don't need a magnetic compass for that. For an intuitive picture of PVC crossing, picture yourself in the northern hemisphere (say at 48 deg north latitude) between the spring and fall equinoxes. Note that the sun rises somewhat to the north of east, and sets somewhat to the north of west. Yet, when it crosses your meridian at noon, it is to the south. If it starts the day to the north of the east-west line, yet is to the south of the east-west line at noon, it follows that it must cross that east-west line on its way south sometime between sunrise and LAN. At that time it will bear due east. That is the morning PVC crossing. Similarly, sometime between noon and sunset, it must again cross the east-west line going north. That is the afternoon PVC crossing, at which time the sun will bear due west. Others have pointed out that you don't always have the benefit of a PVC crossing. For example, at latitude 48 north (where I live), there are no visible PVC crossing between mid-September and mid-March (the equinoxes). As I mentioned earlier, a time sight of the sun can be taken at any time that the sun is visible. To understand the other major reason why time sights were traditionally taken at the time of PVC crossing, try to put yourself in the mindset of an 18th century navigator, before the time of Sumner and St. Hilaire. The concept of a line of position had not yet been introduced. Finding your position meant finding your latitude and then finding your longitude as a separate and distinct process. First, you found your latitude by observing Polaris or by observing the sun at LAN. Note that finding your latitude is equivalent to measuring the distance between you and the equator (or pole) in a north-south direction. Naturally, your observation is of a body that is due north or due south of you. Similarly, finding your longitude was thought of as equivalent to finding the distance between you and the prime meridian (Greenwich for the English-speaking world). What better way to measure an east-west direction than by observing the sun when it bore due east or due west? Given the historical context, this made perfect sense to navigators of the time. After the introduction of the line of position methods developed by Sumner and St. Hilaire in the 19th century (although adoption and acceptance of these methods lagged well into the 20th century), navigators recognized that it was no longer necessary to take separate sights for latitude and for longitude, and that it wasn't necessary to shoot a sight at the time of PVC crossing (or at LAN for that matter). Two LOPs obtained at any time are at least as useful as separate latitude and longitude sights. That is a natural concept for us today, but it would have been incomprehensible to most (if not to all) 18th century navigators. I hope this helps. Best regards, Chuck Taylor North of Seattle --- Robert Gainerwrote: > Chuck said, > >The more traditional way of determining longitude > was > >to use a time sight at the time the sun crosses the > >Prime Vertical (i.e., the time at which the sun is > due > >east or due west of you). ... > > Chuck, > I don?t understand how that will work. The magnetic > variation and the > latitude must be problems in that method. If you are > at 23 degrees north > latitude or greater the sun is never due east or > west. If you do not know > the magnetite variation with some degree of accuracy > wont that have a very > large effect on the method? Is this practical at > all? > All the best, > Robert Gainer > __________________________________ Do you Yahoo!? New and Improved Yahoo! Mail - 100MB free storage! http://promotions.yahoo.com/new_mail