NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Destination from course and distance
From: FS
Date: 2005 Mar 10, 20:51 -0800
From: FS
Date: 2005 Mar 10, 20:51 -0800
--- George Huxtablewrote: > Jeff Schroeder asked, on 17 Feb.- > > >Can someone point me to spherical trig (great circle sailing) > formulas > >for determining destination Lat & Lon, if given departure Lat & Lon, > >true course, and distance travelled? > > > >I have made stabs at trying to flip around the cel nav Hc and Zn > >formulas into what I'm looking for, but must admit the weakness of > my > >math skills. I can't figure out how to get Lat & Lon out of it > without > >already knowing one or the other. > > ================= > > Jeff's question is beguilingly simple, but invites some further > questions. > > He specifies great circle sailing, but then specifies "true course". > And, > of course, in great circle sailing, there's no "true course"; the > course > has to be adjusted all the time to keep to the great circle. What can > be > specified is the "initial course" that you start off with. The > question > Jeff hasn't asked yet (but will need to ask next), if he actually > plans to > steer such a great-circle path, is what adjustments need to be made > to his > course as the voyage proceeds. > > It would be helpful if Jeff were to explain more clearly what he has > in mind. > George- How pleased I am that my beguilingly simple question happened to be the one with which you selected to reawaken the list! Surely it is beguilingly simple to you and many others, but to me it is simply beguiling! As I humbly admitted, I really don't understand trigonometry. I understand the theory behind the navigational triangle, the included sides and angles, and can work the standard altitude and azimuth formulae by rote with considerable acumen, but can neither explain their workings nor disassemble and reassemble them to serve another purpose. I hope this flaw in my character is not too unforgivable for this list - I promise I will try to learn plane and then spherical trigonometry, someday. My goal was simply to determine a new DR Lat & Lon, given a starting position, course, and distance traveled, by calculation rather than plotting, in order to avoid the errors inherent in plotting, e.g. pencil width, inexact measurement, inexact angle transfer, and my bad eyes. I could then plot to the "accurately" calculated point, to avoid introducing my own plotting errors into example problems. I suppose I misstated that I wanted a great-circle course. With the typical length of a DR leg, and my goal, I don't think the difference will be significant. I did assume that calculations based on the great-circle methods would be more accurate than plane calculations, and that's why I worded my question that way. (I'm working on the scale of a standard Universal Plotting Sheet) I actually succeeded in using Paul Hirose's suggestion to "rotate" the triangle, substitute values, and use complements of values (90 - A). But I failed miserably in trying to simplify the formulae by substituting the complementary trig functions. If I knew what I was doing (or received several more hints) I'd bet there was a much simpler formula hiding in there somewhere. Thanks, -Jeff __________________________________ Do you Yahoo!? Yahoo! Small Business - Try our new resources site! http://smallbusiness.yahoo.com/resources/