NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: One-body fix
From: Geoffrey Kolbe
Date: 2009 Apr 27, 07:00 +0100
From: Geoffrey Kolbe
Date: 2009 Apr 27, 07:00 +0100
At [NavList 8049], Peter Hakel wrote : ========================== Thank you, Frank, for the detailed discussion of the rapid-fire fix from multiple observations of a single body during a very short time interval. Coincidentally I have just been looking into the rather academic problem of obtaining a fix from the altitude and azimuth of a body. I understand that this is not done in practice because azimuth is difficult/impossible to measure to sufficient accuracy. Nevertheless, I would like to know just how accurately one can measure azimuth in the field/ocean and what portable devices (besides compasses), are available for this (if any). I hereby display the solutions to this "one-body fix" problem, if only as a curiosity. I expect that these have been worked out before but I haven't found them anywhere so far (references would be much appreciated). The known quantities are the GP (Dec, GHA), observed altitude (Ho), and azimuth to GP (Zn). From the navigation triangle we can calculate the LHA and then the Latitude: ========================== If your position is unknown, the problem with measuring azimuth is knowing where True North is. If you can see Polaris, measuring azimuths on land is not a problem, just use a theodolite. Though for latitudes higher than about 50 degrees it would be difficult to get your eyeball behind the telescope, unless you have a 'broken' theodolite. Too, the errors in measuring azimuths go as (the error in how level your instrument is) times (the tan of the altitude), so the chosen bodies need to be low in the sky. Given a reasonable 30x telescope on an average theodolite, the surveying books say you should be able to see Polaris on a clear day. On a trip to Egypt last November, I spent a frustrating afternoon trying to see Polaris in a reasonably clear sky. No luck. I think it has to be a very clear sky to see this second magnitude star in the daytime. The other thing is that azimuths are not like position lines, which are equally useful regardless of the azimuth of the celestial body. Consider a one-body fix on Polaris, for example. The altitude of Polaris will give you your latitude (pretty much) and the azimuth of Polaris tells you.... what? Regardless of where you are in the Northern Hemisphere, the azimuth of Polaris is going to be pretty much the same and tells you not much more than you are in the Northern Hemisphere! So a one-body fix on Polaris will not be much use to fix your position. Now consider the sun rising in the East or setting in the West at the equinoxes. The local time of this event will give you your longitude - but anybody anywhere on that longitude will see the same event (sunrise in the East or sunset in the West) at the same time, so an azimuth of the sun will not tell you much. So, for useful azimuth measurements, use bodies low in the sky, avoid bodies at the Cardinal points. Geoffrey Kolbe --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---