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Re: Nav exercise - ex-meridian
From: John Cole
Date: 2008 May 23, 15:12 -0700
From: John Cole
Date: 2008 May 23, 15:12 -0700
I used the ex-meridian tables in Burton's Nautical Tables (1963 Edition) 2008 May 18 ZD -10 Lat= 15d 14.0m N Long= 145d 40.0m E For the ex-meridian sight at 2h 8m 46s GMT Dec= 19d 36.4m N LHA= 23h 55.02m; 358.75d; 358d 45.0m Ho= 85d 29.0m (sextant altitude corrected=observed altitude) Hc= 85d 27.9m Az=15.00 Intercept 1.1 toward From Burton: Table I (Dec, Lat): F=25.2 Table II (LHA, F): 10.5 minutes of arc to be added to the observed altitude to determine the altitude at the time of observation Table III second correction to be subtracted from first correction (10.6m)=0.2m Total Correction= 10.3m to be added In Table I, owing to the closeness of Dec and Lat I had only 3 of the 4 entries needed for accurate interpolation so there was some guesswork involved. Corrected Ho = 85d 29.0m + 10.3m = 85d 39.3m Corrected Obs ZD= 90 - 85d 39.3m = 4d 20.7m Lat= Dec-Corrected ZD= 19d 36.4m - 4d 20.7m = 15d 15.7m N DR Lat= 15d 15.7m N No error found. John Cole On May 21, 2:54�am, Anabasiswrote: > � � � � The purpose of the ex-meridian was to get a latitude line even if the > body was obscured at the actual time of meridian passage in the days > before accurate time pieces were the norm. �With an ex-meridian, you > have to double interpolate the tables to get the �a� factor, even if > you use the formula C=a*t^2/60 to get the actual correction. �I am not > fond of this sight, and will just as soon not shoot an LAN then do an > ex-meridian of one. �In my opinion, ex-meridians are next to useless > these days at sea and are really only a good academic exercise. > Frankly, in real life, I will just run a sunline calculation which > would take me far less time, even if I did it by tabular methods. > � � � � All types of bodies can be shot at ex-meridian, and at either upper > or lower transit. �The most common is the sun near LAN, but stars, > planets, and the moon can also be observed. > � � � � My methodology of sight reduction of the ex-meridian is by the > meridian angle (t) method. �This saves me from having to calculate the > time of LAN at the actual position of the sight (if it is even known) > or the DR, which would require a sailing and another iteration of > calculating the time of LAN. > � � � � The first step is to take the sight as you would a sunline, and mark > the exact time. �Next you derive the declination and GHA of the sun at > the time of the sight. �Next find the difference between the GHA of > the sun and your longitude converted to GHA. �The number should be > fairly small as the ex-meridian tables do not allow for too much time > difference between LAN and the sight time. �The number can be either > positive or negative. �Remember meridian angle is not always LHA. > Meridian angle can be measured east or west of your longitude. �Use > the arc to time table or formula for the sun; but for other bodies, > the increments and corrections page in the Almanac should be used to > turn this angular measure into minutes of time. �This will be a big > source of error if it is done incorrectly. > � � � � The �a� factor is found in the navigational tables (Table 24 in the > 2003 Bowditch) and is entered using the declination of the body and > the latitude of the observer. � This table must be double interpolated > in order to obtain an accurate value, especially as the declination > and latitude values get �closer together. � This number is then > entered into the formula C= a*t^2/60; where C is the correction to Ho > that is added for upper transits and subtracted for lower transits, > �a� is from the table, and �t� is meridian angle in minutes of time. > As an alternative, you can enter and interpolate another table (table > 25 in 2003 Bowditch) to get the Ho or �C� correction. �Tabular values > must be interpolated. > � � � � Once Ho is corrected with the �C� correction, the problem is solved > like an ordinary meridian transit problem. > � � � � The tricky part about ex-meridians is that the table and the formula > from which it is derived fails at high altitude sights. �If there is a > blank spot where the declination and latitude meet, the formula can > give error that may be too great for general navigation which usually > occurs when the sun�s declination is the same name as, and very close > numerically, to the latitude of the observer. �This can also occur > when you are near the equator near the equinoxes. � In my example we > have less than 5 degrees of difference between the declination of the > sun and the latitude, so the �a� value will be very large and hard to > calculate accurately. > � � � � In the given example my solution is as follows: > GHA hr � � �210-53.6 > t-corr � � � �2-11.5 > GHA � � � � 213-05.1 > GHA-o � � � 214-20.0 (360 minus East Longitude is the �GHA� of the > observer) > t � � � � � � 1-15.0 = 5 minutes (convert arc to time) > �a� is interpolated from the tables, since it is borderline, it was > only interpolated for Declination which will add a bit of error$, but > since the latitude is fairly close to 15 degrees, the error should not > be unreasonable for general navigation. �I got 22.5 for �a.� �Be sure > to use the table that states Declination and Latitude are the same > name. > C= a*t^2/60 = 22.5*25/60 = 9.4� > > Hs � � � � � 85-22.0 > IC � � � � � � + 1.0 > Dip � � � � � � -9.9 > T/P � � � � � � �0.0 > HA � � � � � 85-13.1 > Body � � � � � +15.8 > Ho � � � � � 85-28.9 > C � � � � � � � +9.4 > Ho� � � � � �85-38.3 > Z-dis (90deg minus Ho�) = 4 deg 21.7� > > Dec hr � � � � � �19 deg 36.3� N > Tcorr(+0.6) � � � � � � + 0.1� > Dec � � � � � � � 19 deg 36.4� N > Z-dis � � � � � �-04 deg 21.7� �(sun dec is same name and > Lat, so > Dec-Z-dis = Lat.) > Latitude � � � � �15 deg 14.7�N > Error 0.7 nm north > > When I ran a sunline using the given DR as the assumed position I > computed an intercept of 0.8 towards an Az of 015 deg. �Very close to > the ex-meridian latitude so the �a� correction and observation must be > fairly accurate. > > Jeremy --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---