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Re: Exercise #12 Daylight Sun/Moon Fix
From: Mike Burkes
Date: 2008 Jun 13, 06:18 -0700
From: Mike Burkes
Date: 2008 Jun 13, 06:18 -0700
Hi folks, as usual great stuff! I noticed a number of members averaged the entire moon set but upon my graphing the set it becomes readily apparent sites 21-01-40 and 21-03-22 are rejected therefore the line of best fit falls nicely thru the remaining 6 sites and solving no 3, the 21-00-48 site, yields an agreeable solution a On Jun 12, 5:53�am, "Andres Ruiz"wrote: > The average in this case is incorrect, see the Hs graph: > > -----Mensaje original----- > De: NavList@fer3.com [mailto:NavList@fer3.com] En nombre de George Huxtable > Enviado el: s�bado, 07 de junio de 2008 15:57 > Para: NavList@fer3.com > Asunto: [NavList 5360] Re: Exercise #12 Daylight Sun/Moon Fix > > I suspect that there are many more unposted attempts at Jeremy's exercises, > > behind the scenes, than actually turn up on Navlist. > > Here's my go at #12. > > Date 28 May 08 > > Start with a position line for the Sun. Without a 2008 almanac, I have to > > rely on my pocket calculator. Its Sun predictions should be good, and should > > correspond to the Almanac's. Someone please tell me if they don't. > > at UT 21h 06m 15s, I get Sun dec +21� 37.5', GHA 137� 13.2', semidiam 15.8' > > corrected altitude from Sun LL is obtained from- > > �16� 43.1 � � Sun sextant altitude > > - � � � 9.9' � �dip from 106 ft. up > > - � � � 3.2 � � refraction > > + � �15.8 � � semidiameter > > + � � �0.1 � � parallax > > ====== > > 16�45.9 corrected altitude. > > Without having alt-az tables for that latitude band, I have to calculate the > > Sun altitude using a program which gives me great-circle course and distance > > in miles from A to B. From an assumed position of N 14� 37.9' and long of E > > 145� 18.6, to Sun at N 21� 37.5', W 137� 13.2', I get a course (= Sun > > azimuth) of 71.4�, and a great-circle distance of 4394.9 miles, > > corresponding to 73�15' zenith distance, or 16� 45' altitude, to compare > > with 16� 45.9' corrected altitude. At the moment of the Sun sight, then, the > > Sun was actually 0.9' higher in the sky, and therefore 0.9 miles closer to > > the Sun's GP, than �was assumed. So it's on a position line, displaced from > > that assumed position �by 0.9 miles in the direction of 71.4�, the line > > being drawn at right angles to that displacement. > > The Sun was on that line at 21h 06m 15s, but with its course due East at > > 14.3 knots, then at 21h 00m it was 1.5 miles further West, so next we shift > > that position line bodily sideways by 1.5 miles to the West. > > Now for the Moon. Averaging the 8 observations, I get the mean altitude of > > 72� 26.0', at a mean time of 21h 01m 57s. Hope others agree. > > For that moment, my pocket calculator predicts Moon dec = -3� 05.2', GHA > > 214�58.6. It's less precise, for the Moon, than it is for the Sun, so I > > wonder what others get. In this exercise, the geometry is such that only the > > dec matters, not the GHA. > > Working from the same Assumed Position as before, and using the same > > technique as for the Sun, I get the calculated Moon altitude to be 72� 16.9 > > at an aziimuth of 179.8�. So the Moon is very nearly due South, and what we > > are finding from it is simply our latitude. > > We need to compare that altitude with the sextant altitude, after all > > corrections have been made, so the next step is to make those corrections. > > 72� 26.0' � Moon sextant altitude. > > - � � � 9.9' � Dip from 106 ft. up > > - � � � 0.3' �refraction > > - � � 15.5' �semidiameter Moon (using UL) > > + � �17.6' �parallax taking HP = 57.6 �and calculating HPcos alt. > > ========== > > 72� 17.9' corrected Moon altitude. This is just 1 mile greater than the > > altitude we calculated from the AP, so therefore we are just 1 mile closer > > to the Moon's position, or 1 arc-minute further South, which puts us on an > > E-W position line at N 14� 36.9. In this case, because that position line > > runs E-W, and the ship travels due East, the position line doesn't shift: it > > was in the same place at 21 h, near as dammit. And a bit of rough sketching > > gives a final longitude just 0.1 miles East of our AP, at 145� 19.6. > > So we can congratulate the people in Fort Worth for doing a remarkably good > > job in the GPS positions they are puttting out. > > Jeremy says "the latitude is consistently off", but it's only a mile out > > from GPS, according to me, so nothing to be ashamed of there. Indeed, it's > > well within the margin of error that can be caused by natural changes in the > > refractive part of the dip. Rather more interesting, to me, is the scatter > > in those Moon altitudes. I wonder why. Was the sea state good, at that time? > > Often, with a high Moon, contrast can be low, especially if the sky is a > > touch milky. That gets worse if you use an all-over horizon mirror, rather > > than a half-and-half split job. If Jeremy had recorded a number of altitudes > > for the Sun, as he did for the Moon, I wonder whether thet, too, might have > > shown scatter. What's his experience? > > I didn't really need to do all those hand-corrections, but could have left > > the lot to my calculator software instead. However, that inflexibly chooses > > a height-of-eye appropriate to the "bridge" of my little craft, at 6ft above > > sea level, rather than to Jeremy's 106 ft. If I adapt Jeremy's altitudes by > > subtracting 7.6' from them first, then it gives the same answer. > > George. > > contact George Huxtable at geo...@huxtable.u-net.com > > or at +44 1865 820222 (from UK, 01865 820222) > > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. > > ================================ > > Exercise #12 �Daylight Sun/Moon fix. > > This exercise is for our math friends. �It is a series of Moon lines > > taken near meridian transit, crossed with an early AM sunline. > > Plotting these lines, you will notice an averaged Moon line giving a > > decent position with lines within 5 degrees of the horizontal. � The > > sun line will be nearly vertical and gives a good Longitude line as a > > cross. > > In this case, my calculations show that Latitude is consistently off, > > but the Longitude is within a couple of tenths. �I am guessing that my > > I wasn't seeing the actual limb of the moon and therefore was off with > > the sextant observations by better than a minute of arc. �The moon is > > a strange mistress to try and shoot with the sextant. > > ---------------------------------- > > UTC date is 28 May 2008. �The 21h 00m UTC �GPS fix was Latitude 14deg > > 37.9' North, Longitude 145deg 18.6' East. �The Ship is sailing course > > 090 at 14.3 knots. �Height of eye is 106 feet, Temp/Pressure is 84 F > > and 1010 MB. �Index error is 0.0. �The following observations were > > made (times in UTC): > > Sun (LL): Hs 16deg 43.1' @ 21h 06m 15s > > Moon (UL) Hs 72deg 25.6' @ 20h 57m 43s > > Moon (UL) Hs 72deg 25.8' @ 20h 59m 14s > > Moon (UL) Hs 72deg 25.8' @ 21h 00m 48s > > Moon (UL) Hs 72deg 27.2' @ 21h 01m 40s > > Moon (UL) Hs 72deg 25.8' @ 21h 02m 20s > > Moon (UL) Hs 72deg 26.4' @ 21h 03m 22s > > Moon (UL) Hs 72deg 26.0' @ 21h 03m 57s > > Moon (UL) Hs 72deg 25.2' @ 21h 05m 08s > > Determine a fix at 21h 00 UTC (07h 00m Local) > > Jeremy > > �image001.gif > 7KViewDownload --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---