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On 16 Oct 2001, at 7:36, Noyce, Bill wrote:

> Better late than never, I hope.
>
> >The weather has been overcast for the past several days. Seas lumpy,
> >and wind variable. On 03/07/2001 at 01:37:00ZT and a distance of 754.0 Nmi
> >on a TC of 267.7d from our last position FIX at (03d 30.0' 097d 30.0'W)
> >30/06/2001 @ 11:53:00UT the navigator orders a turn to a TC of 307d.
> >
> > 1)  What is the DR position at the time of the turn?
> > --  ------------------------------------------------
>
> TC 267.7d = W 2.3d S   Dist 754.0 nmi
> dLat = 30' S  =>                  DR Lat =   3d 0' N
> dep = 754 nmi => dLo = 753' W =>  DR Lon = 110d 3' W

OK

>
> > At 09:27:06ZT that same morning we manage a Sun Lower Limb (Sun LL)
> sight of:
> >     Hs    42d 01.5'
> >
> > TC 307d, Speed 10.4 Kts.
> >
> > 2)  What is the DR position at the time of the Sun sight?
> >     What is the UT/GMT time of the sight?
> > --  ------------------------------------------------------
>
>
> TC 307d = W 37d N  time = 7h 50m 06s => dist = 81 nmi
> dLat = 48' N  =>               DR Lat =   3d 48' N
> dep = 65 nmi => dLo = 65' W => DR Lon = 111d  8' W
> Zone is 7 hours west of Greenwich => UT = 16:27:06

OK

> Working the sight using the DR position as the Assumed position gives:
> GHA 178d 56.1'  dec 22d 54.8' N  Ho 42d 10.6'  Hc 42d 12.2'
> Intercept: 1.6 nmi Away from 062.3d
>
>
> > At a DR position of (04d 10.1'N  111d 32.5'W) at 12:30:22ZT we manage
> > another Sun sight.
> >
> >     Hs    Sun LL: 71d 05.6'
> >
> > 3)  What is 12:30:22ZT Sun sight called?
> >  --  ------------------------------------
>
> It's obviously close enough to local noon to give a LOP oriented
> mostly east/west, so could be called a "Latitude sight".
> A bit of work with the Almanac shows the sun's GHA is within
> a fraction of a minute of our estimated longitude, so this is
> definitely a "LAN sight" or a "Noon sight".  As such, it gives
> Latitude directly with little calculation:
>
> Hs  71d  5.6'   decl 22d 54.1' N
> -IC      2.5'   -ZD  18d 44.5'
> -Dip     3.0'   --------------
> -Refr    0.3'   Lat   4d 9.6' N
> +SD     15.7'   ===============
>    ----------
> Ho  71d 15.5'
> ZD  18d 44.5'

OK.

>
> > 4)  What is the Running FIX(RFIX) position?
> > --  ---------------------------------------
>
> For the RFIX, we must advance the earlier LOP to account for the
> motion from 9:27 to 12:30.  We do this by advancing the Assumed
> Position from which the LOP is drawn.  One way is by advancing
> the position by the given course, speed, and time.  This gives
> a new Assumed Position of 4d 5' N, 11d 34' W.  Since the earlier
> sight was worked with Apos = DR pos, we can simply take the new
> DR position as the place from which to draw the LOP.  Which is
> better depends on why the new DR pos differs from the one I
> assumed for the earlier sight.
>
> Using 4d 5' N,    111d 34' W   => RFIX = 4d 9.6' N, 111d 38.5' W
> Using 4d 10.1' N, 111d 32.5' W => RFIX = 4d 9.6' N, 111d 34' W
>                                   ============================
>
> For the remainder of the problem, I'll use the second solution
> (111d 34' W).

OK

> > 5)  What is the True Course(TC) and distance to the Hawaii landfall
> >     point at (19d 30.0'N  154d 45.0'W)?
> > --  ---------------------------------------------------------------
>
> It's a long way! dLat = 15d 20.4, dLon = 43d 11'
> Even though it's not appropriate, I tried a Mid-Lat solution just to
> see what would happen, and got dist = 2710 nmi, TC = 289.7d.
>
> Using Great Circle, I get      dist = 2687.4 nmi, TC = 296.7 (initial)
>                                =============================
>
>
> The GC course is closer to the pole (expected), but I was surprised
> that the distances came out so close to equal.

OK, but Great Circle is not of much use since on a small sailboat it is just
about impossible to sail it. But you have an idea of how many days to go. Try
using Mercator/Rhumbline calculations, the distance is a bit far for accuracy
from Mid-Latitude.

> > The sky remains a heavy overcast. Winds are variable and indicate a
> slow backing. We maintain at True Course of 289.9d.
> >
> > At the Running FIX position(RFIX) 03/07/2001 @ 19:30:22UT, Current
> Drift 0.7 Kts, Set 095d. Var 9dE, Dev 1.5dE. Speed 10.0 Kts.
> >
> > 6)  What is the Compass Course(CC)/Course-to-Steer?
> > --  -----------------------------------------------
>
> Not sure whether you're asking for TC 289.9d to be translated to a CCTS,
> or for my Hawaii course (TC 296.7d) to be translated to a CCTS.
> I did the latter, and came up with
> Steer 1.4d further West, and SOG = 9.3 kts
> TCTS = 295.3 => TVMDC => CCTS = 284.8d

With Silicon Sea always assume that you are in the cockpit navigating using
traditional navigation methods and equipment.
                         =============
OK. You would think that after all this time I would have learned how to
write a question.

> > We travel for a distance of 646.6 Nmi on a TC of 289.9D.
> >
> > 7)  What is the Dead Reckoning position at this point?
> >     What is the Zone Time(ZT) and Zone Date(ZD) of the DR
> >     position?
> > --  -------------------------------------------------------
>
> Using the given distance and TC directly for DR:
> 289.9d = W 19.9d N
> dLat = 230'  =>                DR Lat =   7d 59.6' N
> dep = 606 nmi => dLo = 604' => DR Lon = 120d 38' W
>                                =====================
> I assumed the distance was distance through the water (measured
> by a log), not distance over the ground, so the time is found
> by dividing by 10.0 kts.  64.66 hrs = 2days 16h 40m
>                                    + July 3 19:30:22 UT
>                                    --------------------
> We're now 8 hours west               July 6 12:10:22 UT
> of Greenwich ==========>             July 6 04:10:22 ZT
>
                                     ==================
OK

> > 8)  What is the UT/GMT time and date at the DR position?
> > --  ----------------------------------------------------
>
> July 6 12:10:22 UT

OK


Dan Hogan
dhhogan@verionmail.com

   

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