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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


> 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

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'


> 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).

> 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.


> 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
                         =============


> 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
                                     ==================

> 8)  What is the UT/GMT time and date at the DR position?
> --  ----------------------------------------------------

July 6 12:10:22 UT

   

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