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> 1)  What is the Compass Course/Course-to-Steer for Aruba Gap(13d
50.0'N
>     70d 00.0'W)?
> --
-------------------------------------------------------------------
Using Mid-Latitude (13d 40')
dLat = +20.0', dLo = +180.0', log dep = 2.24280
TC = 276d 32', dist = 175.8 nm
Current is right behind us, so doesn't affect steering (but
adds to our speed).
CC = 276.5 + 9 = 285.9d
                 ======
> At 14:30:22UT the same day. We take an Sight of the SUN LL. Hs 60d
54.0'.
> Speed 9.5 Kts, TC 276.5d.
>
> 2)  What is the DR position at the time of the 14:30:22UT sight?
> --  ------------------------------------------------------------
Running time 4:51:22.  4.85 hours at 10.2 knots = 49.5 nm.
(Oops - I added the current.  I guess this makes it an EP, not a DR.)
Using the same Mid-Latitude,
dLat = +5.6', log dep = 1.69157, dLo = +50.6'
EP =  13d 35.6' N  67d 50.6' W
      ========================
DR would be about 3.5' east of here: 67d 47.0' W
I worked the sight from  13d 35' N  67d 50' W  and got an intercept of
31.6' Toward 068.9d.  This would mean that nearly 5 hours of running at
10 knots moved us less than 20 miles in the desired direction, so I
looked for blunders.  31.6' is suspiciously close to the sun's diameter.
If we actually observed the Upper Limb, and got the same sextant
altitude, the intercept would be about 0.2' Toward, which seems much
more plausible.
> 3) What is the estimated Zone Time(ZT) of our Local Meridian Passage?
>    Only required to the nearest whole minute.
> -- -------------------------------------------------------------------
14:30 UT = 09:30 ZT using the 75d zone.  Our position is about 7 degrees
east of the zone's center, so LAN will be about a half hour early by ZT.
Estimating our position at 11:30 ZT:
dist @XXX.XXX8'
EP =  13d 37.9' N  68d 11.4' W
At this longitude we are 27 minutes 14 seconds east of the zone center,
so LAN will be at 11:58 - 0:27 = 11:31 ZT
                                 ========
> 4)  What is the Noon latitude?
> --  --------------------------
Sun declination = 22d 7.7' N  is surely north of our position.
Ho = 81d 26.4'  Zenith distance = 8d 33.6'
Latitude = decl - ZD = 13d 34.1' N
                       ===========
> 5) What is the Running FIX(RFIX) position?
> -- ---------------------------------------
Advancing the morning AP to 13d 37.3' N  68d 10.8' W  (this differs
from our EP by the 0.6' I dropped in initially working the sight) and
plotting the intercept, I find it intersects the latitude line at:
- if we really observed LL:    13d 34' N  67d 33' W
- if we actually observed UL:  13d 34' N  68d  7' W
                               ====================
> Speed 9.5Kts, Var 9dW, Dev 1.0dE. Current Set 270.0d Drift 1.0Kts.
(Where does the new current estimate come from?  Books & charts, or
is the estimate changed because our new position is a bit south of
the EP derived from the old current estimate?)
> 6) What is the Estimated Zone Time of Arrival(ETA) at Aruba Gap
>    (13d 50.0'N  70d 00.0'W):
>    ZT time and date?
>    UT time and date?
> -- ------------------------------------------------------------
This requires the distance from #7 (or was this supposed to be a
rough mental estimate?)
If we observed LL in the morning: 143.6 nm at 10.5 kts = 13h 41.4m
                  ETA = 2-Jun 01:12:24 ZT, 2-Jun 06:12:24 UT
                  ==========================================
If we observed UL in the morning: 110.9 nm at 10.5 kts = 10h 32.4m
                  ETA = 1-Jun 22:03:24 ZT, 2-Jun 03:03:24 UT
                  ==========================================
> 7)  What is the TC, Compass Course(CC)/Course-to-Steer, and distance
from
>     the RFIX to Aruba Gap?
> --
----------------------------------------------------------------------
If we observed LL in the morning:
  RFIX = 13d 34' N  67d 33' W  Use Mid-Latitude 13d 42'
  dLat = +16', dLo = +147', log dep = 2.15479
  TC = 276d 24', dist = 143.6 nm.
  ===============================
  Current adjustment: asin( sin(6.4d)*1.0/9.5 ) = 0d 41'
  CTS = TC + 8 + 0.7 = 285.1d
                       ======
If we observed UL in the morning:
  RFIX = 13d 34' N  68d 7' W  Use Mid-Latitude 13d 42'
  dLat = +16', dLo = +113', log dep = 2.04054
  TC = 278d 18', dist = 110.9 nm.
  ===============================
  Current adjustment: asin( sin(8.3d)*1.0/9.5 ) = 0d 52'
  CTS = TC + 8 + 0.9 = 287.2d
                       ======
-- Bill

   

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