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On 9 Apr 2001, at 11:43, Michael Wescott wrote:
> I tried sending this once before but it seems to have gotten lost ...
>
> Well this one has me stumped. I'm either missing something, or I'm
> so rusty that I'm a danger to myself and others should I get on my
> boat anytime soon.
>
> >
> > Dead-Reckoning problem     Leg 69  040401   Test your knowledge!
> > ----------------------     ------  ------   --------------------
> >
> > The last DR position was(10d 27.9'N 52d 26.4'W) on 18/05/2000
> > @XXX.XXX Dev
> > 1.5dE. Current Set 285d Drift 0.5Kts.
>
> Figure roughly 10hrs @XXX.XXX Using traverse tables
> for 289 d we get
>
> D.Lat =  34.8
> Dep   = 101.2
> D.Lo ~= 101.2 / cos 11 = 103.1
>
>         10  27.9N       52  26.4W
>             34.8           103.1
>         =========       =========
>         11  02.7N       54  09.5W
My computed answer DR--11d 01.7'N  54d 06.3'W
You are OK a good answers when using Traverse Tables.
>
> Using A.P. of 11 00.0 N  and  54 00.0 W.
>
> > On that evening we take the following sights:
> >
> >         Body            UT                  Hs
> >
> >         Sirius          22:15:30            28d 16.3'
> >         Spica           22:17:02            42d 20.6'
> >         Avior           22:19:00            15d 55.3'
> >         Bellatrix       22:19:45            13d 26.5
> >         Dubhe           22:20:12            37d 56.1'
>
> > 1)  What is our FIX position?
> > --  -------------------------
>
> Using AP 11N 54W:
>
>              Sirius       Spica     Avior     Bellatrix   Dubhe
> UT          22:15:30    22:17:02   22:19:00    22:19:45  22:20:12
>
> Hs           28 16.3     42 20.6    15 55.3     13 26.5   37 56.1
> IC              -2.5        -2.5       -2.5        -2.5      -2.5
> Dip (9')        -2.9        -2.9       -2.9        -2.9      -2.9
> ========    ========    ========   ========    ========  ========
> Ha           28 10.9     42 15.2    15 49.9     13 21.1   37 50.7
> R               -1.8        -1.1      -3.4         -4.0      -1.2
> =======     ========    ========   ========    ========  ========
> Ho           28 09.1     42 14.1    15 46.5     13 17.1   37 50.7
>
> GHA-A(:00)  206 53.2    206 53.2   206 53.2    206 53.2  206 53.2
> GHA-A(inc)    3 53.1      4 16.2     4 45.8      4 57.1    5 03.8
> SHA         258 43.0    158 41.8   234 22.5    278 43.3  194 04.0
> Long        -54 00.0    -54 00.0   -54 00.0    -54 00.0  -54 00.0
> ==========  ========    ========   ========    ========  ========
> GHA-star    415 29.3    315 51.2   392 01.5    436 33.6  352 01.0
>
> Lat          11 00.0     11 00.0    11 00.0     11 00.0   11 00.0
> Dec         -16 43.2    -11 09.8   -59 30.9      6 20.8   61 45.3
>
> Hc           28 32.3     40 51.1    14 56.3     14 21.0   38 54.8
> Z              243.9       115.4      196.2       173.8     004.8
>
> Delta(dir)    23.2 A      83.0 T     50.2 T      64.0 A    65.3 A
>
> Plotting these gives a fix near 10 00.0 N and 53 00.0W. Reducing sights
> again with A.P. of 10 N and 53 W:
>
> GHA-star    416 29.3    316 51.2   393 01.5    437 33.6  353 01.0
> Lat          10 00.0     10 00.0    10 00.0     10 00.0   10 00.0
> Dec         -16 43.2    -11 09.8   -59 30.9      6 20.8   61 45.3
>
> Hc           28 05.1     42 10.1    15 37.1     13 18.0   37 59.6
> Z              244.8       115.1      196.7       274.2     004.2
>
> Delta          4.0 T       4.0 T      9.4 T       0.9 A    10.1 A
>
> Plotting these gives a good fix at about 9d 50.5'N  53d 00.0' W
>
> This is a bit far off course. What did I get wrong?
My computed answer-- 9d 50.0'N 53d 00.2'W
Don't see anything wrong. Your answers are within 0.5' of accuracy.
> Every thing gets further askew from here on...
>
> > 2)  What is the TC and distance to Barbados(13d 10.0'N  59d 20.0'W)? --
> > ----------------------------------------------------------------
>
> Hmmm ... isn't that a few miles east of Barbados?
Yes. I am using approach positions given in Ocean Passages for the World
and Cornell, World Cruising Routes. You don't want to run up on the
island.
>
> Barbados  13 10.0            59 20.0
> Fix      - 9 50.5          - 53 00.0
>          ========           ========
>  D.Lat =   3 19.5     D.Lo =  6 20.0
>        =    199.5'         =   380.0'
>
> dmp = mp(13d 10.0') - mp(9d 50.5')
>     = 202.3
>
> TC = 270 + arctan(202.3/380.0)
>    = 270 + 28
>    = 298d
>
> Dist = 199.5/sin 28
>      = 424.5
Very OK here.
> > We continue sailing maintaining the same speed and True Course with an
> > overcast sky. Then, with the navigator on deck waiting for an opening
> > for a Sun shot, we see a spot of land on the horizon ahead. It is
> > 20/05/2000 @XXX.XXX
>
> > 3)  What is the DR position?
> > --  ------------------------
>
> S = 10.7 C = 288.9 T,
>
>   20/05/2000 12:13:00 ZT = 20/05/2000 16:13:00 UT
>                           -18/05/2000 22:20:00 UT
>                          ========================
>                             1 day     17:53:00
> or 41.88 hrs
>
> Dist = 41.88 * 10.7 = 448.1 nmi
>
> D.Lat = 448.1 * cos 288.7 = 145.2 = 2d 25.2'
>
> DR Lat = 9d 50.5' + 2d 25.2' = 12d 15.7'
>  dmp = mp(12d 15.7') - mp(9d 50.5')
>      = 147.0
> D.Lo = 147.0 * tan(288.9)
>      = -429.4
>      = -7d 09.4
> DR Lo = -53d  00.0 - 7d 09.4'
>       = -60d 09.4
>
> DR  12d 15.7'N    60d 09.4'W
>
> Actually this is too far off to make any sense.
> We seem to be well past Barbados.
It is off. If you are calculating use a Traverse Table interpolation may
be accumlating an error. A better method would be to use one of the
Sailings methods for DR. For sight reduction at least using a Law of
Cosines formula. If you insist on working it "longhand" download
4mulas.zip from the web site.
> > 4)  What day of the week is this?
> > --  -----------------------------
>
> >From the almanac -- Saturday.
Right
> This I'm (almost) sure I have right :-)
 Your procedure seems OK. It may be the method you are using.
Dan Hogan WA6PBY
Catalina 27 "GACHA"
dhhogan@XXX.XXX
Navigation-L List Owner
http://www.wa6pby.com

   

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