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    Re: New compact backup CELNAV system
    From: Gary LaPook
    Date: 2009 Feb 27, 22:29 -0800

    I've spent several nights at anchor in Cruz Bay and spent time on the
    beach at Trunk Bay. We used to bare boat out of Roadtown or St. Thomas
    pretty much every winter when I lived in Chicago but I haven't been
    there since 1988. I liked sailing to Christiansted and North Sound on
    Virgin Gorda. But since I have lived in California I have only bare-
    boated in Raiatea and in Majorca. I've been to St. Martin three times
    in the last few years but only laid on the beach at orient Bay. I will
    be arriving in Barbados in November aboard the Royal Clipper after
    sailing from Lisbon. (I'll have to bring my SNO-T with me in case the
    captain needs my help and,of course, my Bygrave.)
    
    gl
    
    On Feb 27, 2:55�pm, Hewitt Schlereth  wrote:
    > I thought that might be the case. Way out here in St. John USVI,
    > stores are few and far between. I'll probably be able to find them in
    > St. Thomas. If not, the Internet.
    >
    > Thanx, Gary.
    >
    > Hewitt
    >
    > On 2/27/09, Gary LaPook  wrote:
    >
    >
    >
    > > "Question: Are "plastic transparency sheets" the punched clear
    > > plastic
    > > inserts you see enclosing often-used pages in a three-ring binder or
    > > are they something specially made for ink-jet printing?"
    >
    > > They are something different, the ink won't stick to the sheets you are
    > > talking about. The kind I use are 3M "Transparency Film for Ink Jet
    > > Printers, code number "CG3480" available at Fryes, Office Depot, etc.
    >
    > > Don't try using them with a laser printer they melt and gunk up the printer,
    > > don't ask.
    >
    > > gl
    >
    > > --- On Fri, 2/27/09, Hewitt Schlereth  wrote:
    > > From: Hewitt Schlereth 
    > > Subject: [NavList 7456] Re: New compact backup CELNAV system
    > > To: NavList@fer3.com
    > > Date: Friday, February 27, 2009, 9:13 AM
    >
    > > Gary, this is really neat.
    >
    > > I've printed the scales on 8X11.5 paper and it looks like my printer
    > > has the proportions correct.
    >
    > > Question: Are "plastic transparency sheets" the punched clear
    > > plastic
    > > inserts you see enclosing often-used pages in a three-ring binder or
    > > are they something specially made for ink-jet printing?
    >
    > > I ask because I have nothing transparent here to hand and I really
    > > want to try this.
    >
    > > Thanx, Hewitt
    >
    > > On 2/24/09, glap...---.net  wrote:
    >
    > > > On Feb 24, 12:06 pm,  wrote:
    > > > > There are often posts on the Navlist regarding using celestial as a
    > > backup to GPS and finding a simple way to do this. I think I have found a
    > > method
    > > that is simple, self contained, takes up little space, needs no almanac or
    > > �sight
    > > reduction tables and requires no batteries. This method is meant for those
    > > who
    > > already know celestial navigation and provides a very compact and
    > > self-contained
    > > system needing no books, almanacs or tables.
    >
    > > > > The first part of the kit is simply the long term almanac from H.O.
    > > 249 along with the Polaris tables and the Precession & Nutation table to
    > > allow the use of the tabulated coordinates for the stars for a long period
    > > of
    > > time. Since this almanac only covers the sun and the stars no provision is
    > > made
    > > for handling planets or the moon but that is not that important for a
    > > "backup" celestial method.. However, if you have the Nautical Almanac
    > > then you can work with these bodies as well. I have included a form to use
    > > with
    > > the long term almanac which also includes tables for correction of
    > > observations. The long term almanac consists of nine pages from H.O. 249
    > > plus a
    > > computation form
    > > �which can be printed back to back on only five sheets of paper.
    >
    > > > > The main part of this method relies on my adaptation of the long
    > > extinct Bygrave slide Rule which is elegant in its simplicity but which
    > > produces
    > > altitudes and azimuths within in one or two minutes of arc and takes less
    > > than
    > > two minutes to do the computation. I have included three PDF files that can
    > > be
    > > printed out to create a working copy of my adaptation which consists of
    > > three
    > > sheets containing the modified scales which can be hole punched and kept in
    > > a
    > > thin three ring binder (or in an envelope) with the long term almanac and
    > > extra
    > > forms for recording the computation. The Cotangent scale should be printed
    > > out
    > > on paper and can be sealed in a plastic sheet for good durability. The
    > > Cosine
    > > scale and the Vernier are printed out on plastic transparency sheets in an
    > > inkjet printer and can also be sealed in additional plastic sheets
    > > �for
    > > durability. The entire backup method is contained on a total of only eight
    > > sheets, five for the almanac and three for the Bygrave slide rule!
    >
    > > > > When using the Bygrave slide rule the azimuth and altitude are
    > > calculated in three steps using the same manipulations of the slide rule for
    > > each step. I will first describe the use of the normal cylindrical Bygrave
    > > slide
    > > rule which utilizes a cursor or pointers to align the scales. I have also
    > > enclosed a copy of the original Bygrave instruction book. The Bygrave has
    > > also
    > > been discussed on the Navlist.
    >
    > > > > We first calculate the intermediate value "y" (lower case
    > > y) which is found by the formula:
    >
    > > > > tan y = tan declination / cos H (H = Hour angle)
    >
    > > > > This is the formula listed in the Bygrave manual but, in fact, the
    > > slide rule does the calculation by modifying this formula
    > > �to allow the use of
    > > the cotangent scale. The actual manipulation of the slide rule uses the
    > > re-arranged formula of:
    >
    > > > > cotan y = cotan declination x cos H
    >
    > > > > You accomplish this computation by setting one of the pointers (or
    > > the cursor on my copy) to zero on the cosine scale and while holding it
    > > there
    > > rotate the cosine scale and slide it up or down on the cotangent scale so
    > > that
    > > the other pointer (or cursor) is aligned with the declination on the
    > > cotangent
    > > scale. Now, holding the cosine scale still, rotate the pointer (cursor) to
    > > point
    > > at the hour angle (H) on the cosine scale and then read out "y" from
    > > the other pointer (cursor) where it points on the cotangent scale.
    >
    > > > > Next you find the second intermediate value,"Y" (upper
    > > case Y) by adding "y" to co-latitude (if latitude and declination have
    > > the same name) or by subtracting "y" from co-latitude
    > > �(if of opposite
    > > names.)
    >
    > > > > [I kept the original nomenclature from Bygrave so that the original
    > > literature can be followed . I think it is confusing to use the same letter
    > > of
    > > the alphabet for two variables, "y" lower case y, and "Y"
    > > upper case Y, and I don't know why Bygrave chose this system. I prefer to
    > > replace "y" with "W" in the formulas and have done so on my
    > > forms.]
    >
    > > > > Next we find azimuth with the formula :
    >
    > > > > tan Az = (tan H x cos y ) / cos Y
    >
    > > > > which is re-arranged into the form:
    >
    > > > > cot Az = (cotan H / cos y ) x cos Y
    >
    > > > > Using the same manipulations as before, set one pointer to
    > > "y" on the cosine scale and the other pointer on H on the cotangent
    > > scale, move the cursor to "Y" on the cosine scale and read out azimuth
    > > from the other pointer on the cotangent
    > > �scale.
    >
    > > > > The third step calculates altitude, Hc. using the formula:
    >
    > > > > tan Hc = cos Az x tan Y
    >
    > > > > with the formula re-arranged into the form:
    >
    > > > > cot Hc = cot Y / cos Az
    >
    > > > > set one pointer to Az on the cosine scale with the other pointer to
    > > "Y" on the cotangent scale. move the pointer to zero on the cosine
    > > scale and read out Hc from the other pointer on the cotangent scale.
    >
    > > > > I have developed an even simpler implementation of the Bygrave, one
    > > that is very easy to make since it doesn't require concentric tubes. I made
    > > this by printing out the cotangent scale twice on a piece of paper. I then
    > > printed the cosine scale in red on a transparent sheet so that the cosine
    > > scale
    > > can be placed directly on top of the cotangent scale and aligned much like a
    > > normal slide rule. We follow the same
    > > �steps as already described but it is even
    > > simpler since no cursor needs to be used. I will illustrate how easy it is
    > > to
    > > use with an example. I have include a form and pictures of the scales
    > > showing
    > > this computation.
    >
    > > > > Since the Bygrave doesn't require that the latitude or the LHA
    > > to be whole degrees you can compute Hc for your D.R. position but for
    > > convenience in this example we will use 34� N for latitude, for declination,
    > > 14� N and the LHA is 346�.
    >
    > > > > Look at illustration number 1 (i.jpg) which shows the form to be
    > > used with this simplified model of the Bygrave. The top of the form is used
    > > to
    > > compute hour angle, "H", in the range of 0� through 90�. You enter
    > > the LHA in the proper column and make the computation. You can see in our
    > > example we have placed the LHA, 346�, in the column for LHAs in the range of
    > > 270� to 360�. The form shows that in this case we
    > > �subtract LHA from 360� to
    > > find "H", hour angle, in this example, 14�. We have carried this
    > > 14� down to the "H" blank on the form and we have entered declination
    > > and latitude in the appropriate blanks.(2.jpg)
    >
    > > > > [The scales on the original Bygrave ran from 20' up to 89�
    > > 40' and then back in the reverse direction from 90�20' to 179�40'.
    > > My simplified version eliminates the second set of numbers keeping the scale
    > > less cluttered. The original Bygrave allowed hour angles of 0� to 180� east
    > > and west (which had been normal celestial practice prior to the introduction
    > > of
    > > the concept of LHA) but because my version eliminated the second set of
    > > numbering on the scales it is necessary to get hour angle, "H", into
    > > the range of 0� and 90� which is accomplished on the top part of the form.
    > > Other changes were also necessary because of my simplification of the scales
    > > and
    > > they will be pointed out
    > > �later.]
    >
    > > > > (To avoid confusion I have switched to using "W" to
    > > replace Captain Bygrave's lower case "y.")
    >
    > > > > Next we subtract the latitude from 90� to form co-latitude. If we
    > > were using our D.R. latitude we would subtract it from 89� 60' since this
    > > notation makes it easy to subtract degrees and minutes. In our example the
    > > co-latitude is 56�. We use the top of the form to determine if we will be
    > > adding or subtracting the intermediate value of "W" to co-latitude.
    > > This is determined by the column of the LHA and by the names of the latitude
    > > and
    > > declination. In our example we can see
    >
    > ...
    >
    > read more �
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