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Hi Joel:

Boy, we certainly do jump around - how did we get to Moment of Inertia
from Sextants. The Metacentric Radius (BM) is equal to the Moment of
Inerita of the Load Waterplane divided by the Volume of Displacement,
i.e., BM = I/V, and is a customary value in Stability Calculations. Try
Skene's (of which I have 3-copies) or any SNAME publication for further
explaination.

On Mon, 2 Aug 2004 14:48:06 +0000 Robert Gainer
 writes:
> Joel
> There is a difference in the dynamic and static properties of a
> boat. A
> displacement hull is a shape that will not plane no mater how much
> power you
> add and a �non displacement� hull is a hull that is shaped so that
> the
> dynamic lift it generates causes it to rise up and plane on the
> water
> instead of going though the water. In both cases the boat will
> displace a
> volume of water equal in weight to the weight of the boat when it is
> at
> rest.
>
> The same laws of scaling will apply to any floating object no mater
> what the
> source of power is. When the boat is at rest the engine is just
> another
> weight in the boat.
>
> I don�t ignore the beam or draft, when I scale the length of the
> boat the
> draft will scale in proportion. If the length is 30 feet and the
> beam is 10
> feet when I scale the design 10% up, the length is now 33 feet and
> the beam
> will become 11 feet. Displacement is the same thing. When I scale
> the length
> I also scale the beam and draft, the volume in other words. The
> displacement
> is after all the volume in cubic feet times the weight of water per
> cubic
> foot.
>
> The Moment of Inertia is simply the product of an area multiplied by
> its
> distance squared about an axis. Something squared times something
> squared is
> something to the fourth power. It�s used most often in the design of
> columns
> such as a mast. It also enters into the calculation of stability of
> boats.
>
> I hope this helps; writing has never been my best subject. If you
> need more
> information you might want to check �Principles of Yacht Design� by
> Lars
> Larsson and Rolf Eliasson. I don�t know if �Skene�s Elements of
> Yacht
> Design� is still in print, but that was a good one.
> All the best,
> Robert Gainer
>
>
>
> >From: Joel Jacobs 
> >Reply-To: Navigation Mailing List
> 
> >To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
> >Subject: Re: 7/8 SCALE SEXTANTS MORE
> >Date: Mon, 2 Aug 2004 09:50:49 -0400
> >
> >Thank you for the correction Robert,
> >
> >If you want to be that inclusive don't t you think you should
> differentiate
> >between displacement and non displacement hulls. And between sail
> power and
> >motor driven vessels.
> >
> >I don't want to debate the various formula you present, but just as
> >example,
> >displacement can't possibly be a function of strictly LWL, nor can
> sail
> >area
> >or wetted surface. How can you ignore beam and draft. That makes no
> sense
> >to
> >me. Care to explain?
> >
> >Also I've not seen Moment of Inertia discussed relative to boat or
> ship
> >design where can I read about it.
> >
> >Joel
> >
> >
> >----- Original Message -----
> >From: "Robert Gainer" 
> >To: 
> >Sent: Monday, August 02, 2004 9:21 AM
> >Subject: Re: 7/8 SCALE SEXTANTS MORE
> >
> >
> > > Joel,
> > > Be careful about using the word "everything" when discussing
> scaling a
> > > design. Speed varies as the square root of the waterline, sail
> area and
> > > wetted surface varies as the square of the waterline,
> displacement
> >varies
> >as
> > > the cube of the waterline, stability varies as the fourth power
> of the
> > > waterline and moment of inertia varies as the fifth power of the
> >waterline.
> > > All the best,
> > > Robert Gainer
> > >
> > >
> > >
> > > >From: Joel Jacobs 
> > > >Reply-To: Navigation Mailing List
> 
> > > >To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
> > > >Subject: Re: 7/8 SCALE SEXTANTS MORE
> > > >Date: Mon, 2 Aug 2004 07:53:04 -0400
> > > >
> > > >Let me add something that I thought of after mailing.
> > > >
> > > >In boat and ship design when you scale something up, everything
> changes
> >in
> > > >a
> > > >geometric progression rather than an arithmetic one.
> > > >
> > > >For example, one foot by one foot is one square foot, but if
> you
> >increase
> > > >the size to two feet squared, the result is four square feet or
> four
> >times
> > > >greater.
> > > >
> > > >George, you're the mathematician. Doesn't the reverse hold true
> when
> >you
> > > >shrink something?
> > > >
> > > >Joel
> > > >
> > > >
> > > >----- Original Message -----
> > > >From: "Joel Jacobs" 
> > > >To: "Navigation Mailing List"
> 
> > > >Sent: Monday, August 02, 2004 7:39 AM
> > > >Subject: 7/8 SCALE SEXTANTS
> > > >
> > > >
> > > > > Hello George,
> > > > >
> > > > > Some additional comments on reduced scale sextants (7/8):
> > > > >
> > > > > The small size mirrors collect less light to pass through
> the
> >optical
> > > >system
> > > > > and consequently make twilight observations of stars and
> planets
> >more
> > > > > difficult. There is another equally important disadvantage.
> When
> >taking
> > > >high
> > > > > altitude LAN sights the small surface area of the mirrors
> allows the
> > > >object
> > > > > to jump off the mirror more easily than with large size
> mirrors.
> > > > >
> > > > > In respect to the telescopes on the reduced scale sextants,
> they
> >have
> >a
> > > > > small objective and ocular lens. The Freiberger scope is
> about 2.5 x
> > > >25mm
> > > > > compared to a normal 4 x 40 scope and passes less light
> through the
> > > >system.
> > > > > Again this makes observations of stars and planets more
> difficult.
> > > > >
> > > > > If there are any shooters amongst us, they may comment on
> the
> >preferred
> > > > > weight of a rifle. Some people believe that light weight
> rifles are
> > > >harder
> > > > > to hold on target, and less accurate even though carrying
> them is
> > > >easier.
> > > > > The same holds true of a sextant. A very light weight one is
> thought
> >to
> > > >be
> > > > > more difficult to use.
> > > > >
> > > > > I'm not sure of this, but I think Tamaya was the first to
> introduce
> >a
> > > >7/8
> > > > > scale sextant around 1975. It was the MS 933 Venus which,
> when sold
> > > >today
> > > > > used, sells for about the same as a NEW Freiberger of the
> same size.
> > > > > Freiberger's list price is $600.00. Here's a link to my
> listing of
> >the
> > > > > original Venus sextant. GO:
> > > >http://stores.ebay.com/LAND-and-SEA-COLLECTION
> > > > > It is the fourth one down. I don't know when Tamaya
> discontinued
> > > >production
> > > > > of this model, but they appear on ebay fairly regularly and
> sell
> > > >quickly.
> > > > >
> > > > > Here is a link to a European Freiberger Yachtsman Sextant
> site since
> > > > > Claussen Instrument's is down.
> > > > > http://www.busse-yachtshop.de/dae_Yachtsextant.html Note
> that 600
> >Euros
> > > >is
> > > > > about $720 over there.
> > > > >
> > > > > If you do mostly sun sight navigation, the small size and
> light
> >weight
> > > >might
> > > > > appeal to some, but the 7/8 scale sextant has never had much
> of a
> > > >following
> > > > > by celestial navigators.
> > > > >
> > > > > Joel Jacobs
> > > > >
> > > > >
> > > > > ----- Original Message -----
> > > > > From: "George Huxtable" 
> > > > > To: 
> > > > > Sent: Monday, August 02, 2004 5:40 AM
> > > > > Subject: Re: Celestaire vs Freiberger Yacht Sextant
> > > > >
> > > > >
> > > > > > Joel Jacobs  wrote:
> > > > > >
> > > > > >
> > > > > > >From my experience, if your going to do serious
> navigation
> >relying
> >on
> > > > > > > twilight sights, the 7/8 scale sextants are very
> lacking. Their
> > > >optics
> > > > > are
> > > > > > > not very good, and there small size mirrors are not
> anywhere as
> > > > > effective
> > > > > > > when taking star sights or high altitude sun sights.
> > > > > > ===============
> > > > > >
> > > > > > Something about that puzzles me. Why should it be so, I
> ask?
> > > > > >
> > > > > > First, I should make it clear that I have never even
> handled such
> >a
> > > >7/8
> > > > > > size sextant; and that observations on my own small boat
> have
> >never
> > > >passed
> > > > > > beyond a plastic job, though I have used many "posh"
> sextants,
> > > >belonging
> > > > > to
> > > > > > others. So I make no claims to being an expert on
> sextants.
> > > > > >
> > > > > > Yet, it seems to me that if you were to shrink a sextant
> to 7/8 of
> >its
> > > > > > original size, and shrink its mirrors correspondingly (in
> both
> > > >directions)
> > > > > > while preserving the same angular field-of-view of its
> telescope,
> >then
> > > > > > (because the distance from the eye to those mirrors is
> also
> >reduced
> >to
> > > > > 7/8)
> > > > > > the patch of sky that the mirrors subtend would be exactly
> the
> >same
> >as
> > > > > > before.
> > > > > >
> > > > > > So, in those circumstances, why should the smaller mirrors
> present
> >any
> > > > > > disadvantage?
> > > > > >
> > > > > > George.
> > > > > >
> > > > > >
> ================================================================
> > > > > > contact George Huxtable by email at
> george@huxtable.u-net.com, by
> > > >phone
> > > >at
> > > > > > 01865 820222 (from outside UK, +44 1865 820222), or by
> mail at 1
> >Sandy
> > > > > > Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
> > > > > >
> ================================================================
> > > > >
> > >
> > >
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