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Re: [PSUBS-MAILIST] Weighing
>Something I've been wondering about is the point mass
>vs the properties of the 3 dimentional shape in reality.
>Do anyone think that there is a big difference between
>assuming everything is a point mass?
The "point mass" I assume means the Center of Mass (CM) as though all the
mass was concentrated at that point. Yes, as long as you look at the sub
as a "Static" and not a "Dynamic" system you can consider Centers of
Buoyancy (CB) and the CM as points. Now, because there is mass at various
distances from the CM point, there exists a Moment of Inertial (MI). But,
MI will only come into play when working with factors such as how fast the
nose of your sub responds to changes in the CM. If most of the mass of the
sub were say at the ends, then the sub will be slower to rotate around any
axis but the longitudinal axis. I doubt that this is a very important
factor for small subs. I have heard that some larger subs concentrate the
bulk of their mass as close to the center as possible to avoid this
effect. But, just for static trip purposes, yes, you can consider the CM
as a point of weight downward. You can also consider the CB a point of
lift upward. The sub will ALWAYS in a static condition have the CM
directly below the CB. If the boat is moving and bow or stern dive planes
are employed, then the picture changes as the planes produce torque around
the lateral axis.
BTW, you don't always have to divide up every mass into small cubes. For
example, if you have a metal bar that is 0.5 x 3 x 12 inches you can just
say that the 2.55 pounds of weight is a point of mass exactly in the center
of the bar. If that mass is in water then the buoyancy is 0.325 pounds and
it too can be considered a point source in the center of the bar.
You may need to make two buoyancy tables. The first one is with the sub
completely submerged and everything that can get wet is. The second
buoyancy table is with the sub surfaced with ballast blown. You can have a
CB that is above the CM until you surface when the sub rolls over. Of
course that will happen when you first put it in to the water. A great
point of potential embarrassment. :-)
G. Boucher
>There does seem to be a lot of work involved in dividing
>each object up into small cubes and calculating the CM
>of all the small cubes. Although, I would imagine a
>big advantage when performing CB calculation with parts
>of the submarine out of the water.
>
>At some point I plan on release the submarine design
>application as open source (i.e. free). But I still
>think it has a lot of work left to do before then.
>
>Ian.
>
>On Sun, 04 Aug 2002 19:15:09 -0700
>"Gary R. Boucher" <protek@shreve.net> wrote:
>
> > Mike,
> >
> > I developed that spread sheet years ago with some ancient
> software. I
> > don't think I can even call it up anymore. But, what you need to do is
> > simple. Create two spread sheets, or you can do it in one if you
> > want. You need one for weights and the other for buoyancies. You will
> have
> > the following columns:
> >
> > Name of Component
> > X-position
> > Y-Position
> > Z-Position (optional)
> > Weight (buoyancy for second sheet)
> > X moment
> > Y moment
> > Z moment
> >
> > The direct center of the hull is usually X=Y=Z=0
> >
> > The X,Y,Z positions are the distances in inches from the direct center to
> > each component in their respective directions.
> >
> > To get the X moment for a part you multiply the X position of that part
> > times the weight of that part.
> > The Y's and Z's are done the same way.
> >
> > If the component is behind the direct center, it has a negative X
> value, if
> > below a negative Y, if to the left a negative Z.
> >
> > Add up all the X moments with respect to sign. Do the same with the Y and
> > Z moments to yield three sums.
> > By dividing each sum by the total weight of the boat you will get the
> > location of the CM or what some call the center of gravity.
> >
> > Lets say you have one simple submarine weighing 4000 pounds including all
> > components. You have a hull that is cylindrical, a 200-pound motor
> located
> > at X = -60 inches and a 300-pound battery in the forward end of the
> boat at
> > X = +50 inches. Lets see where the CM is.
> >
> > X moment for Hull = (weight of hull) x (position) =
> (4000)(0) = 0
> > X moment for Motor = ( weight of motor) x (position) = (200)(-60) =
> -12,000
> > X moment for Battery = (weight of Batt) x (position) = (300)(+50) =
> +15,000
> >
> > Sum of the moments = 0 - 12,000 + 15,000 = 3,000
> > Position of CM in the X direction = (total moment for X) / weight = +3,000
> > / 4000 = .75 inch forward of center
> >
> > Does this help your understanding?
> >
> > G. Boucher
> >
> >
> > At 04:04 PM 8/4/2002, you wrote:
> > >On Sun, 04 Aug 2002 11:23:32 -0700 "Gary R. Boucher" writes:
> > >
> > > > The Center of Buoyancy is different. The CB is usually
> > > >calculated. I had a spread sheet that I used where I listed EVERYTHING
> > > >that went into the water. For example; even a steel bar used for
> > > >support had it's volume calculated. It was given an X, and Y position.
> > >Each
> > > >volume multiplied by the weight density of water gave a small upward
> > > >force. Each force was summed as a torque about the X=0 and Y=0 axis
> > > >of my sub. The result is the CB. The CB MUST be located above the CM
> > >or
> > > >the sub will roll inverted. This is good for excitement, but not good
> > >for the
> > > >crew that has to right the mistake.
> > >
> > >Can we see the spreadsheet? Is it on line?
> > >
> > >
> > >
> > >
> > >Mike H.
> > >
> > >
> > >
> > >________________________________________________________________
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> >
>
>
>--
>The moon ate the sun on Monday and it was an awsome sight to see.