Re: [Paddlewise] Skeg Jammers etc

{editing and rearranging done by the moderator since my original only went to Peter and not the list.  Peter worked so hard on his response I felt a need to let it get to everyone}

> Kirk wrote:
> On Thu, 24 Jun 2004 17:15:37 +1000, "Peter Treby" <ptreby_at_ozemail.com.au> said:
> > > However, the easiest way I know of to determine the center of
> > > buoyancy of most existing kayaks is with a level.
> > Since the centre of buoyancy is at the centre of mass of the displaced
> > water, and both are aligned vertically when the kayak is at rest, why
> > isn't
> > the centre of mass of the kayak on land a good approximation to the
> > centre
> > of mass of the water is displaces when floating. Could you explain this
> > use
> > of a level a bit further?
>
> Imagine the "perfect" worst case example.  Your boat is made up of two
> sheets of plywood.
> One sheet perpendicular to the other.  The sheet for the front half of the boat lies parallel to the water.  The sheet for the back half of the boat is centered on the front sheet but vertical to the water.  The CoM is at the intersection of
> the two sheets.
> Now put your "boat" in the water.  The bouyancy of the back section of
> the boat water is minimal (assuming most of the plywood is above water.  The CoB is
> quite a ways into the front sheet of plywood which is parallel to the water.

Kirk:
A kayak is a three dimensional object. We place it in x,y,z axis coordinates
in three dimensions, such that the x axis is the length of the boat, the y
axis is the keel to deck height, and the z axis is the beam to beam section.
Now assume the kayak to have a shadow construct beside it, comprised of two
sheets of plywood at right angles to each other such as you describe. Along
which axes are you placing each sheet of plywood? In what relation to each
other are the two sheets of plywood?
Levelling the floating plywood construct does not give you any information
about the centre of buoyancy or the centre of mass. If you make assumptions
about uniform distribution of mass, which is OK for a sheet of even
thickness plywood, but not for a kayak, or a loaded kayak, or a kayak with a
paddler in it, you can float the ply construction, note that it floats
level, and confirm that with your level, and project a perpendicular from
the centre, vertically, along which the CoM and CoB will lie.
Float the kayak. Use the level on the floor of the cockpit. If the level is
placed lined up with the z axis, beam to beam, then the CoB will lie on a
line perpendicular to the level, up the y axis. If the level is placed along
the length of the kayak, the x axis, it may be level, but it does not supply
any information about where on the x axis the CoB lies.
To locate the CoB, you have to locate the centre of mass of the water
displaced by the kayak. You could construct a three dimensional geometric
model of the hull shape. You could then assume, when it is a bare hull, that
its mass is evenly distributed throughout the volume of the hull. You could
then estimate its mass, for a typical construction method. You then assume
that when floating it displaces an evenly distributed volume of water. The
waterline can then be calculated if you apply considerable mathematical
skill to the hull shape. A bit of integral calculus will come in handy. The
centre of mass of the displaced water, which is the centre of buoyancy, can
no doubt be derived in this way. Hull design programs must use something
like this, to arrive at the centre of buoyancy for a hull supporting a given
mass, distributed evenly throughout the hull.
If you start making assumptions about even distribution of mass in the
kayak, you are begging the question we wish to answer, how to load the kayak
so that it floats at trim.
Mathematics seems the long way.
Take the empty kayak. Lift it by the coaming, and note the point, along the
x axis, the length, at which it balances. Place the kayak seat so that the
paddlers centre of mass will be over the kayak's centre of mass when sitting
in the boat. Load the boat so that it balances along the x axis at the same
point as when unladen. Float the kayak and get into it. It should then float
at trim. Why wouldn't it? Why bother trying to estimate whether you have
placed twice the load in the rear as in the front of the boat?
If I keep asking stupid questions, we can spank Paddlewise along for years!
Cheers, PT
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