[MHml] advantages and optimum uses for proas?
Tom Speer
multihulls at steamradio.com
Tue May 29 03:25:18 EST 2001
-----Original Message-----
From: Rob Denney <carbondesign at one.net.au>
...
>The force that immerses a cat or tri lee hull has 2 causes. First and
>foremost is the heeling load, caused by having the rig upwind of the lee
>hull.
I see no reason why it makes a difference to the heeling load whether the
rig is located upwind or not. The lateral moment generated by the rig is
the same.
It is convenient for analysis purposes to take the moments about a point
below the mast so that the moment arm to the sail's center of effort is a
constant and the force of the sail is acting at right angles to the moment
arm. But you can use an arbitrary point - say, in either hull - and figure
the moments about there. But the final results you get for the loads on
each hull will be the same. For example, consider a catamaran with
identical hulls and the mast in one of three places - windward hull, center,
or leeward hull. Keep the center of gravity at the center for all three
cases.
First take the catamaran case of the mast in the center and sum moments
about a point below the mast and in line with the hulls' centers of
buoyancy. Half of the heeling moment is reacted by an increase in buoyancy
of the lee hull times half the beam and and half of the heeling moment is
reacted by an equal decrease in buoyancy of the windward hull times half the
beam. The total buoyancy remains the same and equal to the weight. So both
the forces and moments balance.
Next take the case with the mast in the windward hull and take moments about
a point below the mast at the level of the center of buoyancy of the
windward hull. Now the moment arm of the windward hull is zero so it does
not contribute to the heeling balance for this reference point. The heeling
moment is reacted by the change in buoyancy of the leeward hull times the
whole beam. This will turn out to be the same change in buoyancy as for the
catamaran, because although the leeward hull is doing the job of both hulls
in the catamaran, the lever arm of the lee hull is doubled (whole beam vs
half beam) so it can react twice the moment (all the moment vs half the
moment) with the same force.
But now the force balance is not right, because if the boat pivots about the
windward hull, now the total buoyancy of the windward hull is the buoyancy
it originally had, plus the increase in buoyancy of the leeward hull. So
the whole boat must rise so as to reduce the buoyancy on the windward hull
by the same amount it is increased on the leeward hull and keep the total
buoyancy the same. So we get back to the same case as for the catamaran -
equal change in buoyancy in each hull.
Finally, consider the pacific proa case with the mast in the lee hull. The
same arguments apply. The heeling moment is reacted by a decrease in
buoyancy in the windward hull. But the decrease in buoyancy has to be
countered by an increase in buoyancy of the lee hull so as to keep the total
buoyancy equal to the weight. So the windward and leeward hulls experience
equal and opposite changes in their buoyancy. Just like the catamaran case.
Where you'll get a difference based on rig location is when the rig produces
a substantial vertical load in addition to its horizontal loads, like an
inclined rig. Then moving the rig will affect the heeling moment because
you're changing the moment arm of the vertical component. So in this case,
the Atalantic proa has an edge because the vertical loads due to the heel
angle of the boat are farthest from the lee hull. But as long as we're
talking about horizontal loads on the rig, you can move it anywhere in a
horizontal plane without affecting the moments - it's only the difference
between the plane of the rig center of effort and the plane of the lateral
resistance that determines the heeling and pitching moment arm.
>...
>A Pacific proa heels (rotates) around the lee hull, thus removing this
>cause of hull burying. Of course, this is at the expense of the righting
>moment achieved by having the tri lee hull offset from the rig. On the
>proa this must be compensated for by having some weight in the weather
>hull. Not a problem, if this is where all the weight is kept anyway....
It's really the weight distribution and total beam that makes the difference
between cat, proa, or tri. The tri makes it easier to have a greater total
beam than the cat or proa for structural purposes. The proa makes it
possible to move the center of gravity to windward compared to having it at
the half-beam location of the tri and cat.
>For the same righting moment, a Pacific proa will have considerably less
>force depressing the leeward bow than will a cat or tri, I think.
As I see it, the Pacific proa will have the same tendency to depress the
leeward bow, given the same loads on the sail. But the total heeling moment
will be limited by the location of the center of gravity of the boat. With
a large hull to leeward and small hull to windward, the c.g. is closer to
the leeward hull and so the boat can't be allowed to generate as much
heeling moment before it starts flying the windward hull.
Take a look at the rig heights compared to the boat lengths of typical proa
and cat/tri designs. A typical tri will have a mast that is half again as
long as the boat. I don't think you see many proa masts that are this long.
If there's a difference in bow burying, I think this is where you'll find
it.
Tom Speer
me at tspeer.com
http://www.tspeer.com
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