Depressing the Leeward Bows of Multihull Craft by Stuart Bloom
Subject: [MHml] advantages and optimum uses for proas?
Date: Tue May 29 14:08:42 EST 2001
From: "Stuart Bloom"
There are a number of reasons for depressing the leeward bows of multihull craft, but the single factor that has the greatest effect seems to have been missed in the discussion so far. The ratio of the lateral stability against the longitudinal stability has IMHO the greatest effect on the pressure that is applied to the leeward bow.
Boats with greater lateral stability will be able to sustain greater sail forces before tipping over sideways, therefore allowing more driving force (and counterbalacing resistance) to be transmitted into the boat and thus resulting in a greater pitching moment depressing the bow. This is why trimarans can be wider than catamarans, because three hulls have more longitudinal stability than two, and the different shapes of the amas and main hull allow the bouyancy to be distributed further forward in the amas relative to the centre of gravity, which is born by the main hull when the boat is at rest. It is also the primary reason proas, that generally have relatively lower transverse stability, do not tend to depress their bows as much.
The effect of moving the rig transversly is to move the point at which the downward rig force(*) is applied, and to a lesser extent, to raise or lower the point of application of the horizontal component of sail forced when the boat is heeled. Moving the rig to leeward will move the vertical component of the sail force (which is resisted by bouyancy and hydrodynamic forces) further to leeward, therefore making a greater (or less negative) contribution to the overturning moment applied by the sails (moments produced by vertical force components about a longitudinal axis). This in turn will reduce the total sail force that can be carried by the platform and therefore reduce the driving force/resistance couple, resulting in a lower pitching moment and thus depressing the bows less. This effect is reduced to a certain degree by the reduction in the height of the center of pressure of the sails when the rig is further to leeward on a heeled boat.
One other factor in rig placement is the yaw acceleration induced into the boat when hit by a gust or when the leeward hull is checked by wave impact. The further the rig is positioned to windward the greater will be the yawing force generated by sudden changes in sail force or hull resistance. If the boat is heeled then some of this yawing force will tend to drive the leeward bow further into the water (sideways).
The overall weight of a boat will directly affect the volume of reserve bouyancy required to resist the pitching moment. Reserve bouyancy is often limited by other physical factors and therefore lighter boats are often capable of withstanding a greater relative pitching moment before "planting" that heavier boats; this is an advantage that a racing catamaran can have over a trimaran, which will generally be heavier all other things being equal. I think this may also contribute towards the apparently high tolerance of proas to bow depression, because they are generally relatively light for their hull length.
I do think that a non-traditional proa that is designed with a high righting moment will exhibit a tendency to depress the leeward bow more when pressed.
Is a proa a good race boat?
Not in my opionion. I think that the relatively low transverse stability will prevent a proa (Pacific) from carrying as much sail power as the equivalent weight racing catamaran or trimaran. Also, the manouvering limitation of proas (shunting) will impact on their racing performance in any non-passage races. I think the real strength of the proa is its ability to sail with the majority of the weight carried by a single slender hull in a wide range of wind conditions, therefore allowing relatively high average speeds compared with other forms of multihulls that generally (but not always) tend to be underpowered in lighter conditions.
My firsthand experience with proas is limited and I would welcome any feedback from those with more practical experience.
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* ed. note: "downward rig force" and change in height of "horizontal component of sail force" are negligible at low angles of heel.
Also: Rig Placement and Heeling Load by Tom Speer
Center of Buoyancy and Center of Gravity Ask A Scientist
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