displacement at 12m/s (23.3 knots), the resistance reduction is still about 25%, but since the powers are larger, the power saving is numerically much greater, at 109kW. But the optimum single hull is now 100m long. This sounds somewhat impracticable for a 100-tonne vessel, though in fact is more or less a 5 scale-up of a rowing eight, which might be 20m long and displace 800 kg. And of course some 80% of the weight of the eight is its “engine”.
The comparison suggests that a narrow-beamed single hull could have some advantage over the catamaran, provided (a) it could be stabilised by “active” means, and (b) that any extra appendages needed for this purpose did not cancel out the reduction in hull resistance.
3. CONTROLLING ROLL ANGLE WITH A RUDDER
Since the lateral force on a rudder usually acts below the mass centre of a vessel, it tends to affect roll as well as yaw. This was studied for a conventional stern-ruddered vessel in [11 and 12] (the latter listing many intermediate references).
augmented with laterally projecting fins, similar to anti- roll stabilisers on ships
but at surface level and
mechanically connected to the rudder. Figure 3 shows a more recent example of a vessel stabilised with a forward rudder. She has a waterline length of 4m, beam of 0.4m and draught to the keel of 0.133m (though the rudder goes down to 0.6m). The mass centre with a typical rider (68 kg) is about 0.75m above the metacentre, which itself is just 0.06m above the waterline. A later vessel (Figure 4) has a beam of 0.5m, draught to the keel of 0.12m, and mass centre typically 0.626m above the metacentre. She is easier to ride than the one in Figure 3, but this is believed
to have more to do
underwater lines than metacentric height.
with her different with the small difference in
But if the rudder is at the stern, there are
two opposing effects. For instance if the rudder is suddenly set for a turn to starboard, the large initial force on it will tend to roll the vessel to starboard. But as the vessel gets into its turn, the rudder force will be reduced, and centrifugal force due to the turn will tend to roll the vessel to port, particularly if the mass centre is high.
In
the language of the control engineer, the action is “non- minimum-phase” (one way first and the other way later), which makes it difficult to use it to stabilise an otherwise unstable roll mode.
Figure 3: “Daring” in 1988
Figure 2: Chapin’s patent of 1926
But if the rudder is at the bow, or at least forward of amidships, both effects are in the same sense, and it becomes relatively simple to use the rudder to keep an otherwise unstable vessel upright, e.g. by correcting a roll to starboard with starboard rudder (i.e. clockwise rotation as seen from above). To the best of the writer’s knowledge, the first person to realise this, or at least to state it in print, was Chapin in 1925 ([1] and Figure 2). He also suggested that the effect of the rudder could be
©2007: Royal Institution of Naval Architects
Figure 4: The vessel used in the mathematical model. The object behind the saddle is a retractable outrigger float, as used in the original version
An additional and occasionally useful consequence of steering with a forward rudder is that sideslip is in the same direction as the turn.
If the helm is put starboard, then most points on the hull start to move to B-3 to
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