rudder, a large bow wave builds up on the inside of the turn, suggesting that the resistance to turning is rather larger than implied by the methods used earlier, and very possibly nonlinear.


to turn, not just the rudder. 6.


SIZE AND POSITION OF RUDDER AND FIN(S)


The rudder needs to be large enough to give sufficiently fast control of the vessel’s path; and there needs to be sufficient fin area to control outward side-slip. But if the rudder and fin are too large, their drag will nullify the advantage got from a narrow single hull, as compared to a catamaran. On the vessel whose mathematical model has been used so far (see Figure 4), and also on “Daring” in Figure 3, these surfaces do indeed appear to be too large, in this sense, influenced by a desire to be “on the safe side”. In both cases twin fins side-by-side have been used, giving the practical advantage that the vessel can be stood stably on the river-bank for assembly etc. But that


retractable stand.


could also be achieved with a removable It had been known from experiment


or


that if one fin was removed from the vessel in Figure 4, there was no perceptible difference in the handling characteristics. And simulation of it with the rudder area reduced to two-thirds and fin area to one quarter of their present values suggested that the behaviour would even then not be significantly affected (though the rudder would operate nearer to the stall).


Such a rudder and


(single) fin have now been made, and a preliminary test with them confirms the simulation, i.e. there is little effect on the handling, at least for straight-line motion or large-radius turns. It is estimated that the modification reduces the combined drag of rudder and fin(s) at 2.2m/s from 4.9N to 2.3N.


These figures should be compared


with the difference between the minimum drags of the single and catamaran hulls in Figure 1b, about 4.4N; and of course the catamaran too would need a rudder or rudders, though no doubt smaller ones.


It is possible to derive from the dynamic model (eqns 1- 7) two possibly useful equations relating to a steady-state turn (at constant v and r, zero p). The “gain” of the rudder is given by:


r  = NvY  YvN Yv(Nr – mxmu0)  Nv(Yr – mu0)


and x0, the x-coordinate of the point of zero sideslip (i.e such that v + rx0 =0) is given by:


x0 =


(Nr – mxmu0)Y  (Yr – mu0)N NvY  YvN


(18)


It seems important that x0 should be behind the mass centre (it comes to –0.936m for the data of Table One). It is perhaps easier to see why in terms of a bicycle (in which the equivalent point is where the back wheel touches the ground). Consider the “line of support”,


B-8 (17)


Ideally the whole bow section needs


joining the points where the wheels touch the ground, and the point on this line which is beneath the mass centre (at least when the bicycle is vertical). When the front wheel is turned to the right, this point has, in inertial terms, a velocity to the right, directly proportional to the steering angle, and to the distance by which it is forward of the rear wheel. It has also an acceleration to the right because of the circular path taken by the bicycle, again proportional to the steering angle. But velocity has a more immediate impact on position than does acceleration, so gives the rider a more immediate means of moving the point of support and hence controlling the roll of the bicycle.


In control system


terms, it puts some phase-advance into the /δ transfer function [5].


Eqn 17 can be used to assess the effectiveness of


alternative sizes and positions of the rudder. It seems that generally, although the rudder should be forward of amidships, it should not be too near the bow.


7. AVOIDING CAPSIZE


Maintaining stability with a forward rudder will not work at very low speeds or when stationary, nor when going astern at whatever speed. Most vessels will need to cope with these circumstances. Those shown in Figures 3 and 4 have a retractable outrigger float, normally


raised


behind the rider, which can be lowered to either side when required. It then locks in that position. That in Figure 3 can be raised only when ashore, but the one in Figure 4 has a mechanism by which it can be raised when afloat. Some vessels built in the USA have had a pair of outrigger floats which fold back in the horizontal plane when not required.


But a vessel so equipped can still capsize as a result of an abnormal event occurring when the floats are retracted, e.g. a large wave, or being brought to a sudden stop by hitting a submerged object, or


just lack of skill or


momentary inattention on the part of the rider. For some sporting purposes these possibilities are acceptable, but they are less so on an all-day cruise, and certainly not on a larger vessel. The remedy seems to be either to widen the vessel’s beam above the waterline, or to fit outrigger floats or auxiliary hulls on either side in a position normally above the waterline, so that contribution to resistance is air resistance.


their only Beyond a


certain angle of heel, one float will enter the water, and at some larger angle the vessel will settle into an attitude of static stability.


The vessel in Figure 4 has been modified in this way. The design considerations were that:


a) the overall beam should be such that the vessel could pass through the 7ft (2.1m) wide locks of the 18th century “narrow canals” of England and Wales;


©2007: Royal Institution of Naval Architects


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