model up with a small heeling moment, and observe if the heel angle increases or decreases during the run at speed. Of course, this is also fraught with difficulties as it will be necessary for the rudder to be deflected to compensate for the yawing caused by the asymmetric underwater shape. Again, the resulting heel angle will be influenced by factors other than the change in transverse stability – in this case the side force caused by the rudder, and the rolling moment generated as a result of the couple between this and the side force caused by the asymmetric underwater shape. An additional complexity is that the equilibrium position will almost certainly occur with a small drift angle, again giving rise to a side force and resulting heeling moment.


Hence, the only reliable way of determining whether a vessel is going to have a problem with loss of dynamic stability is to test a model ballasted with the correct KG value, and observe whether a loll angle develops or not. In principle this could be done either using a captive model or a free running model. Clearly sufficient time at speed is necessary to ensure that any influences of the acceleration are removed, and in practice this is more difficult than at first it may seem!


As the KG value for the full scale vessel will not be known exactly before it is built, it is recommended that the value on the model be set slightly higher than expected. If the model fails to exhibit any problems then this is the best indication that the full scale vessel will not suffer from this phenomenon.


It should be noted that the transverse stability will be dependent on the running sinkage and trim, which in turn are influenced by the propulsion system and appendages, in particular the spray rails. Hence, their effects must be modelled correctly.


Little is known about the scaling of this effect from model to full scale, so the only advice is to use as large a model as possible.


4.2 PORPOISING


Porpoising is a dynamic pitch instability which will result


speed in calm water.


in a pitching behaviour when travelling at high Determination of the


boundary where this occurs can be important, as it clearly not possible to operate at speeds above this.


speed is


It is


well known that high speed craft are likely to experience porpoising problems if there are points of inflexion in the speed/trim curve for Froude numbers between 1 and 2, as shown in figure 4.2. Here the dotted line represents a vessel where porpoising is likely, whereas the solid line represents a vessel where this is not so likely.


The onset of porpoising is due to a complex interaction between sinkage and trim when the vessel is planing, and at this stage it is not possible to accurately predict this


In addition, with small models of high speed craft it can sometimes be difficult to obtain the correct centres of gravity and moments of inertia, as there may not be sufficient movable ballast in the model displacement. For such cases it is essential to construct the model as lightly as possible, and to carefully consider the effect of the placement of any attachment points etc on the centre of gravity and inertias of the unballasted model.


analytically with confidence.


conducted experiments into this


Day and Haag (1952) phenomenon, and


determined that it is influenced by the longitudinal position of the centre of gravity. Blake and Wilson (2001) developed a non-linear time domain model which they showed to have reasonable agreement with experimental results for a series of constant deadrise hard-chine planing craft.


To predict the behaviour of a vessel when porpoising


using a physical model it is necessary to ensure that the towing mechanism properly represents the full scale propulsion, and that the model will have the same vertical


centre of gravity and longitudinal radius of


gyration as the full scale vessel. Both can be difficult to achieve on a small model. It may be possible to determine the porpoising boundary even when the model has the incorrect radius of gyration, however care will have to be used when interpreting the results. On the other hand, the propulsion mechanism is fundamental to the pitching behaviour, and correct simulation of the change in force direction with pitch will be essential. This may require a propelled model, but even then care will have to be taken regarding the model to full scale thrust correlation.


It is known that the onset of porpoising is heavily influenced by running trim angle, and so it is essential that this is represented correctly using a physical model. The propulsion system, and


other


appendages,


particularly spray rails, will have a strong influence on the running trim angle (and the sinkage) so will have to be modelled correctly.


There is not enough known about the effect of scale on the onset of porpoising, so the only advice that can be given is to use as large a model as possible.


5. SEAKEEPING


Predicting the seakeeping behaviour of high speed craft is a particularly challenging task. Existing theories are all based on assumptions that are not valid for small high speed craft undergoing extreme motions, and physical model tests are also fraught with difficulties, not least the small model size, and the problems with constraining/towing the model.


© 2007: Royal Institution of Naval Architects


B-17


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