N v (N -mx )v (N m)r  N   0


    


v v   g r


         z  (N I )r r 


(2)


These are adequate for describing the linear manoeuvring of a conventional ship, and can have additional terms included to


represent non-linearities if required. Coupling with surge can also be added.


However, equations (1) & (2) have two clear drawbacks when used to describe the linear manoeuvring behaviour of a high speed craft.


Firstly, in equations (1) & (2) it is assumed that the so called derivatives:


Y ,Y ,Yr,Y , Y ,N ,N ,N ,N , and Nr v v  r    v v  r  


are all constant, and more importantly, independent of forward speed. Clearly, if the underwater hull shape is varying, either due to significant changes in sinkage and trim, or due to large wave patterns, then this assumption will not be valid. Therefore, equations (1) & (2) have to be written such that these derivatives are all functions of forward speed, U, as follows:


Y (U)v (Y (U) -m)v (Y (U) m)r g


v r    r


N (U)v (N (U) -mx )v (N (U) m)r z


v (N (U) I )r N (U)


    


v  g     r      0


Again, non-linearities can be added as appropriate, however they too will need to be functions of forward speed. Of course, to make use of equations (3) & (4) it is necessary not only to know the values of the derivatives at one speed, but to know their value over the whole speed range. At this stage it is not possible to determine these with sufficient accuracy, and hence they have to be obtained from model experiments, requiring either a rotating arm or a Planar Motion Mechanism.


The second limitation of equations (1) & (2) is that they do not take into account coupling with yaw.


It is well


known that high speed vessels may heel considerably as they turn. As a consequence the underwater shape becomes asymmetrical, thereby causing a swaying force and yawing moment (Renilson & Manwarring, 2000, Renilson & Tuite, 1996, Tuite & Renilson, 1997).


The linear equations in sway and yaw therefore become: 0


(Y (U) mx )r Y (U) Y (U) 


Y (U)v (Y (U) -m)v (Y (U) m)r g


v r (N (U) I )r N (U) N (U)  0


N (U)v (N (U) -mx )v (N (U) m)r z


v  r


 v  


  g   r           v       r   


         


    3. (5) (6) 4.


Chudley J, Grieve D, Dyson PK., 2002, ‘Determination of


Transient Loads on    v        r (Y (U) mx )r Y (U)   


         0


   (3) (4)


Now, the equation in roll is also required, and this can be written as follows:


K (U)v K (U)r K(U) K(U)  


v   r K (U)  0


The major difficulty is in determining the values for the functions:


Y (U)  ; and N (U)  . It has been found that


these vary considerably with hull shape, and that they can not be predicted numerically, (Renilson et al 2001).


7. CONCLUDING COMMENTS


Predicting the performance of a high speed marine vehicle is a particularly challenging task. Numerical techniques are generally not considered sufficiently accurate, and there are particular challenges associated with conducting model experiments on such craft.


Many of the assumptions and simplifications that can be made for conventional craft are not applicable, and great care has to be taken to ensure that the predictions are reliable and not artefacts of the way in which the experiment was conducted.


Distinct techniques have been developed for the experiments associated with the prediction of the performance of high speed craft, and in some cases specialist experimental equipment is required.


8. 1.


REFERENCES


Armstrong, N.A., 1999a, ‘From Model Scale to


Full-size – Towards an


Understanding of the Scaling of Resistance of High-speed Craft’ Fifth International Conference of Fast Sea Transportation, FAST’99, Seattle, USA, August/September 1999.


2.


Armstrong, N.A., 1999b, ‘The Correlation of Model Testing and Full-scale Trials Resistance of High-Speed


Catamarans’,


The hydrodynamics of High-Speed Craft Conference, RINA, London, UK, November 1999.


Blake, J.I.R, and Wilson, P.A., 2001, ‘An Analysis of Planing


Craft Vertical


Dynamics in Calm Water and in Waves’, The 6th International Conference on Fast Sea Transportation, FAST2001, Southampton, September 2001.


      (7)


B-20


© 2007: Royal Institution of Naval Architects


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