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Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec


AVPP DW TWS 5m/s AVPP UW TWS5m/s RVPP DW TWS 5m/s RVPP UW TWS5m/s


0 30 60 Figure 7: wave pattern of the boat at TWA 140°


A plot of the free surface pattern around the yacht broad reaching at a boat speed of 7.13 knots is depicted in Figure 7. On the upper left side the current state variables of the boat are shown.


The polar plot in Figure 8 shows first results of the simulation at a TWS of 5m/s. The solid lines show the results using RVPP whilst the dotted lines have been calculated using AVPP, conventional VPP.


YRU-Kiel’s in-house 120


The results from AVPP have been calculated using the regressions of the Delft Systematic Yacht Hull Series (Keuning [6]) for the bare hull resistance. Coefficients modelling the influence of


lift are also derived on


empirical regressions with some extensions derived from linear lifting surface theory. For more details of the method behind AVPP see Graf [1].


One can see that the results from RVPP are reasonably close to the results from conventional VPP. Naturally one has to expect differences, since the VPP result has been achieved using empirical formulations, whilst the results using RVPP take into account all features of the geometry and do not interpolate hydrodynamic flow forces but rather predict them for the actual sailing state. Given the limited data available, an assessment which of the methods is more accurate is hard to make. However, one could assume RVPP to be more accurate, since it takes the physics into account with a higher level of detail.


Generally said, for sailing states which are fully powered up (broad reach) the velocity potential predicted by RVPP is a little bit higher than that predicted by AVPP. In return, AVPP predicts slightly higher velocities in sailing states which are characterized by less sail forces, e.g. TWA’s greater than 150°.


Consequently, RVPP shows the characteristically hollow of the downwind polar to be more distinctive, clearly urging to avoid a dead run.


180 TWA Figure 8: Velocity Polar plot


For upwind conditions, one can see a similar pattern. The boat speed predicted by RVPP is a little bit higher than the results gained from the conventional VPP. This holds especially true for courses where the boat sails on a beam reach. This is similar to the downwind results where the differences in boat speed were also biggest at the sailing point where the heeling moment acting on the boat was highest.


An important topic when comparing velocity polar plots is the Velocity Made Good, VMG, as a measurement of the boat speed in terms of making way to windward or leeward. The common formulation for VMG is:


VMG  Bu cosTWA  (24)


With boat speed uB, leeway angle ß and true wind angle TWA. Figure 9 shows VMG in m/s for upwind and downwind polar lines for both VPP methods. As a convention, TWA < 90° is considered positive whilst TWA > 90° is negative.


150


90


B-90


©2011: The Royal Institution of Naval Architect


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Boat Speed [m/s] 1


2 3 4


5


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