Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec
parasitic profile drag of blade and rudder profile. RWaves represents the added resistance due to sea state and is often neglected since it is difficult to generalize.
Total heeling force FH (lift perpendicular on flow direction and span) generated by the sailing yacht may be decomposed as:
FH HH HFF F (2)
Here FHß is lift generated due to leeway, FH is Lift due to rudder angle and FH is lift generated by a trim tab, if applicable.
To capture the influence of differing sailing states, the yacht is tested at permutations of speed, heel angle, leeway angle and rudder angle. A typical test matrix is depicted in Figure 1.
Typical numbers of tests for generating the test matrix are:
Non-Lifting tests o 10-20 boat speeds
Leeway angle tests Rudder angle tests
o 3-4 heel angles o 3-5 leeway angles o 5-10 boat speeds
o 2-3 heel angles o 3-5 rudder angles o 3-6 boat speeds
This leads to a large number of test runs, normally
ranging in between 75 to 200 runs. To a certain degree, the matrix can be curtailed by making it dense at special points of interest and sparse at points which are a bit out of place of expected performance.
After performing the investigations, hydrodynamic
coefficients are derived from the resulting forces and moments. These coefficients allow quantifying the characteristics of a sailing yacht at every occurring state by means of interpolation. Figure 2 shows a surface of the dimensionless coefficient for added resistance due to heel over boat speed and heel angle.
The database of hydrodynamic coefficients is fed into the VPP program. In conjunction with the aerodynamic coefficients, the VPP calculates polar plots of maximum boat speed as function of TWA and TWS.
The main drawback of this method is that it inherently incorporates some linearization and interpolation which involves some error. The interpolation error can be reduced by increasing the number of test runs in the test matrix; however this also increases the experimental or computational costs. In turn, if one wants to reduce the number of test runs, this increases the interpolation error.
Figure 2: Coefficients for Added Resistance due to Heel
Here the ratio of added resistance due to Heel is defined as follows:
r RF F
H
UD H RF F
HD H(, 0)
2.2
FH (0, 0) APPROACH USING RVPP
The general idea behind RVPP is to directly implement the calculation of sailing equilibrium into a RANSE Solver. The RANSE solver will calculate hydrodynamic flow forces at conditions for which sail force equilibrium is calculated. Any interpolation is obsolete. To do so, not only the RANS equations have to be solved, but also –
FD( 0, 0) Figure 1: Towing Tank Test Matrix for Sailing Yachts Added Resistance Due to Heel Ratio X Y Z
0.02
-0.08 -0.06 -0.04 -0.02 0
10 20 14 12 10 30 8 6 440
©2011: The Royal Institution of Naval Architects
B-83
U [kts]
Heel [°]
rH [-]
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62