the MAST workshops. Span:
Tip chord: Root chord:
Maximum thickness:
It consisted of a very high
aspect ratio aluminium foil with a uniform NACA 0012 section profile. Its details are given in the table 3.
0.240 m
0.060 m 0.060 m 0.007 m
Table 3: Details of forward rudder
The position of the forward rudder on the hull was located halfway between the keel and the forward perpendicular.
A canting keel with bulb was also manufactured for the experiments. The strut of the new keel was designed with the same profile section as the forward rudder and had a span of 0.24m. At the tip of the keel strut, an aluminium bulb was fitted. It was not optimised for minimal drag
but was designed to simulate
representative canting keel bulb. 3.3
EXPERIMENTAL PROCEDURE
A systematic series of tests was undertaken in which the yaw angle was varied between 0° and 4° and the heel angle between 0° and 20°. For each test series the canting keel angle was varied from 0° to 60° and the measurements were taken over a Froude number range of 0.2 to 0.45.
The gauges used for measuring the forces and displacement have a rated accuracy of ± 1% of the applied load. The error bars shown on the results presented are based on this the gauge accuracy.
It is generally accepted [8] that a yacht usually attains its highest speed when sailing to windward at a Froude number of approximately 0.35. When, for a particular test, the model had to be towed at a constant speed while varying other parameters, a Froude number of approximately 0.35 was chosen every time as a typical cruising speed.
4.
EXPERIMENTAL DISCUSSION
RESULTS AND
4.1 VERTICAL LIFT PRODUCTION BY THE CANTED KEEL
The vertical lift caused by the canting keel while sailing with a leeway angle reduces the wetted surface area of the hull and affects the viscous and the wave resistance of the yacht. The question is whether this effect has a significant influence on the total resistance.
During a test where the upright model was towed at four degrees leeway at several speeds, the change in heave motion was measured, with the keel successively at zero and forty degree canting angles. The differences
©2007: Royal Institution of Naval Architects a Change in heave[mm]
measured between the heave at a certain speed with the keel vertical and the heave at the same speed with the keel canted are plotted in Figure 4.
-0,20 -0,10 0,00 0,10 0,20 0,30 0,40 0,50 0,60
0,200
0,250
0,300
0,350
0,400
0,450
Fn[-]
Figure 4: Change in vertical displacement as a function of the Froude number.
It is noted that at slow speeds the vertical lift force is negative. This is not expected when looking at the theory (figure 1) and taking into account that the boat was trimming bow up at all tested speeds, except for the Fn=0,45 test where she was trimming bow down.
Multiplying this heave difference with the value of the waterplane perimeter (table 1) allows for the calculation of the new wetted surface area to be made for each particular speed. The perimeter is assumed to be constant over
the speed range. Since both the
viscous and wave resistance are proportional to the wetted surface area, and the other parameters in equations (1) and (2) remain unchanged for an equal speed, it follows that:
RV 2 RW2 R 1V RW1 RV1 RW1
Aws Aws
which leads to the results below:
Fn[-] Aws1[m²] Aws2[m²] Rv+Rw change [%] 0,260 0,312
0,345 0,348
0,364 0,353 0,417 0,360 0,437 0,370
Table
0,345 0,349 0,353 0,359 0,369
4: Relative change in
0,050 0,071 -0,048 -0,098 -0,392
viscous and
resistance for the keel canted to forty degrees. Table 4 shows the
wave change in viscous and wave
resistance when the keel is swung sideways from zero to forty degrees as a fraction of the values with the non- canted keel, as a function of Froude number. The viscous and wave resistance change due to vertical lift generated by the canted keel is thus smaller than 0.39% of the original values even for a relatively high speed. This lift effect and its influence on the viscous and
1 2
1 (7)
B-43
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