leeway angle or the distance along the centreline between the two foils and thus increasing the gap.
The theoretical optimal load distribution between two wings can be derived from equation (5):
L L
1 2
b b b b
2 1 1 2
(5)
In theory, the induced drag of a biplane (twin rudders) should always be smaller than or equal to that of a monoplane of the same span and producing the same total lift if the load is distributed in an optimal way [1]. Since the induced resistance is quadratically dependent on the side force (equation (3)), plotting the total resistance against the side force squared for a given heeling angle and forward speed should result straight (RT-SF²) line.
in a
Furthermore, as stated by van Oossanen [8], the induced resistance for a given speed and heeling angle can be found by subtracting the upright drag (no heel and no leeway) and resistance due to heel from the values on the straight line. The resistance due to heel, therefore, can be obtained by extrapolation of the line to the point of zero side force and subtracting the upright resistance.
A convenient method of quantifying the induced drag is provided by the effective draft principle. The effective draft can be regarded as the depth of the tip vortex leaving the
lift generating appendage. A higher
effective draft means that a better induced resistance characteristic for a certain appendage setup is obtained. If the slope of the RT-SF² line is known, the effective draft can be determined [4] using:
Te
1
dS dR
2 F
2 2
V cos (6)
in which dR/dSF² is the slope of the straight line on the RT-SF² graph.
To summarise this section, it should again emphasised that the induced resistance
has be been
defined as being composed of two parts: one part is associated with the induced angle of attack and one with the influence that lift producing bodies have on the free surface waves.
3. THE EXPERIMENTS 3.1 EXPERIMENTAL FACILITIES
The towing tank used for this project is located in the School of Marine Science and Technology (MAST) at
LWL: 1.129 m Tcb: k:
0.072 m 0.077
Aws: Aw:
Waterline perimeter: aft model
0.340 m2 0.294 m2 2.339 m
Table 1: Model principal dimensions The original
rudder was used for the
experiment and has the following dimensions: Span:
Tip chord: Root chord:
Table 2: Details of aft rudder
The forward rudder was designed by one of the authors specifically for the experiment and was constructed in
0.206 m 0.051 m 0.079 m
Figure 3: Yacht model and dynamometer.
The model was fitted with a tripwire, of 1.2 mm diameter, to trigger turbulent boundary layer flow over the whole wetted surface.
The model’s main hull dimensions are summarised in the table below:
the University of Newcastle upon Tyne. It is 40 metres long, 3.75 metres wide and was filled with fresh water of 1.2 metres deep. The carriage, to which the model was attached, can be towed on a monorail system with a maximum forward speed of 3 m/s. The towing post, connecting the carriage to the yacht model, was fitted with a dynamometer measuring the port and starboard drag, and the forward and aft side force. The trim angle and the heave motion were also measured as was the velocity of the towing carriage.
3.2 THE MODEL
The model hull used in the experiments was an existing conventional
1:6.4 scale model of a half tonne
displacement yacht designed by Ed Dubois Naval Architects LTD.
B-42
©2007: Royal Institution of Naval Architects
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