HEELANGLE AND LEEWAY ANGLE ON RESISTANCE AND SIDEFORCE
Sebnem Helvacioglu : Faculty of Naval Architecture and Ocean Engineering, ITUMustafa Insel: Faculty of Naval Architecture and Ocean Engineering, ITU
ABSTRACT
A racing yacht sails in perfect balance of aerodynamic, hydrodynamic and hydrostatic forces with a leeway angle
and a heel angle.The balance of forces and moments must be solved to obtain sailing leeway and heel angles and predictthe speed of the yacht.In this paper, an approach based on towing tank tests and aerodynamic sail data is presented to solvethis task.An elementary background theory of aerodynamic and hydrodynamic forces and moments due to sail and the hullis given to present the balance equations.Aerodynamic forces are introduced by sail lift and drag coefficients.Hydrodynamic forces are derived from towing tank tests for several heel and leeway angles by use of a dedicatedexperimental system based on a six component balance dynamometer.A PC based data acquisition system is utilised tocollect tank data. A typical sailing yacht model at l/8 scale is used for towing tank tests. Towing tank tests are analyzedto investigate the effects of heel angle and leeway angle on the resistance and sideforce generated by the hull. And finally,a VPP analysis is carried out to derive the performance curves.
NOMENCLATUREC0.2.3: ConstantRFC”CRClD: Aerodynamic heeling force coefficient: Aerodynamic driving force coefficient: Induced resistance coefficient: Drag
RIR-rh-vAhG Frictional resistance: Induced resistance: Total resistance: Wave resistance: Sail area: Speed made good: True wind speed: Wetted surface area
: Aerodynamic efficiency angle
FRFN: Aerodynamic driving force: Froude number
VTWSA&AhFvwkLLWLWVMMYL Vertical aerodynamic force: Vertical hydrodynamic force: Form coefficient: Lift: Load waterline: Air trimming moment: Water yawing moment
Y: True wind angle
INTRODUCTIONThere has been recently some interest in sailing yacht racing in Turkey. A study of sailingyacht performance in the design stage has been started Istanbul Technical University, and first stageof this study is presented in this paper.Performance prediction of sailing yachts is of a complex nature, and differs fromconventional ship performance prediction due to presence of leeway angle, hence the sideforceassociated with it.The resistance and side force prediction of a yacht is a complicatedhydrodynamic problem because of asymmetrical flow about the hull. Experimental methods arebeing utilised widely for performance predictions.An experimental approach (Dayi 1991) has been developed to measure the resistance, sideforce, yawing moment, heeling moment, sinkage and trim angle of a yacht sailing in fixed heel angleand leeway angle at a certain speed in ITU., Ata Nutku Ship Model Testing Laboratory (ANSMTL).The approach has been verified by experiments on a sailing yacht model at l/8 scale with fivedifferent keels. The variation of total resistance and sideforce have been investigated by changingthe heel angle, leeway angle, speed and keel characteristics.Hydrodynamic efficiency of the hull(sideforce/resistance) is demonstrated.Based on aerodynamic data and towing tank data, a velocity prediction program has beendeveloped to predict the yacht speed at any arbitrary true wind angle and true wind speed(Helvacioglu and Insel 1994).
THE BALANCE OF AERODYNAMIC AND HYDRODYNAMIC FORCES
The aerodynamic forces acting on a sail and hydrodynamic-hydrostatic forces acting on a hullmust be balanced for a sailing yacht. The forces and their relative positions, hence the moments,are given in Figure 1.Aerodynamic forces are generated by the wind with a true wind speed (p) and at apparent wind speed (V,). Figure 1d is called aerodynamic wind
triangle. It may be observed that speed against wind direction, or speed made good, can becalculated as =V,
F,=R3.
4. MH=MRM,,=MmMOMENTS(1)a) Horizontal plane : If the forces on the horizontal plane are considered (Figure lc), aerodynamicdriving force (FLAT) must be balanced by a hydrodynamic side force
CLR,and COE, must be compensated by rudder moments, which in turn increases the resistance.In awell balanced yacht design, CLR must correspond to COE for optimum performance.b) Cross Sectional Plane :The aerodynamic heeling force
(MPA) is caused by the difference of aerodynamic andhydrodynamic force acting points in vertical direction
&,=L/D).These forces can also be represented in the axis system defined by yacht course, which can beexpressed as driving force and heeling force.D Cos C, S,
F,=L Cos p = 0.5 oA VA2Assuming maximum lift efficiency is obtained for the sail, driving force, heeling force canbe obtained as a function of apparent wind angle
c, =G-l=
(1-a
RT=Rv+Rw+&+R,a) Viscous Resistance
(4): Wave resistance is assumed to be the difference between total resistanceand viscous resistance in upright condition, i.e. zero heel angle and zero leeway angle, mainlyconsists of energy lost in creating waves.Prediction of wave resistance of a yacht is difficult dueto the shape of the hull.Delft yacht series (Gerritsma et al 1991) forms the main data source in theliterature.In practice towing tank test are used as the most reliable method available.c) Resistance due to Heel R,=O.5 Vs2 Fn2
(RI) : As the hull sails with leeway, lift is generated which in turn causes
an increase in the resistance, called induced drag. The induced drag is principally function of theeffective aspect ratio of hull-keel combination and square of the sideforce coefficient.V,z (F,/0.5 V2)2(9)where C, depends on the shape of the keel, Froude number and heel angle, and can be expressed ash=F, (B,+B, p WSA e2 Fn
(11)A hydrodynamic efficiency (cot =F,/R) can be defined similar to the sail case. As
aerodynamic and hydrodynamic forces are balanced, the angle of apperant wind must be equal tosummation of aerodynamic and hydrodynamic efficiency angles Americas Cup designs.Analytical methods are also introduced as an alternative to the tank testing.However theaccuracy of such methods are still limited, and their use are usually restricted to preliminaryinvestigation of design alternatives, to reduce the tank testing expenses.Two types of modelexperiments have been utilised by the experimental tanks (Larsson 1990). Free to heel approachsimulates the aerodynamic forces at the centre of effort (COE) and model is free to trim, heel, andyaw. Hence all the aerodynamic forces must be determined before the experiments and differentset of experiment must be conducted for any change of sail configuration. The second approachfixes the heel angle and leeway angle. Resistance, and sideforce are measured for a set of heelangles and a set of leeway angles.An iterative technique can be applied to find a balance positionfrom this data for a given sail configuration.This approach has been utilised for the current work.A series of yacht tests have been conducted in ITU Ata Nutku Ship Model TestingLaboratory (ANSMTL). The towing tank is 160 m long, 6 m wide, and 3.4 m deep. A typicalyacht model at l/8 scale has been used in the tests (see Table 1). Model and five keels with sectionsof NACA 63A0 15 were built from wood and turbulence studs at 25 % behind the leading edge wereused on both hull and keels.In all tests the model was free to trim and sinkage, but fixed to heel,yaw and sway.
Table 1: Model and yacht characteristicsKeelBCDFHMax Keel Length /Model LengthDepth(m’)0.0703
SweptbackAngle20.0
0.1875
0.187
I0.0703
Measurement system consisted of a six component balance to measure resistance, side force,heeling moment, and yaw moment. An LVDT and a rotary potentiometer have used for sinkage andtrim angle measurements. Bridge balance-amplifier system has been used in combination with sixcomponent balance to amplify signals.All measurement were recorded by a PC based dataacquisition system and averaged (Dayi 1991).The following procedure has been followed in the experiments :a) Upright condition is tested X=00) for 11 speedsbl) Model set for a heel angle 100,
(h=- 120,-80,-40,00,40,80,120)b3) Model tested for four speedsTHE EFFECT OF HEEL ANGLE AND LEEWAY ANGLE ON RESISTANCE ANDSIDEFORCEThe effect of heel on resistance is generally to increase resistance (Figure 8). However someof the tank results show resistance decrease with heel angle increase.This is attributed to the wettedsurface area decrease in heeled conditions.If the hull-keel-rudder combination is considered as an symmetric aerofoil, the lift,i.e.sideforce, and resistance is increased by increase of angle of attack, leeway angle. The increasein resistance, i.e. induced drag (Figure 9), is proportional to the square of the sideforce. This caneasily be seen from Figure 12 and 13.The effect of leeway angle on sideforce is demonstrated in Figure 10. Sideforce isproportional to the leeway angle. At the highest speed tested (10 knots) and at high leeway angles(above 8 degrees), a decrease in sideforce was observed. This is resulted from the separation at highangle of attack similar aircraft stall. A nondimensional plot of leeway angle Firstly two equations are defined from velocity triangle (Figure lc) as:cosy=v, cos V, Sin V, Sin
F,=RFLAT=FS-HORFH(COE&LRZ)=RA A
The iterative method does iterate
(14)Arrod. -f7rot01
Force
Cd5.1..\\IIIFigure 3a: Typical sail driving forcecoefficient curvesFigure 3b: Typicalsailheelingcoefficient curvesforceFigure 4: Prohaska analysis of form factorKeel ,//0.w3//-+\\f3--‘A,.---x--------
-----_-____“9?l20.19 I *,, 0.21 I.0.33 L.*0.40 1.L0 Figure 10: Side force by change of leewayangle and speed0*m-cl----0---.,Figure14:Polarperformanceplotswithkeel aspect ratio changeFigure 1 I: Side force coefficient by changeof leeway angle
fFigure 15: Polar performance plots withkeel sweptback angle change
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