Enhanced Wind Tunnel and Full-Scale Sail Force Comparison Heikki Hansen, Yacht Research Unit, The University of Auckland, Auckland, New Zealand Peter J. Richards, Yacht Research Unit, The University of Auckland, Auckland, New Zealand Peter S. Jackson, College on Engineering, University of Canterbury, Christchurch, New Zealand

ABSTRACT

This paper presents a comparison between wind tunnel and full-scale aerodynamic sail force measurements using enhanced wind tunnel testing techniques to model the full-scale sailing conditions more accurately. The first comparison was conducted by Hansen et al., 2003a, in the Twisted Flow Wind Tunnel (TFWT) at The University of Auckland and followed standard testing procedures. Since then enhancements have been made and two aspects not considered in the original comparison are highlighted here. The interaction of the hull and sail forces is now considered and trim changes of the sails due to wind strength are included.

For the enhanced comparison the interaction between

the hull/deck and the sails is investigated by installing a secondary force balance inside the model to measure the hull/deck forces and by pressure tapping the hull/deck to determine the surface pressure distribution. It is found that

the presence of the sails significantly affects the forces on hull/deck when sailing upwind, which should be accounted for consistently in comparisons of full-scale, wind tunnel, and computational fluid dynamics (CFD) data.

In the original comparison the sails were trimmed in

the wind tunnel to the aerodynamically optimal shape by maximizing the drive force. Trim variations due to wind strength were however noted in full-scale data so that depowering is considered in the enhanced comparison. The sails in the wind tunnel were trimmed based on the full-scale wind strength and the yacht performance by employing a Real-Time Velocity Prediction Program (VPP) to achieve realistically depowered sail shapes.

Utilising the enhanced wind tunnel techniques a

generally good qualitative and quantitative agreement with the full-scale data was achieved, but a conclusive judgment of the accuracy of the comparison cannot be made.

THE 18th CHESAPEAKE SAILING YACHT SYMPOSIUM ANNAPOLIS, MARYLAND, MARCH 2007

NOTATION βT, βA, βeff True, apparent and effective wind angle (°) ∆βeff Change in effective wind angle (°) η Resultant force direction in z-plane (°) φ, θ Heel and pitch (trim) angle (°) ρair Density of air (kg/m3) a Point on central axis closest to coordinate

system origin, a=(ax, ay, az)T (m) AR Aspect Ratio (-) AS Reference sail area according to IMS (m2) ASmain Mainsail cloth area (m2) CD, CDp Drag and parasitic drag coefficient (-) CDi, CDs Induced and separation drag coefficient (-) CF Force coefficient (-) CFx, CFy, Drive and side force coefficient (-) CFz Coefficient perpendicular to deck plane (-) CL, CLopt Lift and optimum lift Coefficient (-) CMx, CMxOpt (Optimum) heeling moment Coefficient (-) cs, e Separation constant and Oswald efficiency (-) I, J Height and length of fore triangle (m) F Force (N) F Force vector, F=(FX, FY, FZ)T (N) fV Wind speed factor (-) M Moment vector, M=(MX, MY, MZ)T (Nm) p Trim parameter power (-) qeff Effective dynamic pressure (Pa) RL Power ratio of lift (-) VA, Veff Apparent and effective wind speed (m/s) xCoE Longitudinal center of effort position (m) zCoE Center of effort height (m) Dyna Name of the Berlin Sail-Force-Dynamometer IMS International Measurement System TFWT Twisted Flow Wind Tunnel VPP Velocity Prediction Program INTRODUCTION

Wind tunnel testing of sails is an effective research and design tool for the developments of yacht sails. It is for example used for obtaining aerodynamic sail force coefficients for the comparison of different sail designs and as input for velocity prediction programs (VPPs). Researchers and designers are generally satisfied that wind tunnel testing of yacht sails and components gives reliable qualitative results. A sail that performs better in the wind tunnel will also perform better in real life. The quantitative agreement is however not well established since a direct comparison between wind tunnel tests and full-scale measurements is complex and rare. Scaling effects are however possible since, for example, the Reynolds Number cannot be matched in wind tunnel tests with soft sails due to strength limitations of the model sail fabrics.

One of the main challenges associated with a direct

comparison between wind tunnel and full-scale measurements is that full-scale aerodynamic sail forces are

very complex to obtain. Due to the large rig forces compared to the relatively small resultant sail forces it is not feasible to obtain the sail forces by simply measuring the forces in the individual rig components but a specially constructed sail force dynamometer is necessary to measure the aerodynamic forces directly. This has only been attempted three times so far by, Milgram et al., 1993, Masuyama and Fukasawa, 1997, and most recently Hochkirch, 2000, who implemented the Berlin Sail-Force-Dynamometer called Dyna. These three sail force dynamometers employed the same principle with an internal structural frame to which all rig components are attached. The frame is connected to the hull by six force transducers to form a six-component force balance.

Dyna, a 10 meter International Measurement System

(IMS) cruiser/racer, is the most sophisticated sailing dynamometer and its data was used by Hansen et al., 2003a, for the earlier comparison to model scale measurements. The wind tunnel tests were conducted in the Twisted Flow Wind Tunnel (TFWT) at The University of Auckland using standard wind tunnel testing techniques. This paper presents an enhanced comparison highlighting two aspects not considered in the original comparison. Firstly the interaction of the hull and sail forces is now considered and secondly trim changes of the sails due to wind strength are included. Other improvements in the wind tunnel set-up and the full-scale data analysis have also been made since the first comparison so that this paper does not directly compare to the original comparison but highlights the differences due to the enhancements of considering hull and sail force interaction and depowering.

Force Coefficients and Center of Effort Position

The aerodynamic forces and moments acting on a yacht are most commonly represented by force coefficients, and a center of effort position. This information is also used by most sail force models in semi-empirical VPPs as input. To approximate the force and moment changes due to heeling of the yacht the effective angle concept is employed, which assumes that the sails are insensitive to span-wise flow that results from heeling as described by, for example, Jackson, 2001. The sails are therefore only influenced by the flow component in the deck plane (z-plane) shown in Figure 1, which heels and pitches (trims) with the yacht. The flow in the z-plane is called the effective flow and is calculated from its geometric relationship to the apparent flow in the horizontal plane. The effective wind angle (βeff) and speed (Veff) are calculated from the apparent wind angle (βA), the heel angle (φ) and the pitch angle (θ) with

[ ]o180,0,cos

sinsincostantan 1 ∈

−= −

effA

eff βθ

φθφββ , (1)

and

( ) θβθφβφβ 222 coscossinsincoscossin AAAAeff VV +−= . (2)

The pitch angle in the wind tunnel is zero and in full-

scale it is still small so that it has no significant effect on the calculations but it is nevertheless considered in the full-scale data analysis. By using the effective angle theory the force coefficients and center of effort position are modeled relative to the z-plane as functions of only βeff instead of βA, φ (and θ). Due to the planetary boundary layer the true wind speed has a vertical speed gradient. The combination of the true wind and the motion of the yacht results in the apparent flow which changes in speed and direction with height. The effective wind speed and angle are therefore defined at the height of the geometric center of sail area above the water, since it can easily be calculated and is a feasible approximation of the center of effort height in this context.

The full-scale forces are measured relative to the

heeled and pitched z-plane, but the wind tunnel forces are measured relative to the horizontal and need to be transformed to the z-plane. Any force coefficient (CF) in the z-plane can be obtained from the corresponding force (F) in the z-plane by using Veff as the reference flow speed with

221

effairSeffSF VA

FqAFC

ρ== , (3)

where AS is the reference sail area, ρair is the density of air and qeff is the effective dynamic pressure. The reference area is taken as the rated IMS sail area defined by Poor, 1986, as

216.1JIAA Smain

S += , (4)

where ASmain is the mainsail cloth area and I is the fore triangle height and J is the fore triangle length. The force coefficients are usually expressed as the coefficient of lift (CL) and drag (CD) defined in Figure 1. The drag coefficient is divided into the separation drag (CDs), induced drag (CDi) and parasitic drag (CDp) components so that

DpL

LsDpDiDsD CeARC

CcCCCC ++=++=π

22 , (5)

where cs is the separation constant, e is the Oswald efficiency and AR is the aspect ratio.

The position of the center of effort is defined as the intersection of the central axis with the centerline plane of the yacht according to Hochkirch, 2000. The central axis is

aligned with the force vector (F) and F can be applied anywhere along the central axis to produce the same moment vector (M). The point (a) on the central axis that is closest to the origin can be determined from

2FMFa ×

= . (6)

The intersection of the central axis and centerline

plane is the center of effort defined by the longitudinal position (xCoE) and the height (zCoE), which can be calculated from

XY

yxCoE F

Fa

ax −= , (7)

ZY

yzCoE F

Fa

az −= . (8)

The center of effort position can be represented as a

function of βeff or of the resultant force direction (η) in the deck plane given by

X

Y

FF1tan −=η . (9)

FULL-SCALE SAIL FORCE ANALYSIS

It is not only a challenge to measure the full-scale sail

forces but also to accurately obtain information regarding the wind environment, such as wind speed and direction, and the yacht performance, such as boat speed and leeway, heel, yaw angle. The full-scale measurement instrumentation is discussed in detail by Hochkirch, 2000. During the data analysis for this comparison it is important to obtain an accurate reference wind speed and direction. An investigation into the calibration of the cup anemometer on top of the mast is therefore conducted as part of the data analysis. The wind direction measurements are corrected for direction vane misalignment and mast twist due to the aerodynamic loads. Data of selected days is still not symmetrical on port and starboard tack. The reason for this asymmetry cannot be determined

βeff

CD

CL

φ (negative)

Zz-plane(deck plane)

z-plane

Veff

Figure 1 - Lift and drag coefficient and effective angle

defined in the heeled (and pitched) z-plane (deck plane)

conclusively but the data is adjusted to give symmetrical results on both tacks.

The reference wind speed and direction are also corrected for the influence of the sails onto the flow above the top of the mast where the cup anemometer and direction vane are located. Wind tunnel measurements were conducted to investigate this with a four-hole Cobra Probe. The change in effective wind angle (∆βeff) at the position of the cup anemometer due to the presence of the sails is shown in Figure 2 plotted against the effective wind angle measured by the Cobra Probe (βeffCobra) with the sails present. The trends are very similar to those shown in the original comparison (Hansen et al., 2003a), but the accuracy is improved due to better measurement instrumentation. The accuracy of angle measurements with the Cobra Probe is typically better than ±0.2°. The tests with mainsail and jib are conducted at three heel angles and a dependency of ∆βeff on heel can be seen. The correction model of the full-scale measurements is therefore a function of βeffCobra and φ and defined by spline surfaces. Figure 2 shows the modeled curves resulting from the response surface at the three tested heel angles. The mainsail with spinnaker combination is investigated only in the upright condition and the correction is modeled as a function of βeffCobra with a 5th order polynomial.

Figure 3 shows the wind speed factor (fV) above the

top of the mast due to the presence of the sails. The accuracy of the Cobra Probe flow speed measurements is estimated at ±0.5% for the low wind tunnel speeds in this study. An increase in flow speed is observed for βeff less than approximately 155° and it is much larger for the spinnaker compared to the jib. The mainsail and jib combination does not show a clear trend with heel angle so that the corrections for both sail sets are functions of just βeff modeled as 5th order polynomials.

WIND TUNNEL TESTING

Since the original comparison by Hansen et al., 2003a, the TFWT has been shortened and relocated within the building to improve the flow quality in the test section. The work for this investigation has been conducted in the upgraded tunnel using upwind and downwind set-up developed for Dyna. The downwind set-up was employed for all mainsail with spinnaker tests and consists of a vertical flow speed gradient and a vertical change in flow direction (twist) generated by the flow twisting vanes (Flay, 1996). The tests were conducted at a flow speed of approximately 2.8m/s. The upwind set-up was used for all mainsail with jib tests and consisted of an vertical flow speed gradient but no twist. Testing was conduced at a flow speed of around 4.1m/s. The flow speeds were selected based on the extensive experience of testing yacht sails at the TFWT. The two main enhancements to the wind tunnel testing process focused on in this paper are the consideration of the hull and sail force interaction and depowering.

Hull and Sail Force Interaction

It is known that the presence of the hull influences the flow around the sails as it partially closes the gap between the sails and the water surface. In wind tunnel tests and CFD simulations the hull is therefore usually modeled. As a result wind tunnel measurements of sails include the forces acting on the hull and rig, also called windage. It is common practice to measure the bare poles windage on the hull and rig without sails in the wind tunnel and subtract it from the measurements with the sails to obtain the sail forces.

In the same way as the sail forces are influenced by

the hull, it can be argued that the hull forces should also be influenced by the presence of the sails, since the sails change the flow field around the hull. The full-scale

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∆β e

ff [°

]

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Figure 2 - Change in effective wind angle (∆βeff) as modeled for the full-scale data correction

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f V [-

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Figure 3 - Wind speed factor (fV) as modeled for the full-scale data correction

measurements do not include the hull forces and the traditional wind tunnel method only provides equivalent results if the hull forces are not affected by the presence of the sails. For the enhanced comparison this interaction between the hull and the sails was investigated by measuring the forces on hull/deck with and without the sails present. A wind tunnel model with an internal structural frame, to which all sail controls are attached, and a hull/deck shell was built. The model can be set up so that the hull/deck shell is connected to the frame by a secondary force balance inside the model. A second hull/deck shell was pressure tapped to measure the surface pressure distribution. This helped to give an understanding of the flow around the hull and, by integration the pressures, provided a second approach of obtaining the hull/deck forces. Figure 4 shows the inside of the model

with the structural frame and the pressure tapped hull/deck shell.

Figure 5 shows the coefficient of drag (CD), lift (CL)

and force perpendicular to the deck plane (CFz) of the hull/deck calculated from force and pressure measurements of the model without sails in the upwind configuration. CFz is positive up the mast as indicated in Figure 1. The experimental error based on the accuracy of the secondary force balance is typically less than ±1%. The pressure measurements have an experimental error of ±1.5% due to the transducer accuracy. The coefficients predicted from the pressure measurements are slightly larger than the coefficients obtained from the force measurements but the two methods produce results that are very similar and show identical trends.

It is found that the presence of the sails significantly

affects the forces on hull/deck when sailing upwind. Most noticeably the lift and drag of hull/deck increase significantly when the sails are present. The drag is at times doubled and the lift produced by the hull/deck with the sails present is up to 8% of the lift produced by the sails whereas it is less than 2.5% without the sails present. The interaction of the hull/deck with the sails is accounted for in the enhanced comparison and it is noted that it should also be considered in comparison involving computational fluid dynamics (CFD) simulations. Figure 6 and Figure 7 show the coefficient of drag (CD) and lift (CL) of the hull/deck for the upright model with and without sails calculated from the pressure measurements. The measurements without sails are shown in the upwind and downwind configuration, which have different vertical speed profiles. In the downwind

Figure 4 – Wind tunnel model of Dyna with internal structural frame and pressured tapped hull/deck shell

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Coe

ffici

ent [

-]

CD (from forces)CD (from pressures)CL (from forces)CL ( form pressures)CFz (from forces)CFz (from pressures)

Figure 5 - Comparison of CD, CL and CFz of hull/deck calculated from force and pressure measurements for

model without sails in upwind configuration at 0° heel

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CD

[-]

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Figure 6 - Drag coefficient (CD) of hull/deck for the model with and without sails in upwind and downwind

configuration

configuration the onset flow is also twisted, i.e. the onset flow angle changes with height, and the model has the spinnaker pole attached. From Figure 6 and Figure 7 it can be seen that the presence of the sails influences the hull forces significantly. The drag coefficient (CD) is almost doubled for many apparent wind angles (Figure 6) and the lift coefficient (CL) is increased by up to a factor of three when sailing upwind (Figure 7). The general shape of the curves is however still very similar to the measurements of hull without sails.

The surface pressure plots in Figure 8 show an increase in the pressure differential between the windward and leeward side of the hull due to the presence of the sails. This indicates that the increase in both lift and drag of the hull is mainly caused by an increase in side force (FY). That this is indeed the case can be shown by plotting the drive force and side force coefficient (CFx and CFy) of the total model with mainsail and jib and of the hull with and without sails in Figure 9 and Figure 10 respectively. The total forces acting on the model are measured with the main wind tunnel force balance which also has an accuracy of typically better than ±1%. The hull forces are again obtained from the pressure measurements. CFx of the hull is

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CL

[-]

Hull windage no sails (upwind)Hull windage no sails (downwind)Hull windage main & jib (upwind)Hull windage main & spi (downwind)

Figure 7 - Lift coefficient (CL) of hull/deck for the model with and without sails in upwind and downwind

configuration

(a) Model without sails

(b) Model with mainsail and jib Figure 8 – Surface pressure plots of upright model on port

tack at βA of 30° showing windward and leeward side

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CFx

[-]

Hull windage no sailsHull windage main & jibTotal force of main, jib, hull and rig

Figure 9 – Drive force coefficient (CFx) of total model with mainsail and jib and of hull/deck with and without

sails for upright model

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CFy

[-]

Hull windage no sailsHull windage main & jibTotal force of main, jib, hull and rig

Figure 10 - Side force coefficient (CFy) of total model with mainsail and jib and of hull/deck with and without sails

for upright model

only small compared to the total drive force coefficient and does not change much due to the presence of the sails. At βeff of 30° it is about 1.5% of the total CFx and at larger angles the percentage is significantly less. CFy of the hull on the other hand is about 3.5% of the total CFy at βeff of 30° without the sails present and increases to 9% with the sails. At βeff of 60° it is as much as 14% of the total CFy. The third force component perpendicular to the deck plane is also investigated with and without the sails present. Figure 11 shows the coefficient of the force perpendicular to the deck plane (CFz) of the hull/deck for the model with and without sails calculated from the pressure measurements. The measurements without sails were again conducted in the upwind and downwind configuration, which explains the differences. The hull/deck acts like a bluff body and the accelerated flow over the deck produces a suction force. For an apparent wind angle of 90° the aspect ratio of the deck is largest and the maximum CFz is produced. From Figure 11 it can also be seen that CFz of the hull/deck is significantly affected by the presence of the sails. For the hull/deck with mainsail and jib, the CFz is close to zero for small effective wind angles (βeff) and increases up to a βeff of 90°, the largest effective angle tested. The pressure plots without sails at small βeff showed an area of high suction close to the bow and slightly negative pressure over the whole deck. At the larger βeff a suction peak at the bow is no longer visible but increased suction can be noted along the windward deck edge, which explains the positive CFz that increases with βeff and peaks at 90°. With mainsail and jib present large areas of the deck experience positive pressure at small βeff, especially in the slot between the jib and the mast. This explains why CFz is close to zero for small βeff. With increasing βeff the

positive pressure exerted by the sails onto the deck reduces which results in an increase in CFz. The suction on the deck is however much less than without the sails present and CFz is significantly less as is shown in Figure 11.

CFz of the hull/deck behaves somewhat differently with the mainsail and spinnaker as can also be seen in Figure 11. It is positive even at small βeff because the spinnaker does not exert as much positive pressure onto the deck due to its significantly larger distance from the deck. As βeff increases and the mainsail and spinnaker are eased, the suction on the foredeck disappears and the flow is directed downwards onto the deck, which reduces CFz and makes it negative for βeff larger than 120°. Unlike CL and CD the force perpendicular to the deck plane is also strongly dependent on the heel angle (Hansen et al., 2006). This is not discussed here but accounted for in the full-scale comparison. It was been shown that the forces on hull/deck are significantly different with the sails present compared to bare poles measurements and that side force contribution of the hull is significant. For the comparison to the hull/scale data the sails and rig component is required and it cannot accurately be determined with the bare poles method. Depowering of Sails in the Wind Tunnel The second main enhancement to the wind tunnel testing process is the consideration of depowering. In the original comparison the sails were trimmed in the wind tunnel to the aerodynamically optimal shape by maximizing the drive force. This assumes that the sails are fully powered-up during the full-scale tests. While this appears to be the case for the downwind tests, indications of sail depowering with respect to the wind strength can be detected for the upwind runs. It is therefore important to also consider the depowering of the sails in the wind tunnel for the comparison with the full-scale measurements. Ideally the full-scale sail shape should be matched in the wind tunnel, but although sail shape recognition was conducted on Dyna, the sail shapes were not recorded simultaneously with the aerodynamic forces. It is therefore not possible to replicate individual full-scale measurements in the wind tunnel but the sail shape data was used as an indicator that the sails were depowered in full-scale. VPPs simulate the depowering of sails with trim parameters, which modify the fully powered-up input data. However, trim parameters do not describe the changes in the force and moment components due to depowering very accurately and in detail. It is therefore desirable to determine realistically depowered trims in the wind tunnel. Trimming sails is a complex task and in the wind tunnel the aerodynamically most efficient fully powered-up sail shape is achieved by maximizing the drive force. The complexity of trimming is further increased when considering depowered sails and Campbell, 1998, and

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CFz

[-]

Hull windage no sails (upwind)Hull windage no sails (downwind)Hull windage main & jib (upwind)Hull windage main & spi (downwind)

Figure 11 - Force coefficient perpendicular to deck plane (CFz) of hull/deck for the model with and without sails in

upwind and downwind configuration

Ranzenbach and Teeters, 2002, introduced techniques to determine realistically depowered sail shapes in the wind tunnel. However, the conceptional difference between trimming sails in the wind tunnel and on the water remained. In real life sails are trimmed based on the performance of the yacht, whereas in the wind tunnel traditionally only the measured forces are available as a guide for trimming. To address this, a Real-Time Velocity Prediction Program for wind tunnel testing has been developed and implemented at the TFWT as described in detail by Hansen et al., 2003b, so that the performance of the yacht is calculated based on the forces measured in the wind tunnel while the sails are trimmed. As illustrated in Figure 12, the Real-Time VPP LabVIEW application measures the forces and moments and passes them to FRIENDSHIP-Equilibrium in coefficient form, which solves for the equilibrium condition in up to six-degrees of freedom employing semi-empirical descriptions to model the hydrodynamic forces. The sails can now be adjusted based on the performance of the yacht in the wind tunnel as well, which makes the trimming process much more similar to the real-life situation.

The Real-Time VPP was employed to achieve

realistically depowered sail trims for the enhanced comparison to full-scale. Figure 13 shows the lift coefficient (CL) for different full-scale true wind speeds (VT) determined with the Real-Time VPP in the wind tunnel. The results for VT of 4m/s correspond to the fully powered-up trim traditionally obtained when trimming the sails to maximum drive force. CL is increasingly reduced for VT above 4m/s and the reduction is greatest for small effective wind angles (βeff). At VT of 6m/s CL is reduced for βeff below about 45° whereas it is reduced for all βeff up to 90° in VT of 14m/s. The measurements show the expected trend that the sails are depowered more with increasing VT and decreasing βeff.

The depowering measurements with the Real-Time VPP were however not conducted together with the hull/deck force measurements to keep the complexity of the testing procedure manageable. The depowering is therefore empirically modeled based on the measurements so that it can be applied to the fully powered-up data that account for the hull/deck interaction. The new depowering model does not aim to describe the physical changes to the sails but simply models the force and moment changes that occur on a realistically depowered sail so that one trim parameter is sufficient to identify the level of depowering. The new trim parameter is called power (p) since it generally describes the level of power produced by the sails. For p=1 the sails are fully powered-up and for p=0 the sails are totally depowered. The main reason for depowering a sail is to reduce the heeling moment so that the level of depowering can be quantified by the reduction in heeling moment as suggested by Ranzenbach and Teeters, 2002. The trim parameter power (p) is defined as the ratio between the heeling moment coefficient (CMx) and the optimum heeling moment coefficient (CMxOpt) for the fully powered-up sails so that

MxOpt

Mx

CC

p = . (10)

In this way each wind tunnel measurement was

assigned a power value and the lift coefficient can now be described as a function of the optimum fully powered-up lift coefficient (CLopt) and the power ratio of lift (RL) so that

Computer A/D card

LP-Filter Pressure transducer LP-Filter

Force balanceAerodynamic forces

Pitot tubeReference pressure

AccelerometerHeel angle (φ)

Parallel port

Result file

Electric motorHeel angle (φ)

Controller

FS-Equilibrium

RT-VPPLabVIEWapplication

Figure 12 - Schematic description of the implementation of the Real-Time VPP (RT-VPP) in the TFWT

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CL

[-]

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Figure 13 - Lift coefficient (CL) for all tested true wind speeds (VT) from Real-Time VPP and modeled by power

),()( pRßCC effLeffLoptL β= , (11)

where CLopt is modeled as a function of βeff as shown in Figure 14. For the comparison to the full-scale data CLopt is obtained from the measurements that have the correct hull/deck forces subtracted. The power ratio for lift (RL) is obtained from the Real-Time VPP measurements and modeled as a function of power (p) and βeff by the response surface shown in Figure 15. The reduction in lift relative to the reduction in heeling moment shows little dependency on βeff. Similarly the change in center of effort height (zCoE) relative to power is also fairly independent of βeff. However, the change in parasitic drag with power requires modeling the dependency on βeff. As expected, the changes in CL, CDp and zCoE are the most significant when

depowering and their modeling affects the performance prediction most noticeably.

With the empirical ‘power’ model the depowered sail trims obtained with the Real-Time VPP can be described accurately. Figure 13 in addition to the measured CL also shows CL obtained with equation (11). The modeled CL is only calculated for each wind tunnel measurement and the points are connected by straight lines since the power values at other βeff are not known. CL is modeled in good detail but some of the discontinuities due to measurement inaccuracies are smoothed out. The average absolute error between the CL measurements and the response surface is 1.2% and the maximum absolute error is 4.5%. The error is calculated relative to the fully powered-up trim at each βeff. MAINSAIL WITH SPINNAKER COMPARISON

Figure 16 to Figure 18 shows the force coefficients

obtained from the full-scale measurements and the wind tunnel tests with mainsail and spinnaker. Point-symmetric full-scale measurements on starboard tack are mirrored about the origin and plotted as one data set together with the port measurements. All wind tunnel measurements are conducted on port tack so that βeff is negative and point-symmetric data is plotted against -βeff. Axis-symmetric data is plotted against |βeff|. Wind tunnel results for the total model including the hull/deck and results for the rig and sails only are shown. The difference between the wind tunnel data sets is the hull/deck contribution towards the forces including the interacting with the sails, which has been discussed earlier. It can be seen from Figure 17 that the hull/deck makes a significant contribution to the side force coefficient at small βeff but that it does not affect the

Figure 14 - The optimum lift coefficient (CLopt) as a function of effective wind angle (βeff)

Figure 15 - Surface describing the lift coefficient ratio RL=CL/CLopt as a function of βeff and power

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CFx

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Full scale

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Rig, main & spi

Figure 16 - Comparison of CFx from full-scale and wind tunnel runs with mainsail and spinnaker vs. βeff

other force coefficients much. The data for rig and sails are equivalent to the full-scale measurements since the rig force balance on Dyna did not measure the aerodynamic forces on the hull/deck. These measurement points are joined by straight lines to highlight them.

The range of the force coefficient plots in Figure 16 to Figure 18 is the same and the amount of scatter in the full-scale data is similar for all three coefficients. From the full-scale rig force balance calibration Hochkirch, 2000, calculated the average deviation in the x and y-direction to be 2.3% and 1.5% in the z-direction. As a first general assessment it can be said that the wind tunnel and full-scale measurements clearly show very similar trends for all force and moment coefficients and that the magnitude of the coefficients is very comparable; a clear scaling effect cannot be noticed.

The scatter in the full-scale data is probably caused,

to a large degree, by differences in the flying shape of the sails. This is not only caused by differences in sail trim but also due to higher frequency fluctuations in the wind speed and direction to which the sail trimmer and the helmsman cannot react but which change the flying shape of the sails relative to the wind direction. In the controlled test environment of the wind tunnel the sails are trimmed to the aerodynamically optimal shape, which is not always achieved in real life. It can therefore be expected that the driving force measured in the wind tunnel forms an upper bound for the full-scale measurements. Figure 16 shows that this is the case, where for βeff larger than 120° only very few full-scale measurements are as high as the wind tunnel measurements. Between βeff of 90°-110° a few full-scale measurements are significantly higher than the wind tunnel results and do not form a smooth curve with the other measurements. It could therefore be argued that these

measurements are not reliable. To some degree the force perpendicular to the deck plane is also related to CFx, a properly trimmed spinnaker that is fully inflated has a higher CFz. It is therefore not surprising that the wind tunnel measurements of CFz in Figure 18 form an upper bound for the full-scale measurements.

The side force coefficient (CFy) for a poorly trimmed

sail can be higher or lower than for the optimally trimmed sail so that the full-scale measurements could be expected to fluctuate about the wind tunnel measurements. For small βeff and βeff close to 180° non-optimum trim of the sails is unlikely to result in |CFy| much larger than the optimum trim and the wind tunnel measurements should be close to the maximum full-scale data. For βeff above 140° this is the case for CFy in Figure 17. For βeff less than 80° the full-scale CFy is however significantly smaller than measured in the wind tunnel. The moment coefficients are not plotted but their behavior can easily be summarized. The heeling moment, although it is strongly related to the side force, exhibits good agreement between wind tunnel and full-scale measurements but the yawing moment about the z-axis has a similar trend to CFy. It agrees well for larger βeff but for βeff less than 100° the full-scale measurements of the yawing moment are also much lower.

As discussed earlier it is difficult to determine the

full-scale βeff accurately due to mast twist, direction vane misalignment, wind shear or other factors. Inaccuracies would shift the full-scale coefficients along the x-axis but would only change the coefficient value by a small amount. Therefore the discrepancy of CFy at small βeff cannot be caused simply by an error in βeff.

The difference in CFy for small βeff is significant and is the source of discrepancies when the coefficient

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Figure 17 - Comparison of CFy from full-scale and wind tunnel runs with mainsail and spinnaker vs. βeff

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Figure 18 - Comparison of CFz from full-scale and wind tunnel runs with mainsail and spinnaker vs. βeff

measurements are processed further. The lift coefficients (CL) shown in Figure 19 agree well for βeff larger than 80° where the wind tunnel measurements form an upper bound for the full-scale data. For βeff below 80° the full-scale data are smaller than the wind tunnel measurements because of the smaller CFy component. Figure 19 also shows the lift coefficient calculated from the IMS coefficients for mainsail and spinnaker following the method by Poor, 1986, but assuming no blanketing effect between the sails. For large βeff the IMS coefficients fall within the scatter of the full-scale data and are smaller than the wind tunnel measurements. For small βeff they lie in-between the full-scale and wind tunnel data.

From the total measured drag coefficient the parasitic drag coefficient (CDp) can be approximated using equation (5) and assuming the same efficiency in the induced drag calculation as obtained by Hochkirch, 2000, for mainsail with jib. CDp is shown in Figure 20 and also agrees well for lager βeff but at smaller angles is significantly less in full-scale because of the smaller CFy component. Since CDp cannot be negative the full-scale values seem unrealistically small. Also shown in Figure 20 is CDp calculated according to the IMS formulation by Poor, 1986. It shows a similar trend to the measurements but it is lower than the wind tunnel measurements and higher than the full-scale data for small βeff.

Looking at the lift to drag ratio in Figure 21 eliminates any differences in measured force magnitudes between full-scale and wind tunnel tests. The lift to drag ratio is much greater for the full-scale measurements at small βeff because of the big difference in CD, which is caused experimentally by the low side force measurements in full-scale. For some measurements the full-scale lift to drag ratio is twice the ratio obtained in the wind tunnel. The lift to drag ratio predicted by the IMS formulation is higher than the wind tunnel results at small βeff but matches the wind tunnel data much better than the full-scale measurements. βeff below 40° represent unrealistic sailing conditions under spinnaker so that the discrepancies are less important.

Figure 22 shows the center of effort height zCoE

calculated from the central axis approach described earlier plotted against the resultant force direction (η) defined in equation (9). Plotting zCoE against η makes the asymptotic behavior when the resultant force (F) is inline with the yacht centerline (x-axis), η=0°, easier to interpret. For small η (which corresponds to large βeff) zCoE from wind

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Figure 19 - Comparison of CL from full-scale and wind tunnel runs with mainsail and spinnaker vs. βeff

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Figure 20 - Comparison of CDp from full-scale and wind tunnel runs with mainsail and spinnaker vs. βeff

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Figure 21 - Comparison of CL/CD from full-scale and wind tunnel runs with mainsail and spinnaker vs. βeff

tunnel and full-scale measurements agree well but for large η (small βeff) zCoE from the full-scale measurements increases while zCoE from the wind tunnel tests stays fairly constant around the height of the geometric center of the mainsail. At large η (small βeff) zCoE is largely driven by the side force and the heeling moment coefficients so that the reduced CFy for the full-scale measurements results in an increased zCoE.

Before assessing the differences between the wind tunnel and full-scale data further the comparison between the upwind data with mainsail and jib needs to be considered to see if similar trends exist.

MAINSAIL WITH JIB COMPARISON For the mainsail with jib comparison the fully

powered-up sail and rig forces are obtained from the total forces acting on the wind tunnel model by subtracting the hull/deck forces measured as discussed earlier. The effects of depowering are accounted for by employing the ‘power’ model described earlier. As an example the ‘power’ model description of the lift coefficient is given in equation (11) and the power ratio based on the Real-Time VPP wind tunnel tests is shown in Figure 15. The full-scale measurements are divided into two data sets: one including tests conducted in VT less than 4m/s and the other with VT between 6-8m/s. For the comparison the wind tunnel predictions are therefore shown for VT of 4, 6, and 8m/s.

The drive force coefficient in Figure 23 shows that the full-scale measurements with VT between 6-8m/s are smaller than with VT<4m/s for small βeff. For larger βeff the maximum values are not very different for the two data sets. This agrees well with the wind tunnel measurements which also show the drive force coefficient reduced with VT of 6 and 8m/s due to depowering. Due to their interdependence the pitching moment coefficient has the same trends. The side force coefficient in Figure 24 shows a significant reduction in magnitude at small βeff for both full-scale and wind tunnel data. It needs to be remembered that the side force is negative and that a reduction in magnitude makes CFy less negative. The largest magnitudes of the full-scale measurements in VT between 6-8m/s are still smaller than the wind tunnel prediction for VT of 8m/s but many full-scale measurements in 6-8m/s VT fall in between the wind tunnel predictions for VT of 6 and 8m/s. The heeling moment coefficient behaves very similar to CFy. A trend of slightly reduced force coefficient perpendicular to the deck plane with increasing VT at small

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Figure 22 - Comparison of zCoE from full-scale and wind tunnel runs with mainsail and spinnaker vs. η

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Figure 23 - Comparison of CFx from full-scale and wind tunnel runs with mainsail and jib vs. βeff

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Figure 24 - Comparison of CFy from full-scale and wind tunnel runs with mainsail and jib vs. βeff

βeff can be seen in Figure 25 from both full-scale and wind tunnel measurements.

The lift coefficient in Figure 26 shows a number of trends discussed earlier. The wind tunnel and full-scale measurements agree well for larger βeff whereas the full-scale lift coefficient is less at small βeff, particularly near βeff of maximum lift. The level of depowering seems to be very similar in the wind tunnel and full-scale. The maximum of the IMS coefficients agrees well with the wind tunnel measurements but the curve is shifted to the left. However, the IMS formulation does not account for the lift produced by the hull, which has been subtracted from the wind tunnel measurements. From the total

measured drag coefficient the parasitic drag coefficient (CDp) is again approximated using equation (5) and shown in Figure 27. Similarly to the mainsail with spinnaker investigation, the full-scale parasitic drag coefficient is unrealistically small but both the full-scale and wind tunnel results agree that there is little change in parasitic drag due to depowering at small βeff. The IMS coefficients agree well with the wind tunnel data at small βeff but increase less rapidly with βeff than the wind tunnel and full-scale measurements. Figure 28 shows the center of effort height (zCoE) calculated from equation (8) plotted against βeff. The fully powered-up wind tunnel and full-scale results show zCoE

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Figure 25 - Comparison of CFz from full-scale and wind tunnel runs with mainsail and jib vs. βeff

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Figure 26 - Comparison of CL from full-scale and wind tunnel runs with mainsail and jib vs. βeff

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Figure 27 - Comparison of CDp from full-scale and wind tunnel runs with mainsail and jib vs. βeff

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Figure 28 - Comparison of zCoE from full-scale and wind tunnel runs with mainsail and jib vs. βeff

close to the geometric center of sail area. The wind tunnel measurements show an increase in zCoE at small βeff which cannot be seen in the full-scale measurements. This indicates that the sails in full-scale may have been trimmed with more twist even in light winds or that the top of the mainsail generated less lift in light wind at small βeff for some other reason. The medium wind strength results from full-scale and wind tunnel measurements agree very well. The zCoE is reduced by a very similar amount.

One of the main discrepancies between the full-scale

and wind tunnel data is again in the side force coefficient at small βeff. As for mainsail with spinnaker the side force coefficient is less for the full-scale measurements for mainsail with jib as well, which again results in a too low CL and CD at small βeff. Plotting the lift to drag ratio in Figure 29 shows that it is much larger for the full-scale measurement compared to the wind tunnel data and IMS predictions, which agree well. The graph is very similar in trend to the mainsail with spinnaker case in Figure 21. The full-scale lift to drag ratios seem unrealistically high and a basic sample calculation for βeff of 20° also predicts CL/CD of around 6, which is very similar to lift to drag ratio achieved in the wind tunnel and predicted by the IMS formulation. The full-scale ratios on the other hand are much larger. This seems to be a systematic error since it has been observed for both sailing configurations. It is very unlikely that sails in full-scale produce much greater lift to drag ratios than predicted using standard aerodynamic principles since extensive research has been carried out in aeronautics and the principles of wing theory are well understood. The parasitic drag coefficient has a great influence on CL/CD since it is the only component in equation (5) not dependent on CL and the low CDp measurements cause the unrealistically high CL/CD.

The low CDp could be caused by an error in βeff due to, for example, errors in the mast twist measurements or the ∆βeff approximation. An offset to increase βeff makes CDp and CL/CD more realistic but the trends of other variables such as CFx and CFy agree less well with the wind tunnel data. Another possible reason for the low CDp is the low measurement of CFy relative to CFx for small βeff due to for examples inaccuracies in the calibration matrix for these load cases. In addition, for small βeff inaccuracies in the force measurements have a greater influence on the resulting CL and CD since the drive force is very small compared to the much larger side force. It is difficult to measure a small drive force accurately when a much larger side force and a significant heeling moment are present due to cross talk between the force transducers of the multi component force balance. From the available full-scale data it is unfortunately not possible to determine with certainty what caused the unrealistically small CDp at small βeff. In spite of this likely problem the wind tunnel and full-scale data agree very well in general. As far as possible with the scatter in the full-scale data, no clear scaling effect can be seen between the wind tunnel and full-scale measurements and the same trends are observed in the different data sets.

CONCLUSIONS

It has been shown that the interaction of the hull/deck with the sails has a significant effect on the side force and the force perpendicular to the deck plane and that this needs to be accounted for consistently when comparing full-scale, wind tunnel and CFD data. The full-scale aerodynamic sail force coefficients obtained with Dyna show a dependency on wind speed and by considering the depowering of the sails in the wind tunnel based on the full-scale wind speed, the comparison is improved.

Generally good agreement with the full-scale measurements can be achieved when employing these advanced wind tunnel testing techniques. No obvious scaling effect was notices but the scatter in the full-scale data makes a quantitative judgment on the accuracy difficult. The most noticeable difference is the unrealistically low drag at small effective wind angles in full-scale for which no conclusive cause could be determined. The qualitative trends between wind tunnel and full-scale tests agree well. ACKNOWLEDGEMENTS

The authors thank all their colleagues at The University of Auckland, the Technical University Berlin and FRIENDSHIP SYSTEMS who contributed to this

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Figure 29 - Comparison of CL/CD from full-scale and wind tunnel runs with mainsail and jib vs. βeff

work, especially Dr. Karsten Hochkirch and David Le Pelley. REFERENCES Campbell, I. M. C. "The Performance of Offwind Sails Obtained from Wind Tunnel Tests." The Modern Yacht Conference, RINA, Portsmouth, 1998.

Flay, R. G. J. "A twisted flow wind tunnel for testing yacht sails." Journal of Wind Engineering and Industrial Aerodynamics, Vol. 63, pp. 171-182, 1996.

Hansen, H., Jackson, P. S., and Hochkirch, K. "Comparison of Wind Tunnel and Full-Scale Aerodynamic Sail Force." International Journal of Small Craft Technology (IJSCT), Vol. 145 Part B1, pp. 23-31, 2003a.

Hansen, H., Jackson, P. S., and Hochkirch, K. "Real-Time Velocity Prediction Program for Wind Tunnel Testing of Sailing Yachts." The Modern Yacht Conference, RINA, Southampton, pp. 79-87, 2003b.

Hansen, H., Richards, P. J., and Jackson, P. S. "An Investigation of Aerodynamic Force Modelling for Yacht Sails using Wind Tunnel Techniques." 2nd High Performance Yacht Design Conference, RINA, Auckland, pp. 89-97, 2006.

Hochkirch, K. "Entwicklung einer Meßyacht zur Analyse der Segelleistung im Orginalmaßstab (Design and Construction of a Full-Scale Measurement System for the Analysis of Sailing Performance)," PhD-Thesis, Technische Universität Berlin, Berlin, 2000.

Jackson, P. S. "An Improved Upwind Sail Model for VPPs." The 15th Chesapeake Sailing Yacht Symposium, SNAME, Annapolis, pp. 11-18, 2001.

Masuyama, Y., and Fukasawa, T. "Full Scale Measurement of Sail Force and the Validation of Numerical Calculation Method." The 13th Chesapeake Sailing Yacht Symposium, SNAME, Annapolis, pp. 23-36, 1997.

Milgram, J. H., Peters, D. B., and Eckhouse, D. N. "Modeling IACC Sail Forces by Combining Measurements with CFD." The 11th Chesapeake Sailing Yacht Symposium, SNAME, Annapolis, pp. 65-73, 1993.

Poor, C. L. "A Description of the New International Rating System." Publications of the United States Yacht Racing Union, USYRU, Washington D.C., 1986.

Ranzenbach, R., and Teeters, J. "Enhanced Depowering Model for Offwind Sails." High Performance Yacht Design Conference, RINA, Auckland, pp. 163-172, 2002.