Journal of Technology 2020, Volume 5, Issue 1, pp. 61 – 81. The Society of Naval Architects and Marine Enginesers.

VPP–Driven and Foil Trim Optimization for the Olympic NACRA 17 Foiling

Kai Graf Univ. Appl. Sciences Kiel, Germany, [email protected]

Oliver Freiheit German Sailors Association, Germany

Paul Schlockermann Univ. Appl. Sciences Kiel / Yacht Research Unit, Germany

Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 Jan C. Mense Univ. Appl. Sciences Kiel / Yacht Research Unit, Germany

Manuscript received September 11, 2020; revision received December 13, 2020; accepted December 14, 2020.

Abstract. The Nacra-17 catamaran is currently the only type of that participates in the Olympic Games. It features semi-L-shaped , allowing the to foil. For maximizing boat speed, the sailors have to cope with a large set of trimming parameters. Boat speed depends on sail trim, but additional trim parameters also have a strong impact on boat speed: the rake of the and the , the platform trim and heel angle and the rudder angle. The project described here tries to assist the sailors in finding an optimized set of trim parameters. This is done with the help of a proprietary velocity prediction program, which—besides solving for equilibrium of all forces acting on the boat—searches for the set of daggerboard and rudder rake, rudder angle, heel angle and platform trim, for which performance yields a maximum. The paper describes the method as well as some of the results.

Keywords: Nacra 17; foiling; velocity prediction; CFD; wind tunnel tests; optimization.

NOMENCLATURE

AD Drag area [m²] AD0 AD at zero LW and pitch [m²] AL Lift Area [m²] AL0 Lift area at zero LW and pitch [m²] ARef Reference sail area [m²] AS Spanwise force area [m²] AS0 AS at zero LW and pitch [m²] AWA Apparent wind angle [°] AWS Apparent wind speed [m s.1] cD Drag coefficient [-] cD0 Drag coefficient at zero lift [-] cD sailed Drag coefficient of depowered sail [-] CE Efficiency coefficient [-] cL Lift coefficient [-] cL DOWN Downwind sail set lift coefficient [-] cL sailed Lift coefficient of depowered sail [-] cL UP Upwind sail set lift coefficient [-] df Daggerboard response surface coefficient [-]

61 dU Daggerboard response surface coefficient [-] EMAR Effective main sail aspect ratio [-] FL Aerodynamic lift force [N] Height of origin above water plane [mm] flat Sail depowering factor [-] Fn Froude number ( ugL/( )1/2) G Gravitation constant, 9.8065 [m s-2] kpp Sail parasitic profile drag coefficient [-] L Daggerboard lift [N] lf Daggerboard response surface coefficient [-] lU Daggerboard response surface coefficient [-] LW Leeway angle [°] pitch,rake Daggerboard rotation around transverse axis [°] RA Rudder angle [°] sf Daggerboard response surface coefficient [-] sU Daggerboard response surface coefficient [-] Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 SOG Speed over ground [m s-1] speed Boat speed [m s-1] TWA True wind angle [°] TWS True wind speed [m s-1] U Boat speed [m s-1] V Buoyancy of the [m3] VMG Velocity made good [m s-1] z Height above water plane [m] �, heel Platform heeling angle [°] � Density of water [1000 kg m-3] -3 �Air Density of air [1.25 kg m ]

BRICS Blended reconstructed interface capturing scheme CFD Computational DLS Drag lift span coordinate system DOF Degrees of freedom ORC Offshore Racing Council, this abbreviation is widely used for the ORC measurement system RANS Rynolds Averaged Navier Stokes VMG Velocity made good, component of boat speed in wind direction VPP Velocity Prediction Program XYZ Boat longitudinal, transverse, upright coordinate system

1 INTRODUCTION The Nacra 17 catamaran, Figure 1, sailed by a mixed crew, has been the Olympic multihull class since the Olympic Games of 2016. In 2017, the class association decided to change the shape of the daggerboards. The previously used C-shaped daggerboards were replaced by semi-L-shaped ones, which, together with T-, allow the catamaran to fly, see Figure 2.

While this increased the attractiveness of the boat class significantly, the catamaran turned out to be very complicated to sail at optimum speed. Due to the shape of the daggerboards and rule constraints, a wide set of trim parameters have to be optimized in order to maximize boat speed: daggerboards have to both remain in downward position while racing and have the ability to be pitched independently. The rudder can be pitched prior to, but not during, racing. Due to the daggerboard shape, no obvious choice can be made on the best heeling angle, and the rudder angle has some impact on the ability of the boat to fly. In addition, the crew may change the pitch of the entire platform by moving longitudinally. Including the sail trimming, flattening, twisting, rake and the like, the degree of freedom of all the trimming possibilities may be too large for the sailors to obtain maximum performance experimentally (i.e., by sailing).

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Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 Figure 1. Nacra 17 foiling Source: Kohlhoff/Stuhlemmer Sailing Team, Photo: Felix Diemer

Figure 2. Semi-L daggerboards and T-rudders of the Nacra 17

Table 1. Nacra 17 main dimensions Length: 5.25 m : 2.59 m Weight empty: 138 kg Sail Area Upwind: 20.1 m² Downwind: 39.6 m² Designer: Morrelli & Melvin

63 In order to aid the sailors in their efforts to optimize boat speed, a dedicated velocity prediction program (VPP) has been developed, aiming to find the optimal set of the mentioned platform and sail trimming parameters. The VPP estimates boat speed by calculating force and moment equilibrium in four degrees of freedom, while constraints are taken into account for two degrees of freedom. The optimal combination of sail and foil trim parameters are found using a nonlinear constraint optimization method. Flow forces are predicted using various flow analysis methods. Sail forces are taken from wind tunnel test results with a 1:5.6-scale model of the Nacra 17. Hull and daggerboard forces are derived from free-surface RANS flow simulations, which execute a large simulation test matrix, taking into account a range of fly-, leeway-, pitch- and heel-states, as well as velocity.

The following chapters describe the used flow force prediction methods as well as the optimization procedure before results are shown.

2 BACKGROUND

The base of any sailing boat VPP are methods for prediction of all the flow forces acting on the Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 boat. In this project, wind tunnel tests have been used for the prediction of aerodynamic forces, free-surface RANS simulations have been used for the prediction of the hydrodynamic forces of the hull and the daggerboards, and empirical methods have been used for the rudder force prediction. Beside flow forces, weight of the boat in sailing trim including crew and the center of effort have to be known. Wind tunnel tests were conducted at our twist flow wind tunnel, utilizing a 1:5.6 scale model of the Nacra 17. A general description of the wind tunnel test procedure for is given in Clauthon et al. (1998). The twist flow wind tunnel of the Yacht Research Unit at University of Applied Sciences Kiel has been described in Graf and Mueller (2005). The general method to predict lift and drag coefficients for the sailing yacht from wind tunnel tests follows principles described in Hazen (1980). A proprietary solution method based on the OpenFOAM framework was used for free-surface RANS simulations of flow around hull and daggerboards. The RANS equation solver is described in Meyer et al. (2016) and its validation and application to fast sailing yacht flow problems are described in Graf et al. (2017). For the prediction of flow forces generated by the rudder, simple empirical formulas for the lift and drag coefficients of profiles and wings are used. Profile lift and drag can be derived from standard text books (Hoerner, 1964) while 3D-phenomena are calculated with empirical formulas from Schlichting (1969).

It is well known that high-speed catamaran daggerboards are subject to significant deflections due to the hydrodynamic loads. In addition ventilation and/or cavitation may occur. Taking cavitation into account in a RANS based flow simulation context is a challenging task by itself. The same holds for dynamic fluid-structure interaction of the hydrofoils. Taking both into account within a VPP is even more challenging and would properly change the focus of this study completely. It has thus been assumed that the foils are rigid and do not cavitate. Ventilation on the other hand will inherently be detected by a free-surface RANS code as the one used in this study.

The general solution method for the velocity prediction is based on constraint optimization. No effort has been undertaken to implement or adapt a proprietary solution method for the particular purpose of this project. Instead, we used the framework for numerical calculations, Matlab™. For details of the available numerical methods within Matlab, please refer to https://de.mathworks.com/.

Melvin (2016) presented predictions of the Nacra 17 performance. His results have been used for comparison. No field measurements of the Nacra 17 at full scale have been found in the literature. Consequently some validation data has been collected within this project using standard measurement techniques like GPS and paddle-wheel wind anemometers.

64 3 COORDINATE SYSTEM Two coordinate systems are used: The drag-lift-span (DLS) coordinate system is a local coordinate system used for the daggerboard, rudder and sails. The DLS-axes are oriented in the flow direction, perpendicular to flow and span, and in spanwise direction. Drag, lift and spanwise force are calculated in this coordinate system. Since the spanwise force is a lift as well, the definition of the lift and spanwise direction are a bit arbitrary. The origin of these local coordinate systems are set to:

• The intersection of the leading edge with the hull for the daggerboard. • The intersection of the rudder leading edge with a virtual smooth hull extension for the rudder. • The gooseneck, projected to the water surface for the sail.

Forces from sail, hull and appendages are transformed to a platform-fixed coordinate system (XYZ), with its x-axis pointing in longitudinal direction and its y-axis pointing in transverse direction, parallel to the water surface. The origin of this global coordinate system is amidships, longitudinally and vertically at the intersection of the leading edge of the daggerboard and the hull. Figure 2 Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 shows the local DLS-coordinate system for the port rudder (see the red-green-blue arrows near the of the port hull) and the global XYZ-coordinate system (see the red-green-blue arrows below the mast on waterplane level).

4 AERODYNAMIC FLOW FORCES Aerodynamic flow forces of the Nacra 17 were investigated in the wind tunnel of the yacht research group at our university. The wind tunnel, see Figure 3, is an open, constant-pressure type tunnel, generating twisted flow, mimicking the height-dependent apparent wind a sailing yacht encounters while sailing. The wind tunnel is equipped with a high precision 6-DOF force balance and - Doppler anemometry for wind speed measurements.

Figure 3. Twist Flow Wind Tunnel

65 A model of the Nacra 17 with a scale factor of 1:5.6 was built. While the rig is modelled quite accurately, the shape of the hull is only approximated, and a box equipped with servo motors was placed between the hulls to host the trim actuators (see Figure 4). Measurement results were obtained by trimming the sails manually for maximum driving force in an upright position (no heel). Tests have been conducted for the upwind case with a and a and for the downwind case, in which an additional has been used. Two simplified dummy bodies account for the drag of the crew in condition.

Lift and drag coefficients cL and cD from the wind tunnel tests are further processed according to the work of Hazen (1980): A drag coefficient at zero lift cD0 is calculated from:

2 (1) ccCEcDD0 =- × L where CE is an efficiency coefficient, taking into account the parasitic profile drag and the effective span of the rig in order to calculate induced drag:

Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 1 CE=+ kpp (2) p EMAR

Here kpp is the parasitic profile drag coefficient and EMAR the effective main sail aspect ratio, see Hazen (1980) for details.

Figure 4. Nacra 17 model, scale 1:5.6

Figure 5 shows lift coefficient cL and drag coefficient at zero lift cD0 over apparent wind angle AWA for the upwind and downwind sail sets. Note that total aerodynamic forces are shown, including windage elements, such as hull and crew. This leads to a small error, since the activator box windage element does not exist at full scale. In addition, no attempt has been made to apply a Reynolds number correction, leading to a small over-prediction of viscous drag cD0.

66 Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021

Figure 5. Lift and drag coefficient of Nacra 17 rig

Aerodynamic forces under true sailing condition are calculated from the wind tunnel test results using an additional trim factor flat, taking into account the depowering of the sails in stronger wind conditions:

ccflatLsailed= L × (3)

22 (4) cD sailed=+ c D CE c L flat

Lift and drag are calculated from cL sailed, cD sailed, the reference sail area ARef and the apparent wind speed AWS using (5). AWS takes into account height-dependent true wind speed TWS(z), true wind angle TWA, leeway angle LW and heel angle f as to (6):

2 (5) FAWSzcAL= 0.5r Air ( ) L sailedRe f and a respective formula for the drag.

2 AWS( z) =++( TWS( z)cos TWA U cos( LW )) ... (6)

2 ++(TWS( z)sin TWA cosf U sin( LW )) Since wind speed measurements in the wind tunnel are taken at mast , the true wind speed is also valid at this height in reality.

The flat-factor accounting for the depowering of the sail is calculated within the VPP from the maximization condition for boat speed:

¶¶Uflat/0= (7)

67 5 RANS FLOW SIMULATIONS Flow forces generated by the daggerboards and hull are predicted using our proprietary OpenFOAM-based free-surface RANS equation solver. This solver has been described in Meyer et al. (2016) and a yacht-related investigation employing this solver has been presented at a previous INNOV’SAIL conference (Graf et al. 2017). The above publications include an intensive validation study for sailing yacht applications, albeit for appended hulls only. Due to a lack of respective experimental data no validation study of surface piercing foils has been conducted so far.

Compared to the standard OpenFOAM solver for free-surface flow, interFoam, our solver features some advanced algorithms for the treatment of the free surface:

• The Blended reconstructed interface capturing scheme (BRICS) is implemented for the discretization of the convective term of the volume-of-fluid conservation equation. • Pressure reconstruction for proper modelling of the pressure gradient near the free surface is used. • A variation of the turbulence model is implemented, taking into account the variable density in Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 a mixture of water and air. • A reliable, non-reflective method accounts for damping of waves at the exit of the flow domain. • A stable method for the solution of the equation calculates movement, in particular, trim and sinkage.

The main advantages of this free-surface solver compared to the OpenFOAM interFoam are:

• A non-diffusive sharp air-water interface. • Suppression of numerical ventilation of submerged flow bodies. • Numerical robustness of the solver. • Increased computational efficiency, in particular the solver remains stable at quite large Courant-numbers.

This proprietary flow solver is used for the prediction of the forces acting on the daggerboard and the hull, as described in the following chapters. For the RANS flow simulations, various grid generators have been used as described below. For the generation of grids, surface models have to be available. These have been produced employing laser-based 3D scan methods, as they are used for the Offshore Racing Councils (ORC) measurement system; this has resulted in STL-files.

6 DAGGERBOARD FLOW FORCES Daggerboard flow forces are predicted from RANS flow simulation using a grid of approximately 2.6 million grid cells. The grid is generated using the split-cartesian approach with OpenFOAM’s snappyHexMesh tool (Figure 7). Average normalized wall distance of the innermost cell is approximately y+=50. Inlet boundary conditions are set to given flow speed and turbulence intensity of 0.1% and a length scale of 2 mm, approximately the average boundary layer thickness. The simulation uses the k-�-SST turbulence model, see Menter (1992) . The following test matrix was executed: • Leeway angle LW = -4°, 0°, 4° • Pitch angle pitch = -4°, 0°, 4° • Fly height fly = 0 mm, 200 mm, 400 mm, 600 mm • Speed U = 5 m/s, 10 m/s, 15 m/s yielding a test matrix of 108 test runs. The fly height is the distance of the intersection of the daggerboards leading edge and the hull from the undisturbed water plane. A positive height gives a dry hull, while a negative fly height is linked to some buoyancy of the hull.

68 Figure 8 shows wave patterns at a velocity of U=15m/s at zero leeway and pitch. Flow force results of the daggerboard investigation have been integrated by a response-surface-method approach. Flow forces are converted into force areas by normalizing them with the dynamic pressure. For the lift L, the lift area AL is calculated as follows: L AL = (8) 1 2 2 rU with the density of water ρ and the flow speed U. Similar expressions are used for the drag force area AD and spanwise force area AS.

Forces’ areas are approximated using the following equations: æö¶¶AL AL AL=+ç÷ AL0 LW + pitch èø¶¶LW pitch (9) fly ×-(1lUms )( / 10 / ) lu f 1000mm Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 æö¶¶AS AS AS=+ç÷ AS0 LW + pitch èø¶¶LW pitch (10) fly ×-(1sUms )( / 10 / ) su f 1000mm ¶¶AD AD ¶2 AD AD=+( AD LW + pitch + LW 2 0 ¶¶LW Pitch ¶ LW 2 ¶¶2*AD AD ++pitch2 LWp itch) (11) ¶¶¶pitch2 LW pitch fly ×-(1dUms )( /10 / )du f 1000mm ¶¶AL AL The coefficients AL; ;; l; l and respective expressions for drag and spanwise force are 0 ¶¶LW pitch fU derived from the simulation results using least-square-minimization. Figure 6 demonstrates the accuracy of the fit for lift area AL and spanwise force areas AS (left) and drag area AD (right).

Figure 6. Fit of the regression against CFD results

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Figure 7. Split Cartesian Grid around Nacra 17 daggerboard

Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021

Figure 8. Nacra 17 daggerboard wave pattern at 15 m/s, zero leeway

Rotation angles of the daggerboard around longitudinal axis caused by canting of the daggerboard or heeling of the entire catamaran have been taken into account by rotation of the flow force vector around the longitudinal axis of the boat. A single RANS test validated that this approach is acceptable as long as the heeling angle does not exceed 10°.

Two additional RANS tests have been conducted: the daggerboard lift and drag coefficients have been predicted for a rigid water surface, mimicking the situation for a non-flying hull. From the result, a correction factor for lift and effective span has been derived. A second additional test case investigates the geometry of a hull together with a daggerboard in a setup, in which the hull just touches the free water surface. It was found that the effect of the hull at the root of the daggerboard can be neglected with acceptable accuracy compared to the fully submerged daggerboard at the free surface.

7 HULL RESISTANCE The resistance has been predicted for a single hull, neglecting wave reflection and interaction effects. In addition, the impact of trim and leeway on the hull resistance has been neglected as well. The rationale behind these simplifications is the effort to reduce the test matrix to be investigated. After all, sailing states, where both hulls are immersed, are rare. Usually at least one hull is flying and the optimizer within the VPP will always find optimal solutions with this sailing state. If the hulls are not at all or only one hull is flying, the leeway angles are quite small as well as the additional resistance of the hull encountering a non-zero leeway angle. Consequently, a test matrix with a permutation of boat speeds and buoyancies has been investigated.

The computational grid was generated using the ANSA© meshing tool and uses dodecahedra cells in the far field of the flow domain, pentagon prisms to resolve the free surface, and prism layers around the hull for the resolution of the boundary layer (Figure 9). Approximately 2.5 million grid cells are used. This type of computational grid gives excellent grid quality in terms of orthogonality and skewness and usually produces better simulation results compared to a grid of tetrahedral or hexahedral cells with a similar grid cell number, see Peric (2004) for a description of a study on

70 grid cell type. A drawback of this method is a grid influence on the undisturbed free surface as can be seen in Figure 10. It has been accepted in the study, assuming that it’s impact is small.

Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 Figure 9. Polyhedral grid around Nacra 17 hull The setup of the hull resistance investigation is similar to the one used for the daggerboards (see previous chapter). However, to simplify interpolation the hull was allowed to translate in vertical direction and rotate around the transverse axis, in order to balance the hydrodynamic and hydrostatic forces with the weight m⋅g and center of gravity. The computational grid follows the motion of the hull using a grid morphing approach. Flow speed and buoyancy has been set as follows:

• Flow speed: U = 3 m/s; 6 m/s; 9 m/s • Buoyancy: V = 0.1 m³; 0.2 m³; 0.340 m³

The following contour plots show the wave pattern around the hull with a buoyancy of 0.34 m³ and for various flow speeds. At a hull speed of U = 3 m/s (Fn=0.42), a rather conventional wave pattern can be seen, while at U = 9 m/s, the wave pattern is very narrow, indicating the high Froude number of this hull speed. It can also be detected that some spray covers the zone of the hull at the highest speed.

The results of the hull RANS investigation manifest themselves in a single diagram showing the hull resistance over hull speed and fly height (Figure 13). Remember that negative fly heights stand for some immersion of the hull. Figure 14 shows the mapping of fly height and hydrostatic lift. Here, a small error is introduced because only the undisturbed water surface was considered for the calculation of hydrostatic lift.

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Figure 10. Wave pattern around hull at u = 3 m/s

Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021

Figure 11. Wave pattern around hull at u = 6 m/s

Figure 12. Wave pattern around hull at u = 9 m/s

Figure 13. Nacra 17 resistance diagram

72 0 -50 -100 -150 -200 -250 Fly [mm] height -300 -350 0 1000 2000 3000 4000 5000 Hydrostatic lift [N]

Figure 14. Mapping of fly height vs. hydrostatic lift at zero platform pitch

8 VELOCITY PREDICTION Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 Constraint optimization methods have been used in order to predict the velocity of the Nacra 17. Boat speed was calculated using:

minf (x ) (12) where f is the objective function, set to f=-U for maximization of boat speed and fU=-×cos( TWALW + ) for VMG maximization. x is the vector of free variables:

T (13) x={pitchLW,,,,,,, pitch pitch PR pitch heel flat fly RA} where pitchL,W,R,P are the pitch angles of the leeward and windward daggerboard, the rudder, and the entire platform. Heel is the heeling angle of the platform, flat is the flattening of the sails, fly is the fly height of the platform and RA is the rudder angle. Mathematical flattening of the sails is any linear reduction of the sail’s lift coefficient, regardless of the means by which this is established. Flattening can be done by reducing sail profile depth or decreasing the angle of attack by opening the sail. This is a widely used abstraction of the sail trimming process used by the Hazen (1984) sail force model.

As a nonlinear equality constraint, the equilibrium of the aerodynamic and hydrodynamic flow forces and weight are considered. For the platform, pitching and heeling moment nonlinear inequality constraints are used, which ensure that the maximum righting moment around longitudinal axis is not exceeded. The maximum -up pitching moment is calculated from the longitudinal metacentre and crew trimming.

Moment equilibrium around upright axis is not taken into account. It is assumed that the mast is raked to a degree, which ensures that a yawing moment balance with the optimum rudder angle is achieved. This is of major importance for a semi-L-foil, as described later.

Beside the nonlinear equilibrium and inequality constraints, bounds are given for all free variables. These are set to reasonable values derived from mechanical limits due to class rules and construction of the hull and daggerboard. Some of the bounds (for example heel) are assumed from general sailor consensus.

The VPP is implemented using the Matlab© computational environment. For the constraint optimization, the interior point method is used in a black box style. No effort was made to enhance or improve the methods readily available in Matlab. In order to find a global optimum within the entire design space, a global optimization method has been used. It combines the interior point method for local constraint optimization with a Sobol sequence for the specification of initial values.

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9 RESULTS 9.1 Upwind Polar Figure 15 shows the velocity polar, the diagram depicting boat speed as a function of a true wind angle TWA of 35° ≤ TWA ≤ 90°, and a true wind speed TWS of 4m/s ≤ TWS ≤ 9m/s. Generally, the diagram shows that boat speeds higher than two times wind speed can be achieved for lower wind speeds. As expected, these high boat speeds occur on the beam reach.

A few additional observations can be made: • For TWS = 4 m/s, no transition to the flight state can be seen. • For higher wind speed, the transition to flight condition can be identified with the steep increase in boat speed. • At TWS = 5 m/s, the boat starts to fly at TWA = 60°, but velocity made good (VMG) is higher for a non-flying state at TWA ≈ 40°.

• At TWS = 6 m/s, the previously described pattern changes: Maximum VMG is reached with a Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 TWA ≈ 55°. • For higher true wind speeds, flying is possible at TWA ≥ 45°.

Note that some combinations of TWS and TWA do not converge when searching for optimum speed. At TWS=8m/s and 9m/s no results could be achieved for TWA=50°. Due to a time lack the reason for this has not been further investigation. The respective speed values have been replaced by a linear interpolation of the neighboring values.

The velocity polar at TWS = 6 m/s is of particular interest. Here, two local maxima of VMG can be seen: at TWA = 40° at a non-flying state and an even higher VMG at TWA = 55° at a flying state. It is now expected that an upwind course of TWA = 55° is favored, due to the higher VMG. However, a discussion with the sailors and the coaches unveiled that such a high TWA would be a tactical disadvantage in a race and is usually avoided. Nonetheless, the information is of high value for the sailors, since situations may occur in which a risky tactical decision is advisable if it is coupled with a higher VMG.

Figure 15. Nacra 17 upwind velocity polar

74 9.2 Max VMG Upwind Nacra 17 races are usually up-and-down-races. Consequently, optimization of VMG is more interesting to the sailors than speed optimization for a given true wind angle. For VMG maximization, the objective function f for the optimization is not the negative speed of the catamaran, but rather:

fU=-cos( TWALW+ ) (14)

In this particular case, the true wind angle is an additional free variable subject to optimization.

Figure 16 shows achievable boat speed as well as optimized values for true wind angle TWA and fly height over true wind speed TWS. First of all, we can see that the Nacra 17 can fly on an upwind course as soon as the true wind speed is larger than 5 m/s. This is not fully in agreement with sailing practice of this boat class in a race. However, this is linked to a quite large true wind

angle, which may be disadvantageous in terms of race tactics, as previously mentioned. Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021

It can be seen that for TWS < 4.5 m/s, the boat does not fly (fly < 0). At higher TWS the fly height changes quite rapidly, and the boat seems to jump to a stable flying state. From practical observation it is known that at flight heights where the knee of the daggerboard is getting dry, the flight stability drops. Sailors usually avoid this, applying respective longitudinal trimming. For the VPP this is taken into account by limiting the flight height to 60 cm.

The TWA reaches a maximum as soon as the flight state settles and decreases again for higher wind speed. For TWS > 9 m/s, the diagram shows a loss of boat speed together with a reduction of the flight height, albeit the boat is still flying (fly > 0). We can only assume that at higher wind speeds the transverse force achieves a level where the respective force equilibrium constraint demands higher immersion of the daggerboard.

Figure 16. Nacra 17 speed, fly-height and TWA as a function of TWS

Figure 17 can be seen as a sailing instruction for the daggerboards and the rudder. It shows the pitch angles of the two daggerboards, the rudder and the total platform over true wind speed TWS. Note that the hydrodynamic pitch of the daggerboard is the sum of the geometric pitch of the daggerboards and the platform. For the rudder, a respective relationship holds. However, pitch of the platform and the daggerboards have to be treated independently, since platform pitch changes the immersion of the rudder as well as the moment balance around the transverse boat axis.

From Figure 17 we can derive that in non-flying states, the daggerboards and the rudder should be used in a position where they generate only little vertical lift. The daggerboard-induced drag due to

75 vertical lift seems to be higher than the reduction of the hull drag due to the reduction of buoyancy, which is a consequence of the vertical lift. However, as soon as the boat starts to fly with increased wind speed, the leeward daggerboard has to be set to a position where maximum vertical lift is generated while the opposite holds for the windward daggerboard. For medium TWS, the platform is trimmed such that the platform pitch aids the vertical lift production, while for higher TWS, this seems to be dispensable. The rudder is pitched in such a way that it generates vertical lift over the entire range of TWS. For 5 m/s < TWS < 8 m/s, the rudder pitch is set to a value only limited by the mechanical constraints of the rudder fittings. Outside of this interval rudder pitch is smaller.

Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021

Figure 17. Pitch (rake) angles of daggerboards, rudder and platform

Figure 18 shows optimized rudder and heel angle over true wind speed. This diagram can also be used as part of an instruction for sailors. One can observe that the heel angle is close to zero over almost the entire true wind speed regime. However, at the transition from the non-flying to flying state, the heel angle shows a peek of a view degrees of leeward heel. It can also be seen that a negative rudder angle is found to generate maximum performance as soon as the boat flies.

Figure 18. Nacra 17 optimized rudder and heel angles

Due to the shape of the daggerboards and the class rule, which says that both daggerboards must be used in a downward position at any time, the heeling and the rudder angle need some special attention: for a catamaran utilizing L-shaped daggerboards, a slightly windward heeling angle

76 usually generates maximum performance because the righting arm is larger than for upright or leeward heel (Figure 19, left). This does not for the Nacra 17 semi-L-daggerboard. When heeled to leeward, the immersion, and thus the drag, of the windward daggerboard is reduced. In addition, the leeward daggerboard is better suited to generate sufficient lift to let the boat foil at lower boat speeds (Figure 19, right). This works fine only in light wind conditions, since only there can the lack of righting arm be acceptable.

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Figure 19. Righting moment and lift generated by L- and Semi-L daggerboards

Regarding the proper rudder angle, a forward rake of the rig causing a negative rudder angle (helmet to lee) will put additional side force load on the daggerboard. Due to the semi-L-shape of the Nacra 17 daggerboard, side force is linked to daggerboard vertical force, thus increasing daggerboard side force will increase daggerboard vertical force, which will allow the boat to fly earlier.

This well-established theoretical reasoning is reflected in Figure 18. To aid the boat achieving a flying state as soon as possible, the boat is heeled to leeward at a wind speed of TWS = 4.5 m/s. This heel angle is reduced to zero as soon as a stable flight state is reached. Negative rudder angle is used when flying to generate more vertical force except in very low wind speeds, where vertical force production is not advantageous, as previously described. In reality, such a large negative rudder angle will not be used. Most sailors don’t feel comfortable if a boat on a windward tack asks for lee helm.

9.3 Downwind Performance The downwind polar (Figure 20) shows the expected pattern: maximum boat speed is achieved on a broad reach, and flying states are achieved at true wind speeds TWS ≥ 5 m/s.

There is a general drawback with our downwind velocity prediction. For smaller true wind angles TWA ≤ 100°, the boat speed is far too slow. From race observation it is known that the jib-to- gennaker crossover takes place at true wind angles smaller than 90°. Some race observations suggest that even on an upwind course in light-wind conditions, a higher VMG can be achieved with a gennaker than with main/jib only (when this was observed for the first time, the class rules were changed, prohibiting setting the gennaker on a course to a windward ).

Our downwind velocity polar does not reflect these observations. The only interpretation we have for this pattern is the shape of the gennaker. The used in our wind tunnel are usually models of (slow) ORC-like gennakers. The gennaker of a fast flying catamaran definitely looks different, very flat and more -like.

A new test series with a revised gennaker is being conducted, but the results were not yet available when this paper went to press.

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Figure 20. Nacra 17 downwind velocity polar

10 COMPARISON WITH FULL SCALE TESTS Full scale resistance tests have been conducted by simply towing the Nacra 17 with a . Field tests generally lack some accuracy compared to towing tank tests, since impact of environmental changes can never be entirely excluded. At the time of the resistance tests, a light breeze prevailed. In order to minimize its impact on the measured resistance, two towing tests have been conducted, one attempt with headwind, another with wind from astern. These tests were conducted without daggerboards, but rudders were necessary in order to keep the boat on track. Figure 21 shows the result of the towing tests compared to computational resistance results. In this case the calculated resistance consists of Computational Fluid Dynamics (CFD) results for the hulls and some empirical formulas for the rudder resistance. The windage of the platform with crew on board has been derived from a tare wind tunnel measurement.

Figure 21. Resistance field test results and comparison with numerical prediction

78 Given the expected inaccuracy of field test results, the agreement of the field test with computed resistance seems to be acceptable.

Only incomplete data has been available for the comparison of measured and VPP-predicted boat speed. Field measurements have been conducted using an onboard GPS-unit, giving speed over ground SOG. A wind sensor has only been available on the coach’s chase-boat, measuring apparent wind speed. From both data true wind speed TWS has been calculated, assuming leeway to be zero. No attempt has been made to measure true or apparent wind angle. It is assumed that the sailors sail the boat at optimum VMG and the measurements have been compared with respective VPP results, without considering true wind angle.

It could be observed, that the catamaran was mainly sailing in non-flying condition when trying to maximize VMG. Consequently the comparison of measured and predicted boat speed was based on non-foiling states. To this end, additional VMG-predictions have been generated suppressing any foiling. Instead two additional constraints for the fly height have been taken into account: a non-foiling state, where 2/3 of the boat weight is balanced by hydrostatic buoyancy, and a Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 skimming state, where the foils generate vertical forces balancing 100% of the boat’s weight, however the hull was not allowed to raise above the water plane.

The comparison of measured and predicted boat speed under the above constraints is shown in Figure 22. Three solid graphs show the VPP-predicted boat speed over true wind speed: the blue line indicates boat speed at maximum VMG for the catamaran free to foil, the green line indicates speed for skimming mode and the red line indicates the boat speed with floating hull. Individual dots mark measurement samples.

Generally lots of data noise can be observed for measured boat speed, and to a quite high degree this is expected. For the vast majority of measurement samples, comparison unveils that the VPP- results mark an upper bound of measured boat speed. Taking into account, that a VPP inherently predicts the maximum achievable boat speed, Figure 22 confirms the validity of the VPP results to a quite satisfying degree.

Figure 22 shows a quite large boat speed increase at flying states compared to non-flying states. This can be expected since maximum VMG states are predicted for flying states at much higher true wind angle than for non-flying states. Only few data samples are available for upwind flying states and they show much lower boat speed. A reason for this discrepancy is simply the fact, that the crew on the Nacra 17 usually avoids bearing away to achieve flying states on an upwind tack because this is usually associated with a tactical disadvantage in the race. Consequently it can be assumed that the few data points for flying state in Figure 22 are obtained at smaller true wind angles than would be optimal to achieve maximum upwind VMG. This will be further investigated in the near future by an intensive validation study.

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Figure 22. Comparison of measured boat speed with VPP predictions

11 CONCLUDING REMARKS The subject of the project described here was finding a method to aid the sailors of the Nacra 17 Olympic catamaran in their effort to maximize the performance of the boat. This was solved by means of a VPP, which calculates the maximum achievable boat speed from a force and moment equilibrium with a set of optimized boat trim parameters. The VPP is able to quantify many optimum trim settings, such as daggerboard and rudder rake, which so far are optimized by the sailors through practical sailing or reasoned conclusion.

Numerous topics of investigation could not yet be addressed, and are reserved for a continuation of this study:

• Rudder forces are predicted with empirical formula that do not take into account the free surface. • Validation of the daggerboard flow forces is missing. • The Hazen sail force model does not take into account a twist parameter, allowing the maximization of boat speed by twisting the sail. • Deflection of the foils is neglected so far. • Cavitation of the foils is not investigated. • For the higher wind speed range, some implausible results are obtained. • Validation of the method by comparing computed results with practical measurements while sailing have to be extended.

A continuation of the study for the next Olympic cycle 2020 to 2024 is planned. It will lead to refinements of the building blocks of the method presented here, in particular the flow forces generated by the rudder and a twisted main sail. This will lead to better reliability of the results, which will further increase the value of the procedure.

80 12 REFERENCES Clauthon, A., Wellicome, J. and Shenoi, A. (1998), 'Sailing Yacht Design, Theory', Addison Wesley Longman Limited, Essex, UK.

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Hazen, G.S. (1980), 'A Model of Sail Aerodynamics for Diverse Rig Types', Proc. New England Yacht Symposium, New London, Connecticut, USA.

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Graf, K., Meyer, J., Renzsch, H. and Preuss, C. (2017), 'Investigation of modern sailing yachts Downloaded from http://onepetro.org/jst/article-pdf/5/01/61/2478399/sname-jst-2020-02.pdf by guest on 02 October 2021 using a new free-surface RANSE code', Cite de la Voile Eric Taberly and Naval Academy Research Institute (Ed.): Innovation in high performance sailing yachts (INNOV'SAIL 2017), Lorient, .

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Peric, M. (2004), 'Flow simulation using control volumes of arbitrary polyhedral shape', ERCOFTAC Bulletin. 62, 25-29.

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