Extreme manoeuvres for America\'s Cup catamarans

Trans RINA, Vol 155, Part B1, Intl J Small Craft Tech, Jan-Jun 2013

EXTREME MANOEUVRES FOR AMERICA’S CUP SAILING CATAMARANS J R Mansbridge and J R Binns, Australian Maritime College, Australia SUMMARY This paper explores the manoeuvring aspects of the 34th International Americas Cup catamarans as the current rule draft allows [1] using the Futureship GmbH developed program FS_Equilibrium. With the results of this analysis the implications of implementing other manoeuvring solutions including varying the size of the rudder and the implementation of a pure drag rudder are investigated. The effectiveness of varying the rudder size was tested by specifying different lateral areas with a consistent chord length and profile shape. It was concluded that increasing the rudder size allowed the vessel to turn sharper but reduced overall speed due to the increased drag. In addition it was shown that the optimum rudder size for the manoeuvre specified, had a lateral area of 1 m2 and a wetted surface area of 2m2. This rudder size was then tested against a new proposed design, here termed the pure drag rudder in order to determine any possible performance gains. It was concluded that the addition of the pure drag rudder caused the vessel to turn with a much smaller radius at the expense of forward speed. It was determined however that this loss in forward speed was outweighed by the smaller radius of the turn and the potential tactical gains to be had from sailing further to windward and as such the pure drag rudder is a viable method of turning the vessel. NOMENCLATURE AWA TWA u v r X Y Z Vs



VPP NURBS AC72 AC45 1

Apparent wind Angle ( deg) True wind Angle (deg) Surge ( m ) Sway ( m ) Yaw ( Deg ) Force in the X direction ( N ) Force in the Y direction ( N ) Force in the Z direction ( N ) Vessel Velocity ( m/s ) Rudder angle (Deg ) Velocity Prediction Program Non-uniform rational basis spline Americas cup vessel Americas cup world series vessel

INTRODUCTION

The Americas cup race was conceived in 1851 with a challenger and defender format. Since then the format has changed many times over the years along with the Class rules. The Class rules are restrictive by nature which encourages teams to think outside the box and implement new and innovative solutions in order to gain an advantage over the other team, Australia II being the prime example of this[2]. Australia II used a radical new wing keel in order to gain an advantage over their American rivals with a very similar boat. For the purposes of this research project the second draft of the Americas Cup class rules was used as this was the latest draft available at the time. These rules dictate a radically new style of design, a 22m Catamaran with a displacement of 5400kg with a 38m tall wing sail [1]. This design is currently being trialled albeit in a smaller scale in the form of the AC World Series. The AC World Series is a competition between the nations for a chance

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to challenge for the Americas cup. Races are being held around the world using smaller versions of full-sized America’s cup race boats known as AC45’s. These AC45’s have a length of 13.7m, a beam of 6.9m and a displacement of 1600kgs. The AC World Series not only determines the challenger for the cup, it also serves to train the crews on how to deal with boats of this style. The results thus far are quite encouraging, AC 45s are sailing much faster than the wind when reaching and beating, producing very exciting racing. As with any type of professional yacht racing there has been a large amount of research performed into the performance characteristics of these boats by the teams involved in the race and to a lesser degree by inspired amateurs. Due to the competitive nature of the Americas cup this research is not in the public domain, however the GPS data for all AC45 World Series races and practice sessions are available on the Americas cup website. This data was used to validate the results of a stationary VPP and tune the coefficients of lift and drag for the sails.[2] The objective of this research project was to explore the manoeuvring characteristics of the AC72’s as they currently are and explore different methods of making them turn at greater rates and at greater speeds. Currently the AC72 rules allow for a 1.5m span rudder with a limit of motion of 10 degrees either side of the centreline. The first method investigated was the effect of varying the projected area of the rudder whilst keeping the chord length the same. These results were then collated and recommendations made based on which vessel configuration results in the highest performance in terms of distance travelled to windward after a set amount of time. In order to test these manoeuvring characteristics the program Futureship was employed. This program has both a stationary solver and an instationary solver. The stationary solver was used to check the validity of the

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Trans RINA, Vol 155, Part B1, Intl J Small Craft Tech, Jan-Jun 2013

simulation against published AC45 data and the instationary solver was used to assess the manoeuvring characteristics of these vessels and determine any possible performance gains. 2

BACKGROUND

Performance prediction of racing yachts has been around for a very long time. Due to the large amount of money involved in performance racing and the relative importance of very slight efficiency gains this has driven a lot of the research in to the fields of resistance, sail aerodynamics and any other field that could be an advantage. However, none of these areas operate in isolation so it is necessary to consider all aspects when determining performance. The result of this is the creation of the VPP or velocity prediction program as a tool used in order to predict performance in different environmental conditions.[3] Velocity prediction programs (VPP’s) can be broken up into two distinct categories, steady state or instationary [4]. FS equilibrium contains both of these types of VPP. For the purposes of this research project the stationary solver was used to assess the performance of the simulation when tested against real world data and the instationary simulation was used to assess the manoeuvring options. Steady state VPP’s “freeze” the vessel at an instant in time and using the assumption that there are no accelerations acting on the vessel, i.e. the model is balanced, the forces acting on the vessel cancel out. Hence, if the resistance and righting moment data are known a leeway and heel angle can be calculated for a given wind direction (relative to the vessel). Then resolving all the known forces, a force in the direction of travel of the vessel can be determined. This in combination with resistance data can then be used to determine the forward speed. Using this approach polar plots can be generated that can be used to determine a vessels theoretical speed from a given wind direction and speed. [5] Instationary VPP’s are a progression of the steady state VPP. Instationary VPPs operate on a principal similar to the steady state VPP by computing the forces acting on the rig and hull. These forces are then used to determine the velocity of the vessel using a time stepping algorithm in combination with the equations of motions [6]. The instationary VPP contained within Futureship was used in this research project in order to predict the performance of an AC72 during a round up manoeuvre. During any performance analysis it is necessary to know the resistance of the vessel. For this research project slender body theory was used. Slender body theory was formulated by Ernie Tuck [7] using work done by Michell in 1898. This method computes the wave resistance of a slender symmetrical mono hull that is

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operating in the displacement regime. This method was used to determine the resistance of the AC72 and AC45 hulls. There are several ways to predict added mass coefficients and damping coefficients of a hull including full scale measurements, model experiments, empirical formulas developed by Clarke and Lewis transformations. For the purpose of this research project the author used strip theory and conformal mapping as developed by Lewis and Clarke [8] .This method determines the coefficients by integrating two-dimensional sub domains along the length of the hull [6]. As the title implies this method is only valid for slender bodies but has had some success predicting the coefficients in performance racing yachts[5]. FS_Equilibrium is a velocity prediction program developed by Futureship a GL company and used internationally for the performance prediction of sailing yachts[5]. The manoeuvring simulator has also been used successfully to predict the manoeuvring of powered craft. It works by using a quasi-steady instationary analysis using Runge-Kutta methods to step forward in time.[9]. It uses the hydrodynamic models described later in this document and a module based system to represent the external forces acting on the vessel such as the force from the sails and the resistance of the hull. Each of these modules operates independently of each other as mini force calculators in their own right. The forces determined by these modules are then output to the main program in the form of a force in each of the principle directions and a moment about each of the principle axes. These forces are then summed in order to determine the total forces acting on the vessel. Using this information and the equations of motion the simulation is stepped forward in time. 3

MANOEUVRE

For the purposes of this investigation the selected manoeuvre is the round up. This manoeuvre starts with the vessel sailing down wind at a TWA of 120 degrees at a constant speed of 7m/s. This would be indicative of a vessel approaching the bottom mark preparing to round up. A rudder movement is applied to starboard to cause the vessel to start to turn to port. As the vessel comes round to a wind heading of 30 degrees the rudder is returned back to close to its original position and the vessel continues to advance on this heading, this is illustrated in Figure 1. For the purpose of this simulation it was assumed that all necessary sail changes have been made before the manoeuvre is started. This can be one of the most important manoeuvres in a race because it is generally one of the last manoeuvres performed before the finish line.

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Trans RINA, Vol 155, Part B1, Intl J Small Craft Tech, Jan-Jun 2013

AC45’s, this was used to compare against published data and test the sail coefficients. The lift and drag coefficients were taken from a NACA 0012 series foil then these were adjusted to correlate with the AC45 race data.

Figure 1 Round up manoeuvre 4

DESIGN METHODOLOGY

Due to the competitive nature of Americas Cup racing it is not possible to obtain information on the hulls that will be used. To work around this it was decided to design within the box rules and apply some simple design methodology and basic Naval Architecture principals. The overriding goal of these boats is to go fast and ultimately win the race; to this end several design decisions have been made. The maximum allowable length is 22m (72ft)[1, Section B, 4.3] for resistance purposes it was decided to use this maximum length. The maximum allowable beam to the outside of the demi hulls is 14m [1, Section B, 4.5 ], it was decided to maximise this beam in order to maximise the righting moment. The beam of the demi hulls is limited by the inboard beam waterline which must be no less than 11.5m [1, Section B, 4.7 ]. This limits the beams of the demi hulls to 1.25m. It was decided to maximise the beam of these demi hulls in order to minimise to draft (for a constant displacement) which in turn minimises the angle at which a the vessel will fly a hull and the resistance loss from flying a hull is much larger than the gain from the increased demi hull beam. The displacement is limited to between 5200kg-5400kg [1, Section B, 4.10 ] the minimum displacement of 5200kg has been chosen. To simulate likely fairing of the hull the deepest point of the hulls surface is at the midpoint of the hull. This draft has been determined by the limiting displacement to be 359mm. the hull reaches its maximum beam at 11m fwd. of the stern and then continues at this beam all the way aft to the stern plate. The draft reaches its maximum amidships (11m fwd. of the stern plate) and reduces to 0 at both the bow and stern in a linear fashion. For the design of the sail the dimensions were mapped out using the AC72 class draft [1] and the prescribed area was taken from this document as well. In addition to the above design, a design was produced using the same design methodology that reflected the

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5

RESULTS

5.1

STATIONARY

The highly competitive nature of America’s Cup racing means that data regarding the attainable speeds of the AC72’s is impossible to obtain and the first boat was not launched till July 31st of 2012. In order to partially verify the accuracy of this simulation a model was created that accurately represented the AC45 Catamarans; this was then tested against varying wind speeds. These results were then compared to published speed trial GPS data of the AC45’s. For this comparison data from the Venice leg of the Americas Cup World Series was used. This data was chosen for several reasons, it gave a range of wind speeds that were of interest and the wind data was consistent in speed and direction. The AC45’s are very similar to the AC72’s in overall concept and the proportions are approximately to scale as shown in Table 1. Table 1 Principal Particulars Particular AC 45

AC 72

Lwl (m)

13.72

21.95

Beam (m)

6.9

14

Rig Height (m)

21.5

40

Displacement (kg)

1400

5700

85

260

Total sail area (m )

133

580

Construction

Nomex/prepreg

-

Crew

5

11

2

Wing area (m ) 2

In order to check the validity of this simulation polar diagrams were produced using the stationary solver and a simulation that accurately represented the AC45’s. These polar plots were then compared to publish GPS data from the AC45’s in order to determine if the results match closely. The results so far are encouraging Figure 2 shows a polar plot produced by FS_Equilibrium of an AC45 at a true wind speed of 8 knots. This polar plot is indicative of the limiting speeds of the AC45’s i.e. the fastest possible speeds they can attain in ideal conditions. The polar plot shows a typical racing yacht shape, namely an increase in speed between 180° and 120° as the spinnaker becomes effective and then another slight increase as the wing sail becomes most effective around 100°. When comparing to the published data, it can be seen the upwind speeds generated by FS_Equilibrium are

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Trans RINA, Vol 155, Part B1, Intl J Small Craft Tech, Jan-Jun 2013

Figure 2 Polar plot produced by FS_Equilibrium at 8 knots overlayed with AC45 Data race data taken from Venice on May 15th to 20th 70 90 110 130 150 170 -45

-50 4 3.5

Latitude (m)

-55

3 2.5

-60

2 1.5

-65

1.2 1

-70

0.9 -75

0.85 Longitude (m)

0.75

Figure 3 Positional plot of varying rudder sizes

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Trans RINA, Vol 155, Part B1, Intl J Small Craft Tech, Jan-Jun 2013

5.2

INSTATIONARY RESULTS

As stated earlier in this document the manoeuvre for this simulation consists of a round up manoeuvre as shown in Figure 1. For the purpose of this simulation when time = 0 the vessel is at a longitude of 0 and a latitude of 0. At time equals to 15 seconds a rudder angle is applied and the vessels begins to turn around the marker at position 1 To determine the effectiveness of varying the rudder size the simulation was run with varying rudder lateral and wetted surface areas. In order to make the result comparable the chord length was kept constant and the span was adjusted. This was done primarily because the thickness is determined by structural reasons and the chord is determined by the thickness in order to keep a constant section shape and thickness ratio. The various sizes are shown in Table 2. Table 2 Varying rudder results

Rudder area (m2) 0.75 0.8 0.9 1 1.2 1.5 2 2.5 3 3.5 4

Time (s)

Long (m)

35.02 34.99 34.87 34.61 34.69 34.82 35.18 35.45 35.72 35.99 36.35

199.25 197.41 197.41 196.53 197.3 195.69 194.71 193.34 191.94 190.56 189.26

A plot of the tracks of vessels with the various rudder sizes is shown in Figure 3 and a table showing the time taken to return to the zero latitude position is shown in Table 2.

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From Figure 3 it can be seen that the larger rudder is causing the vessel to turn tighter however the tightness of the turn needs to be weighed against the speed loss created by the increased resistance of the larger rudder. This is quantified in Table 2; this table shows the relative positions and times that the vessel reaches the 0 latitude point again after the manoeuvre. This shows that the vessel with the 1m2 rudder reaches the same latitude faster than the vessels with the larger rudders. The rudders that are smaller than 1m2 have also caused the vessel to turn slower. It was noted by the author that the rudders smaller than 1m2 required a much higher variation in angle of attack in order to steer a straight course than the larger rudders. This increased operation means that the smaller rudders were again creating more drag than the 1m2 rudder and hence slowing the vessel. Rudder sizes smaller than 0.75m2 were tested but it was found to be very difficult to get the vessel to sail in a straight line and hence were not included in this analysis.

Time (s)

very close to that produced by the AC45. Between the angles of 20 and 40° the simulation is very close to the maximum recorded speeds. Futureship is very slightly under predicting the speed at angles of attack between 160° and 140°. Another useful conclusion that can be gained from this data is that these boats do the predominant amount of their sailing at very low and very high TWA’s; this is consistent with match racing. At angles greater than 40° Futureship appears to be overestimating the attainable speeds. This may be due to a lack of data in this region, but is more likely due to the coefficients of lift of the sail being too high, this could possibly be corrected with further research however for the purpose of this research project accuracy at headings of 40 and 120 are much more important.

36.6 36.4 36.2 36 35.8 35.6 35.4 35.2 35 34.8 34.6 34.4 0

2

4

Rudder Projected area

6 (m2)

Figure 4 Varying rudder size against time to return to 0 latitude If the times to return to the zero latitude mark are plotted against rudder area (Figure 4) it is possible to see a potential for optimisation. For this manoeuvre, with this boat the optimum rudder size is a lateral area of 1m2. This rudder size will be used to compare against other manoeuvring options. The curve of the data is not exactly smooth this is due to the smaller rudders having difficulty getting the vessel on the correct course after the manoeuvre. This error could possibly be reduced if the PID controller that was used were to be tuned finely to each rudder simulation however in order to make the results comparable this was not done. The rudder sizes larger than 1m2 show a linear trend in time to reach the zero latitude mark this is consistent with the increase in drag caused by the greater wetted surface area.

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Trans RINA, Vol 155, Part B1, Intl J Small Craft Tech, Jan-Jun 2013

THE PURE DRAG RUDDER (P.D.R)

The overriding goal of this research was to optimise the hydrodynamic turning forces in terms of maximising the performance of these vessels. Up until this point the methods explored were conventional. From this point forward this paper will focus on an unconventional method proposed by Doctor Jonathan Binns. The pure drag rudder takes the form of a retractable flat plate orientated perpendicular to the flow of water along the hull. The plate or P.D.R would be extended vertically out of the bottom of the inside hull of the turn, this will create large amounts of drag force on that hull. Causing the vessel to pivot about this hull and hence turn with a much smaller radius. The design of this P.D.R was determined primarily by the need for it to be retracted back into the hull. To this end the same profile as the cross section of the hull is used for the lower edge of the plate and the width is determined by the width of the hull. Some optimisation of this design could be useful but is beyond the scope of this research project. To simulate the P.D.R for this manoeuvre the universal force module within Futureship was used. This module allows the user to describe a force in any direction as a function of a number of variables to do with the vessel. For this simulation the force in the x direction as a function of speed was calculated using the following equation. FD 

1 CD AV 2  2

(0.0.1)

The area for this plate was calculated using Rhinoceros to be 1.28m2. Density of the water was assumed to be 1025kg/m3 and a drag coefficient of 2 was used [10]. The velocity used in this equation is the velocity parallel to the hull (VX).

vessel to turn much faster and with a smaller radius, the final position of the vessel after the turn is also much further upwind (closer to the next mark or finish line) than that of the standard configuration. Being upwind is a tactical advantage because it allows the upwind vessel to control the race by sailing parallel to the downwind boat and ‘covering’ or by sailing closer to the downwind boat at significantly increased speed. Additionally the upwind boat can ‘cover’ the downwind boat, when he tacks, you tack and theoretically using this approach there is no possible way for the downwind vessel to gain distance on the upwind vessel, due to naturally occurring wind angle shift. The third advantage that can be gained from being upwind is the upwind vessel can influence the air the downwind vessel is getting. This so called dirty air can severely affect the performance of racing yachts.

HDG

-20

Position

-30

Latitude (m)

6

-40

-50

-60

-70

40

60

80

100

120

Longitude (m)

Figure 6 Position with heading for P.D.R Figure 6 shows the position of the AC72 during the flat plate manoeuvre as well as the instantaneous heading. As it can be seen during the manoeuvre the vessel is developing large leeway angles very quickly. In addition to this once the vessel has reached the desired heading and the plate has been retracted the vessel straightens out quite quickly and continues on its way, this is most likely due to a combination of the low weight of these vessels and the power generated by the wing sail.

Figure 5 Flat plate mounted behind daggerboard Figure 5 shows the relative positions of the standard configuration and the P.D.R configuration for a breeze of 8 knots. It can be seen that the plate is allowing the

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The overriding purpose of these boats is to win the race so whilst the tightness of the turn is important the position with respect to time is even more important. For this reason the preceding figures show the position of two boats through the round up manoeuvre, one with a P.D.R and one without (see Figure 8). At the start of the round up manoeuvre (fifteen seconds); both boats are in the same position and travelling at 7

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Trans RINA, Vol 155, Part B1, Intl J Small Craft Tech, Jan-Jun 2013

m/s. An instant after this point the plate is deployed from the vessel with the dashed trail.

degrees and is sailing with a steady leeway angle of 11 degrees. The vessel with the P.D.R is 8.5m to the stern of the vessel with the conventional rudder, this may seem like a disadvantage but the fact that the vessel with the P.D.R is at the desired heading means it can start to accelerate out of the turn and start gaining position to windward.

9 8 Velocity (m/s)

7 6 5 4 3

Conventional Rudder

2

P.D.R

1 0 0

10

20 30 40 50 Time (s) Figure 7 Velocities of both configurations during the manoeuvre At the 16.3 second mark the plate is retracted, the retraction point of the plate was tested thoroughly by the author of this paper and it was found that 16.3 seconds was the optimum time to retract the plate in terms of gaining distance to windward. The vessel with the plate has reached a heading of 90 degrees and has a leeway angle of approximately 60 degrees. This means the vessel’s velocity is mostly perpendicular to its heading; both the rudder and the dagger board have stalled a long time ago and as such are no longer producing lift. At time equals 18 seconds the vessel with the P.D.R has reached the desired heading of 30 degrees; however it still has a residual leeway from the P.D.R of 25 degrees. The vessel without the P.D.R has reached an angle of 98

At time equals 26 seconds (Figure 8) the vessel without the P.D.R has reached a heading of 30 degrees and is sailing at a steady leeway of 3 degrees. However it is a full boat length (22m ) behind the vessel with the P.D.R. The standard vessel is also a full boat length downwind this is a huge tactical disadvantage because it limits the skippers options in terms TWA and puts the vessel at a disadvantage in the tacking manoeuvre that will be performed later in the race. The vessel without the plate reaches the same latitude 4.9 seconds after the vessel with the plate. Figure 7 shows the relative forward velocities of the two vessels. It can be seen that the vessel with the plate experiences a speed loss from 7 to 3 m/s in a period around 1 second which is very significant; however the vessel regains this speed very quickly as well. This is most likely due to the very low mass of these vessels and the large power developed by the wing sail in comparison to the inertia of the vessel. The vessel without the plate experiences a small initial speed loss due to the drag of the rudder and then an increase as it goes through the turn. This increase is most likely due to the vessel passing through a more favourable TWA. This speed increase would obviously depend on the ability of the crew to trim the sail effectively and quickly but is not outside the realms of possibility.

Longitude 80

90

100

110

120

130

140

150

160

170

180

-10 -20

Latitude

-30 Conventional Rudder

-40

P.D.R -50 -60 -70 Figure 8 Positional plots of both configurations

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Trans RINA, Vol 155, Part B1, Intl J Small Craft Tech, Jan-Jun 2013

ACCELERATIONS

When considering the implementation of this pure drag rudder it is necessary to consider the effect this will have on the crew and the rig. The most direct effect of the pure drag rudder will be the accelerations imposed on the vessel during the manoeuvre. In order to assess the accelerations generated by the P.D.R it was necessary to determine the accelerations generated in the standard turn. The point where these accelerations were recorded was at the stern, this was determined to be the place where the greatest accelerations occur and is indicative of what the skipper of the vessel experiences. Figure 9 shows the result of these analyses. As can be seen there are some initial longitudinal accelerations due to the model settling down after the start of the manoeuvre. At the 15 second mark the rudder is put to an angle of 10 degrees causing an initial longitudinal deceleration due to the increased drag then a longitudinal acceleration due to more power being developed in the sail due to the more favourable wind angles. At the 21 second mark the longitudinal accelerations go negative again as the vessel slows down as it starts to go up wind. The lateral accelerations follow a similar trend. The largest lateral acceleration is experienced just after the start of the turn at the 15.3 second mark with a peak of negative 2.24 m/s2 caused by the stern accelerating to starboard due to the rudder. This acceleration drops off gradually as the leeway develops and the vessel settles into a steady turn. At the 22.8 second mark the acceleration becomes positive as the rudder is returned back to approximately centre and the vessel comes out of the turn. This then settles to approximately zero as the manoeuvre finishes. For the turn with the P.D.R the longitudinal and transverse accelerations are as per Figure 10.

Accelerations (m/s2)

5 0 0

20

30

40

Longitudinal acceleration Lateral accelerations

-10 -15 -20

Time (s)

Figure 10 Lateral and Longitudinal accelerations during pure drag rudder manoeuvre It can be seen that the accelerations are very large when compared to the standard configuration rudder but occur almost exclusively in the 6 seconds after the plate is deployed, a smaller timescale view of this is present in Figure 11. 5 0 14

16

18

20

22

-5 Longitudinal acceleration

-10

Lateral accelerations

-15 -20

1.5

10

-5

Accelerations (m/s2)

6.1

Time (s)

Acceleration (m/s2)

1 Figure 11 Lateral and Longitudinal accelerations during pure drag rudder manoeuvre

0.5 0

-0.5

0

10

20

40

Longitudinal acceleration Lateral accelerations

-1

-1.5 -2 -2.5

30

Time (s)

Figure 9 Lateral and longitudinal accelerations for standard rudder

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This enhanced view shows that the lateral and longitudinal accelerations are both negative the entire time the plate is deployed then jump to being positive when the plate is retracted. The lateral accelerations have another jump as port rudder is applied at the end of the manoeuvre to correct the leeway. The maximum acceleration is the lateral acceleration which peaks at – 15.94 m/s2 for a period of 0.02 seconds. For perspective this is as fast as the today’s fastest production cars accelerate [11]. The effect of these accelerations on the crew has yet to be quantified, however would most likely require them to be harnessed to the boat.

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Trans RINA, Vol 155, Part B1, Intl J Small Craft Tech, Jan-Jun 2013

For the purpose of this paper we can consider this as the highest estimate of acceleration due to a number of factors. Firstly this model assumes the plate starts acting the instant it is deployed, in reality the plate would take a finite amount of time to deploy and as such the build-up of the force would be much more gradual. Secondly the measurement point for these accelerations is at the stern and as such the largest lateral accelerations anywhere on the vessel are experienced at this point. Figure 12 shows the acceleration 2/3rds of the way up the mast for the pure drag rudder manoeuvre, as is to be expected the longitudinal accelerations remain the same but the lateral accelerations are much reduced. These accelerations are important to know because they have structural implications on the wing sail. 2 0 Acceleration (m/S2)

14

16

18

20

22

-2 -4 -6

Longitudinal acceleration

-8

Lateral accelerations

-10

Time(s)

Figure 12 Lateral and Longitudinal accelerations during pure drag manoeuvre at the mast 7

The P.D.R is very close to the surface and as such it is likely that during some of the more high speed manoeuvres the plate will cavitate or ventilate to the surface. This would have a significant effect on the resistance of the plate and the hull as well as the effectiveness of the rudder. This would obviously alter the effectiveness of the plate but the effect is likely to be limited to effecting the magnitude of the drag force [10]. The large leeway angles developed when using the pure drag rudder make it necessary to retract the plate much earlier than the vessel reaches desired heading. This leads to the problem of timing, for this manoeuvre with these set up conditions the ideal time to retract the rudder was found to be 16.3 seconds into the manoeuvre, when the vessel was at a heading of 90 degrees. This was as a result of performing the manoeuvre several times with exactly the same conditions and using trial and error with very accurate heading and leeway data. In reality, this data would not be available to skippers at the accuracy and speed required for this manoeuvre and the skipper will only get one chance at each manoeuvre. Deploying the plate for an extra 0.2 seconds leads to an overshoot 20 degrees at the end of the manoeuvre. 8

-12 -14

turn faster because of the lower added mass and damping. Changing any of the aforementioned parameters would affect the result significantly.

EVALUATION

The implementation of a pure drag rudder is a viable option for several reasons. Firstly the extreme beam of these vessels means they have very large righting moments and therefore can have a large sail area. This large beam also allows the plate to be positioned at a large distance from the centreline, increasing the turning moment without increasing the drag. The third reason is the lightness of these vessels, 5400 kg is a very small displacement for a boat of this length, this lack of weight means the vessels have a very low inertia meaning they can accelerate quickly and cancel out the penalty drag imposed by the plate. The fourth reason that makes this pure drag rudder a viable option is the high forces with respect to the inertia generated by the wing sail allows the vessel to accelerate quickly and reach very high speeds which increases the effectiveness of the plate. The final reason is the low resistance of the hull which is much smaller than the forces generated by the sails, daggerboards and rudders, this low resistance not only allows the vessels to attain high speeds it also means they

©2013: The Royal Institution of Naval Architects

CONCLUSIONS

Varying the rudder size lead to the conclusion that the rudder size could be optimised with respect to the quickest time to return to a specified latitude up wind of the marker. For this manoeuvre the optimum rudder size has a lateral area of 1 m2, any smaller and the rudder has trouble keeping the vessel going in a straight line and any larger the induced drag outweighs the increased straight line stability. In summary for the manoeuvre involving the P.D.R the vessel is initially travelling at a steady speed and direction then the plate is deployed, the vessel turns in, leeway rapidly develops, rudder and keel stall, leeway continues to develop, plate is retracted leeway slackens off, the rudder and dagger board catch, sail power develops and the vessel shoots forward. The implementation of the pure drag rudder results in 20m gain in position over a standard rudder and a tactical advantage of being tighter in the turn and higher to windward over the standard boat. The maximum accelerations acting on the crew and the rig during the round up manoeuvre with the standard configuration are 2.24 m/s2 transversely and 0.24 m/s2 longitudinally at the stern and 0.81 m/s2 transversely and 0.24m/s2 longitudinally at the mast respectively. With the implementation of the pure drag rudder these accelerations increase to 15.94 m/s2 laterally and 11.26 m/s2 longitudinally at the stern and 3.34m/s2 laterally

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11.26 m/s2 longitudinally for the rig, this may or may not present as a problem for structure or personnel. The implementation of the pure drag rudders as a total manoeuvring solution was also considered. This would involve the complete removal of the rudder and partially extending and retracting the plate on each hull whenever it was necessary to adjust the heading slightly. 9

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