22nd Australasian Fluid Mechanics Conference AFMC2020 Brisbane, Australia, 7–10 December 2020 https://doi.org/10.14264/2c425c2

Unsteady Aerodynamics of Turning Maneuvers in Olympic Class Sailboats

S. Morris1 and C.H.K. Williamson1

1 Sibley School of Mechanical and Aerospace Engineering Cornell University, Ithaca NY 14853, USA

Abstract The VMG is defined by the true wind angle (TWA), that is the angle between the true wind speed (TWS) and the boats speed In this research, we use a “sports-mimetic” approach to study over ground (SOG): unsteady sail motion techniques, inspired by the bodyweight motions of Olympic sailors as they maneuver their sailboats when racing. One such technique is for sailors to use body- VMG = SOG|cos(TWA)| (1) weight movements to roll the boat about its longitudinal axis. This motion is used especially when turning in light winds, by We take the absolute value of cos(TWA) such that VMG is pos- either “roll tacking” (upwind sailing) or “roll gybing” (down- itive for both upwind and downwind sailing. wind sailing). When roll tacking and roll gybing, sailors dy- namically roll the boat to propel their boats faster than using wind alone; this is in contrast to flat tacking and flat gybing, wherein the sailor keeps the boat level (and mast vertical) while turning. These motions are characterized in on-the-water ex- periments using an Olympic Laser and a 420 sailboat equipped with a GPS, IMU, wind sensor and GoPro camera array. We study the underlying vortex dynamics using these characteristic motions, along with full-scale flow visualization.

Keywords sports aerodynamics; vortex dynamics

Introduction Figure 2. (a) The velocity made good (VMG) is defined as the compo- nent of the boats speed (SOG) in the direction of the true wind (TWS). (b) The true wind angle (TWA) is the angle made by the TWS and SOG.

Experimental Methods Experiments are carried out on Cayuga Lake in Ithaca, NY, us- ing two different boats outfitted with custom built instrumen- tation: a full rig single-handed Olympic Laser sailboat, and a 420 two-person sailboat. These are sailed by various members of the Cornell Sailing Team. A chase boat is employed to fol- low the test boat, allowing us to capture images from a DSLR camera and to provide instruction to the sailors. Figure 1. Cornell Sailing Team member Ben Rizika performing a roll The boats’ motion on the water is characterized using a custom- gybe in an Olympic Laser Sailboat at Cayuga Lake in Ithaca, NY. built inertial measurement unit (IMU) [4]. The IMU is housed in a Pelican 1020 waterproof case and placed on the deck of Olympic sailboats range in size from small rockable boats, to the boat, directly in front of the mast. The heel (HEEL), heel larger keel boats. In small rockable sailboats, sailors can use un- rate, and heading (HDG) are captured at a rate of 50Hz, and steady sailing techniques to generate extra propulsion for their the boats GPS position, speed over ground (SOG), and bearing boat, as shown in figure 1. The majority of research to date into (BRG) are captured at 10Hz. For a full description of the IMU sailing turning maneuvers has been focused on large boats (e.g. and its capabilities, see Schutt and Williamson [4,5]. GoPro [1,3]). In this paper, we focus on turning maneuvers in small Hero5 Session cameras are placed on the deck of the boat near rockable sailboats, and examine the vortex dynamics of down- the cockpit, and at the top of the mast of the boat. A boom wind sailing. This follows the work of small sailboat aerody- mount is used when we want to capture the shape of the sail namics by Schutt and Williamson [4,5]. from below. Two of the parameters we measure in this work are the heel A Kestrel 5500 anemometer measures the TWS. The anemome- angle and heading angle of the boat. The heel of the boat mea- ter is located at the edge of the dock at the Cornell Merrill Sail- sures how much the boat is rolling about its longitudinal axis; ing centre, as close to our testing region as possible. In order to the heading is the direction the boat is traveling with respect to reduce the error of wind gusts traveling across the lake, we take true north. The “effectiveness” of how the boat is sailing is mea- an average of the TWS over the entire time period for each set sured via a parameter called “velocity made good”, or VMG. of tests. To ensure accuracy in calculating the true wind direc- The VMG is a measure of how quickly the boat is traveling in tion (TWD), we calculate the TWD based on the time-averaged the direction of the true wind, and is taken as the component of bearing (BRG) of the boat before and after a turning maneuver, the boats speed in the direction of the true wind (see figure 2). as described by Williamson and Schutt [7]. This is given by BRGpre−tack + BRGpost−tack TWD = (2) 2

This method relies on the expertise of the sailor to sail the boat correctly: the sailor will sail at the same relative angle to the wind in each direction immediately preceding and following a turning maneuver.

During testing, the sailor is asked to perform a combination of Figure 6. Sailor performing a roll tack in a Laser sailboat. flat tacks, roll tacks, flat gybes, and roll gybes. The sailor per- forms 10-20 of each maneuver, ensuring an even distribution of starboard to port, and port to starboard turns. Olympic Laser Sailboat

Tacking Results

Figure 3. Schematic of a boat performing a tack. As the boat tacks, it turns its bow through the wind, changing the direction the wind blows.

The first turning motion we investigate is “tacking”. Tacking is the way a sailor turns their boat while traveling upwind. A Figure 7. Results of a Laser undergoing a flat tack (blue) and a roll tack sailboat cannot travel directly into the wind, and so it travels at (red) in light wind (∼ 2kn). an angle to the wind (see figure 3). As the boat tacks, it turns its bow through the wind, changing the direction the wind blows Figure 7 shows the results of data collected of a Laser sailboat from one side of the boat to the other. This change in direction performing flat and roll tacks. Each set of data is an average of moves the boom to the other side of the boat, and the sailor can 10-12 tacks. continue traveling upwind as the boat sails across the wind. As one would expect, we observe a large variation in Heel be- tween the two types of tacks. Whilst the flat tack remains rel- atively level, the sailor can reach heel angles of more than 50◦ when roll tacking. The change in HDG (the measure of the boats direction) is similar in both cases. The important differ- ence we note is in the velocity made good. Whilst both the flat and roll tacks experience an increase in VMG as they enter the tack, after completing the turn the VMG of the flat tack signif- icantly decreases. This is contrast to the roll tack, where the sailor experiences a boost in VMG as they bring the boat back to vertical. This is beneficial for racing sailors, who want to sail in the direction of the true wind as quickly as possible. Figure 4. GPS data of a series of tacks performed in front of the Cornell Merrill Sailing Centre at Cayuga Lake. 420 Sailboat

The signature of tacking upwind is therefore a “zig-zag” pattern. Figure 4 shows our GPS data of a series of tacks performed in front of the Cornell Merrill Sailing Centre at Cayuga Lake. When a sailor is tacking, they can choose to perform either a “flat” tack, or a “roll” tack. When flat tacking, the sailor keeps the boat level (and mast vertical) while turning, as shown in figure 5. When a sailor performs a “roll” tack, they use their bodyweight to dynamically roll the boat through the turn, as shown in figure 6.

Figure 8. Results of a 420 sailboat undergoing roll tacks with a wind speed of 4.1kn (blue) and 5.7kn (red).

Figure 5. Sailor performing a flat tack in a Laser sailboat. In contrast to a Laser sailboat, a 420 sailboat is sailed with two sailors. Whilst for the Laser we compared flat and roll tacking, in the case of the 420 we examine the effect of sailing in two angle to the wind they would like to sail. Here, we look at different wind speeds: 4.1kn and 5.7kn. two types of gybes: a beam reach to beam reach (B2B) roll gybe in a Laser sailboat, and a downwind to downwind (D2D) Figure 8 shows the Heel and VMG recorded for the two dif- roll gybe in a 420 sailboat. The GPS trajectory of the boat is ferent wind speeds. Whilst both roll tacks result in large Heel vastly different between these two types of gybes, as shown in angles, we notice that the VMG of the boat stays below average figure 11. When performing a B2B gybe, the sailor is travelling for significantly longer in the higher wind. This is consistent nearly perpendicular to the true wind speed (TWS) immediately with results observed by Williamson and Schutt [7] for a Laser prior to and after the gybe. In contrast, the sailors remain nearly sailboat, wherein the VMG of a Laser performing roll tacks was parallel with the TWS when performing a D2D gybe. found to be substantially higher in lighter wind conditions. Olympic Laser Sailboat Gybing Results

Figure 9. Schematic of a boat performing a gybe. As the boat turns, the direction the wind blows changes from one side of the boat to the other, moving the boom across the boat.

The second turning maneuver we investigate is “gybing”. Gy- bing is the downwind counterpart to tacking: it is the way a Figure 12. Results of a Laser sailboat undergoing a beam reach to beam sailor turns the boat when the wind is coming from behind them, reach roll gybe. as shown in figure 9. As the sailor performs a gybe and the boat turns, the wind direction changes from one side of the boat to Figure 12 shows the results of a Laser sailboat performing a the other. Because of this, there will come a point where the B2B roll gybe. The SOG of the boat decreases as the sailor boat cannot turn any further without the wind getting behind heels the boat over, however increases back to its original speed the sail, moving the boom to the other side of the boat. Once as the sailor dynamically flattens the boat. the boom has crossed the boat, the boat can continue to sail downwind. Davison [2] describes the gybe as the hardest sail- It is interesting to note the large spike in VMG. As aforemen- ing maneuver to perform in a Laser. tioned, when sailing downwind, the sailor can choose the angle they make with the wind. In the case of a sailor performing a series of B2B gybes, the course of the boat is frequently not aligned with the true wind direction. As such, the TWA between the SOG and TWD vector is quite large. As the boat performs the gybe, the SOG will momentarily be in line with the TWD (TWA = 180◦). If we recall the equation for VMG, this will result in the second term (|cos(TWA)|) to become a maximum, corresponding with a peak in VMG.

420 Sailboat Figure 10. Sailor performing a roll gybe in a Laser sailboat.

As with tacking, when a sailor is gybing they can choose to perform either a “flat” gybe or a “roll” gybe. When roll gy- bing, sailors use their bodyweight to dynamically roll the boat through the turn to increase their speed, as shown in figure 10.

Figure 13. Results of a 420 sailboat undergoing a downwind to down- wind roll gybe.

Figure 11. (left) GPS with SOG vectors of a Laser performing a series In contrast to the Laser performing a B2B roll gybe, we now of beam reach to beam reach roll gybes. (right) GPS with SOG vectors examine a 420 sailboat performing a D2D roll gybe. As shown of a 420 performing a series of downwind to downwind roll gybes. in figure 11, the path of the D2D roll gybe remains almost per- fectly in line with the TWD, with only small fluctuations off When a sailor is sailing downwind, they can choose at what the downwind course. Because of this, the VMG very closely follows the SOG of the boat; the |cos(TWA)| term decreases only at the peak of the gybe, when the boat is pointed furthest from the TWD. This is reflected in figure 13. The heel of the boat reaches a maximum as the SOG reaches a minimum, and the SOG dramatically increases as the boat is brought back to vertical. The VMG follows this curve, quickly returning to its original value.

Flow Visualization A series of experiments were conducted using smoke flow vi- sualization. This technique is an effective means of visualizing flow dynamics, as described by Smits and Lim [6]. To create a smoke cloud big enough to see the large-scale flow features around the sail, we use an Enola Gaye WP40 Smoke Grenade. The WP40 is a wire-pull smoke grenade that generates a bril- Figure 15. (left) Flow visualization of a clockwise vortex form- liantly colored smoke cloud for 60-90 seconds. The smoke is ing around the leech of a downwind-sailing boat. (right) PIV of a ignited by pulling a ring at the top of the grenade: we can there- downwind-sailing sail, showing the same clockwise vortex around the fore trigger the grenade by hand from the chase boat, or re- leech (Williamson & Schutt [7]). motely via pulleys and strings on the mast itself. For gybing sailboats, the direction of the boat contributed greatly to the observed VMG. For sailboats sailing nearly per- pendicular to the wind in broad reach to broad reach gybes, a spike in VMG was observed at the point of the gybe where the boat was facing directly downwind. Using flow visualization, we also show the “signature” of a gybing sailboat. A counter- rotating vortex pair is formed from the combined motion of heeling and flattening the boat, and observed in full-scale smoke flow visualization.

Acknowledgements We would like to thank the following members of the Cornell Sailing Team, Ben Rizika, Clark Uhl, Gabby Rizika, and Gabbi DelBollo. Clark Uhl, Alex Bebb, and Thomas Balk helped in the laboratory. Many thanks to Phillipe Williamson for use of his Laser, and the Cornell University Merrill Family Sailing Figure 14. (left) A vortex is formed on the outside of the sail as the Centre for use of their facilities and chase boats. sailor heels the boat over in a roll gybe. (right) A vortex of opposite sign forms on the new outside of the sail, as the sailor flattens the boat. References

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