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The aerodynamics of symmetric spinnakers
ARTICLE IN PRESS
Journal of Wind Engineering and Industrial Aerodynamics 93 (2005) 311–337 www.elsevier.com/locate/jweia
The aerodynamics of symmetric spinnakers William C. Lasher, James R. Sonnenmeier, David R. Forsman, Jason Tomcho The Pennsylvania State University at Erie, The Behrend College, Erie, PA 16563-1701, USA Received 11 March 2004; received in revised form 7 January 2005; accepted 23 February 2005 Available online 2 April 2005
Abstract Twelve parametric spinnaker models were built and tested in a wind tunnel. In these models, five sail shape parameters were varied—cross-section camber ratio, sail aspect ratio, sweep, vertical distribution of camber, and vertical distribution of sail width. Lift and drag forces were measured for a range of angles of attack, and the results were analyzed for three points of sail. It was found that low sweep (more vertical) spinnakers are faster than spinnakers with high sweep, and that the optimum camber ratio depends on both the point of sail and aspect ratio of the sail. On a run (sailing directly downwind), the only significant geometric parameter is projected sail area. The implications of these results to sail trim are discussed. A description of the sail shapes and corresponding force coefficients is presented for future validation of Reynolds Averaged Navier-Stokes simulations of spinnaker flow fields. r 2005 Elsevier Ltd. All rights reserved. Keywords: Sail aerodynamics; Spinnaker aerodynamics; Downwind sailing
1. Introduction A sailing boat can sail at various angles to the wind, from about 401 to 1801. The approximate angle between the boat and the wind is referred to as a point of sail, as shown in Fig. 1. When a boat is sailing either upwind or on a close reach, the sails are pulled in tight to the boat and are relatively flat, so they act very much like Corresponding author. Tel.: +814 898 6391; fax: +814 898 6125.
E-mail address: [email protected] (W.C. Lasher). 0167-6105/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2005.02.001
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Nomenclature A sail area ANOVA analysis of variance AR aspect ratio AWA apparent wind angle CD drag coefficient, D/(0.5rV2A) C Df frictional drag coefficient C Din induced drag coefficient, C2L/(p AR) C Dp pressure drag coefficient, C D C Din C Df CFD computational fluid dynamics CL lift coefficient, L/(0.5rV2A) CT thrust coefficient D aerodynamic drag DOE design of experiment IMS International Measurement System L aerodynamic lift r air density RANS Reynolds averaged Navier-Stokes S sweep V air velocity
Wind
Upwind
Close Reach
Beam Reach
Broad Reach
Run
Fig. 1. Points of sail.
traditional airfoils. In these conditions, the flow over the sails is mostly attached, and traditional inviscid aerodynamic theory can be used. For example, Milgram [1] first employed panel techniques to this problem with some success. More recently, researchers have been using vortex particle methods [2] on this problem. When the wind is at approximately 901 (beam reach) or further aft (broad reach or run), the sails used for upwind sailing become very inefficient, so sailors use a spinnaker (Fig. 2). Spinnakers can be either symmetric (Alinghi) or asymmetric (Team New Zealand). Asymmetric spinnakers are more efficient at low angles (for example, when beam
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Fig. 2. Alinghi leads Team New Zealand on a run in the final race of the 2003 America’s Cup.
reaching), while symmetric spinnakers provide a broader range of application. At most sailing angles the flow over symmetric spinnakers is largely separated, so inviscid techniques do not apply [3]. As a result of the separated flow, the options for analyzing spinnakers are limited to full scale testing, wind tunnel testing, or computation using Reynolds-Averaged Navier Stokes (RANS) simulation. The difficulties associated with each of these techniques are detailed by Lasher [4]. For example, Milgram et al. [5] and Masuyama and Fukasawa [6] ran careful experiments on full-scale sailing dynamometers, but due to the problems associated with making accurate measurements and with fluctuations in sailing conditions, their data show an excessive amount of scatter in force coefficients (a standard deviation of approximately 13% of the mean). Wind tunnel testing, while highly controlled, suffers from well-known problems such as blockage and lack of true similitude, as well as sailing-specific problems due to the fact that boats sail in an atmospheric boundary layer [7,8]. While RANS simulation is rapidly maturing as a technology, there are still problems associated with turbulence modeling, and to date there has been little validation of RANS models appropriate for spinnaker aerodynamics. Until recently, little has been published on downwind sail aerodynamics, largely as a result of the problems outlined above. The information that is currently available in the literature does not allow for a fundamental understanding of the aerodynamics of spinnakers, often due to the proprietary nature of the work. Fallow [9] reports that over 300 model sails were built and tested for the America’s Cup, but does not provide data. Ranzenbach and Mairs [10] tested 23 different sails and reported force coefficients but not sail geometry. Ranzenbach and Teeters [11] tested five different sails flying under different conditions and describe the basic sail, but do not provide detailed geometric data. Other researchers have done either experimental or computational work on downwind sail aerodynamics, including Flay and Vuletich [7], Hedges et al. [12], Richards [3], Caponnetto et al. [13], and Richards et al. [14],
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but these have all been for a single sail configuration, and thus do not allow for an understanding of the effect that sail shape has on performance. In an effort to address the deficiency in published data, wind tunnel experiments were performed on a parametric series of symmetric spinnaker models. The models are small, rigid sails tested in isolation (that is, they were positioned in the center of the tunnel without other sails). Using rigid sails allows for a highly controlled experiment where one shape parameter can be varied at a time, providing an understanding of the impact that each parameter has on performance. Testing the models in isolation ensures that the results are uncomplicated by interactions with the water surface or with other sails. While these conditions are different than what is actually seen by a boat on the water, it allows for study of the aerodynamics of the spinnakers isolated from other issues, including the complex fluid-structure interaction of the spinnaker with the wind. In this paper, the aerodynamic objectives of downwind sailing will first be discussed, followed by an overview of how spinnakers are flown. The construction and testing of the models will then be detailed, followed by the results and discussion. The objectives of the work are to enhance the understanding of the basic aerodynamic issues regarding symmetric spinnakers, and to develop a database of force coefficients that can be used for validation of RANS simulation.
2. Aerodynamic objectives of downwind sailing In upwind sailing, as in traditional aerodynamic applications, the objective is to maximize the lift to drag ratio. This is not the case in downwind sailing, where the aerodynamic objective depends on the point of sail. For example, consider the three points of sail shown in Fig. 3. In all cases the goal is to maximize the driving force (the force component in the direction of motion of the boat) and minimize the side force (the force component perpendicular to the direction of motion of the boat).
D
L
L
D Wind
D
L driving force Wind Wind
side force Fig. 3. Aerodynamic forces in downwind sailing.
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For a boat on a run, this means maximizing the drag and minimizing the lift, which is the exact opposite of the goal in upwind sailing. The sailor will adjust (or trim) the sail to achieve maximum driving force. When a boat is on a broad reach, the lift and drag forces are of approximately the same magnitude, so maximum drive occurs at the point of maximum total force. This corresponds to a very small side force, since the lateral components of lift and drag approximately cancel. For a boat on a beam reach, the goal is to minimize the drag for a given lift, or to maximize the lift for a given drag. This is not exactly the same as maximizing the lift to drag ratio. For example, consider two sails A and B. Sail A might have a slightly lower lift to drag ratio than sail B, but at the same time generate a significantly larger driving force. In this case, assuming the boat is not overpowered, one would select the shape of sail A for more power, even though the lift to drag ratio is lower than sail B. Note that in real sailing conditions there is an interaction between the spinnaker and the mainsail, and that the objective is to optimize total performance, not just the performance of the spinnaker. For example, on a run the mainsail will partially block the flow of air to the spinnaker, so it is important to trim the spinnaker in such a way as to minimize the impact of the mainsail. This may result in a spinnaker trim that is different than what would be desired if the spinnaker were flying in isolation, and will be discussed later. On a broad reach sail there is still some interference from the mainsail, but it is relatively small, so the spinnaker is trimmed about as it would be if the mainsail were not present. When a boat is on a beam reach, the wind is far enough forward that the mainsail does not have a significant adverse impact on the spinnaker.
3. Primer on spinnaker flying The shape of a flying spinnaker is determined by several factors—the dimensions of the rig (determined by the boat designer); the shape of the cloth panels (determined by the sailmaker); and adjustments made by the sailor on the boat. While all three factors are important, the first two are highly controlled and produce an envelope of shapes in which the sail will fly. The third factor is more open-ended and a complete understanding of spinnaker aerodynamics requires a knowledge of what adjustments can be made on the boat, and what impact they have on sail shape. The basics of spinnaker trim will be outlined here; the reader interested in more details should refer to one of several excellent references on sail trim, such as Whidden and Levitt [15]. The basic setup for a spinnaker is shown in Fig. 4. The top (head) of the sail is attached to the mast. The windward corner (tack) is attached to a line (guy) that runs through a spinnaker pole, then to the side of the boat. This pole can be rigidly positioned through the use of the guy and other lines attached directly to the pole, and can be adjusted both fore and aft, and up and down. The third corner (clew) is attached to another line (sheet) that runs to the back of the boat. The clew is free to
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Head
Leech Spinnaker
Luff
Mainsail Foot
Clew
Tack
(Behind Mainsail)
Sheet
Pole Guy
Fig. 4. Controls for a spinnaker.
float up and down depending on the location of the spinnaker pole and the pressure on the sail. For a given setting of the guy and sheet, the spinnaker will settle to an equilibrium position. This is one of the factors that makes spinnaker aerodynamics so complicated—the shape of the sail depends on the pressure distribution, which in turn depends on the sail shape. The basic rules of spinnaker trim are as follows: the pole is set approximately perpendicular to the wind, and at an elevation where the tack and the clew are at approximately the same height. The sheet is eased (the sheet is let out and the clew is allowed to move forward) until the leading edge (luff) of the spinnaker starts to curl over (see Alinghi in Fig. 2), which generally corresponds to the angle of maximum lift. By adjusting the pole position forward or aft, the angle of attack of the sail relative to the wind can be changed, as well as its camber. Pulling the pole aft spreads the tack and clew apart and flattens the cross-section of the sail and increases projected area. The shape of the sail can also be affected by adjusting the vertical position of the pole. When the pole is brought down, tension increases in the luff and leech (trailing edge), which causes the edges to come together and increase the camber, slightly reducing projected area. A lower pole also reduces the vertical
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curvature of the sail which increases projected area. Generally the reduction in vertical curvature causes a greater increase in projected area than the decrease in projected area caused by the increased camber; however, if the pole is lowered too far there can be a net decrease in projected area.
4. Development of the experimental models Initially, a series of eight rigid parametric spinnaker models (see Figs. 5–7) were built and tested according to the theory of statistical Design of Experiments (DOE) [16]. The details of this initial experiment and the results are discussed by Lasher et al. [17]. Three sail shape parameters were varied in these models—camber ratio (camber at the bottom, or foot, divided by chord at the foot), aspect ratio (AR, length of the vertical centerline divided by length along the foot), and sweep (S, the vertical angle between the head and the centerline at the foot). The three parameters (or factors) were varied at two levels—a minimum value and a maximum value, which were selected to encompass the expected range of values typically found on actual boats. The results from this initial set were analyzed using Analysis of Variance (ANOVA) to determine if the performance of the sails (the lift and the drag coefficients) was affected in a statistically significant way by the variation of the three sail shape parameters. If so, this would indicate that there was some functional dependence of sail performance on the parameters. The ANOVA was based on a confidence interval of 95%, and showed that a difference of less than approximately 3% in the force coefficients for a given sail parameter was statistically insignificant and cannot be distinguished from experimental error over the range of values of the parameter tested. This would indicate that performance did not depend on the parameter over that range. In the original analysis, which was limited to a boat sailing on a run, the results of the ANOVA showed that aspect ratio was not a significant parameter over the range of aspect ratios tested. This is due to the fact that aspect ratio is only a concern if there is induced drag due to lift, and lift is absent on a run. Following the initial testing four additional models were built to extend the range of the models, as well as to investigate two additional parametric variations, radius of curvature variation of the sail camber line up to the sail shoulder, and shoulder width, as discussed below. The analysis was also extended to include broad and beam reaching. The spinnaker model shape was designed not so much to duplicate exactly what is found in a real spinnaker, but to allow for controlled parametric variation of shapes that are characteristic of spinnakers. First, an elliptical arc was created to form the centerline of the spinnaker when viewed from the side (Fig. 5). This arc is vertical at the foot and has an angle of 201 from the horizontal at the head. The dimensions of the centerline arc, along with the major and minor axis of the ellipse, were determined based on the spinnaker area, aspect ratio, and sweep angle. All spinnakers were designed with the same surface area. Next, a circular arc of the specified camber ratio was created at the foot (Fig. 6). This arc was swept along the
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20°
Shoulders Sweep Angle
Fig. 5. Side view of model.
Shoulders Foot
Fig. 6. Foot view of model.
ellipse, with the arc remaining perpendicular to the ellipse. For all but model 11 the arc radius of curvature increases linearly from foot to head. The radius of curvature at the shoulders, which are located 45% of the centerline arc length from the head, is
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Shoulders
Fig. 7. Sample spinnaker geometry.
twice the radius at the foot (radius ratio ¼ 2). For model 11 the radius of curvature was held constant from foot to head (radius ratio ¼ 1). For all but model 12 the halfwidth of the spinnaker is constant from the foot to the shoulders, tapering to zero at the head. The rate of taper was determined by passing a cubic polynomial from the shoulders to the head, with the polynomial tangent to the half-width line at the shoulders. For model 12 the half-width at the shoulders was 80% of the half-width at the foot. An isometric outline of one of the models is shown in Fig. 7, and the parameters are summarized in Table 1. All twelve models were constructed in Pro/ENGINEER, a solid modeling package. The models are 0.11 in. thick and a support structure for mounting the model to the wind tunnel dynamometer was built into the back of the model at the center. The nominal area of the spinnakers (centerline arc length times foot arc length) is 37.3 sq. in., and the actual area is 31.3 sq. in. The physical models were then built using a Z-402 three-dimensional printer. This technology prints a binder on a thin (0.003 in.) layer of plaster, building layer after layer, creating a solid three-dimensional model. After printing and drying, the models were infiltrated with urethane to provide additional strength. Due to the low Reynolds number of the tests, the models were intentionally left rough to stimulate turbulence. One of the models was scanned on a three-dimensional Roland LPX-250 laser scanner and compared with the Pro/ENGINEER model. The maximum difference between the physical model and the Pro/ENGINEER model was less than 0.009 in. (about 0.1% of maximum camber). A model was also photographed in the wind tunnel at the test speed, and the deflection of the
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Table 1 Model parameter combinations Model ]
Camber ratio at foot
Aspect ratio
Sweep angle (deg.)
Radius ratio
Shoulder/foot ratio
1 2 3 4 5 6 7 8 9 10 11 12
0.25 0.45 0.25 0.45 0.25 0.45 0.25 0.45 0.15 0.25 0.25 0.25
1.4 1.4 2.0 2.0 1.4 1.4 2.0 2.0 2.0 2.0 2.0 2.0
33.69 33.69 33.69 33.69 21.80 21.80 21.80 21.80 21.80 11.30 21.80 21.80
2 2 2 2 2 2 2 2 2 2 1 2
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8
model was measured. The change in camber ratio due to model deflection was less than 1%.
5. Experimental procedure The models were tested in an Engineering Laboratory Design (ELD) open-circuit wind tunnel. The test section is 2400 2400 , with a length of 4800 . The forces were measured with an ELD 2-component beam dynamometer, which was mounted approximately 1200 downstream of the leading edge of the test section, and corrected for tare. The dynamometer was calibrated using dead weights, and calibration error was estimated to be negligible. The models were located in the center of the test section, and were supported from the rear with a rod approximately 500 in front of the dynamometer to minimize the influence of the mounting fixture (Fig. 8). The models were tested at a nominal velocity of 84 ft/s. This corresponds to a Reynolds number based on the square root of the area of 197,000, and an apparent wind speed of approximately 1.4 knots on a spinnaker for a typical 24 foot boat, such as a J-24. The velocity was measured using two pressure ports in the wind tunnel walls upstream of the test section. The pressure difference was measured with a differential digital pressure transducer with a resolution of 0.01% of full scale, and was calibrated with a water manometer. The total error in measured velocity was estimated to be less than 2%. Since the flow is unsteady due to separation, the lift and drag forces were averaged over a period of 30 s. Blockage corrections were not made for three reasons. First, the model surface area is less than 512% of the wind tunnel cross-sectional area, so blockage effects were assumed to be small. Second, since the primary objective of the present work is to compare force coefficients for different sail shapes, it was not necessary to make
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Fig. 8. Model mounted on dynamometer.
blockage corrections. Third, since one of the objectives is to build a database of force coefficients that can be used for CFD validation, it is preferable to have uncorrected data, since it is computationally easier to mesh a small contained area than to apply infinite domain boundary conditions. Due to the small size of the supporting mount (approximately 0.3% of the total sail area) and location of the support relative to the model (in the separated flow region behind the sail), interference effects were also assumed to be small. These assumptions were assessed by building three models of different sizes—one at the nominal size, one with an area 21% larger than nominal, and one with an area 46% larger than nominal. Lift and drag coefficients CL and CD for each of these models were calculated, and the variations were within experimental error (less than 3%) except close to the stall point. These results indicate that blockage was not a factor, and since the supporting structure was the same size for each model, that interference was not significant. Additional tests were run to assess repeatability and the impact of Reynolds number on force coefficients. The repeatability was generally very good (less than 1% difference in measured forces between two runs). One of the models was run at five different nominal velocities ranging from 29 to 164 ft/s. Over this range the force coefficients at a given angle of attack were approximately constant (a variation of less than 5%), with no evident trend in the data. The models were mounted with the spinnaker centerline horizontal, since the dynamometer measures the lift in the vertical direction. In this orientation, the models created a side force that resulted in a significant measured component in the lift direction due to the design of the dynamometer. This was eliminated by
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testing the models twice, with the head pointing in alternate directions, and averaging the results. The cross-talk between side force and drag could not be eliminated in this experiment, but was neglected since it was less than 3%. The crosstalk between lift and drag was less than 1%, and was also neglected. For the bulk of the testing, each of the models was mounted in both sideways orientations at angles of attack ranging from 901 to 351 in increments of 51, with 901 being the condition for a run. The angle of attack is defined as the angle between the incoming free stream and the chord line of the model at the foot. The error in measuring angle of attack was estimated to be less than 0.51. In the final analysis, angle of attack is not a critical factor, since the important parameter is lift-drag ratio; however, the angle measurement can introduce some error since the models had to be set at identical angles for each of the two orientations.
6. Results Initially, model ]1 was tested at angles of attack from 901 to 01. Since the models are rigid they are capable of producing lift at all angles. This is not true of a real spinnaker, which would collapse at angles significantly less than about 351, so only model ]1 was tested to zero degrees. The lift and drag coefficients are shown as a function of angle of attack in Fig. 9. The lift shows a characteristic drop due to stall at approximately 451, with a somewhat smaller drop in drag. This drop in drag, which has not been evident in other force data for spinnakers found in the literature, can be explained as follows. The induced drag for an elliptically loaded wing is given by the following equation, and is also shown in Fig. 9: C 2L . p AR This formula does not strictly apply to spinnakers, since they are not elliptically loaded, but provides an estimate of the induced drag. Also shown in Fig. 9, the pressure (or form) drag coefficient C Dp ; which is the total drag coefficient minus the induced drag coefficient C Din and the skin frictional drag coefficient C Df : In spinnaker aerodynamics the frictional drag coefficient C Df is small compared to the other two components and can be neglected. The drop in induced drag at stall parallels the drop in total drag, and the pressure drag curve is approximately constant in this region. This shows that the drop in drag can be attributed to a drop in the induced drag, corresponding to the drop in lift. The lift and drag coefficients are replotted in Fig. 10 as a lift-drag polar, which is more useful for sailing analysis. In this figure, a 901 angle of attack corresponds to the point of maximum drag and zero lift. As the angle of attack decreases, the drag for model ]1 slowly decreases until it reaches a local minimum at an angle of attack of about 501, followed by an increase in both lift and drag. This ‘‘bump’’ in the polar is due to the increase in induced drag described above. This characteristic that has not been evident in other lift-drag polars found in the literature for spinnakers, such as the data from Richards et al. [14], although there is a similar but smaller bump in C Din ¼
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Model #1 force coefficients 1.4
Force coefficient
1.2 1 0.8 0.6 0.4 0.2 0 0
20
40 Angle of attack
60
80
Legend: Lift coefficient, CL Drag coefficient, CD Induced drag coefficient, CDin = CL2/(π•AR) Pressure drag coefficient, CDp = CD - CDin Fig. 9. Force coefficients for model ]1.
the polar for a single mainsail as reported by Marchaj [18]. This effect is less pronounced in the data for sails with higher aspect ratio due to a lower induced drag, which has implications in terms of performance when reaching, as will be discussed later. In general the magnitude of the force coefficients in Fig. 10 are consistent with those published in the literature. For example, at zero lift coefficient, van Oossanen [19] reports a value for the International Measurement System (IMS) spinnaker drag coefficient of 1.10, and Richards et al. report a value of 1.12. These drag coefficients compare well with the present data, which range from 1.06 to 1.36. The differences between the present results and those previously published can be reasonably attributed to differences in spinnaker geometry. It can be shown that the point of maximum driving force for a given sail can be determined by locating the point on the polar diagram where a line drawn perpendicular to the apparent wind angle is tangent to the polar curve. For example, on a run the apparent wind angle is 1801, so the perpendicular line would be vertical, and the point of maximum driving force would be the zero lift point (i.e., the sail angle of attack would be 901). For a broad reach, the apparent wind angle is 1351, so the line is tangent to the polar curve at the point of maximum total force. On a beam reach, the apparent wind angle is 901, so the line would be horizontal, corresponding
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Model #1 polar 1.5
broad reach
beam reach
1.2
CL
0.9
0.6
0.3 run 0 0
0.3
0.6
0.9
1.2
1.5
CD Fig. 10. Polar diagram for model ]1.
to the point of maximum lift. Each of these three lines is shown in Fig. 10, and the optimum point corresponds to the optimum aerodynamic condition discussed earlier. Note that at the optimum condition for a broad reach for model ]1, the lift coefficient is approximately 1.2, and the drag coefficient is approximately 1, so the side force components will approximately cancel. It should be noted that in regions where the slope of the lift-drag polar does not significantly change from point to point, the driving force is relatively insensitive to angle of attack, whereas the side force is not. In this case the optimum trim would be the location of minimum side force—that is, the spinnaker would be eased as much as possible. On a run the maximum driving force (and minimum side force) occurs when the angle of attack is 901, which would correspond to an over-trimmed situation. In practice even on this point of sail, the spinnaker is eased and the sail is at an angle of attack significantly less than 901 (see Fig. 3). This is done both to create sufficient air flow over the sail to keep it flying, and also to keep it away from the mainsail. In the present case hard sails were being tested in the absence of a main, and so getting the sails to fly was not an issue, nor was blanketing by the main. The effect that each of the parameters has on performance can be analyzed by comparing the polar diagrams for two sails, where only the parameter of interest has been changed. For example, Fig. 11 shows a comparison of the polars for sails 3 and 4. Sail 3 has a 25% camber at the foot, while sail 4 has a 45% camber. All of the other parameters are the same. For a run, the objective is to maximize the drag. Sail 3 (the flatter sail) has a higher maximum drag coefficient than sail 4, so sail 3 would
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Camber comparison
1.5
1.2
CL
0.9
0.6
0.3
0 0
0.3
0.6
0.9
1.2
1.5
CD Sail 3 - 25%
Sail 4 - 45%
Fig. 11. Polars for sails 3 and 4.
be faster. The difference in this case is small (about 3%) and close to the experimental error. In other comparisons the difference for a run is significant—as much as 14%. On a broad reach, the objective is to maximize total force, and sail 4 is faster than sail 3. On a beam reach, both sails produce approximately the same maximum lift, but sail 3 has a significantly lower drag, so it would be faster. This analysis can be repeated for all combinations of sail shapes, and the results are summarized in Table 2. The remaining comparison polar diagrams are shown in Appendix A for reference. The data in Table 2 can be analyzed to draw the following conclusions about the performance of different shapes on different points of sail: 1. Low sweep (i.e., more vertical) is always better than high sweep. The average differences between the various combinations is approximately 10% on a run, 13% on a broad reach, and 16% on a beam reach. 2. Flat sails (i.e., low camber) are always better on a run and on a beam reach. On a run, the flat sails average 6% more driving force than the full sails. On a beam reach the low aspect ratio combinations (5 & 6; 1 & 2) show that flat sails have an average of 7% more lift at the same drag than full sails; for the high aspect ratio combinations (3 & 4; 7 & 8; 7 & 9) the flat sails average 19% less drag for the same lift. 3. On a broad reach, the effect of camber depends on the sail aspect ratio. The low aspect ratio combinations show an average of 5% more driving force for the flat
326
Table 2 Relative performance comparison of sail combinations
Models compared
Increase in driving force for faster sail (%)
of sails with different sweep Low sweep 9 Low sweep 8 Low sweep 14 Low sweep 9 Low sweep 10 of sails with different camber Low camber 6 Low camber 3 Low camber 7 Low camber 7 Low camber 6 of sails with different aspect ratio Low AR 4 Draw 1 Draw 0 Draw 0 of sails with different radius ratio 2 5 of sails with different shoulder width Full width 16
Beam reach
Parameter of fastest sail
Increase in driving force for faster sail (%)
Parameter of fastest sail
Difference in force for faster sail
Low Low Low Low Low
13 16 12 10 15
Low Low Low Low Low
sweep sweep sweep sweep sweep
16% 18% 10% 16% 20%
Low camber High camber Low camber High camber High camber
6 11 4 9 7
Low Low Low Low Low
camber camber camber camber camber
8% more lift 23% less drag 6% more lift 13% less drag 20% less drag
Low Low Low Low
23 5 25 10
High High High High
AR AR AR AR
39% 18% 40% 22%
sweep sweep sweep sweep sweep
AR AR AR AR
1 Full width
7 29
more more more more more
less less less less
lift lift lift lift lift
drag drag drag drag
2
20% less drag
Full width
28% more lift
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Comparison 1&5 2&6 3&7 4&8 7 & 10 Comparison 1&2 3&4 5&6 7&8 7&9 Comparison 1&3 2&4 5&7 6&8 Comparison 7 & 11 Comparison 7 & 12
Parameter of fastest sail
Broad reach
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5.
6.
7.
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sails, while the high aspect ratio combinations show an average of 9% more driving force for the full sails. The effect of aspect ratio on performance is negligible on a run. Only one of the four combinations (1 & 3) shows a statistically significant difference (4%), and this is barely above the estimated 3% experimental error. On a broad reach the low aspect ratio sails are always faster, while on a beam reach the high aspect ratio sails are always faster. The two flat combinations (1 & 3; 5 & 7) show an average of 24% more driving force for the low aspect ratio sails on a broad reach, and an average of 40% less drag for the high aspect ratio sails on a beam reach. The two full combinations (2 & 4; 6 & 8) show an average of 7% more driving force for the low aspect ratio sails on a broad reach, and an average of 20% less drag for the high aspect ratio sails on a beam reach. The sail with the uniform radius of curvature (sail 11) produced 7% more driving force on a broad reach than the corresponding sail with reduced camber at the shoulders. Sail 7, with a flatter cross section at the shoulders, produced 5% more driving force on a run and 20% less drag on a beam reach than the sail with uniform camber. The sail with full girth at the shoulders (sail 7) is always better than the sail with reduced shoulders (sail 12). The difference in driving force is approximately 16% on a run and 29% on a broad reach. On a beam reach the full-shoulder sail produces 28% more lift for the same drag.
7. Discussion 7.1. Running When running, factors that increase projected area always result in an increased driving force. Reducing sweep and camber both increase projected area. The sail with reduced camber at the shoulders (sail 7) will also have increased projected area compared to the sail with uniform camber, as will the sail with full girth at the shoulders. All of these factors produce increased driving force on a run. To further understand the impact of projected area on a run, all of the force coefficients were recalculated using projected area rather than actual sail area, and the different combinations were compared. The average of the differences between the highest and lowest driving force coefficient was less than 2%, which is below the estimated experimental error of 3%. For two of the combinations the difference was slightly more than 4%, which is close enough to the estimated error to be considered insignificant. From this analysis it can be concluded that the only geometric factor that significantly influences performance on a run is projected area. Boat designers can directly and significantly influence sweep and aspect ratio by varying the dimensions of the mast and spinnaker pole, and they can have a small, indirect influence on camber. A longer pole and wider beam (hull width) allow for a
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wider sheeting base, which flattens the sail. Sailmakers can have minimal influence on aspect ratio, since this is usually determined by class or handicapping rules; however, they can have a significant influence on all of the other parameters by changing the shape of the sail panels. Once a sail has been selected, sailors can significantly influence both sweep and camber by adjusting the positions of the spinnaker pole. The fact that reduced sweep is beneficial suggests that it is best to keep the pole low when running to increase projected area. There is a limit, however. Lowering the pole also increases camber, which reduces projected area, especially near the head of the sail. There will be a point at which the increase in projected area due to reduced sweep is offset by a decrease in projected area due to increased camber. Also, since these models were tested in the absence of a vertical velocity gradient due to the atmospheric boundary layer, this conclusion may not be valid in some conditions—especially light air, where the velocity gradients are high. The conclusion regarding camber suggests that the pole should be pulled back to flatten the sail. On the other hand, as previously mentioned, the optimum aerodynamic condition for a run is to create maximum drag and zero lift (i.e., no side force). This suggests that when running the spinnaker should be kept in front of the boat as much as possible and trimmed so that it is at an angle of attack of 901. In practice this is not done in order to pull the sail out from the shadow of the main, and also to increase flow over the surface of the sail to help it fly. While neither of these were a factor in the present work due to the use of hard sails tested without a mainsail, it does suggest that the common practice of pulling the pole back as far as possible and easing the sheet until the leading edge curls on itself, which indicates that the sail is near the minimum angle of attack (see Alinghi in Fig. 2), may not be optimum. Further investigation will be required to definitively resolve this issue. In general, conventional wisdom for sail trim is consistent with the results presented here; that is, when running, the pole should be pulled down and aft, as long as the sail shape is not distorted and the sail is able to properly fly. 7.2. Beam reaching As shown in Table 2, the fact that low sweep, flat sails, and high aspect ratio are all desirable when beam reaching is not surprising, since the aerodynamic objective on this point of sail is to maximize lift and minimize drag. In addition to increasing projected area, a reduction in sweep also forces more of the air to go around the cross-section of the sail, as opposed to down and toward the water surface, increasing the lift (see Fig. 12). It is interesting that the flat sails are always faster on a beam reach, but for different reasons. The low aspect ratio flat sails have more lift than the full sails, while the high aspect ratio flat sails have less drag than the full sails. This difference can be explained by considering the ratio of induced to pressure drag. Since the flat sails will have less trailing edge separation than the full sails, they will have a higher
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Fig. 12. Spinnaker model at a low angle of attack (beam reaching conditions). The air is moving from right to left, with the viewer looking perpendicular to the air stream. Most of the flow goes around the sail, while some is deflected downward due to the sail sweep.
maximum lift and a lower drag. For the low aspect ratio sails, induced drag is very high, so the reduction in pressure drag is not as significant a factor as the increase in lift. For the high aspect ratio sails, induced drag is small and pressure drag dominates, so the reduction in pressure drag is a more significant factor than the increase in lift. When comparing two sails of different aspect ratio on a beam reach, the full sails show less of a decrease in drag with increased aspect ratio than the flat sails. Separation drag is much higher for the full sails, so pressure drag is a more significant factor, and increasing the aspect ratio will not reduce the total drag by as high a percentage as it will for the flat sails. The fact that the sail with the flatter cross-section at the shoulders (sail ]7) has less drag than the sail with uniform camber (sail ]11) is consistent with the discussion above since they are high-aspect ratio models. The sail with the full-width shoulders, having more actual area, will generate a higher force than the sail with reduced shoulders. Since the coefficients are based on the same area for all sails (handicapping and class rules give no credit for reducing the shoulder width), this will lead to higher coefficients for the full-shoulder sails. While the fact that the fullsize sail is faster than the sail with reduced shoulders is not surprising, it is interesting to see how significant the effect is. Sailmakers sometimes reduce the shoulder width intentionally, since it allows the top of the sail to fly flatter. The significantly reduced driving force on the reduced shoulder sail (especially when reaching) shows that this may not be the best strategy.
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The implications of these results for sailors is similar to those for a run—decrease sweep by lowering the pole, and decrease camber by pulling the pole aft. Since the effect of camber is more important on a beam reach than on a run, it is more critical to not lower the pole too far, since this will result in an excessively full cross-section near the head, which will significantly reduce performance. It is also possible to pull the pole too far aft, causing the sail to luff (flutter); however, the conventional wisdom of pole aft and down as long as it does not distort the shape of the sail is supported by these results. It should be noted that the mainsail has minimal impact on the spinnaker on this point of sail. 7.3. Broad reaching When broad reaching, low sweep and low aspect ratio are always desirable. Low sweep increases projected area, which increases total force. Since lift is present on this point of sail, low aspect ratio increases induced drag, which increases total driving force. It is interesting that low aspect ratio sails should be flat and high aspect ratio sails should be full. This is again explained by examining the ratio of induced to pressure drag. Since induced drag is more important for low aspect ratio sails, the increase in lift due to a flat cross section is greater than the decrease in pressure drag due to reduced separation. For high aspect ratio sails the opposite is true—since pressure drag is so significant, the best way to increase total force is to increase the amount of separation by increasing the camber. In the comparison of sails ]7 and 11, which are both high aspect ratio models, the fuller of the two sails (]11) has more drag and thus is faster. The impact of the broad reach results for sailors is interesting. While it is good to maintain a low pole position, the question of whether it is best to pull the pole back as far as possible or not depends on the aspect ratio of the spinnaker. Pulling the pole aft will flatten the sail, increasing the lift and net driving force for low aspect ratio sails, and decreasing the drag and net driving force for high aspect ratio sails. Conventional wisdom maintains that it is best to maximize projected area, but this is clearly not always the case, at least for high aspect ratio sails. Since lowering the pole decreases sweep and increases camber at the shoulders, the results suggest that this is the appropriate thing to do for high aspect ratio sails, whereas for low aspect ratio sails it would be advantageous to leave the pole a bit higher to maintain a flatter cross-section aloft. Further research or on-the-water testing will be necessary to determine the optimum pole position for various aspect ratios.
8. Limitations The limitations of applying the results of the present work to the downwind sailing problem are recognized. The size of the models is such that it was not possible to match Reynolds number with full-scale yachts under typical sailing conditions. The size and testing speed in the present work were limited by the durability of the
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models and the stiffness of the dynamometer. While it would be better to test larger hard sails made from metal or composites in larger wind tunnels, the testing speed would still be limited by the fact that the flow is highly separated and flow-induced vibration can be a significant problem. This limitation is not significantly different than the problem facing researchers who use soft sails, where the wind speed is limited by the strength of the cloth. In spite of this limitation, there are several reasons to believe that the general conclusions of the present results are valid for full-size yachts. First, the conclusions are generally consistent with sailing practice, although there are some interesting differences. Second, the magnitudes of the force coefficients are similar to those published by other researchers. Third, Fallow [9] states that previous wind tunnel data compared well with full scale testing, in spite of the fact that no attempt was made to match Reynolds number. Finally, the effects of parameters such as sweep, projected area, and aspect ratio are probably not influenced by Reynolds number. While Reynolds number certainly influences separation and the impact of camber on performance, the general trends identified here should still be valid at full scale. Another limitation of the present work is that hard spinnakers were tested in isolation (to the main). Richards et al. [14] show in their testing that, except when running, there is minimal interaction between the mainsail and spinnaker. So, while not perfect, spinnaker testing in isolation can provide useful data. Additionally, in the present case the spinnaker was tested in the center of the tunnel in the absence of walls or the yacht hull, whereas the measurements of Richards et al. were taken from a rigged yacht model. Whether the present conclusions would change if the models were tested closer to one of the walls to simulate the surface of the water is an area for further study; however, the results seem reasonable, and this is probably not an issue. Richards et al. also show that wind tunnel data from a hard spinnaker and a soft spinnaker compare well, except in the range of angle of attack close to where the soft spinnaker will collapse. It should be noted that a soft sail might collapse before reaching the point of maximum lift used on a beam reach; whether this would impact the present results can only be determined by testing soft sails. While it is understood that the use of a hard sail is not a perfect simulation of what happens on the water, it does have three significant advantages. First, it is possible to change only one parameter at a time, gaining a fuller understanding of the effect that each parameter has on performance. This is not a possibility when testing soft sails. Second, since the sail is rigid the shape is known in detail without the need for expensive and time-consuming in situ measurement. This allows for a controlled understanding of the relationship between sail shape and force coefficients. Third, the combination of testing hard sails and testing in isolation to the main provides a different perspective than testing sails on an actual yacht or yacht model. In real sailing, it is not possible to separate the fundamental aerodynamic issues from other issues, such as how the sail will fly, or whether it can be trimmed to achieve the desired shape. This different perspective allows for an understanding of why a certain shape is fast, as opposed to simply what shape is faster.
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A final limitation of the present work is the absence of a vertical velocity gradient and twist of the incoming free stream. The presence of a vertical velocity gradient would be expected to significantly impact the effect of aspect ratio and sweep on thrust coefficient, since a higher aspect ratio sail or higher sweep sail would see a different average velocity. This is probably an important factor in determining the optimum vertical pole position for the various points of sail. The presence of twist in the flow would undoubtedly change the values of the force coefficients, but would probably not change the general conclusions for the parameters investigated here. It is the intent of the authors to perform RANS simulations on these spinnakers in the future, where it would be possible to computationally assess the impact of several realistic conditions, including vertical velocity gradient, twist, higher Reynolds number, blockage due to the main, and interference from the water surface.
9. Conclusions The primary objective of the present work was to understand the effect that each of several sail geometric parameters has on spinnaker performance. It was shown that more vertical sails were always faster; flat sails were usually faster, except for high aspect ratio sails on a broad reach; and the optimum aspect ratio depended on the point of sail. Aspect ratio was an insignificant factor on a run; low aspect ratio was better on a broad reach; and high aspect ratio was better on a beam reach. Furthermore, projected area is the only significant factor on a run. These results are, of course, tempered by the fact that the sails were rigid, and the question of which of the shapes would fly better was not addressed. This is an important issue that needs to be investigated if we are to fully understand spinnaker aerodynamics, but the present work provides at least a partial understanding of this complex problem. An additional objective of this project was to create a database of force coefficients with a complete description of the spinnaker shape which could be used for verification of Reynolds averaged Navier-Stokes (RANS) simulations. Due to the complexities of the flow, the predicted force coefficients from RANS simulations may not match experimental results, although it will be interesting to see if RANS can capture the effect that each of the parameters has on the force coefficients. If so, this would help validate the concept of a ‘‘virtual wind tunnel’’ [20], and would allow the yacht research community to address some of the remaining questions regarding downwind sails.
Acknowledgements This work was supported by grants from the Council on Undergraduate Research Student Summer Research Fellowships in Science and Mathematics, and the Behrend College Undergraduate Students Summer Research Fellowship Program.
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Appendix A. Polars for all parameter comparisons
Sweep comparison
1.2
1.2
0.9
0.9
CL
1.5
CL
1.5
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
0
0.3
0.6
CD
0.9
1.2
1.5
CD
Sail 1-33.69
Sail 5 - 21.8
Sail 2-33.69
1.5
1.2
1.2
0.9
0.9
CL
CL
1.5
Sail 6 - 21.8
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
CD Sail 3 - 33.69
0.3
0.6
0.9
1.2
1.5
CD Sail 7 - 21.8
Sail 10 -11.3
0
Sail 4-33.69
Sail 8 - 21.8
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Camber comparison
1.2
1.2
0.9
0.9
CL
1.5
CL
1.5
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
0
0.3
CD
0.6
0.9
1.2
1.5
CD
Sail 1 - 25%
Sail 3 - 25%
Sail 2 - 45%
1.5
1.2
1.2
0.9
0.9
CL
CL
1.5
Sail 4 - 45%
0.6
0.6
0.3
0.3 0
0 0
0.3
0.6
0.9
1.2
1.5
0
0.3
0.6
CD Sail 5 - 25%
0.9
1.2
1.5
CD Sail 6 - 45%
Sail 8 - 45%
Sail 7 - 25% Sail 9 - 15%
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Aspect ratio comparison
1.2
1.2
0.9
0.9
CL
1.5
CL
1.5
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
0
0.3
0.6
CD
0.9
1.2
1.5
CD
Sail 1 - 1.4
Sail 3 - 2.0
Sail 2 - 1.4
1.5
1.2
1.2
0.9
0.9
CL
CL
1.5
Sail 4 - 2.0
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
CD Sail 5 - 1.4
0
0.3
0.6
0.9
1.2
1.5
CD Sail 7 - 2.0
Sail 6 - 1.4
Sail 8 - 2.0
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Camber uniformity
Reduced shoulders 1.5
1.2
1.2
0.9
0.9
CL
CL
1.5
0.6
0.6
0.3
0.3 0
0 0
0.3
0.6
0.9
1.2
CD
1.5
0
0.3
0.6
0.9
1.2
1.5
CD
Sail 7-non-uniform
Sail 7 - full
Sail 11-uniform
Sail 12-reduced
References [1] J.H. Milgram, The analytical design of yacht sails, Trans. Soc. Naval Architect. Marine Eng. (1968). [2] T. Charvet, S. Huberson, Numerical calculation of the flow around sails, Eur. J. Mech. B/Fluids 11 (5) (1992) 559–610. [3] P.J. Richards, The effect of wind profile and twist on downwind sail performance, J. Wind Eng. Ind. Aerodyn. 67&68 (1997) 313–321. [4] W.C. Lasher, On the Application of RANS Simulation for Downwind Sail Aerodynamics, Proceedings of the Fourteenth Chesapeake Sailing Yacht Symposium, Annapolis, MD, January 29–30, 1999, pp. 157–170. [5] J.H. Milgram, D.B. Peters, D.N. Eckhouse, Modeling IACC sail forces by combining measurements with CFD, Proceedings of the Eleventh Chesapeake Sailing Yacht Symposium, Annapolis, MD, January 1993, pp. 65–73. [6] Y. Masuyama, T. Fukasawa, Full scale measurement of sail force coefficients and the validation of numerical calculation method, Proceedings of the Thirteenth Chesapeake Sailing Yacht Symposium, Annapolis, MD, January 24–25 1997, pp. 23–36. [7] R.G.J. Flay, I.J. Vuletich, Development of a wind tunnel test facility for yacht aerodynamic studies, J. Wind Eng. Ind. Aerodyn. 58 (1995) 231–258. [8] R. Ranzenbach, C. Mairs, Experimental Determination of Sail Performance and Blockage Corrections, Proceedings of the Thirteenth Chesapeake Sailing Yacht Symposium, Annapolis, MD, January, 24–25, 1997, pp. 245–259. [9] J.B. Fallow, America’s Cup sail design, J. Wind Eng. Ind. Aerodyn. 63 (1996) 183–192. [10] R. Ranzenbach, C. Mairs, Wind tunnel testing of offwind sails, Proceedings of the Fourteenth Chesapeake Sailing Yacht Symposium, Annapolis, MD, January 29–30, 1999, pp. 171–179. [11] R. Ranzenbach, J. Teeters, Aerodynamic performance of offwind sails attached to sprits, Proceedings of the Fifteenth Chesapeake Sailing Yacht Symposium, Annapolis, MD, January 26–27, 2001, pp. 181–191. [12] K.L. Hedges, P.J. Richards, G.D. Mallinson, Computer modelling of downwind sails, J. Wind Eng. Ind. Aerodyn. 63 (1996) 95–110.
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[13] M. Caponneto, A. Castelli, P. Dupont, B. Bonjour, P.-L. Mathey, S. Sanchi, M.L. Sawley, Sailing yacht design using advanced numerical flow techniques, Proceedings of the Fourteenth Chesapeake Sailing Yacht Symposium, Annapolis, MD, January 29–30, 1999, pp. 97–104. [14] P.J. Richards, A. Johnson, A. Stanton, America’s Cup downwind sails—vertical wings or horizontal parachutes?, J. Wind Eng. Ind. Aerodyn. 89 (2001) 1565–1577. [15] T. Whidden, M. Levitt, The Art and Science of Sails, A Guide to Modern Materials, Construction, Aerodynamics, Upkeep, and Use, St. Martin’s Press, New York, 1990. [16] G.E.P. Box, W.G. Hunter, J.S. Hunter, Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building, Wiley, New York, 1978. [17] W.C. Lasher, J.R. Sonnenmeier, D.R. Forsman, C. Zhang, K. White, Experimental Force Coefficients for a Parametric Series of Spinnakers, Proceedings of the 16th Chesapeake Sailing Yacht Symposium, Annapolis, MD, March 21–22, 2003, pp. 153–160. [18] C.A. Marchaj, Aero-Hydrodynamics of Sailing, Dodd, Mead and Co., New York, NY, 1979. [19] P. van Oossanen, Predicting the speed of sailing yachts, Trans. Soc. Naval Architect. Marine Eng. 101 (1993) 337–397. [20] H.J Richter, K.C. Horrigan, J.B. Braun, Computational Fluid Dynamics for Downwind Sails, Proceedings of the Sixteenth Chesapeake Sailing Yacht Symposium, Annapolis, MD, March 21–22, 2003, pp. 19–28.
Journal of Wind Engineering and Industrial Aerodynamics 93 (2005) 311–337 www.elsevier.com/locate/jweia
The aerodynamics of symmetric spinnakers William C. Lasher, James R. Sonnenmeier, David R. Forsman, Jason Tomcho The Pennsylvania State University at Erie, The Behrend College, Erie, PA 16563-1701, USA Received 11 March 2004; received in revised form 7 January 2005; accepted 23 February 2005 Available online 2 April 2005
Abstract Twelve parametric spinnaker models were built and tested in a wind tunnel. In these models, five sail shape parameters were varied—cross-section camber ratio, sail aspect ratio, sweep, vertical distribution of camber, and vertical distribution of sail width. Lift and drag forces were measured for a range of angles of attack, and the results were analyzed for three points of sail. It was found that low sweep (more vertical) spinnakers are faster than spinnakers with high sweep, and that the optimum camber ratio depends on both the point of sail and aspect ratio of the sail. On a run (sailing directly downwind), the only significant geometric parameter is projected sail area. The implications of these results to sail trim are discussed. A description of the sail shapes and corresponding force coefficients is presented for future validation of Reynolds Averaged Navier-Stokes simulations of spinnaker flow fields. r 2005 Elsevier Ltd. All rights reserved. Keywords: Sail aerodynamics; Spinnaker aerodynamics; Downwind sailing
1. Introduction A sailing boat can sail at various angles to the wind, from about 401 to 1801. The approximate angle between the boat and the wind is referred to as a point of sail, as shown in Fig. 1. When a boat is sailing either upwind or on a close reach, the sails are pulled in tight to the boat and are relatively flat, so they act very much like Corresponding author. Tel.: +814 898 6391; fax: +814 898 6125.
E-mail address: [email protected] (W.C. Lasher). 0167-6105/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2005.02.001
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Nomenclature A sail area ANOVA analysis of variance AR aspect ratio AWA apparent wind angle CD drag coefficient, D/(0.5rV2A) C Df frictional drag coefficient C Din induced drag coefficient, C2L/(p AR) C Dp pressure drag coefficient, C D C Din C Df CFD computational fluid dynamics CL lift coefficient, L/(0.5rV2A) CT thrust coefficient D aerodynamic drag DOE design of experiment IMS International Measurement System L aerodynamic lift r air density RANS Reynolds averaged Navier-Stokes S sweep V air velocity
Wind
Upwind
Close Reach
Beam Reach
Broad Reach
Run
Fig. 1. Points of sail.
traditional airfoils. In these conditions, the flow over the sails is mostly attached, and traditional inviscid aerodynamic theory can be used. For example, Milgram [1] first employed panel techniques to this problem with some success. More recently, researchers have been using vortex particle methods [2] on this problem. When the wind is at approximately 901 (beam reach) or further aft (broad reach or run), the sails used for upwind sailing become very inefficient, so sailors use a spinnaker (Fig. 2). Spinnakers can be either symmetric (Alinghi) or asymmetric (Team New Zealand). Asymmetric spinnakers are more efficient at low angles (for example, when beam
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Fig. 2. Alinghi leads Team New Zealand on a run in the final race of the 2003 America’s Cup.
reaching), while symmetric spinnakers provide a broader range of application. At most sailing angles the flow over symmetric spinnakers is largely separated, so inviscid techniques do not apply [3]. As a result of the separated flow, the options for analyzing spinnakers are limited to full scale testing, wind tunnel testing, or computation using Reynolds-Averaged Navier Stokes (RANS) simulation. The difficulties associated with each of these techniques are detailed by Lasher [4]. For example, Milgram et al. [5] and Masuyama and Fukasawa [6] ran careful experiments on full-scale sailing dynamometers, but due to the problems associated with making accurate measurements and with fluctuations in sailing conditions, their data show an excessive amount of scatter in force coefficients (a standard deviation of approximately 13% of the mean). Wind tunnel testing, while highly controlled, suffers from well-known problems such as blockage and lack of true similitude, as well as sailing-specific problems due to the fact that boats sail in an atmospheric boundary layer [7,8]. While RANS simulation is rapidly maturing as a technology, there are still problems associated with turbulence modeling, and to date there has been little validation of RANS models appropriate for spinnaker aerodynamics. Until recently, little has been published on downwind sail aerodynamics, largely as a result of the problems outlined above. The information that is currently available in the literature does not allow for a fundamental understanding of the aerodynamics of spinnakers, often due to the proprietary nature of the work. Fallow [9] reports that over 300 model sails were built and tested for the America’s Cup, but does not provide data. Ranzenbach and Mairs [10] tested 23 different sails and reported force coefficients but not sail geometry. Ranzenbach and Teeters [11] tested five different sails flying under different conditions and describe the basic sail, but do not provide detailed geometric data. Other researchers have done either experimental or computational work on downwind sail aerodynamics, including Flay and Vuletich [7], Hedges et al. [12], Richards [3], Caponnetto et al. [13], and Richards et al. [14],
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but these have all been for a single sail configuration, and thus do not allow for an understanding of the effect that sail shape has on performance. In an effort to address the deficiency in published data, wind tunnel experiments were performed on a parametric series of symmetric spinnaker models. The models are small, rigid sails tested in isolation (that is, they were positioned in the center of the tunnel without other sails). Using rigid sails allows for a highly controlled experiment where one shape parameter can be varied at a time, providing an understanding of the impact that each parameter has on performance. Testing the models in isolation ensures that the results are uncomplicated by interactions with the water surface or with other sails. While these conditions are different than what is actually seen by a boat on the water, it allows for study of the aerodynamics of the spinnakers isolated from other issues, including the complex fluid-structure interaction of the spinnaker with the wind. In this paper, the aerodynamic objectives of downwind sailing will first be discussed, followed by an overview of how spinnakers are flown. The construction and testing of the models will then be detailed, followed by the results and discussion. The objectives of the work are to enhance the understanding of the basic aerodynamic issues regarding symmetric spinnakers, and to develop a database of force coefficients that can be used for validation of RANS simulation.
2. Aerodynamic objectives of downwind sailing In upwind sailing, as in traditional aerodynamic applications, the objective is to maximize the lift to drag ratio. This is not the case in downwind sailing, where the aerodynamic objective depends on the point of sail. For example, consider the three points of sail shown in Fig. 3. In all cases the goal is to maximize the driving force (the force component in the direction of motion of the boat) and minimize the side force (the force component perpendicular to the direction of motion of the boat).
D
L
L
D Wind
D
L driving force Wind Wind
side force Fig. 3. Aerodynamic forces in downwind sailing.
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For a boat on a run, this means maximizing the drag and minimizing the lift, which is the exact opposite of the goal in upwind sailing. The sailor will adjust (or trim) the sail to achieve maximum driving force. When a boat is on a broad reach, the lift and drag forces are of approximately the same magnitude, so maximum drive occurs at the point of maximum total force. This corresponds to a very small side force, since the lateral components of lift and drag approximately cancel. For a boat on a beam reach, the goal is to minimize the drag for a given lift, or to maximize the lift for a given drag. This is not exactly the same as maximizing the lift to drag ratio. For example, consider two sails A and B. Sail A might have a slightly lower lift to drag ratio than sail B, but at the same time generate a significantly larger driving force. In this case, assuming the boat is not overpowered, one would select the shape of sail A for more power, even though the lift to drag ratio is lower than sail B. Note that in real sailing conditions there is an interaction between the spinnaker and the mainsail, and that the objective is to optimize total performance, not just the performance of the spinnaker. For example, on a run the mainsail will partially block the flow of air to the spinnaker, so it is important to trim the spinnaker in such a way as to minimize the impact of the mainsail. This may result in a spinnaker trim that is different than what would be desired if the spinnaker were flying in isolation, and will be discussed later. On a broad reach sail there is still some interference from the mainsail, but it is relatively small, so the spinnaker is trimmed about as it would be if the mainsail were not present. When a boat is on a beam reach, the wind is far enough forward that the mainsail does not have a significant adverse impact on the spinnaker.
3. Primer on spinnaker flying The shape of a flying spinnaker is determined by several factors—the dimensions of the rig (determined by the boat designer); the shape of the cloth panels (determined by the sailmaker); and adjustments made by the sailor on the boat. While all three factors are important, the first two are highly controlled and produce an envelope of shapes in which the sail will fly. The third factor is more open-ended and a complete understanding of spinnaker aerodynamics requires a knowledge of what adjustments can be made on the boat, and what impact they have on sail shape. The basics of spinnaker trim will be outlined here; the reader interested in more details should refer to one of several excellent references on sail trim, such as Whidden and Levitt [15]. The basic setup for a spinnaker is shown in Fig. 4. The top (head) of the sail is attached to the mast. The windward corner (tack) is attached to a line (guy) that runs through a spinnaker pole, then to the side of the boat. This pole can be rigidly positioned through the use of the guy and other lines attached directly to the pole, and can be adjusted both fore and aft, and up and down. The third corner (clew) is attached to another line (sheet) that runs to the back of the boat. The clew is free to
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Head
Leech Spinnaker
Luff
Mainsail Foot
Clew
Tack
(Behind Mainsail)
Sheet
Pole Guy
Fig. 4. Controls for a spinnaker.
float up and down depending on the location of the spinnaker pole and the pressure on the sail. For a given setting of the guy and sheet, the spinnaker will settle to an equilibrium position. This is one of the factors that makes spinnaker aerodynamics so complicated—the shape of the sail depends on the pressure distribution, which in turn depends on the sail shape. The basic rules of spinnaker trim are as follows: the pole is set approximately perpendicular to the wind, and at an elevation where the tack and the clew are at approximately the same height. The sheet is eased (the sheet is let out and the clew is allowed to move forward) until the leading edge (luff) of the spinnaker starts to curl over (see Alinghi in Fig. 2), which generally corresponds to the angle of maximum lift. By adjusting the pole position forward or aft, the angle of attack of the sail relative to the wind can be changed, as well as its camber. Pulling the pole aft spreads the tack and clew apart and flattens the cross-section of the sail and increases projected area. The shape of the sail can also be affected by adjusting the vertical position of the pole. When the pole is brought down, tension increases in the luff and leech (trailing edge), which causes the edges to come together and increase the camber, slightly reducing projected area. A lower pole also reduces the vertical
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curvature of the sail which increases projected area. Generally the reduction in vertical curvature causes a greater increase in projected area than the decrease in projected area caused by the increased camber; however, if the pole is lowered too far there can be a net decrease in projected area.
4. Development of the experimental models Initially, a series of eight rigid parametric spinnaker models (see Figs. 5–7) were built and tested according to the theory of statistical Design of Experiments (DOE) [16]. The details of this initial experiment and the results are discussed by Lasher et al. [17]. Three sail shape parameters were varied in these models—camber ratio (camber at the bottom, or foot, divided by chord at the foot), aspect ratio (AR, length of the vertical centerline divided by length along the foot), and sweep (S, the vertical angle between the head and the centerline at the foot). The three parameters (or factors) were varied at two levels—a minimum value and a maximum value, which were selected to encompass the expected range of values typically found on actual boats. The results from this initial set were analyzed using Analysis of Variance (ANOVA) to determine if the performance of the sails (the lift and the drag coefficients) was affected in a statistically significant way by the variation of the three sail shape parameters. If so, this would indicate that there was some functional dependence of sail performance on the parameters. The ANOVA was based on a confidence interval of 95%, and showed that a difference of less than approximately 3% in the force coefficients for a given sail parameter was statistically insignificant and cannot be distinguished from experimental error over the range of values of the parameter tested. This would indicate that performance did not depend on the parameter over that range. In the original analysis, which was limited to a boat sailing on a run, the results of the ANOVA showed that aspect ratio was not a significant parameter over the range of aspect ratios tested. This is due to the fact that aspect ratio is only a concern if there is induced drag due to lift, and lift is absent on a run. Following the initial testing four additional models were built to extend the range of the models, as well as to investigate two additional parametric variations, radius of curvature variation of the sail camber line up to the sail shoulder, and shoulder width, as discussed below. The analysis was also extended to include broad and beam reaching. The spinnaker model shape was designed not so much to duplicate exactly what is found in a real spinnaker, but to allow for controlled parametric variation of shapes that are characteristic of spinnakers. First, an elliptical arc was created to form the centerline of the spinnaker when viewed from the side (Fig. 5). This arc is vertical at the foot and has an angle of 201 from the horizontal at the head. The dimensions of the centerline arc, along with the major and minor axis of the ellipse, were determined based on the spinnaker area, aspect ratio, and sweep angle. All spinnakers were designed with the same surface area. Next, a circular arc of the specified camber ratio was created at the foot (Fig. 6). This arc was swept along the
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Shoulders Sweep Angle
Fig. 5. Side view of model.
Shoulders Foot
Fig. 6. Foot view of model.
ellipse, with the arc remaining perpendicular to the ellipse. For all but model 11 the arc radius of curvature increases linearly from foot to head. The radius of curvature at the shoulders, which are located 45% of the centerline arc length from the head, is
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Shoulders
Fig. 7. Sample spinnaker geometry.
twice the radius at the foot (radius ratio ¼ 2). For model 11 the radius of curvature was held constant from foot to head (radius ratio ¼ 1). For all but model 12 the halfwidth of the spinnaker is constant from the foot to the shoulders, tapering to zero at the head. The rate of taper was determined by passing a cubic polynomial from the shoulders to the head, with the polynomial tangent to the half-width line at the shoulders. For model 12 the half-width at the shoulders was 80% of the half-width at the foot. An isometric outline of one of the models is shown in Fig. 7, and the parameters are summarized in Table 1. All twelve models were constructed in Pro/ENGINEER, a solid modeling package. The models are 0.11 in. thick and a support structure for mounting the model to the wind tunnel dynamometer was built into the back of the model at the center. The nominal area of the spinnakers (centerline arc length times foot arc length) is 37.3 sq. in., and the actual area is 31.3 sq. in. The physical models were then built using a Z-402 three-dimensional printer. This technology prints a binder on a thin (0.003 in.) layer of plaster, building layer after layer, creating a solid three-dimensional model. After printing and drying, the models were infiltrated with urethane to provide additional strength. Due to the low Reynolds number of the tests, the models were intentionally left rough to stimulate turbulence. One of the models was scanned on a three-dimensional Roland LPX-250 laser scanner and compared with the Pro/ENGINEER model. The maximum difference between the physical model and the Pro/ENGINEER model was less than 0.009 in. (about 0.1% of maximum camber). A model was also photographed in the wind tunnel at the test speed, and the deflection of the
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Table 1 Model parameter combinations Model ]
Camber ratio at foot
Aspect ratio
Sweep angle (deg.)
Radius ratio
Shoulder/foot ratio
1 2 3 4 5 6 7 8 9 10 11 12
0.25 0.45 0.25 0.45 0.25 0.45 0.25 0.45 0.15 0.25 0.25 0.25
1.4 1.4 2.0 2.0 1.4 1.4 2.0 2.0 2.0 2.0 2.0 2.0
33.69 33.69 33.69 33.69 21.80 21.80 21.80 21.80 21.80 11.30 21.80 21.80
2 2 2 2 2 2 2 2 2 2 1 2
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8
model was measured. The change in camber ratio due to model deflection was less than 1%.
5. Experimental procedure The models were tested in an Engineering Laboratory Design (ELD) open-circuit wind tunnel. The test section is 2400 2400 , with a length of 4800 . The forces were measured with an ELD 2-component beam dynamometer, which was mounted approximately 1200 downstream of the leading edge of the test section, and corrected for tare. The dynamometer was calibrated using dead weights, and calibration error was estimated to be negligible. The models were located in the center of the test section, and were supported from the rear with a rod approximately 500 in front of the dynamometer to minimize the influence of the mounting fixture (Fig. 8). The models were tested at a nominal velocity of 84 ft/s. This corresponds to a Reynolds number based on the square root of the area of 197,000, and an apparent wind speed of approximately 1.4 knots on a spinnaker for a typical 24 foot boat, such as a J-24. The velocity was measured using two pressure ports in the wind tunnel walls upstream of the test section. The pressure difference was measured with a differential digital pressure transducer with a resolution of 0.01% of full scale, and was calibrated with a water manometer. The total error in measured velocity was estimated to be less than 2%. Since the flow is unsteady due to separation, the lift and drag forces were averaged over a period of 30 s. Blockage corrections were not made for three reasons. First, the model surface area is less than 512% of the wind tunnel cross-sectional area, so blockage effects were assumed to be small. Second, since the primary objective of the present work is to compare force coefficients for different sail shapes, it was not necessary to make
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Fig. 8. Model mounted on dynamometer.
blockage corrections. Third, since one of the objectives is to build a database of force coefficients that can be used for CFD validation, it is preferable to have uncorrected data, since it is computationally easier to mesh a small contained area than to apply infinite domain boundary conditions. Due to the small size of the supporting mount (approximately 0.3% of the total sail area) and location of the support relative to the model (in the separated flow region behind the sail), interference effects were also assumed to be small. These assumptions were assessed by building three models of different sizes—one at the nominal size, one with an area 21% larger than nominal, and one with an area 46% larger than nominal. Lift and drag coefficients CL and CD for each of these models were calculated, and the variations were within experimental error (less than 3%) except close to the stall point. These results indicate that blockage was not a factor, and since the supporting structure was the same size for each model, that interference was not significant. Additional tests were run to assess repeatability and the impact of Reynolds number on force coefficients. The repeatability was generally very good (less than 1% difference in measured forces between two runs). One of the models was run at five different nominal velocities ranging from 29 to 164 ft/s. Over this range the force coefficients at a given angle of attack were approximately constant (a variation of less than 5%), with no evident trend in the data. The models were mounted with the spinnaker centerline horizontal, since the dynamometer measures the lift in the vertical direction. In this orientation, the models created a side force that resulted in a significant measured component in the lift direction due to the design of the dynamometer. This was eliminated by
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testing the models twice, with the head pointing in alternate directions, and averaging the results. The cross-talk between side force and drag could not be eliminated in this experiment, but was neglected since it was less than 3%. The crosstalk between lift and drag was less than 1%, and was also neglected. For the bulk of the testing, each of the models was mounted in both sideways orientations at angles of attack ranging from 901 to 351 in increments of 51, with 901 being the condition for a run. The angle of attack is defined as the angle between the incoming free stream and the chord line of the model at the foot. The error in measuring angle of attack was estimated to be less than 0.51. In the final analysis, angle of attack is not a critical factor, since the important parameter is lift-drag ratio; however, the angle measurement can introduce some error since the models had to be set at identical angles for each of the two orientations.
6. Results Initially, model ]1 was tested at angles of attack from 901 to 01. Since the models are rigid they are capable of producing lift at all angles. This is not true of a real spinnaker, which would collapse at angles significantly less than about 351, so only model ]1 was tested to zero degrees. The lift and drag coefficients are shown as a function of angle of attack in Fig. 9. The lift shows a characteristic drop due to stall at approximately 451, with a somewhat smaller drop in drag. This drop in drag, which has not been evident in other force data for spinnakers found in the literature, can be explained as follows. The induced drag for an elliptically loaded wing is given by the following equation, and is also shown in Fig. 9: C 2L . p AR This formula does not strictly apply to spinnakers, since they are not elliptically loaded, but provides an estimate of the induced drag. Also shown in Fig. 9, the pressure (or form) drag coefficient C Dp ; which is the total drag coefficient minus the induced drag coefficient C Din and the skin frictional drag coefficient C Df : In spinnaker aerodynamics the frictional drag coefficient C Df is small compared to the other two components and can be neglected. The drop in induced drag at stall parallels the drop in total drag, and the pressure drag curve is approximately constant in this region. This shows that the drop in drag can be attributed to a drop in the induced drag, corresponding to the drop in lift. The lift and drag coefficients are replotted in Fig. 10 as a lift-drag polar, which is more useful for sailing analysis. In this figure, a 901 angle of attack corresponds to the point of maximum drag and zero lift. As the angle of attack decreases, the drag for model ]1 slowly decreases until it reaches a local minimum at an angle of attack of about 501, followed by an increase in both lift and drag. This ‘‘bump’’ in the polar is due to the increase in induced drag described above. This characteristic that has not been evident in other lift-drag polars found in the literature for spinnakers, such as the data from Richards et al. [14], although there is a similar but smaller bump in C Din ¼
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Model #1 force coefficients 1.4
Force coefficient
1.2 1 0.8 0.6 0.4 0.2 0 0
20
40 Angle of attack
60
80
Legend: Lift coefficient, CL Drag coefficient, CD Induced drag coefficient, CDin = CL2/(π•AR) Pressure drag coefficient, CDp = CD - CDin Fig. 9. Force coefficients for model ]1.
the polar for a single mainsail as reported by Marchaj [18]. This effect is less pronounced in the data for sails with higher aspect ratio due to a lower induced drag, which has implications in terms of performance when reaching, as will be discussed later. In general the magnitude of the force coefficients in Fig. 10 are consistent with those published in the literature. For example, at zero lift coefficient, van Oossanen [19] reports a value for the International Measurement System (IMS) spinnaker drag coefficient of 1.10, and Richards et al. report a value of 1.12. These drag coefficients compare well with the present data, which range from 1.06 to 1.36. The differences between the present results and those previously published can be reasonably attributed to differences in spinnaker geometry. It can be shown that the point of maximum driving force for a given sail can be determined by locating the point on the polar diagram where a line drawn perpendicular to the apparent wind angle is tangent to the polar curve. For example, on a run the apparent wind angle is 1801, so the perpendicular line would be vertical, and the point of maximum driving force would be the zero lift point (i.e., the sail angle of attack would be 901). For a broad reach, the apparent wind angle is 1351, so the line is tangent to the polar curve at the point of maximum total force. On a beam reach, the apparent wind angle is 901, so the line would be horizontal, corresponding
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Model #1 polar 1.5
broad reach
beam reach
1.2
CL
0.9
0.6
0.3 run 0 0
0.3
0.6
0.9
1.2
1.5
CD Fig. 10. Polar diagram for model ]1.
to the point of maximum lift. Each of these three lines is shown in Fig. 10, and the optimum point corresponds to the optimum aerodynamic condition discussed earlier. Note that at the optimum condition for a broad reach for model ]1, the lift coefficient is approximately 1.2, and the drag coefficient is approximately 1, so the side force components will approximately cancel. It should be noted that in regions where the slope of the lift-drag polar does not significantly change from point to point, the driving force is relatively insensitive to angle of attack, whereas the side force is not. In this case the optimum trim would be the location of minimum side force—that is, the spinnaker would be eased as much as possible. On a run the maximum driving force (and minimum side force) occurs when the angle of attack is 901, which would correspond to an over-trimmed situation. In practice even on this point of sail, the spinnaker is eased and the sail is at an angle of attack significantly less than 901 (see Fig. 3). This is done both to create sufficient air flow over the sail to keep it flying, and also to keep it away from the mainsail. In the present case hard sails were being tested in the absence of a main, and so getting the sails to fly was not an issue, nor was blanketing by the main. The effect that each of the parameters has on performance can be analyzed by comparing the polar diagrams for two sails, where only the parameter of interest has been changed. For example, Fig. 11 shows a comparison of the polars for sails 3 and 4. Sail 3 has a 25% camber at the foot, while sail 4 has a 45% camber. All of the other parameters are the same. For a run, the objective is to maximize the drag. Sail 3 (the flatter sail) has a higher maximum drag coefficient than sail 4, so sail 3 would
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Camber comparison
1.5
1.2
CL
0.9
0.6
0.3
0 0
0.3
0.6
0.9
1.2
1.5
CD Sail 3 - 25%
Sail 4 - 45%
Fig. 11. Polars for sails 3 and 4.
be faster. The difference in this case is small (about 3%) and close to the experimental error. In other comparisons the difference for a run is significant—as much as 14%. On a broad reach, the objective is to maximize total force, and sail 4 is faster than sail 3. On a beam reach, both sails produce approximately the same maximum lift, but sail 3 has a significantly lower drag, so it would be faster. This analysis can be repeated for all combinations of sail shapes, and the results are summarized in Table 2. The remaining comparison polar diagrams are shown in Appendix A for reference. The data in Table 2 can be analyzed to draw the following conclusions about the performance of different shapes on different points of sail: 1. Low sweep (i.e., more vertical) is always better than high sweep. The average differences between the various combinations is approximately 10% on a run, 13% on a broad reach, and 16% on a beam reach. 2. Flat sails (i.e., low camber) are always better on a run and on a beam reach. On a run, the flat sails average 6% more driving force than the full sails. On a beam reach the low aspect ratio combinations (5 & 6; 1 & 2) show that flat sails have an average of 7% more lift at the same drag than full sails; for the high aspect ratio combinations (3 & 4; 7 & 8; 7 & 9) the flat sails average 19% less drag for the same lift. 3. On a broad reach, the effect of camber depends on the sail aspect ratio. The low aspect ratio combinations show an average of 5% more driving force for the flat
326
Table 2 Relative performance comparison of sail combinations
Models compared
Increase in driving force for faster sail (%)
of sails with different sweep Low sweep 9 Low sweep 8 Low sweep 14 Low sweep 9 Low sweep 10 of sails with different camber Low camber 6 Low camber 3 Low camber 7 Low camber 7 Low camber 6 of sails with different aspect ratio Low AR 4 Draw 1 Draw 0 Draw 0 of sails with different radius ratio 2 5 of sails with different shoulder width Full width 16
Beam reach
Parameter of fastest sail
Increase in driving force for faster sail (%)
Parameter of fastest sail
Difference in force for faster sail
Low Low Low Low Low
13 16 12 10 15
Low Low Low Low Low
sweep sweep sweep sweep sweep
16% 18% 10% 16% 20%
Low camber High camber Low camber High camber High camber
6 11 4 9 7
Low Low Low Low Low
camber camber camber camber camber
8% more lift 23% less drag 6% more lift 13% less drag 20% less drag
Low Low Low Low
23 5 25 10
High High High High
AR AR AR AR
39% 18% 40% 22%
sweep sweep sweep sweep sweep
AR AR AR AR
1 Full width
7 29
more more more more more
less less less less
lift lift lift lift lift
drag drag drag drag
2
20% less drag
Full width
28% more lift
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Comparison 1&5 2&6 3&7 4&8 7 & 10 Comparison 1&2 3&4 5&6 7&8 7&9 Comparison 1&3 2&4 5&7 6&8 Comparison 7 & 11 Comparison 7 & 12
Parameter of fastest sail
Broad reach
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5.
6.
7.
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sails, while the high aspect ratio combinations show an average of 9% more driving force for the full sails. The effect of aspect ratio on performance is negligible on a run. Only one of the four combinations (1 & 3) shows a statistically significant difference (4%), and this is barely above the estimated 3% experimental error. On a broad reach the low aspect ratio sails are always faster, while on a beam reach the high aspect ratio sails are always faster. The two flat combinations (1 & 3; 5 & 7) show an average of 24% more driving force for the low aspect ratio sails on a broad reach, and an average of 40% less drag for the high aspect ratio sails on a beam reach. The two full combinations (2 & 4; 6 & 8) show an average of 7% more driving force for the low aspect ratio sails on a broad reach, and an average of 20% less drag for the high aspect ratio sails on a beam reach. The sail with the uniform radius of curvature (sail 11) produced 7% more driving force on a broad reach than the corresponding sail with reduced camber at the shoulders. Sail 7, with a flatter cross section at the shoulders, produced 5% more driving force on a run and 20% less drag on a beam reach than the sail with uniform camber. The sail with full girth at the shoulders (sail 7) is always better than the sail with reduced shoulders (sail 12). The difference in driving force is approximately 16% on a run and 29% on a broad reach. On a beam reach the full-shoulder sail produces 28% more lift for the same drag.
7. Discussion 7.1. Running When running, factors that increase projected area always result in an increased driving force. Reducing sweep and camber both increase projected area. The sail with reduced camber at the shoulders (sail 7) will also have increased projected area compared to the sail with uniform camber, as will the sail with full girth at the shoulders. All of these factors produce increased driving force on a run. To further understand the impact of projected area on a run, all of the force coefficients were recalculated using projected area rather than actual sail area, and the different combinations were compared. The average of the differences between the highest and lowest driving force coefficient was less than 2%, which is below the estimated experimental error of 3%. For two of the combinations the difference was slightly more than 4%, which is close enough to the estimated error to be considered insignificant. From this analysis it can be concluded that the only geometric factor that significantly influences performance on a run is projected area. Boat designers can directly and significantly influence sweep and aspect ratio by varying the dimensions of the mast and spinnaker pole, and they can have a small, indirect influence on camber. A longer pole and wider beam (hull width) allow for a
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wider sheeting base, which flattens the sail. Sailmakers can have minimal influence on aspect ratio, since this is usually determined by class or handicapping rules; however, they can have a significant influence on all of the other parameters by changing the shape of the sail panels. Once a sail has been selected, sailors can significantly influence both sweep and camber by adjusting the positions of the spinnaker pole. The fact that reduced sweep is beneficial suggests that it is best to keep the pole low when running to increase projected area. There is a limit, however. Lowering the pole also increases camber, which reduces projected area, especially near the head of the sail. There will be a point at which the increase in projected area due to reduced sweep is offset by a decrease in projected area due to increased camber. Also, since these models were tested in the absence of a vertical velocity gradient due to the atmospheric boundary layer, this conclusion may not be valid in some conditions—especially light air, where the velocity gradients are high. The conclusion regarding camber suggests that the pole should be pulled back to flatten the sail. On the other hand, as previously mentioned, the optimum aerodynamic condition for a run is to create maximum drag and zero lift (i.e., no side force). This suggests that when running the spinnaker should be kept in front of the boat as much as possible and trimmed so that it is at an angle of attack of 901. In practice this is not done in order to pull the sail out from the shadow of the main, and also to increase flow over the surface of the sail to help it fly. While neither of these were a factor in the present work due to the use of hard sails tested without a mainsail, it does suggest that the common practice of pulling the pole back as far as possible and easing the sheet until the leading edge curls on itself, which indicates that the sail is near the minimum angle of attack (see Alinghi in Fig. 2), may not be optimum. Further investigation will be required to definitively resolve this issue. In general, conventional wisdom for sail trim is consistent with the results presented here; that is, when running, the pole should be pulled down and aft, as long as the sail shape is not distorted and the sail is able to properly fly. 7.2. Beam reaching As shown in Table 2, the fact that low sweep, flat sails, and high aspect ratio are all desirable when beam reaching is not surprising, since the aerodynamic objective on this point of sail is to maximize lift and minimize drag. In addition to increasing projected area, a reduction in sweep also forces more of the air to go around the cross-section of the sail, as opposed to down and toward the water surface, increasing the lift (see Fig. 12). It is interesting that the flat sails are always faster on a beam reach, but for different reasons. The low aspect ratio flat sails have more lift than the full sails, while the high aspect ratio flat sails have less drag than the full sails. This difference can be explained by considering the ratio of induced to pressure drag. Since the flat sails will have less trailing edge separation than the full sails, they will have a higher
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Fig. 12. Spinnaker model at a low angle of attack (beam reaching conditions). The air is moving from right to left, with the viewer looking perpendicular to the air stream. Most of the flow goes around the sail, while some is deflected downward due to the sail sweep.
maximum lift and a lower drag. For the low aspect ratio sails, induced drag is very high, so the reduction in pressure drag is not as significant a factor as the increase in lift. For the high aspect ratio sails, induced drag is small and pressure drag dominates, so the reduction in pressure drag is a more significant factor than the increase in lift. When comparing two sails of different aspect ratio on a beam reach, the full sails show less of a decrease in drag with increased aspect ratio than the flat sails. Separation drag is much higher for the full sails, so pressure drag is a more significant factor, and increasing the aspect ratio will not reduce the total drag by as high a percentage as it will for the flat sails. The fact that the sail with the flatter cross-section at the shoulders (sail ]7) has less drag than the sail with uniform camber (sail ]11) is consistent with the discussion above since they are high-aspect ratio models. The sail with the full-width shoulders, having more actual area, will generate a higher force than the sail with reduced shoulders. Since the coefficients are based on the same area for all sails (handicapping and class rules give no credit for reducing the shoulder width), this will lead to higher coefficients for the full-shoulder sails. While the fact that the fullsize sail is faster than the sail with reduced shoulders is not surprising, it is interesting to see how significant the effect is. Sailmakers sometimes reduce the shoulder width intentionally, since it allows the top of the sail to fly flatter. The significantly reduced driving force on the reduced shoulder sail (especially when reaching) shows that this may not be the best strategy.
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The implications of these results for sailors is similar to those for a run—decrease sweep by lowering the pole, and decrease camber by pulling the pole aft. Since the effect of camber is more important on a beam reach than on a run, it is more critical to not lower the pole too far, since this will result in an excessively full cross-section near the head, which will significantly reduce performance. It is also possible to pull the pole too far aft, causing the sail to luff (flutter); however, the conventional wisdom of pole aft and down as long as it does not distort the shape of the sail is supported by these results. It should be noted that the mainsail has minimal impact on the spinnaker on this point of sail. 7.3. Broad reaching When broad reaching, low sweep and low aspect ratio are always desirable. Low sweep increases projected area, which increases total force. Since lift is present on this point of sail, low aspect ratio increases induced drag, which increases total driving force. It is interesting that low aspect ratio sails should be flat and high aspect ratio sails should be full. This is again explained by examining the ratio of induced to pressure drag. Since induced drag is more important for low aspect ratio sails, the increase in lift due to a flat cross section is greater than the decrease in pressure drag due to reduced separation. For high aspect ratio sails the opposite is true—since pressure drag is so significant, the best way to increase total force is to increase the amount of separation by increasing the camber. In the comparison of sails ]7 and 11, which are both high aspect ratio models, the fuller of the two sails (]11) has more drag and thus is faster. The impact of the broad reach results for sailors is interesting. While it is good to maintain a low pole position, the question of whether it is best to pull the pole back as far as possible or not depends on the aspect ratio of the spinnaker. Pulling the pole aft will flatten the sail, increasing the lift and net driving force for low aspect ratio sails, and decreasing the drag and net driving force for high aspect ratio sails. Conventional wisdom maintains that it is best to maximize projected area, but this is clearly not always the case, at least for high aspect ratio sails. Since lowering the pole decreases sweep and increases camber at the shoulders, the results suggest that this is the appropriate thing to do for high aspect ratio sails, whereas for low aspect ratio sails it would be advantageous to leave the pole a bit higher to maintain a flatter cross-section aloft. Further research or on-the-water testing will be necessary to determine the optimum pole position for various aspect ratios.
8. Limitations The limitations of applying the results of the present work to the downwind sailing problem are recognized. The size of the models is such that it was not possible to match Reynolds number with full-scale yachts under typical sailing conditions. The size and testing speed in the present work were limited by the durability of the
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models and the stiffness of the dynamometer. While it would be better to test larger hard sails made from metal or composites in larger wind tunnels, the testing speed would still be limited by the fact that the flow is highly separated and flow-induced vibration can be a significant problem. This limitation is not significantly different than the problem facing researchers who use soft sails, where the wind speed is limited by the strength of the cloth. In spite of this limitation, there are several reasons to believe that the general conclusions of the present results are valid for full-size yachts. First, the conclusions are generally consistent with sailing practice, although there are some interesting differences. Second, the magnitudes of the force coefficients are similar to those published by other researchers. Third, Fallow [9] states that previous wind tunnel data compared well with full scale testing, in spite of the fact that no attempt was made to match Reynolds number. Finally, the effects of parameters such as sweep, projected area, and aspect ratio are probably not influenced by Reynolds number. While Reynolds number certainly influences separation and the impact of camber on performance, the general trends identified here should still be valid at full scale. Another limitation of the present work is that hard spinnakers were tested in isolation (to the main). Richards et al. [14] show in their testing that, except when running, there is minimal interaction between the mainsail and spinnaker. So, while not perfect, spinnaker testing in isolation can provide useful data. Additionally, in the present case the spinnaker was tested in the center of the tunnel in the absence of walls or the yacht hull, whereas the measurements of Richards et al. were taken from a rigged yacht model. Whether the present conclusions would change if the models were tested closer to one of the walls to simulate the surface of the water is an area for further study; however, the results seem reasonable, and this is probably not an issue. Richards et al. also show that wind tunnel data from a hard spinnaker and a soft spinnaker compare well, except in the range of angle of attack close to where the soft spinnaker will collapse. It should be noted that a soft sail might collapse before reaching the point of maximum lift used on a beam reach; whether this would impact the present results can only be determined by testing soft sails. While it is understood that the use of a hard sail is not a perfect simulation of what happens on the water, it does have three significant advantages. First, it is possible to change only one parameter at a time, gaining a fuller understanding of the effect that each parameter has on performance. This is not a possibility when testing soft sails. Second, since the sail is rigid the shape is known in detail without the need for expensive and time-consuming in situ measurement. This allows for a controlled understanding of the relationship between sail shape and force coefficients. Third, the combination of testing hard sails and testing in isolation to the main provides a different perspective than testing sails on an actual yacht or yacht model. In real sailing, it is not possible to separate the fundamental aerodynamic issues from other issues, such as how the sail will fly, or whether it can be trimmed to achieve the desired shape. This different perspective allows for an understanding of why a certain shape is fast, as opposed to simply what shape is faster.
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A final limitation of the present work is the absence of a vertical velocity gradient and twist of the incoming free stream. The presence of a vertical velocity gradient would be expected to significantly impact the effect of aspect ratio and sweep on thrust coefficient, since a higher aspect ratio sail or higher sweep sail would see a different average velocity. This is probably an important factor in determining the optimum vertical pole position for the various points of sail. The presence of twist in the flow would undoubtedly change the values of the force coefficients, but would probably not change the general conclusions for the parameters investigated here. It is the intent of the authors to perform RANS simulations on these spinnakers in the future, where it would be possible to computationally assess the impact of several realistic conditions, including vertical velocity gradient, twist, higher Reynolds number, blockage due to the main, and interference from the water surface.
9. Conclusions The primary objective of the present work was to understand the effect that each of several sail geometric parameters has on spinnaker performance. It was shown that more vertical sails were always faster; flat sails were usually faster, except for high aspect ratio sails on a broad reach; and the optimum aspect ratio depended on the point of sail. Aspect ratio was an insignificant factor on a run; low aspect ratio was better on a broad reach; and high aspect ratio was better on a beam reach. Furthermore, projected area is the only significant factor on a run. These results are, of course, tempered by the fact that the sails were rigid, and the question of which of the shapes would fly better was not addressed. This is an important issue that needs to be investigated if we are to fully understand spinnaker aerodynamics, but the present work provides at least a partial understanding of this complex problem. An additional objective of this project was to create a database of force coefficients with a complete description of the spinnaker shape which could be used for verification of Reynolds averaged Navier-Stokes (RANS) simulations. Due to the complexities of the flow, the predicted force coefficients from RANS simulations may not match experimental results, although it will be interesting to see if RANS can capture the effect that each of the parameters has on the force coefficients. If so, this would help validate the concept of a ‘‘virtual wind tunnel’’ [20], and would allow the yacht research community to address some of the remaining questions regarding downwind sails.
Acknowledgements This work was supported by grants from the Council on Undergraduate Research Student Summer Research Fellowships in Science and Mathematics, and the Behrend College Undergraduate Students Summer Research Fellowship Program.
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Appendix A. Polars for all parameter comparisons
Sweep comparison
1.2
1.2
0.9
0.9
CL
1.5
CL
1.5
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
0
0.3
0.6
CD
0.9
1.2
1.5
CD
Sail 1-33.69
Sail 5 - 21.8
Sail 2-33.69
1.5
1.2
1.2
0.9
0.9
CL
CL
1.5
Sail 6 - 21.8
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
CD Sail 3 - 33.69
0.3
0.6
0.9
1.2
1.5
CD Sail 7 - 21.8
Sail 10 -11.3
0
Sail 4-33.69
Sail 8 - 21.8
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Camber comparison
1.2
1.2
0.9
0.9
CL
1.5
CL
1.5
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
0
0.3
CD
0.6
0.9
1.2
1.5
CD
Sail 1 - 25%
Sail 3 - 25%
Sail 2 - 45%
1.5
1.2
1.2
0.9
0.9
CL
CL
1.5
Sail 4 - 45%
0.6
0.6
0.3
0.3 0
0 0
0.3
0.6
0.9
1.2
1.5
0
0.3
0.6
CD Sail 5 - 25%
0.9
1.2
1.5
CD Sail 6 - 45%
Sail 8 - 45%
Sail 7 - 25% Sail 9 - 15%
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Aspect ratio comparison
1.2
1.2
0.9
0.9
CL
1.5
CL
1.5
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
0
0.3
0.6
CD
0.9
1.2
1.5
CD
Sail 1 - 1.4
Sail 3 - 2.0
Sail 2 - 1.4
1.5
1.2
1.2
0.9
0.9
CL
CL
1.5
Sail 4 - 2.0
0.6
0.6
0.3
0.3
0
0 0
0.3
0.6
0.9
1.2
1.5
CD Sail 5 - 1.4
0
0.3
0.6
0.9
1.2
1.5
CD Sail 7 - 2.0
Sail 6 - 1.4
Sail 8 - 2.0
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Camber uniformity
Reduced shoulders 1.5
1.2
1.2
0.9
0.9
CL
CL
1.5
0.6
0.6
0.3
0.3 0
0 0
0.3
0.6
0.9
1.2
CD
1.5
0
0.3
0.6
0.9
1.2
1.5
CD
Sail 7-non-uniform
Sail 7 - full
Sail 11-uniform
Sail 12-reduced
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