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Measuring the Speed of a Model Land Yacht with Varying Sail Shape and Wind Power Moore, Joanna Jun 1, 2010

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SCIENCE ONE PROGRAM 09/10  Measuring the Speed of a Model Land Yacht with Varying Sail Shape and Wind Power Joanna Moore Science One Program The University of British Columbia Vancouver, Canada April 2010  1  Measuring the Speed of a Model Land Yacht with varying Sail Shape and Wind Power Abstract: To determine the influence sail area and sail shape has on the speed of a sailing yacht, it is less ambiguous using a model land yacht, eliminating the forces acting upon it from water related forces such as current, tide, heel angle etcetera. This report looks at the relationship between yacht speed and the force generated by the sail with varying wind speeds, sail area and sail shape. Introduction: Sailing is one of the oldest modes of transport for our civilization, allowing societies to explore and discover the globe. The evolution of yacht racing began with the oldest sporting trophy in history, the first America’s Cup in 1851. The 33rd America’s Cup in Valencia, Spain was won by the USA yacht the BMW Oracle and these yachts as well as those participating in the global Volvo Ocean Race are the finest examples of highly optimized yachts with breakthrough technology. The modelling of yachts currently relies extensively on twisted wind tunnels and computer programs such as the velocity prediction programs for optimization. This extensive and expensive equipment is a more accurate version of the procedure and data found in this experiment and used for more highly tuned yachts such as those racing in the Volvo Ocean Race or the Louis Vuitton America’s Cup. Sailing relies on tactical intelligence, yacht handling and fitness but also heavily depends on yacht design. This paper looks to analyze the best optimization of a sail on a run, 180 ̊ from the true wind by varying sail area, shape and wind speed.  of sail, the sail produces no lift forces. The top part of the sail is referred to as the head of the sail. The edge of the sail closest to the mast is called the luff and the edge furthest away is the leech. The stern of the yacht is the back of the yacht. The pole supporting the sail is the mast and the pole perpendicular to this is the boom. Methods: The model yacht was constructed of two wooden dowels 0.70m ±0.01m and 0.50m ±0.01m with the shorter fastened with zapstraps perpendicular to one end of the longer wooden dowel that created the stern. At either end of the stern, a Lego wheel was taped with two Lego wheels taped to the bow of the yacht. The mast was made of carbon fibre and measured 0.975m±0.01m and placed roughly 10cm from the bow of the yacht. The carbon fibre boom, measured 0.40m±0.01m was attached to the mast ~0.145m above the hull. The sails were constructed from clear 0.20mm plastic sheets of two shapes. One shape was a triangle, while the other was roughly the shape of half an elongated semicircle. A schematic representatio n of the sails used, A to D is shown in Figure 1. A digitizer converts an analog signal of a discrete set of points into digital  The centre of effort on a sail is the geometric centre (please refer to Figure 5) where all wind forces are assumed to act and be optimized. The wind forces on a run are purely a thrust force and unlike all other points  Table 1: Table of initial parameters of sail areas. The mass of the boat found on an analytical balance and the friction force found with a gram-force spring scale. The friction force calculated by pulling the yacht at rest until breaking the friction barrier.  2  wind power, by using the low, medium and high fan settings. A photograph of this setup is shown in Figure 3. Results & Discussion: Influence of Sail Area of Average Speed Figure 2: Photograph of the digitizer equipment used.  The average times for each of the sets of data are shown in Table 2 and the calculated average speed of the model yacht. It is clearly shown in Table 2 and Figure 3 that as the wind speed increases the average speed of the yacht increases, regardless of sail shape or area. A sail with smaller area was attempted at 16.53cm2±0.005cm2 but the yacht only travelled 0.73m±0.005m in comparison to sails A through D which would roll off the end of the 1.20m±0.05m table.  form. The digitizer equipment used shown in Figure 2. Using a digitizer, Sail A had a surface area equal to 23.06cm2±0.005cm2 and sails B, C and D areas of 21.62 cm2±0.005cm2, 21.63 cm2±0.005cm2 and 20.22 cm2±0.005cm2. All sails required a 0.241m±0.01m baton to prevent the head collapsing, placed 0.15m from the head at a 115 ̊angle. The mass of the yacht with the sail was measured using a digital scale and the static friction using a 110g-force spring scale. The parameters of the yacht used in this experiment are shown in Table one with the difference of sail weight between A and D falling within the tolerance parameters outlined.  Analyzing Figure 3, it is shown that the slope of the best fit lines for the same sail with the same speed yet different fan placements have different vertical placements on the graph; however, the slope of the lines are the same. The slope of the best fit line for Sail A aligned with the centre of the sail is 0.035ms-1vwind-1 and slope for the best fit line aligned with the mast is 0.033 ms-1vwind-1. This shows that the fan placement is causing the difference in average speed rather than varying airflow across the sail since the slopes are the same. The same slope shows that the increase in wind speed correlates to the same increase in average speed implying the placement results in the difference in speed. To average the force applied to the yacht the average force generated by the two different fan placements are used. The averaging of power generated by the difference in fan placement results in Figure 5.  The yacht was placed on a Figure 3 - Photograph take of model yacht with Sail D. polished cherry wood table at least a metre and a half long. A Honeywell household fan was placed at one end of the table, angled so that the yacht will travel 1.02m±0.05m on a run. The yacht was then timed to travel the set distance with varying  3  The slope and placement of Sails B and C with a difference of 0.01cm2 have best fit lines almost on top of each other in Figure 5. This demonstrat es sail area is one of the main determinan ts in yacht speed. The slopes of  aerodynamics of the small triangular sail. Influence of Sail Area of Yacht’s Net Force The yacht for each trial and variable change is on a run at 180 ̊to the true wind and there is no lift created by the sail as explored in a twisted wind tunnel by Richard et al.  the best Figure 4 - Graph of the average speed of Sails A, B, C and D to travel from rest, 1.20m with [1] and only fit lines varying wind speed and fan placement found from twenty trials at each data point. a thrust force for Sails driving the A, B, C and D are 0.018 ms-1vwind-1, 0.017 ms- yacht forwards. Using Newtonian Mechanics, 1 vwind-1 , 0.018 ms-1vwind-1 and 0.022 ms-1vwind𝐹 = 𝑚𝑎 (1). 1 . The same slope reveals that an increase in wind speed relates to a linear increase in The thrust force provided by the wind, as average speeds for sails A, B, and C. For sail discussed by Flay et al. [2] is equivalent to D it is slightly higher which may be due to the 𝐹𝑡𝑕𝑟𝑢𝑠𝑡 = 0.01917𝐴𝑠𝑎𝑖𝑙 𝑣𝑤2 , (2) where Asail is the surface, area of the sail in metres squared and vw2 is the wind velocity squared. The wind velocity was not found in this experiment, as the equipment to do so was not available. The force resisting motion was the static and kinetic friction. The kinetic friction is slightly less than the static friction; however, the tread used in the rubber Lego wheels causes both static friction and kinetic friction. To simplify the friction force, as the static friction measured is the entire friction force opposing the yacht’s motion. Since all yacht models have the same weight, they also  Table 2: Table of Average Times for each trial of Sail A, B, C and D to travel 1.2m  4  hand side of Eq.8 as shown in the Net Force column of Table 3. The trend shown in Table 3 is that both wind speed and sail area are proportional to the net force. Using the calculated net force for Sail A at various wind speeds, the estimated value is proportional to the decrease percentage in area. Most estimated values were slightly more than the calculated value. The estimated value should be slightly more due to the rolling tread friction from the Lego tire wheels not accounted for. The anomalies are present in Sails B and C at low and high wind speeds.  Figure 5 – Graph of average speed of Sails A, B, C and D travelling 1.20m with the fan placement averaged for the average wind speed over the entire sail.  Influence of Sail Shape on Average Speed  have the same friction as calculated in Table 1 and restated as: 𝐹𝑓 = 5.88 × 10−2 𝑁  In studies done by Hochkirch et al. [4] the aerodynamics of sail shape are discussed with emphasis on how the height and placement of the centre of effort on a sail affect the speed of the yacht. Due to the variation in sail shape of B and C and thus the alteration of the geometric optimization of a sail’s centre of effort, the force generated varies even with the same area. To evaluate how the centre of effort placement on sails B and C affect the overall speed of the yacht is shown in Figure 6. Figure 6 reveals Sail C has the extreme values and thus the averaging of fan placement speeds decreases the estimated net force. The slopes of the trend line for sail B and C with the fan aligned with the centre of the sail are 0.044ms-1vwind-1 and 0.041ms1 vwind-1 versus sails B and C aligned with the  3 .  By substituting equations 2 and 3 into 1: 𝐹𝑛𝑒𝑡 = 𝑚𝑎 = 𝐹𝑡 − 𝐹𝑓 , 𝐹𝑛𝑒𝑡 = 0.01917𝐴𝑠𝑎𝑖𝑙 𝑣𝑤2 − 5.88 × 10−2 𝑁 4 .  The formula for the average speed, as referred to from Semat [3] is 𝑉𝑜 +𝑉𝑓 5 , 2 where Vavg is the average velocity, Vo is the initial velocity and Vf is the final velocity. Since the model yacht started from rest, Eq.5 is transformed into 𝑉𝑎𝑣𝑔 =  2𝑉𝑎𝑣𝑔 = 𝑉𝑓  6 .  Semat [3] also discusses a formula for acceleration, stated as 𝑉𝑓 − 𝑉𝑜 7 𝑑𝑡 moreover, by substituting Eq. 6 into Eq. 7 the new transformation of Eq.4 is 𝑎=  2𝑚 𝑉𝑎𝑣𝑔 𝑑𝑡  = 0.01917𝐴𝑠𝑎𝑖𝑙 𝑣2𝑤 − 5.88 × 10−2 𝑁 8 .  From Eq.8, the net force acting upon the model yacht should change proportionally to the change in sail area. The net force can be calculated by multiplying mass and the left 5  Table 3 - Table of the difference between the net force estimated by the change in sail area and the calculated net force from Eq. 4 and 7.  Conclusion: In this experiment, by eliminating the water component of sailing the effects of sail area, sail shape and wind speed are more apparent. To optimize a yacht’s performance, a larger sail area increases the thrust force generated by the wind on a run thus increasing the speed. An increase in wind speed linearly increases the average speed of yachts. The centre of effort of sails is determined by shape and the closer the wind force is centralized to the centre of effort, the average speed of yachts increased. Skippers and crew must take this information into account and as such causes the constant trimming of sails when racing.  Figure 6 - Graph of the average speeds of Sail B and C with varying wind speed. The dashed lines are when the fan is aligned with the centre of the sail and the solid lines are when the fan is aligned with the mast.  centre of the sail of 0.030ms-1vwind-1and 0.028 ms-1vwind-1. This can be explained because the luff of the sail is not in use when the fan is more aligned with the sail centre causing the decreased average speed values in comparison.  References: [1] Richards, P.J., Johnson, A., Stanton, A. America’s Cup Downwind Sails – Vertical Wings or Horizontal Parachutes? Journal of Wind Engineering and Industrial Aerodynamics. 89, 1565-1577 (2001). [2] Flay, R.G.J., Vuletich, I.J. Development of a Wind Tunnel Test Facility for Yacht Aerodynamic Studies. Journal of Wind Engineering and Industrial Aerodynamics. 58(3), 231-258 (1995). [3] Semat, H. Fundamentals of Physics. Soil Science. 59(4), 337-343 (1945). [4] Hochkirch, K., Krebber, B. Numerical Investigation on the Effects of Trim for a Yacht Rig. Paper presented at: 2nd High Performance Yacht Design Conference. 2, 1321 (2006).  Sail C had faster average speeds than B when the fan was aligned with the centre of the sail. Sail B had faster average speeds when the fan was aligned with the mast. Crudely using the methods outlined by Hochkirch et al. [4] the geometric centre of effort for sails B and C are shown in Figure 7. By aligning the fan with the mast, the thrust force is closer to Sail B’s centre of effort and as such has higher average speeds. Figure 7 - Crude of the In comparison, aligning Diagram difference in the the fan with the centre Centre of Effort of Sail of the sail, the thrust B and C force is closer to the centre of effort of Sail C and as such has higher average speeds than Sail B.  6  


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