2 HOT 2 SAIL

This project investigates the effect of sail factors on yacht speed. Mainly, the factors of the yacht sails affect the aerodynamics of the boat which determines the speed of the boat. But due to budget factors, this investigation was done with a model boat.

Focus questions

a) The effects of material, angle, shape and surface area of the sail on yacht speed.

b) The effect of the sail's shape on the yacht's optimum surface area.

c) The effect of perimeter reinforcement on yacht speed.

a)We had five treatments for each material, shape, and surface area, and four treatments for each angle.

 Variable Treatments Material Sail, Paper, Cardboard, Plastic, Cloth Angle 45º, 90º, 135º, 180º (to the boat's platform when traveling towards the wind) Shape Circle, Square, Rectangle, Triangle, Pentagon Surface area 130cm2, 160cm2, 190cm2, 220cm2, 250cm2

b) For the shapes: circle, square, rectangle and triangle, we had the surface areas: 190cm2, 210cm2, 250cm2, 270cm2.

c) For 270cm2 sails, we reinforced the shapes: circle, square, rectangle and triangle.

For each treatment we took 20 measurements.

In these investigations, we measured how long it took for tour model yacht to cross a 76cm tub. Then we calculated the speed of the boat. For all the treatments, we had to control a few variables. We kept the fan a constant distance from the tub and at a constant speed all the time. We also worked in a closed off room which would prevent all external winds. The same boat was used for each test. The surface area of the sails were always kept constant except where it was the independent variable. When we tested the reinforcements of the sails we kept the sail weights the same.

Results

a) results of investigation a

 material sail cardboard plastic cloth paper Ave. time (s) 4.67 4.32 4.02 4.08 4.21 Ave. speed (cm/s) 16.41 17.89 19.18 18.79 18.34 Stand dev. (time) 0.44 0.63 0.5 0.4 0.53 Stand dev. (speed) 1.48 2.05 2.33 1.76 2.24

 Angle to boat platform 135 180 45 90 Ave. time (s) 4.64 10.3 6.61 3.83 Ave. speed (cm/s) 16.66 8.15 11.73 20.07 Stand dev. (time) 0.6 4.62 0.88 0.39 Stand dev. (speed) 2.18 1.94 1.79 2.07

 Shape triangle square circle pentagon rectangle Ave. time (s) 3.73 3.78 3.73 4.15 3.38 Ave. speed (cm/s) 20.53 20.25 20.49 18.47 22.58 Stand dev. (time) 0.31 0.3 0.3 0.36 0.18 Stand dev. (speed) 1.67 1.55 1.55 1.63 1.27

 Surface area 130cm2 160cm2 190cm2 220cm2 250cm2 Ave. time (s) 3.73 3.19 2.89 2.75 3.71 Ave. speed (cm/s) 20.46 23.94 26.59 27.75 27.79 Stand dev. (time) 0.19 0.25 0.31 0.14 4.78 Stand dev. (speed) 1.1 1.72 2.98 1.38 6.37

b) results of investigation b

 triangle Surface area cm2 160 190 230 270 310 350 Ave. time (s) 5.45 5.47 4.72 4.67 4.32 4.04 Ave. speed (cm/s) 13.9 13.9 16.12 16.29 17.6 18.81 Stand dev. (time) 0.45 0.31 0.33 0.31 0.28 0.24 Stand dev. (speed) 1.03 0.87 1.14 1.07 1.27 1.15

 rectangle Surface area cm2 160 190 230 270 310 350 Ave. time (s) 3.21 3.04 2.7 2.49 2.63 2.33 Ave. speed (cm/s) 23.7 24.98 28.17 30.57 28.82 32.37 Stand dev. (time) 0.14 0.18 0.17 0.18 0.15 0.19 Stand dev. (speed) 1.02 1.49 1.64 2.12 1.78 2.21

 square Surface area cm2 160 190 230 270 310 350 Ave. time (s) 3.8 3.43 3.23 3.21 3.25 3.27 Ave. speed (cm/s) 19.98 22.17 23.52 23.71 23.41 23.24 Stand dev. (time) 0.14 0.34 0.13 0.2 0.19 0.13 Stand dev. (speed) 0.75 2.15 0.98 1.54 1.4 1.07

 circle Surface area cm2 160 190 230 270 310 350 Ave. time (s) 5.03 3.91 3.5 3.4 3.39 2.77 Ave. speed (cm/s) 15.1 19.43 21.71 22.41 22.45 27.42 Stand dev. (time) 0.36 0.15 0.14 0.17 0.34 0.16 Stand dev. (speed) 1.1 0.79 0.95 1.12 2.34 1.65

c) results of investigation c

 reinforcement Surface area cm2 triangle rectangle square circle Ave. time (s) 3.13 2.78 3.22 3.03 Ave. speed (cm/s) 24.3 27.38 23.62 25.86 Stand dev. (time) 0.14 0.15 0.17 0.16 Stand dev. (speed) 1.13 1.47 1.24 1.31 Difference between reinforced and not 8.02 -3.19 -0.09 3.45

Discussion

In the material investigation, plastic did the best. We think that this is because it is impermeable, unlike cloth and sail material. It is also the lightest of all the materials we used. But, real scale yachts would not easily be able to use plastic sails due to their weakness: they can tear very easily. A torn sail cannot be used anymore because the wind will not be able to push the sail.

An increase in surface area increases speed until an optimum point – when the accompanying increase in mass has a greater negative effect than the increase in surface area has a negative effect. To find the optimum surface area, we increased surface area until the largest size the yacht's mast could fit. Our data suggests that the optimum surface area could not be reached with the mast size we have, although in some graphs we found a slight dip (when graphed) in the highest readings, showing an optimum was soon to be reached.

When we decided to reinforce some of our sail shapes, we hypothesized that this would increase speed. We reasoned that if adding perimeter reinforcement caused improvement through adding tautness, then the speed obtained with the circular sail (which is slack without reinforcement) should be improved by perimeter reinforcement relative to others. While this was found in relation to square and rectangle, reinforcement of the triangle improved speed considerably relative to all the shapes, despite the fact that this was accompanied by little affect on tautness. This made us deduce that tautness might not be the most influential factor altered by perimeter reinforcement. We think that our observations could probably be explained by considering the effect that the different distribution of mass (due to perimeter reinforcement of each shape) had on the stability of each sail. The lower the distribution of mass in a structure, the more stable the structure, so adding mass along the perimeter of a rectangle (if orientated with its long axis perpendicular to the boat deck) stabilizes the structure.

In treatments in which the perimeters were reinforced, the top mast, used in previous treatments was removed. This would also have increased the circular sail's stability, and would explain why its speed improved relative to the square and rectangular sails. It seems, therefore, that stability is an important factor in affecting yacht speed.

Only two forces act on the boat: the force of gravity and the upward push of the water. If we take the contact point of the boat and the water as the pivot, only gravity has a nonzero torque. With triangular sails, the torque die to gravity is counter clockwise and causes the boat to remain in an upright position. With rectangular sails, gravity make a clockwise torque and so causes the boat to be very unstable. When the boat is very unstable it slows it down quite allot. This can be an explanation for the triangular and the rectangular sail's performances when they were reinforced.

Conclusion

a) The higher the effective surface area (that part of the sail which intercepts the wind), the higher the boat speed, up to an optimum point. Effective surface area can be increased by increasing:

• sail impermeability

• sail tautness

• the angle between the sail and the long axis of the boat's platform

• sail's surface area.

b) Square sails reach and optimum at lower surface areas than rectangular, circular or triangular shapes; although the speed at this optimum point is lower than that obtainable with rectangular or circular sails. Optimum surface area for triangular and circular sails fell out of the range of data obtainable.

c) Where perimeter reinforcement and the opportunity this offers to remove the top horizontal mast, increases stability, it increases speed relative to other cases.

Acknowledgments

• Franz Huber gave us the wood for the boat and also carved it out for us

• Bill Hailstones gave us the yacht mast and the testing tub

• Angella Stott gave us advice on the investigation.

Bibliography

www.yachtsails.com

Bueche F.J (1988) Principles of Physics. McGraw-Hill. New York.

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