Table of Contents1. Introduction2. Sail Boat Design Considerations3.1 Model Hull Test3.2 Model Sail Test4. Prototype Performance Predictions1Wooden Shoe RegattabyDan SchwarzSchool of EngineeringGrand Valley State UniversityEGR 365 – Fluid MechanicsSection 01Instructor: Dr. S. FleischmannAugust 3, 20072Table of Contents1. Introduction…….….….….……….…………..………………………………..………..……..32. Sail Boat Design Considerations…….….….….……….………….……………………..…….33.1 Model Hull Test…………………..……………….……………………….…………….……43.2 Model Sail Test..…………….…...…….…………….………..………..….……….…..…..…54. Prototype Performance Predictions…………….…………………….…………….….……….55. Conclusions……………………….…………….…………………….……………….……….76.1 Appendix A - Hull Performance Sample Calculation …..….….………….………………….76.2 Appendix B - Hull Performance Data ……………………...……..…..…….…….………….96.3 Appendix C - Hull Error Propagation Sample Calculation …………………….…………….96.4 Appendix D - Sail Performance Sample Calculation …………………………….……….….96.5 Appendix E - Sail Performance Data ……………….…………….………….…….……….1031. IntroductionThe purpose of the wooden shoe regatta project was to design a 1/12th scale model of a 10foot long, single hull sailboat. The model hull was constructed first and tested using a 12’ towingtank to measure drag forces as a function of velocity. A sail model was also tested using a windtunnel to determine the forward thrust provided by the sails. These test results were scaled usingFroude’s Hypothesis and Reynolds number matching to predict the performance of a full scalesailboat.2. Sail Boat Design ConsiderationsThe hull of the model was constructed from a 10”x2”x4” block of basswood. Figure 1shows the hull design with dimensions included. It was designed with gradual contours andsmooth surfaces in an attempt to maintain laminar flow and minimize flow separation. Thewidth of the hull was made as narrow as possible to reduce ‘form’ drag. The height of the hullwas made smaller than the width to prevent instability of the boat when transverse forces areapplied by wind blowing against the sails.Figure 1: The 1/12th scale boat hull was designed with gradual contours to reduce flow separation (Dimensionsin inches).The model sails, shown in Figure 2, were constructed from rip stop material because it islight and durable. The height of each sail was designed to be short relative to its length so thatthe centroid was closer to the boat without making the sail area smaller. A low centroid wasintended to reduce the moment arm between the wind forces on the sail and the center of mass.Since the moment arm created by wind forces was quite small, it was not necessary to make akeel for stability.4A rudder was built using an aluminum rod and sheet. The rudder could be set in one of17 positions to counteract any forces that tend to rotate the boat as it sails. The rudder assemblyis shown in Figure 2.Figure 2: The 1/12th scale model is shown complete with sails and a rudder.3.1 Model Hull TestA hull test was performed in a 12 foot towing tank which was filled with water. Aharness was attached to the top of the hull which was attached to a cantilever beam on the sled.The sled pulled the hull through the water at a constant velocity and resultant beam deflectionswere measured by a strain indicator. A calibration curve was used to convert strainmeasurements into drag forces. Finally the drag forces and velocities could be used to calculatethe residual drag coefficients for each test. The residual drag coefficient is plotted with respectto the Froude number as shown in Figure 3. Figure 3 indicates that the residual drag coefficientbecomes less significant as the Froude number increases. See Appendix A for details about thedrag coefficient calculations and Appendix B for detailed results.5Figure 3: The residual coefficient is graphed as a function of the Froude Number.The main source of error in this test was error propagation. An equation describing errorpropagation in the drag coefficient calculation was derived from the drag equation. The totaluncertainty was found using Equation 1. See Appendix C for details.2224AUVUDragUUUCUAVDragDCrCDr(1)The wetted surface area of the model hull was found using CAD methods and thus theuncertainty in area was considered to be negligible. However, there was significant uncertaintyin both the velocity and drag force measurements. 3.2 Model Sail TestA sail test was performed in the wind tunnel using copper sails because rigidity is neededfor high velocity testing. The test was performed at a static pressure reading of 3 inches alcohol.The yaw angle was changed from 0 to 90 degrees in 10 degree increments. At each incrementthe sail forces were measured parallel and perpendicular to the flow direction. See Appendix Efor test data.4. Prototype Performance PredictionsFroude’s Hypothesis and Reynolds number matching methods were used to predict theperformance of a prototype based on the model’s performance. Details of the methods are shownin Appendix A and Appendix D. The predicted prototype hull drag is plotted with respect to theFroude number in Figure 4. Figure 4 shows that the drag force increases as the fluid velocityand corresponding shear stresses increase.6Figure 4: The hull drag force is graphed as a function of the Froude Number.The hull drag values were converted into effective horse power to determine how muchpower is needed to propel the hull at a particular speed. Figure 5 shows the effective horsepowercurve for the prototype. This data could be used to size an engine to provide auxiliary power forthe boat when wind power is insufficient.Figure 5: The EHP is graphed as a function of the Froude Number.Reynolds number matching was used to determine the thrust provided by the prototypesails. Thrust is plotted with respect to the yaw angle in Figure 6. The Figure 6