1 Wooden Shoe Regatta by Dan Schwarz School of Engineering Grand Valley State University EGR 365 Fluid Mechanics Section 01 Instructor Dr S Fleischmann August 3 2007 2 Table of Contents 1 Introduction 3 2 Sail Boat Design Considerations 3 3 1 Model Hull Test 4 3 2 Model Sail Test 5 4 Prototype Performance Predictions 5 5 Conclusions 7 6 1 Appendix A Hull Performance Sample Calculation 7 6 2 Appendix B Hull Performance Data 9 6 3 Appendix C Hull Error Propagation Sample Calculation 9 6 4 Appendix D Sail Performance Sample Calculation 9 6 5 Appendix E Sail Performance Data 10 3 1 Introduction The purpose of the wooden shoe regatta project was to design a 1 12 th scale model of a 10 foot long single hull sailboat The model hull was constructed first and tested using a 12 towing tank to measure drag forces as a function of velocity A sail model was also tested using a wind tunnel to determine the forward thrust provided by the sails These test results were scaled using Froude s Hypothesis and Reynolds number matching to predict the performance of a full scale sailboat 2 Sail Boat Design Considerations The hull of the model was constructed from a 10 x2 x4 block of basswood Figure 1 shows the hull design with dimensions included It was designed with gradual contours and smooth surfaces in an attempt to maintain laminar flow and minimize flow separation The width of the hull was made as narrow as possible to reduce form drag The height of the hull was made smaller than the width to prevent instability of the boat when transverse forces are applied by wind blowing against the sails Figure 1 The 1 12th scale boat hull was designed with gradual contours to reduce flow separation Dimensions in inches The model sails shown in Figure 2 were constructed from rip stop material because it is light and durable The height of each sail was designed to be short relative to its length so that the centroid was closer to the boat without making the sail area smaller A low centroid was intended 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 a keel for stability 4 A rudder was built using an aluminum rod and sheet The rudder could be set in one of 17 positions to counteract any forces that tend to rotate the boat as it sails The rudder assembly is shown in Figure 2 Figure 2 The 1 12th scale model is shown complete with sails and a rudder 3 1 Model Hull Test A hull test was performed in a 12 foot towing tank which was filled with water A harness 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 deflections were measured by a strain indicator A calibration curve was used to convert strain measurements into drag forces Finally the drag forces and velocities could be used to calculate the residual drag coefficients for each test The residual drag coefficient is plotted with respect to the Froude number as shown in Figure 3 Figure 3 indicates that the residual drag coefficient becomes less significant as the Froude number increases See Appendix A for details about the drag coefficient calculations and Appendix B for detailed results 5 Figure 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 error propagation in the drag coefficient calculation was derived from the drag equation The total uncertainty was found using Equation 1 See Appendix C for details U Cr Cr U CD UD U Drag Drag 2 U 4 V V 2 U A A 2 1 The wetted surface area of the model hull was found using CAD methods and thus the uncertainty in area was considered to be negligible However there was significant uncertainty in both the velocity and drag force measurements 3 2 Model Sail Test A sail test was performed in the wind tunnel using copper sails because rigidity is needed for 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 increment the sail forces were measured parallel and perpendicular to the flow direction See Appendix E for test data 4 Prototype Performance Predictions Froude s Hypothesis and Reynolds number matching methods were used to predict the performance of a prototype based on the model s performance Details of the methods are shown in Appendix A and Appendix D The predicted prototype hull drag is plotted with respect to the Froude number in Figure 4 Figure 4 shows that the drag force increases as the fluid velocity and corresponding shear stresses increase 6 Figure 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 much power is needed to propel the hull at a particular speed Figure 5 shows the effective horsepower curve for the prototype This data could be used to size an engine to provide auxiliary power for the 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 prototype sails Thrust is plotted with respect to the yaw angle in Figure 6 The Figure 6 indicates that as the sail is turned perpendicular to the flow direction the trust is increased The figure also 7 indicates that the prototype would not sail when the relative wind velocity is 8ft s since the initial hull drag is approximately 30 lbs However if the wind velocity is increased the boat would be most likely to sail with a yaw angle of 40 degrees or higher Figure 6 The forward driving force is graphed as a function of the sail yaw angle 5 Conclusions A working 1 12th scale model of a 10 foot sail boat was built Hull tests indicate that reasonably small drag forces can be expected for the prototype A small engine could be used for auxiliary power to move the prototype at speeds under 7 ft s with approximately 1 hp Sail tests indicate that the prototype would require more than 8 ft s relative wind velocity to sail The boat would be most likely to sail with yaw angles between 40 and 90 degrees 6 1 Appendix A Hull Performance Sample Calculation Test conditions for the sample calculations are Re sis tan ce Force M 0 0386lbf AM 0 24 ft 2 V M 2 ft s and L M 1 74 ft The total resistance