WOODEN SHOE REGATTA:MODEL SAIL BOAT REPORTEGR 365 – FLUID MECHANICSINTRODUCTION:PRELIMINARY DESIGN STATEMENT:THE DESIGN:TESTING:MODEL CALCULATIONS:PROTOTYPE CALCULATIONS:SAIL CALCULATIONS:DISCUSSION:CONCLUSION:Grand Valley State UniversityThe Padnos School of EngineeringWOODEN SHOE REGATTA: MODEL SAIL BOAT REPORTEGR 365 – FLUID MECHANICSBrad Vander Veen July 30, 2003INTRODUCTION:The purpose of this project is to design, build, and test a 1/12 model recreational sailboat.After this model has been tested, calculations will then be performed to predict how the full-scale prototype will behave. The hull for the model boat is to be made from a 2” x 4”x 10” block of basswood. The design must be a single hull design, and the entire hull must be made only of the basswood. The boat must also be powered only using sails to harness the wind. The boat must also be design so that it would look appealing to customers wanting to buy a sailboat.PRELIMINARY DESIGN STATEMENT:The boat I have build was designed using the following criteria:- high width to depth ration (for increased stability)- low weight- shape will be similar to real sailboat- use two sails (main sail and jib sail)- adjustable rutterTHE DESIGN:Figure 1 below shows a picture of the model sailboat:Figure 1 – Picture of Model SailboatThe completed model design had a waterline length of 15”, and a wetted surface area of 67 square inches. The mast reached a height of 16” from the surface of the deck.TESTING:The model hull was put through a hull test in a towing tank. Drag on the model was found for a range of different speeds. In Table 1 below, the test results can be seen.speed_model [ft/s] drag_model [lbf] 0.35 0.01320.63 0.02420.91 0.01651.18 0.02641.47 0.01651.74 0.03301.95 0.03082.22 0.04842.48 0.0660Table 1 – Drag Test ResultsMODEL CALCULATIONS:Using the wetted surface area of the model and the model speed, the total resistance coefficient can be calculated.25.0 AVDragCtTable 2 below shows the resistance coefficient at each speed:speed_model [ft/s] total_resistance_coefficient_model 0.35 0.23990.63 0.13580.91 0.04441.18 0.04221.47 0.01701.74 0.02431.95 0.01802.22 0.02192.48 0.0239Table 2 –Total Resistance CoefficientThe Froude Number can also be calculated for each speed.gLVFn Table 3 below shows the Froude Number for each speed:speed_model [ft/s] Froude Number 0.35 0.05520.63 0.09930.91 0.14341.18 0.18601.47 0.23171.74 0.27431.95 0.30742.22 0.34992.48 0.3909Table 3 – Froude NumberIn Figure 2 below, the hull resistance is plotted vs. the Froude Number:Drag Force0.000.010.020.030.040.050.060.070.080.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45Froude NumberDrag ForceFigure 2 – Drag vs. Froude Number For ModelUsing the Reynolds Number for the model and the waterline length of the model and the model speed, the friction coefficient can be calculated.210)2Re(log075.fCTable 4 below shows Reynolds Number and the friction coefficent for each speed.speed_model [ft/s] Reynolds Number (Model) friction_coefficient_model 0.35 36157 0.011460.63 65083 0.009470.91 94008 0.008481.18 121901 0.007881.47 151860 0.007411.74 179752 0.007081.95 201446 0.006872.22 229339 0.006642.48 256198 0.00646Table 4 – Reynolds Number and Friction CoefficientThe residual coefficient can now be calculated.ftrCCC Table 5 below shows the residual coefficient:speed_model [ft/s] residual_coefficent 0.35 0.228490.63 0.126300.91 0.035881.18 0.034341.47 0.009591.74 0.017191.95 0.011172.22 0.015232.48 0.01744Table 5 – Residual CoefficientPROTOTYPE CALCULATIONS:Now that the Froude Number is matched, calculations can be made for the prototype sailboat.Using the Froude Number, the prototype sailboat speed can be calculated.21mpmpLLVVTable 6 below shows the speed of the prototype sailboat:speed_model [ft/s] Froude Number prototype_velocity [ft/s] 0.35 0.0552 1.2120.63 0.0993 2.1820.91 0.1434 3.1521.18 0.1860 4.0881.47 0.2317 5.0921.74 0.2743 6.0281.95 0.3074 6.7552.22 0.3499 7.6902.48 0.3909 8.591Table 6 – Prototype VelocityThe Reynolds Number for the prototype can now be calculated, and using the Reynolds Number, the prototype friction coefficient can be calculated.210)2Re(log075.fCTable 7 below shows Reynolds Number and the friction coefficient for the protoype:prototype_velocity [ft/s] Reynolds Number (Prototype) friction_coefficient_prototype 1.212 1503019 0.004302.182 2705435 0.003823.152 3907850 0.003564.088 5067322 0.003395.092 6312681 0.003256.028 7472153 0.003166.755 8373965 0.003097.690 9533437 0.003038.591 10649965 0.00297Table 7 – Prototype Reynolds Number and friction coefficientThe total resistance coefficient for the prototype can now be calculated.rftCCC Table 8 below shows the total resistance coefficient for the prototype:prototype_velocity [ft/s] total_resistance_coefficient_prototype 1.212 0.232792.182 0.130123.152 0.039444.088 0.037735.092 0.012856.028 0.020356.755 0.014267.690 0.018258.591 0.02041Table 8 – Prototype Total Resistance CoefficientThe total drag force for the prototype can now be calculated:25.0pptVACDragTable 9 below shows the total drag force on the prototype:prototype_velocity [ft/s] drag_prototype [lbf] 1.212 22.1292.182 40.0753.152 25.3464.088 40.7715.092 21.5456.028 47.8096.755 42.0837.690 69.8058.591 97.402Table 9 – Prototype Drag ForceThe horsepower needed to overcome this drag force can also be calculatedsec5501lbfftHpVDragHppTable 10 below shows the horsepower calculation for the prototype:prototype_velocity [ft/s] EHP [hp] 1.212 0.0492.182 0.1593.152 0.1454.088 0.3035.092 0.1996.028 0.5246.755 0.5177.690 0.9768.591 1.521Table 10 – Prototype Horsepower CalculationFigure 3 below shows a plot of the necessary horsepower to overcome the drag force of the prototype:Prototype Horsepow er0.000.501.001.502.002.500.00 0.10 0.20 0.30 0.40 0.50Froude Num berEHP [hp]Prototype Horsepow erFigure 3 – Horsepower Needed to Overcome DragSAIL CALCULATIONS:SEE APPENDIX A FOR SAIL DATA:To get model sail data, a copper sail was placed in a wind tunnel. This sail was also a 1/12 scale, so Reynolds scaling was used to match sail forces. The model sail was put into a wind tunnel with a model wind velocity of 136 ft/second. This corresponds to a prototype wind velocity 11.35 ft/s.Table 11 below shows the forward force generated due to the wind:yaw angle [deg] Forward Force @ 5'' or 11`.35 ft/s [lbf] 0