Wooden Shoe Regatta ProjectBy Joshua Robinson School of EngineeringGrand Valley State University EGR 365-Mechanics and Machines Section 903 Instructor: Dr. Ali MohammadzadehJuly 29th , 2020Purpose: The purpose of this project is to design, build and test a 1/35th scale model of a recreational sailboat, while also predicting the performance of a prototype based on the results ofthe model tests.Introduction: The largest consideration taken into the of the boat was the limitations set by the tool available. To maximize my efforts, the main goal was to reduce the frontal projected area to reduce drag. Symmetry of the boat was also a consideration in the boat design in order to keep the bow pointed in the direction of travel, as well as maintaining aesthetics.Model Tests- Hull: 1.Based on principal, we could match the Froude number for model and prototype to achieve kinematic similarity. Because of the requirements derived from the equation this would require the use of a fluid with a viscosity of 4.829∗10−3 times the viscosity of water. Froude had thought of this and proved that the total drag coefficient could be split into a wave-making coefficient reliant and a friction coefficient reliant on Reynolds number.Ct(ℜ , Fn)=Cf(ℜ)+Cr(Fn)Both functions are derived from experimental results and have proven yield reliable results.1. Results0.2500 0.3000 0.3500 0.4000 0.4500 0.5000 0.5500-0.0100-0.0080-0.0060-0.0040-0.00200.00000.00200.0040Cr vs Fn for barge modelFnCr0.2500 0.3000 0.3500 0.4000 0.4500 0.5000 0.5500 0.6000-0.0080-0.0060-0.0040-0.00200.00000.00200.00400.00600.00800.01000.0120Cr vs Fn for sailboat modelFnCr2. If you have tests for a barge shape and for a more streamlined shape, can you conclude anything about the effect of streamlining on performance based on your tests? Based on the results from the tests, the streamlined shape sailboat had higher velocities than the barge with the same drag force applied. 3. What were the largest sources of error in your hull tests?The largest sources of error include the measuring of the wetted area and the speed of the gravity driven model. The measurement of the wetted area was very inaccurate and involve a large amount of human error. The timing of the model runs introduced a large error into the speed values of the models. Other sources of error include friction in thepulleys and drag due to pull rope. Looking at the total resistance calculated for the prototype we see significant error propagation.Resistance=0.5 Ctρ ApVp2Expanding this equation out into the calculated values we get the following:Resistance=0.5[((Resistancemodel0.5 ρ AmodelVmodel2−Cfmodel)+Cfprototype)ρ(Amodel∗362)(Vmodel(36)12)2]Because of kinematic similarity we can ignore the friction coefficients.Uresistance=Resistance√122+2(1i n2Are amodel)2+8(0.1ftsVmodel)2Model Tests – Sails: 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00-25.00-20.00-15.00-10.00-5.000.00Cd vs Yaw angleYaw angle (deg) Cd0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00-5.000.005.0010.0015.0020.00Cl vs Yaw angleYaw angle (deg)ClPrototype Predictions: The model results will be followed by your prototype predictions. The purpose of this analysis is to determine possible points of sail. For those who completed the 1/35 scale models do this for one of the hulls that you tested. Include at least 3 graphs in this section:1. Hull Resistance (drag) vs Fn for the prototype. (include error bars)0.2500 0.3000 0.3500 0.4000 0.4500 0.5000 0.5500 0.6000-500.00000.0000500.00001000.00001500.00002000.00002500.00003000.00003500.0000Hull resistance vs FnFnHull Resistance 2. EHP vs Fn for the prototype. (useful if you wish to choose a motor)0.2500 0.3000 0.3500 0.4000 0.4500 0.5000 0.5500 0.6000-10.00000.000010.000020.000030.000040.000050.000060.0000EHP vs FnFnEHP1. Forward Force vs Yaw Angle for the sail at a given prototype relative windspeed.0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00-8.00-6.00-4.00-2.000.002.004.006.008.00Forward Force vs Yaw angleYaw angle (deg)Force (lbf)Selecting a boat speed of 6.13 ft/s there is a hull resistance of 99.6 lb. The sail would not be adequate for the at a 5mph winds. Although using the corresponding Froud number at 6.13 ft/s we find that a 1 ¼ HP motor will have enough power to overcome the resistance of the hull.Sample CalculationsCtbarge=Resistance force0.5∗ρ∗A∗V215.8 i n2(1 f t2144 in2)∗(82.2fts)2¿0.5∗62.3lbf t3∗¿Ctbarge=4.99 g (6.8522∗10−5Slugsg)(32.2fts)¿F nm−barge=V(gL)12=.82fts[(32.2fts2)(.2917 ft)]1 /2=.2689R em−barge=VmLmγm=(.82fts)(.2917 ft )(1.126∗10−5f t2s)=21348Cf=0.075(Lo g10ℜ−2)2=0.075(Lo g1021348.5−2)2=1.382∗10−2Cr=Ct−Cf=4.74∗10−3−1.382∗10−2=−9.08∗10−3Vprototype=Vm(LpLm).5=(.82fts)(35).5=4.875ftsResistancep=(.5)(Ct)(ρ)(Ap)(Vp2)=(.5) (−.0056)(62.3lbf t2)(134.4 f t2)(4.87fts)2=−557.9EHP=Resistanc ep(Vp)(1 hp550ft lbfs)=(−557.9) (4.876)(1550)=−4.946 hpUresistance=Resistance√122+2(1i n2Are amodel)2+8(0.1ftsVmodel)2122+2(1i