Grand Valley State University The Padnos School of Engineering WOODEN SHOE REGATTA MODEL SAIL BOAT REPORT EGR 365 FLUID MECHANICS Brad Vander Veen July 30 2003 INTRODUCTION 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 rutter THE DESIGN Figure 1 below shows a picture of the model sailboat Figure 1 Picture of Model Sailboat The 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 63 0 91 1 18 1 47 1 74 1 95 2 22 2 48 0 0132 0 0242 0 0165 0 0264 0 0165 0 0330 0 0308 0 0484 0 0660 Table 1 Drag Test Results MODEL CALCULATIONS Using the wetted surface area of the model and the model speed the total resistance coefficient can be calculated Ct Drag 0 5 AV 2 Table 2 below shows the resistance coefficient at each speed speed model ft s total resistance coefficient model 0 35 0 63 0 91 1 18 1 47 1 74 1 95 2 22 2 48 0 2399 0 1358 0 0444 0 0422 0 0170 0 0243 0 0180 0 0219 0 0239 Table 2 Total Resistance Coefficient The Froude Number can also be calculated for each speed Fn V gL Table 3 below shows the Froude Number for each speed speed model ft s Froude Number 0 35 0 63 0 91 1 18 1 47 1 74 1 95 2 22 2 48 0 0552 0 0993 0 1434 0 1860 0 2317 0 2743 0 3074 0 3499 0 3909 Table 3 Froude Number In Figure 2 below the hull resistance is plotted vs the Froude Number Drag Force 0 08 0 07 0 06 0 05 0 04 0 03 0 02 Drag Force 0 01 0 00 0 00 0 05 0 10 0 15 0 20 0 25 0 30 0 35 Froude Number Figure 2 Drag vs Froude Number For Model 0 40 0 45 Using the Reynolds Number for the model and the waterline length of the model and the model speed the friction coefficient can be calculated Cf 075 log10 Re 2 2 Table 4 below shows Reynolds Number and the friction coefficent for each speed speed model ft s Reynolds Number Model friction coefficient model 0 35 0 63 0 91 1 18 1 47 1 74 1 95 2 22 2 48 36157 65083 94008 121901 151860 179752 201446 229339 256198 0 01146 0 00947 0 00848 0 00788 0 00741 0 00708 0 00687 0 00664 0 00646 Table 4 Reynolds Number and Friction Coefficient The residual coefficient can now be calculated C r C t C f Table 5 below shows the residual coefficient speed model ft s residual coefficent 0 35 0 63 0 91 1 18 1 47 1 74 1 95 2 22 2 48 0 22849 0 12630 0 03588 0 03434 0 00959 0 01719 0 01117 0 01523 0 01744 Table 5 Residual Coefficient PROTOTYPE 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 1 Lp 2 V p Vm Lm Table 6 below shows the speed of the prototype sailboat speed model ft s Froude Number prototype velocity ft s 0 35 0 63 0 91 1 18 1 47 1 74 1 95 2 22 2 48 0 0552 0 0993 0 1434 0 1860 0 2317 0 2743 0 3074 0 3499 0 3909 1 212 2 182 3 152 4 088 5 092 6 028 6 755 7 690 8 591 Table 6 Prototype Velocity The Reynolds Number for the prototype can now be calculated and using the Reynolds Number the prototype friction coefficient can be calculated Cf 075 log10 Re 2 2 Table 7 below shows Reynolds Number and the friction coefficient for the protoype prototype velocity ft s Reynolds Number Prototype friction coefficient prototype 1 212 2 182 3 152 4 088 5 092 6 028 6 755 7 690 8 591 1503019 2705435 3907850 5067322 6312681 7472153 8373965 9533437 10649965 0 00430 0 00382 0 00356 0 00339 0 00325 0 00316 0 00309 0 00303 0 00297 Table 7 Prototype Reynolds Number and friction coefficient The total resistance coefficient for the prototype can now be calculated C t C f C r Table 8 below shows the total resistance coefficient for the prototype prototype velocity ft s total resistance coefficient prototype 1 212 2 182 3 152 4 088 5 092 6 028 6 755 7 690 8 591 0 23279 0 13012 0 03944 0 03773 0 01285 0 02035 0 01426 0 01825 0 02041 Table 8 Prototype Total Resistance Coefficient The total drag force for the prototype can now be calculated Drag 0 5 C t A pV p 2 Table 9 below shows the total drag force on the prototype prototype velocity ft s drag prototype lbf 1 212 2 182 3 152 4 088 5 092 6 028 6 755 7 690 8 591 22 129 40 075 25 346 40 771 21 545 47 809 42 083 69 805 97 402 Table 9 Prototype Drag Force The horsepower needed to overcome this drag force can also be calculated 1Hp Hp Drag V p ft lbf 550 sec Table 10 below shows the horsepower calculation for the prototype prototype velocity ft s EHP hp 1 212 2 182 3 152 4 088 5 092 6 028 6 755 7 690 8 591 0 049 0 159 0 145 0 303 0 199 0 524 0 517 0 976 1 521 Table 10 Prototype Horsepower Calculation Figure 3 below shows a plot of the necessary horsepower to overcome the drag force of the prototype Prototype Horsepow er 2 50 2 00 EHP hp Prototype Horsepow er 1 50 1 00 0 50 0 00 0 00 0 10 0 20 0 30 0 …