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<br />I" <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br /> <br />(fable 4). (When referring to the <br />hazard curve, the scale on the <br />vertical axis represents velocity, <br />while the same scale represents <br />the product number when <br />referring to the product number <br />curve. ) <br /> <br />When these plots are <br />superimposed with respect to the <br />hazard envelope (Figure 11), a <br />"controlling product number" <br />curve is generated for a given <br />configuration of weight, <br />geometry, and coefficients. It is <br />this "controlling product <br />number" curve which is used to <br />compare different configurations <br />in the remainder of this analysis. <br /> <br />Controlling <br />Product Number <br /> <br />10 <br /> <br />..__.. .:0:_ 511ppoge PN <br /> <br />..- Toppllng PN <br /> <br />:0: :0: .0- Controlling PN <br />...........-.~~;oc~:::tr.'.!=.".=l~.?;.~:r:....x;;.;:x::.I............................... <br /> <br />~ 5 .-ol!.' o..o..Q..().;;;o.. -:J :0:':0:,_ <br /> <br />t ~o~ :0:,_ <br />~~- <br /> <br />m.m....m................. ........................._..... ..........m................... ..................~..... <br /> <br />P <br />r <br />o <br />d <br /> <br />., <br /> <br />o <br />o <br /> <br />3 <br /> <br />4 <br /> <br />2 <br />Depth <br /> <br />Figure 11 <br /> <br />Figure II is a composite of product numbers for slippage and toppling hazards. At lower depths, <br />the product number is controlled by slippage while at greater depths the product number is <br />controlled by toppling up to a limited depth where buoyancy controls. The peak represents the <br />intersection of the product number curves for slippage and toppling. <br /> <br />Sensitivity Analysis <br />As part of this analysis, the validity of the assumptions slated above were explored by studying the <br />effects of various parameters on the curves shown earlier. <br /> <br />As stated previ- <br />ously, the coeffi- <br />cient of drag (Cd) <br />is based upon <br />losses due to fric- <br />tion with the <br />ground surface <br />and momentum <br />changes due to <br />variations in flow, <br />and is a function <br />of velocity and <br />flow regime (Ref- <br />erence 5). While <br />the "Colorado <br />Floodproofing <br />4 Manual" states <br />that a minimum of <br />1.25 should be <br />Figure 12 used for rectan- <br />gular objects, the relatively small size of the objects under consideration led to the use of a value of <br />1.0 as a base coefficient. This value was varied from 1.0 to 1.5 to test the sensitivity of the param- <br />eter (Figure 12), and a median value of 1.25 was ultimately chosen for purposes of comparing the <br />effects of body geometry. <br /> <br />Product Number as a Function of <br />Coefficient of Drag <br /> <br /> - Bose PN <br />- .. .. <br /> .... Cd=l .25 <br />...._........................m.......... .......................................... .......................................... <br /> - Cd= 1.5 <br />./. .' ...............- <br />.... - <br />~~.,-1.- ~." <br />~ ...~ <br /> ......... <br /> ..~~.... <br /> ~ "~ <br />..-........................._........ ........................................... ...........................-.~.. ..~;::O:,...................... <br /> ~ <br /> .... <br /> <br />10 <br /> <br />P <br /> <br />r <br />o <br />d <br />u 5 <br />c <br />t <br /> <br />., <br /> <br />o <br />o <br /> <br />2 <br />Depth <br /> <br />3 <br /> <br />- 11- <br />