Shockwave Examples - practice PDF

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SignalShockwaveExampleProblem(Text6.11) Given: u1=40mph k1=44veh/mi/lane qs=1950veh/hr/lane ks=51veh/mi/lane kj=120veh/mi/lane a) Whatisthelengthofthequeueattheendoftheredphase? First,determinetheinitialvehicularflow: q1=u1k1=40*44=1760veh/hr/lane Next,findthespeedofBackwardFormingShockwave: ωBF=‐q1/(kj‐k1)=‐1760/(120‐44)=‐23.2mph Converttofeet/second: ωBF=‐23.2mph*1.47fps/mph=‐34.0fps Finally,determinequeuelength: LQr=ωBF*r=‐34.0*30=1020ft  b) Whatisthemaximumqueuelength? Fromparta,weknowωBF=‐34.0fps. NextweneedtosolveforωBR. ωBR=q2/(k2‐kj)=1950/(51‐120)=‐28.3mph Converttofeet/second: ωBR=‐28.3mph*1.47fps/mph=‐41.5fps Finally,determinequeuelength: LQmax=(ωBR*ωBF*r)/(ωBR‐ωBF)=(‐41.5*‐34.0*30)/((‐41.5)‐(‐34.0))=5644ft  c) Howlongwillittakeafterredforqueuetodissipate? Tadd=(ωBF*r)/(ωBF‐ωBR)=(‐34.0*30)/((‐34.0)‐(‐41.5))=137sec    

Example6.5inText q1=1500veh/hr q2=1000veh/hr k1=25veh/mi k2=100veh/mi u2=10mi/hr L=2.5mi  Howmanyvehicleswillbeintheplatoonbythetimethetruckleaves?       1500   1000       6.67        25   100         10 

    6.67    16.67    

 2.5    .25   10 

       .25  16.67 #       100

 

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 4.17

 4.17  417...