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Homework #7 solution

# Homework #7 solution - Determine flow and free-flow speed...

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Unformatted text preview: Determine flow and free-flow speed. at maximum ﬂow q := 2900 u := 30 and d—q =2-a-u+ b=0 du b:—2-a-u atq = 2900 and u = 30 q = a-u2 + b-u q = a-u2 + (—2-3-u)-u a = —3.222 b := —2-a-u b = 193.333 now, when q:=1400 q= 3-le + b-u U1= 8.424| u2 = 51.53 mifh at q = 0, the free ﬂow speed is as follows q:=0 q = avu2 + bvu u = 50 mi.-'h Problem 5.2 (given) (given) (given) Problem 5.3 Determine the ca aci S eed at ca aci and densi at one Quarter caQaCiEH. q(k) := (SD-k — 0.156-k2) (given) d—q(k) —) 50 _ .312-k dk o : 50 _ .3124:ca P kcap := 160 veh qcap := q(kcap) qcap = 4006.4 7 qcap mi ”cap := k ”cap = 25.04 I cap at 25% of capacity ._ E q -- 4 veh q = 1001.6 — h 2 q cap 50-k—0.156- — =0 veh k1 = 21.5 — m veh k2 = 299 — Problem 5.5 Determine the time-mean sgeed and space-mean speed. Lane 1 Lane 2 Lane 3 30 mifh 45 mifh 60 mifh 1 vehicle every 60 sec 1 vehicle every 40 sec 1 vehicle every 30 sec For 30 minutes t := 30 Num1 :2 60 Num2 :240 Num3 :2 30 60 1 Lane1 :2 t- Lane1 = 30 Num1 J 60 \ Lane2 := t- Lane2 = 45 Numz J 60 \ Lane3 := t- Lane3 = 60 Num3J Speed1 :2 30 Speedz :2 45 Speed3 :2 60 Speed1-Lane1 + SpeedZ-Lanez + Speed3-Lane3 ut_bar :— Speed1 + Speedz + Speed3 ut bar = 48.33 milh 1 L's—bar} m [so-[é] + 45-[%] + 30-[%]] 45 mifh l"':._bar = Determine the time-mean sgeed and space-mean speed. Problem 5.6 5280 5280 U1E=195-— U1 = 286 W5 U2:=190-— U2 = 278.667 3600 3600 5280 5280 U3 := 185-— U3 = 271.333 U4E=130-— U4 = 264 3600 3600 2.55280 secperlap1 := — secperlap1 = 46.154 u1 2.5-5280 secperlap2 := — secperlapz = 47.368 U 2 2.55280 secperlap3 := — secperlap3 = 48.649 u3 2.5-5280 secperlap4 := — secperlap4 = 50 U 4 total_sec := 30-60 total_sec = 1800 tota|_sec tota|_sec laps1 := — laps1 = 39 Iap52 := — secperlap1 secperlap2 tota|_sec tota|_sec laps3 := — laps3 = 37 laps4 := — secperlaps secperlap4 total_laps := laps1 + laps2 + laps3 + laps4 total_|aps = 150 laps1-U1 + lapsz-UZ + laps3-U3 + laps4-U4 ms:— total_|aps 3600 . TMS = 275.244 ftfs TMS-— = 187.67 mllh 5280 1 SMS :— 1 I 1 I 1 I 1 I 1 \ —- as-—+as-—+as-—+as-— tota|_|aps p 1 U1 p 2 U2 p 3 U3 p 4 U4) 3600 . SMS = 275 W5 SMS-— =137.5 mlfh 5280 lapsz = 38 laps4 = 36 ...
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