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Unformatted text preview: Determine flow and freeflow speed. at maximum ﬂow q := 2900 u := 30 and d—q =2au+ b=0
du b:—2au atq = 2900 and u = 30 q = au2 + bu q = au2 + (—23u)u a = —3.222
b := —2au
b = 193.333 now, when q:=1400 q= 3le + bu 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) := (SDk — 0.156k2) (given) d—q(k) —) 50 _ .312k
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
50k—0.156 — =0
veh
k1 = 21.5 —
m
veh
k2 = 299 — Problem 5.5
Determine the timemean sgeed and spacemean 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
Speed1Lane1 + SpeedZLanez + Speed3Lane3
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 timemean sgeed and spacemean 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
2.55280
secperlap2 := — secperlapz = 47.368
U
2
2.55280
secperlap3 := — secperlap3 = 48.649
u3
2.55280
secperlap4 := — secperlap4 = 50
U
4 total_sec := 3060 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 laps1U1 + lapszUZ + laps3U3 + laps4U4 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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 Fall '08
 KATZ

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