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(civl261)[2009](s)Quiz2solutions~PPSpider^_10067.pdf
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CIVL 261 Traffic and Transportation Engineering
Tutorial 1A Quiz 2
Name: Student ID: Week 3, 20 Feb 2009
Question 1:
Frank observes a cyclic traffic flow on Queens Road East from his table through the coffee shop window. Three groups of vehicles arrived in the 15min period. Red vehicles arrive with a rate of 5veh/min at speed 50km/hr. Green vehicles arrive at 60km/hr with headway of 30sec. 20 Purple vehicles arrive, each at speed 80km/hr. Compute the space mean speed and time mean speed of the traffic flow.

Solution:

Volume:
QR =5*60 =300 veh/hr
QG =3600/30 =120 veh/hr
QP =20*60/15 =80 veh/hr

The time mean speed is:
Vt =(300*50+120*60+80*80)/500 =57.20km/hr

Consider if Dr. Poon takes a photo for a road segment of length 1000m from the top of the Hopewell Centre, he will find 6 red, 2 green, and 1 purple vehicles. This is derived by considering the density of each group:
KR =(300veh/hr) / (50km/hr) =6 veh/km
KG =(120veh/hr) / (60km/hr) =2 veh/km
KP =(80veh/hr) / (80km/hr) =1 veh/km

Thus, the space mean speed is
Vs =(6*50+2*60+1*80)/9 =55.56km/hr

Notes: It would also turn out to be correct to use the harmonic mean for space mean speed. In this case, the amount of vehicles we should include is, respectively, 75, 30, and 20, instead of 6, 2, & 1. Thus, the space mean speed is

Vs =125/(75/50+30/60+20/80) =55.56km/hr

Question 2:
From the video, one observes a cyclic traffic flow over time with two groups of cars traveling along an observation section of Wong Chuk Hang Road. All cars in Group A are running at a speed of 40km/hr while the spacing is 50m. Group B vehicles are running at 30 km/hr with headway of 4sec. Determine the space mean and time mean speeds of the traffic flow.

Solution: (by formula)

Instantaneous observation: for distance of 1km, we have 20 Group A vehicles and 30 (=1000*3.6/30*4) Group B vehicles. Thus,


Vs =(20*40+30*30)/50 =34.0km/hr
Vt =(20*402+30*302)/(20*40+30*30) =34.7km/hr

Solution: (by definition)

Consider for distance of 1km, we have 20 Group A vehicles and 30 Group B vehicles. Thus,

Vs =(20*40+30*30)/50 =34.0km/hr

Consider observing at a point (OP) for one hour. At the end of the hour, the first Group A (B) vehicle that passed OP will be 40km (30km) away from OP. We count back from that first vehicle. The headway for Group A (B) is 50m (33.3m). Then we have 40,000/50=800 Group A vehicles and 30,000/33.3=900 Group B vehicles. Thus,

Vt =(800*40+900*30)/1700=34.7km/hr

Remarks:

A better way of computation is to always follow the definition of SMS and TMS. The former observes over space and the latter over time. We have another example to show.