1. A rapid-transit system employing single vehicles is scheduled at constant hea

Question

1. A rapid-transit system employing single vehicles is scheduled at constant headways. For safety regime b (Table 3.2.1), plot the relationship between spacing in feet (ft) and speed in feet per second (ft/s) using the following data: perception-reaction time 1.5 s, normal deceleration 8 ft/s2, emergency deceleration 32 ft/s2, vehicle length - 40 ft, and safety clearancex, 4 ft. 2. Repeat the solution to Exercise 1 for safety regime a. 3. For Exercises 1 and 2, calculate the maximum flows in vehicles per hour (veh/h) and the corre- sponding speeds

Explanation / Answer

1. First car applies emergency brakes, second car applies normal brakes. From figure(b) S is given by the following relation

S+(v^2/2dl)=v(delta)+(v^2/2df)+L+(safety clearance)

S=1.5v+40+4+(v^2/16)-(v^2/64)

S=3v^2/64 +1.5v + 44

3.Flow per hour ,F= (3600v)/S =(3600v)/(3v^2/64+1.5v+44)

Putting dF/dv=0 we get

44/v^2=3/64

or v=30.6 ft/s

For v=30.6ft/s, Maximum flow=823 vehicles per hour

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