CIVE 7385 Public Transportation Hwk 7: Rail Operations

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CIVE 7385 Public Transportation

Hwk 7:  Rail Operations

1. Line Capacity. Calculate the line capacity (persons/hr in the peak direction) of the following facilities (some cases are simplified). Make reasonable assumptions about average occupancy when a vehicle capacity is not specified.

a. New York City 8th Avenue Express subway, 10 car trains, 210 persons/car, minimum headway = 140 s.

b. Boston's Southeast Expressway (I-93) (4 lanes in each direction).

c. Route I-66 in the Virginia suburbs of D.C. during peak hours. 2 lanes per direction, only carpools with at least 2 persons allowed.

d. New Jersey Route 495, bus-only contraflow freeway lane approaching and through Lincoln Tunnel. It carries one bus every 7 s, and could carry one bus every 2.8 s. (Calculate capacity with both actual and minimal headway.)

e. Green Line Central Subway, 2-car trains, 140 persons per car, assuming minimum headway = 70 s.

f. Seattle downtown bus tunnel as it operated 20 years ago. Arriving buses have a waiting area where they form platoons of 4 buses. The tunnel can handle one platoon every 90 s.

2. Minimum Headway Analysis, Including Sketch. Analyze the minimum headway for two alternative metro operations by making, for each, a sketch of the trajectory of two successive metro trains entering and leaving a station. Alternative  (A) is a well-controlled, modern, low-minimum-headway operation; you should find that its minimum headway is between 90 and 120 s. Alternative (B) a traditional operation, not-well-controlled operation that results in a long minimum headway in the range of 180 to 220 s.

In space the sketch should show

· the platform at the station (make it 150 m long)

· both the front and rear of each train as it moves along (trains are 150 m long)

· minimum safety separation if one train is forced to stop behind another

· the decision point for whether to stop an approaching train:

o Altertative A. As close to the station as possible, based on minimum safety separation

o Alternative B. 800 m before the station, assuming that’s the block boundary in a block system 

In time, the sketch should show:

· dwell time (wheels not moving).

o Outside the sketch, provide a table showing how dwell time is the sum of 3 parameters: door open time, time waiting for doors to open, and time waiting after doors close.

· delay due to deceleration and delay due to acceleration

· operating buffer (extra time needed in the headway to allow some variation in running time without forcing trains to wait for each other)

· resulting headway for case (A) and for case (B) 

In time and space, the sketch should show the two trains in normal operation, and also the trajectory of the following train if the leading train has to stay at the station (say, due to a medical emergency).

Outside the sketch, provide a typed list of all the parameters, with reasonable default values, upon which the analysis is based. In the lecture, reasonable values for these parameters were discussed; if you wish, feel free to ask for advice on reasonable parameters.

3. Minimum headway and capacity of a metro without a sketch. Find the capacity of a metro line, in pax/h, based on the limit imposed by the control system. Solve the base problem on paper, and then put the calculations into a spreadsheet for the variations that will follow. Use SI units in your calculations. As part of your solution, indicate the length of blocks R and S.

a. Base Case. The line has 8-car trains, with each car 25 m long, and each car has a capacity of 210 pax. The control system is designed for the 90^th percentile dwell time at the busiest station, which is 36 s. On the segments leading into and out of that station, cruising speed is 60 km/h (37.5 mph), or 16.67 m/s. Deceleration and acceleration will be 1.2m/s². The station block, called block S, extends from 30 m before the platform to 30 m after it. The block before the station block, called block R, will be sized long enough for a full-speed train to stop at 50% of the standard deceleratino, plus a 60 m safety separation. The control logic will be that when a train enters block R, it must decelerate to a stop if block S is occupied. For the schedule to be resilient, there should be a buffer of at least 20 s in the schedule, meaning that if a train is 19.9 seconds late in leaving the station, the following train will not be delayed.

b. Traditional Operation. Like the base case, except that (1) Block R, instead of being sized for an efficient operation,  is 800 long; (2) because of load variability, the 90^th percentile dwell time is 45 s; and (3) because of headway variability, the needed headway buffer is 30 s.

c. Lower Speed, Fixed Blocks. Like the base case, except (1) trains are ordered to go no faster than 40 km/h (25 mph). Block R’s boundary is the same is in the base case.

d. Lower Speed, Variable Blocks. Like case (c), except that Block R’s boundary is recalculated to be as close to the station as possible while still satisfying the safety constraints.

Write a summary of your findings:  How do the various changes of cases b, c, and d affect the line’s capacity?

4. Single Track Operation – Minimum Headway. The Old Colony line (trains from South Station to Fall River / New Bedford, Plymouth, and Scituate) has a single track section 2.6 miles long in Dorchester and South Boston, with the JFK/UMass station at the midpoint of this section. If trains alternate inbound – outbound – inbound, find the minimum headway for inbound trains. Draw a schematic showing block boundaries in each direction. Organize your calculations in a neat table (by hand, or with a spreadsheet).

· Cruise speed = 30 mph both within the single-track section and in the neighboring sections

· Deceleration rate = 1.2 mph/s

· Acceleration rate = 0.6 mph/s (Limited power because propulsion is from diesel engine)

· Scheduled dwell time at JFK/UMass station = 90 s (from wheels stop to wheels roll)

· Maximum train length = 1000 ft

· Block boundaries inbound and outbound may differ

· How far back from the junction a waiting train should wait: 500 ft

· How far beyond the junction a moving train must clear for the junction to be considered clear: 300 ft.

· Length of the deceleration blocks leading to the single track section = double the distance needed for normal deceleration.

· You may ignore control elements needed to keep same-direction trains apart; they will be provided, of course, but don’t affect the separation needed between opposite direction trains.

5. Minimum headway for track shared by local and limited stop trains. A commuter rail line with 2 tracks (1 per direction) is 15 miles long, and has 13 stations, numbered 1 (most distant) to 13 (city center). Stations are all 1.5 miles apart, for a total line length of 18 miles. Limited stop trains serve stations 1, 2, 3, 4, 8, 12, and 13. Local trains turn back at station 4, and so they serve only stations 4, 5, …, 13. Local and express trains will alternate. Between stops, all trains operate at 45 mph. Time lost per stop is 1.75 minutes (that accounts for decel / accel delay and dwell time). Minimum safety headway between successive trains is 4 minutes (i.e., if one train arrives at time t, the next train may not arrive between time t + 4 minutes. Note that “headway” is from arrival time to arrival time, not from departure time to arrival time.) Find the maximum service frequency for alternating local / limited stop services can operate, and then round it to clockface headways (something that repeats every hour). Then make a time-space diagram showing the inbound service schedule, large enough that the diagram has at least 2 complete limited stop and 2 complete local trips.