Williamsburg Bridge Capacity

[bobtehpanda]

On 3/28/2019 at 8:02 PM, Around the Horn said:

That's just plain not true. In 1954 the Williamsburg Bridge handled 26 tph in peak. We currently run 18 tph.

Also note that it says the upper limit for the bridge is 32 tph. Better operating practices can support that level of service.

That's also before we discovered the Williamsburg was built with shitty cabling, though. Do we know that we can run a more intensive service these days?

[Enjineer]

21 hours ago, bobtehpanda said:

That's also before we discovered the Williamsburg was built with shitty cabling, though.

The bridge also was rehabbed in the late 90's, no? Wouldn't that mitigate said problems? 

[RR503]

22 hours ago, bobtehpanda said:

That's also before we discovered the Williamsburg was built with shitty cabling, though. Do we know that we can run a more intensive service these days?

I vaguely remember @RailRunRob knowing something about this... 

[Trainmaster5]

On 3/28/2019 at 11:02 PM, Around the Horn said:

That's just plain not true. In 1954 the Williamsburg Bridge handled 26 tph in peak. We currently run 18 tph.

Also note that it says the upper limit for the bridge is 32 tph. Better operating practices can support that level of service.

Look at the flow chart and add some context. 26 trains across the bridge.  How were the signals spaced?  The 11 Myrtle Chambers,  14 Broadway Brooklyn local,  and the 15 Jamaica line all crossing into Manhattan and terminating at 3 separate locations. Another service entering at the southern end through the Montague tunnel but not using the Williamsburg.  I see the chart showing 173 cars on both sides of the bridge but the  maximum capacity is lower on the Manhattan side. There is something missing in the chart, IMO, and I'm not sure but I think it relates to train length and signal blocks. IIRC we used to run n/b trains at 2 minute intervals from approximately 4:45 -5:25 PM through Bowling Green and I seriously doubt that any route crossing a bridge with timers could approach that frequency on a sustained basis. This is just my opinion and I could be looking at this incorrectly. Either way kudos to Essex and DeKalb  towers for trying to make the terminal operations work. Carry on. 

[RR503]

3 hours ago, Trainmaster5 said:

Look at the flow chart and add some context. 26 trains across the bridge.  How were the signals spaced?  The 11 Myrtle Chambers,  14 Broadway Brooklyn local,  and the 15 Jamaica line all crossing into Manhattan and terminating at 3 separate locations. Another service entering at the southern end through the Montague tunnel but not using the Williamsburg.  I see the chart showing 173 cars on both sides of the bridge but the  maximum capacity is lower on the Manhattan side. There is something missing in the chart, IMO, and I'm not sure but I think it relates to train length and signal blocks. IIRC we used to run n/b trains at 2 minute intervals from approximately 4:45 -5:25 PM through Bowling Green and I seriously doubt that any route crossing a bridge with timers could approach that frequency on a sustained basis. This is just my opinion and I could be looking at this incorrectly. Either way kudos to Essex and DeKalb  towers for trying to make the terminal operations work. Carry on. 

The biggest thing permitting that level of service was, if I'm not mistaken, the fact that the middle track at Marcy used to run through to the bridge. That basically solved the curve/dwell issue coming off the bridge. The reason the max capacity is listed as being lower on the Manhattan side is because BOT as a matter of course listed triple track segments as having a capacity of 40tph (not without good reason, if I may say so -- as late as 1949, the 3rd Avenue El was running 42tph). Of course, west of Marcy, there were only two tracks, which brought achievable capacity to 32. 

FWIW, all the timed bridge crossings once ran good throughputs -- WillyB is above, and the two sides of the MannyB once ran a combined 50 (30 north, 20 south). The issue with them isn't the GTs, in both cases it's what lies at their ends -- Marcy/Essex, Dekalb. 

[RR503]

I had a 45mins to kill this morning so I dug up some ancient signalling diagrams (1965) that @RailRunRob shared with me to delve deeper into the issue of historical capacity at Marcy/Essex. The math here will, by its nature, miss some nuances of train operation, acceleration profiles and the like, but should give a rough outline of capacity. If you see any significant errors, please let me know. 

Let's start with Marcy. If you need a primer on how to read these diagrams, go here. This is the relevant portion of the diagram for Marcy:

Digging in. A train occupying the platform at Marcy would have let a following train creep up on it as far as signal J1-150 if its last car was at or behind J1-155, or J1-153 if its last car was forwards of signal J1-155. That means that there would have been either 1000 +/- 100 or 700 +/- 100 feet (+/- 100 as each signal position is rounded to the nearest hundred feet, giving each one an error of +/- 50, which is multiplied by two when dealing with two positions) between the front of the following train and signal J1-160, which we are approximating as our stopping position for the purposes of this exercise. 

Leaving Marcy, let's assume everyone goes local. Per this RFW video (train acceleration is hard to estimate beyond the first few mph, as the acceleration curve becomes really a curve), the time it takes to vacate the platform is approximately 20 seconds (I arrived at that by taking the time from the platform to when we passed signal J3-165 on the express track, and then rounded up from 19 to 20). Almost as soon as a train starts moving, a train at J1-150 would be able to move up to J1-153, with 20 seconds being sufficient time to cover that distance.  As such, we're gonna just consider the time from J1-153 to the platform.

After 20 seconds, J1-153 would clear to yellow, and a train, moving per the six MPH limit shown in the diagram, would take 79.5 +/- 11.4 seconds to arrive at the stopping point at the platform. In the best case distance, 20 + 68.1 = 88.1 seconds have elapsed since the leading train left, and in the worst, 20 + 90.1 = 110.9 seconds. Dwell time is the final variable here. At 30 seconds, the best case distance gives us a minimum cycle time of 118.1 seconds (or 30.4tph) and in the worst, a time of 140.9 seconds for 25.6 tph. It seems, given the statistics available, that distances were probably closer to the best case situation than the worst case, and that it's possible that ops took the curve at more than 6mph (the latter change would have a real impact -- moving at an average of 10 rather than 6 means the travel time becomes 47.6 +/- 6.4 sec). 

Contrast to today, when the equivalent of J1-150 (J1-149) has a control line long enough that it takes about 18 seconds for it to clear to yellow after a train starts moving out of Marcy. This is key. That length of separation in a slow speed area is one of the more significant places where capacity is lost on the WillyB. 

It's worth looking at the other direction for a second or two (I'm running short on time now -- if anything here/below bears more analysis, do let me know). A train in Marcy would hold a following train at J2-165, or about 500' back from the platform. 165 would clear to yellow as the leading train passed 154, which it would do (per the 6mph limit) 61s after beginning to move. Given that all signals between 165 and the platform's stopping point had control lines that did not extend beyond the platform, this would be the only time point of importance. So, when a leader passed 154, a train at 165 could accelerate at 2.5mphps (=3.7 ft/sec^2) to, say, 25mph (=36.7 ft/sec^2), decelerate at 2.5mphps, and arrive at the platform about 40 seconds later (1100 foot distance +/- 100, combined accel./decel. time of 20s, average speed in those intervals of about 18.35 ft/sec, distance covered in accel/decel of 367ft, remaining distance of 733 ft covered in 19.9 seconds @ 36.7ft/s). This means a total movement cycle time of 101 seconds. Add a 30 sec dwell, and we're at 131 seconds for 27.4tph. 

Superficially, this would seem the problem area; it would not surprise me if that was true back in the 1960s. But unlike in 1965, the entrance to Marcy going west seems to have ST aspects on its signals (those box-shaped hoods below the three lights on automatics, or between the three sets of three on the homes) which suggests to me that a following train could close better on its leader today. If someone can speak to the presence of ST in the area, or provide a video of two trains following at close distance through the area, I'd be very appreciative. 

Now Essex:

The signal system here is insane. A train could pull up to J2-70 provided the leading train's last car was clear of J2-69. When a leader left the station, a follower could be a third of the way in. Given that the entrance speed here is 15, not 10, and that the signal system allows for truly close following, I don't even see the need to bore y'all with a further analysis of historical capabilities. Today, there are fewer signals (and thus following distance is probably longer), but given that I can't find an RFW where one train follows the next at close distance into Essex, I can't put my finger on an exact figure. It suffices to say that, given they've preserved the 15mph entrance speed, it's still somewhat capable of good capacity, provided controlled dwell times and good ST use. 

[RR503]

3 hours ago, RR503 said:

It's worth looking at the other direction for a second or two (I'm running short on time now -- if anything here/below bears more analysis, do let me know). A train in Marcy would hold a following train at J2-165, or about 500' back from the platform. 165 would clear to yellow as the leading train passed 154, which it would do (per the 6mph limit) 61s after beginning to move. Given that all signals between 165 and the platform's stopping point had control lines that did not extend beyond the platform, this would be the only time point of importance. So, when a leader passed 154, a train at 165 could accelerate at 2.5mphps (=3.7 ft/sec^2) to, say, 25mph (=36.7 ft/sec^2), decelerate at 2.5mphps, and arrive at the platform about 40 seconds later (1100 foot distance +/- 100, combined accel./decel. time of 20s, average speed in those intervals of about 18.35 ft/sec, distance covered in accel/decel of 367ft, remaining distance of 733 ft covered in 19.9 seconds @ 36.7ft/s). This means a total movement cycle time of 101 seconds. Add a 30 sec dwell, and we're at 131 seconds for 27.4tph. 

There's a mistake here. In the diagram above, I idiotically missed the GT20 within station limits at Marcy. The calculations now look like: 

-61 seconds for J2-165 to clear

-8 seconds to accelerate to 20mph at 2.5mphps

-29.5 seconds at 20mph

-8 seconds to decelerate to a stop 

=106.5 seconds 

+30 second dwell

=136.5 seconds, or 26.4 trains per hour. In all likelihood, trains took less than 61 seconds to exit the station (either through overspeeding or shorter consist length or both) bringing capacity upwards. 

[RailRunRob]

On 3/31/2019 at 4:56 PM, RR503 said:

I vaguely remember @RailRunRob knowing something about this... 

Yep the Cabling on the Willy B wasn't Galvanized so no corrosion protection in a nutshell.