How to Determine Signal Block Length

Trains Magazine General Discussion
1

Hello, everyone. So I’m trying to determine the block length for a track. My teacher references AREMA for a lot of his notes. In the notes, it says, “For block signals, length of block = at least as long as longest normal stopping distance for any train on the route traveling at its maximum authorized speed” and “The longest stopping distance will be used to establish the design block length for the signal system”. The notes don’t mention anything else on calculating the stopping distance. So if anyone could help me with this problem that would be great.

I have 70 cars. 140-ton fully loaded, 40 empty

5 four-axle locomotives with 4000hp (145ton)

Desired speed of 40mph

minimum speed of 10mph

How do I start finding the stopping distance?

2

It’s complicated. But there’s a simple approximation** - the key is to use basic high school physics to figure out far (and how long) it’ll take the train to stop.

40 MPH ~ 60 ft./ sec.; stopped = 0 mph = 0 ft./sec.

Figure 2 to 3 seconds for the engineer to see the signal, process it, and react and set the brakes (that’s 120 to 180 ft. right there). EDIT: This time lag is essentially the same calculation as for the stopping distance of a car or truck on the highway.

Then the brake signal needs time to propagate to the rear of the train so that all brakes are set. Your train is ~4,550 ft. long (70 * 60’ or so + 5 * 70’ or so), so at 500 ft./ sec. (guess-timate) it’ll take 9 seconds for that to happen. To be safe, we’ll assume little or no braking effect during that time, although they would come on gradually.

Then work out stopping distance from 60 ft./ sec. at 0.1g (g= gravity = 32.2 ft./ sec.2) or about 3.2 ft./ sec. per sec., ~2.2 MPH per sec. - it’ll take about 19 secs., during which time the train will travel about another 580 ft. (1/2at2).

The 0.1g is my estimate of a reasonable deceleration rate to avoid slipping wheels or damaging cargo, also taking into account load-empty sensors, TPOB, brake system leverage, brake shoe performance, etc.

**You didn’t mention grade, but that’s a huge parameter - see: “Going Down” in “What is a Tough RR Grade?” at http://hm.evilgeniustech.com/alkrug.vcn.com/rrfacts/gradetuf.htm Essentially you add or subtract it (decimal, so 3% = 0.03) as appropriate from the stopping coefficient above.

See also:

http://hm.evilgeniustech.com/alkrug.vcn.com/rrfacts/rrfacts.htm <

3

A Google search for “rail signal block length” found these 2 articles with nice diagrams (among others):

http://railway-technical.blogspot.com/2011/07/braking-curve.html

http://railway-technical.blogspot.com/2011/07/thameslink-ato-im-struggling.html - similar calculations, though a little more conservative - about 2.1 ft./ sec.**2 deceleration rate, instead of my 3.2.

See also: https://en.wikipedia.org/wiki/Railway_signalling#Fixed_block

  • PDN.
4

I guess this isn’t really answering the question from a physics perspective, but on most railroads block signals are spaced 2-3 miles apart, which is generally somewhere in the range of a brake application.

However, it is worth noting that with signal indications, it is generally setup in such a way that the crew ends up with boatloads of time to make the necessary changes to trainhandling in anticipation of the track ahead. That’s where the Clear, Approach, Stop progression comes into play.

Hence for a clear, the crew knows they’ve got two blocks of uninterrupted running ahead of them, at least, so they can go along their merry way to the next signal. If they need to slow for either another train or take a diverging route, the signals begin to let them know at least one block in advance, so figure at least double the stopping distance, if a block length is a good estimate.

Most railroads add in an additional indication between “clear” and “approach” for when crews might need to stop/be way slower at the 2nd signal, where the distance between the next and that second signal is shorter than usual. This can happen in areas where interlockings are fairly close togther.

In speed signalling, that is generally handled by an advanced approach, which I believe is a flashing yellow on both UP and BNSF (western fans, correct me if I’m wrong), along with NS’s standardized rules which they use on all new installations. Meanwhile, CSX employs most often, as far as I have seen it, an approach limited indication, which you’d think would be shown to trains which are getting a limited clear at the next signal, but where I’ve seen it employed, is generally used for short blocks, where trains may have to slow to “slow speed” in short order between the first and second signal.

The interesting aspect of this block dilemma going forward is of course moveable blocks or “computerized blocks”, which

5

As I recall, one reason for the plethora of possible signal aspects (interlocking notwithstanding) was the increase in speeds, along with the lengthening of trains, both of which increased stopping distance.

Relatively short trains, running at moderate speeds, is what most signals were spaced for. Thus three, or four, aspects was all that was needed.

As speeds increased, and trains got longer, it became necessary to create more aspects in order to maintain safe following distances.

6

There’s another simple way: look at some of the technical material by ECP providers, which contain ‘stopping curves’ for consists of various speeds, weights, and composition. That will give you a handle on some of the ‘empirically derived’ constants that would have to be incorporated in a meaningful mathematical equation for train stopping distance.

7

Here’s a link to a FRA study/ report that addresses some of these issues:

https://www.fra.dot.gov/Elib/Document/3327

“Development of an Operationally Efficient PTC Braking Enforcement Algorithm for Freight Trains” - August 2013

Abstract:

Software algorithms used in positive train control (PTC) systems designed to predict freight train stopping distance and enforce a penalty brake application have been shown to be overly conservative, which can lead to operational inefficiencies by interfering with normal train operations. Federal Railroad Administration contracted Transportation Technology Center, Inc. to investigate approaches to improve these algorithms and to reduce the associated operational inefficiencies. As part of this program, several new approaches to PTC enforcement were introduced and were shown, through simulations and field testing, to improve the operational efficiency of the algorithm. An appropriate safety objective for these algorithms was established from a fault-tree analysis of the accidents PTC was conceived to prevent. A standard methodology was also established by which any PTC enforcement algorithm can be evaluated against design safety and performance measures. This methodology involves a statistical evaluation of the algorithm by means of a Monte Carlo simulation process, as well as limited, focused field testing, which provides more confidence in the safety and performance of the software at less cost than traditional field testing methods. This methodology was then used to evaluate PTC supplier algorithms that incorporate concepts introduced in this project.

EDIT: The little table on pg.49 might be of interest to the Origina

8

What’s even scarier is that the term “Monte Carlo simulation” was originally used to model the path neutrons took in the pit of an A-bomb. The “gambling” aspect came from using a random number generator (e.g. roulette wheel) to provide parameters for the neutron’s path, such as distance to next collision, angle of scattering, etc. This is still the basis for most code simulating radiation transport.

“Monte Carlo simulation process” for most other engineering analysis is tweaking some of the parameters in a simulation (e.g. coefficient of adhesion) and then running the simulation multiple times with differring tweaks. In the radiation transport problem, the random number generator would be called billions of times in a simultion, where in other forms of “Monte Carlo simulation process” the random number generator may be called a few dozen to a few thousand times.

9

Paul’s result is 540 feet of set up time plus 580 feet of travel with the brakes set, or 1120 feet from 40 MPH, at I presume full service application. He did not say. As I read your statement of the problem, your train is 111 Tons Per Operative Brake, which I calculated as (70140+4033)/110. TPOB is the prefered railroad short hand in limiting speed since it is a rough predictor of stopping distance. Basic concept is that trains with high TPOB are often limitied to something lower than track speed. See specific carrier and territory Special Instructions

10

The prefered method of speed control on Class 1’s these days is the use of Dynamic Brakes. Air is to be used only when the engineer deems it necessary to resolve the situation properly. Slowing for slow orders, complying with less than clear signal indications and any other of a number of operating situations the main form of speed control will be done with dynamic braking - this minimizes wear on brake shoes on the cars of the train, it also minimizes the oportunity of a brake valve on a car in the train malfunctioning and initiating an emergency brake application throughout the train. Train handlng in mountain territory can be complicated -

[quote user=“CSX Batimore Division Timetable”]

  1. INSTRUCTIONS RELATING TO AIR BRAKE AND
    TRAIN HANDLING RULES
    5559 STEEP GRADE (1% OR MORE) TRAIN HANDLING

1. Unit Trains:
For head-end movement only, the allowable speed is 15
MPH while descending the following grades:
BA 207.8 and BA 223.0 - Seventeen Mile Grade
BA 242.3 and BA 252.3 - Cranberry Grade
BA 255.1 and BA 259.3 - Cheat River Grade
BA 262.0 and BA 267.4 - Newburg Grade

2. All Trains – If speed cannot be maintained at or below
the authorized speed for the train descending the
grades listed above:
A. The train must be stopped immediately by making an
emergency brake application of the air brakes including the
operation of the two-way EOT emergency toggle switch.
B. The train dispatcher must be contacted.
C. After stopping a minimum of 50% of train hand brakes
must be applied before the recharging procedure is initiated.
D. The brake pipe must be recharged for a minimum of 20
minutes. The rear car air pressure must be within 5 PSI of
the pressure shown on the HTD when the head end of the
train began the descent.
E. A

11

The dynamic brake interlock is supposed to keep the locomotive’s brake from applying when an air brake application is made. We are to still bail off incase this feature isn’t working properly.

Jeff

12

Jeff,

Thank you for the correction.

Mac

13

For me, it’s virtually automatic - dynamics or not - make a set, bail off.

14

Are retainers still used today or has dynamic totally obsoleted them?

BaltAC,there is no mention of retainers in your rules so I suspect they are no longer used. I remember back in 1954 while returning from Washington DC on the B&O, the trainman setting up the retainer valves on the cars after we got into the grades somewhere west of Cumberland. The show from the vestibule door of the headlight lighting the side if the mountain and a line of fire from the brakes makes me wish had had a camera.

15

The only way Retainers come into play is if a train gets out on the territory and for whatever reason the Dynamic’s fail. After the crew confers with the Trainmaster, they may be instructed to set Retainers on a portion of the train so they can continue their trip using air brakes only - like in steam times. I have had this happen during my tours of duty - but it is exceedingly rare. The TTSI I posted are only a portion of the train handling instructions for the Mountain Sub.

The NTSB report of a runaway on the Mountain in about 1994 it was disclosed that regular clasp brakes on coal cars would fade to ineffectiveness at any speeds over 15 MPH on the grades of the Mountain Sub. That is why the max speed is listed as 15 MPH. On the train that ranaway, there were 3 units - the Engineer thought he had dynamics operating on all engines, in reality they were only operating on the lead engine. At the time I believe max speed of 25 MPH was allowed. Train got upto 27 MPH on a portion of the grade where normal dynamic & air brake actions should have had speed at 20 MPH. Engineer then knew he was in trouble and put the train in emergency, however the train didn’t slow down as the air brakes had already faded away and the emergency application stopped the

16

In Ootawa we are building a new light rail system (although to “heavy metro” standards with no grade crossings or street running) of 13 km and 13 stations. The middle third will be be in a deep tunnel through the downtown core. It will use moving block signals with indicators in the cab. There is even provision for “hands off” operations. In Toronto, the TTC is replacing its 50yr+ electo-mechanical signalling and emergency stop system on subway Line 1 (Yonge-University-Spadina etc) with a moving block system. The EW line should follow.

17

I don’t know if I missed it somewhere, but you have to consider the equipment’s braking ratio. Freight car are built so that they don’t slide wheels when empty. Typically 20-25% braking ratio - 20 to 25% of the car’s weight is available as braking force, in emergency. But, loaded, the same braking force is available, which means much slower deceleration can occur.

This is the reason freight trains take so long to stop.

18

So, roughly:

a car with a 80,000# light weight will provide braking force of roughly 20% of that x 75% for full service vs. emergency = 12,000#

12,000/286,000 = .042 g = 1.35 ft/s^2 decel rate

Add some time for reaction and brake set up. It’s just kinematics after this…

19

BaltACD: reference “On the train that ranaway, there were 3 units - the Engineer thought he had dynamics operating on all engines, in reality they were only operating on the lead engine”…was this the time when a pin # ?? of the MU cable did not pass along the DB command? endmrw0411171510

20

https://www.ntsb.gov/investigations/AccidentReports/Reports/RAR0202.pdf