How to Determine Signal Block Length

[ACPH]

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? 

[Paul_D_North_Jr]

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. (1/2*a*t**2).

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 

- PDN. 

[Paul_D_North_Jr]

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.

[Saturnalia]

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 would incorporate PTC's calculations of train stopping and braking distances into signalling. The system would take all of those metrics and basically give the crew a "clear" cab signal indication unless their stopping distance dropped below the calculated distance, plus some safety net value. Thus physical block signals would become unnecessary. In theory, absolute signals could be cut as well, but the railroads are a bit more hesitant to cut those for obvious reasons. 

Alas, moving blocks are not being inrocporated into the first generation PTC systems, which is unfortunate because that is probably where most of the savings on the railroad's part would come from, in terms of increased fluidity, and eliminating the need for the majorty of lineside signals, those being the intermediate types. 

[tree68]

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.

 

[RME]

Paul_D_North_Jr

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.

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.

[Paul_D_North_Jr]

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 Original Poster, 

as it shows stopping distances for 7 runs of 10, 40, and 75 loaded 

cars (315K) at several speeds - 5 of which were at 40 MPH - 

and the effects of varying grades.

- PDN. 

P.S. - "Monte Carlo simulation process", eh ?  

While I know what that means from an Engineering Science course 

a few decades ago, it might be not too reassuring to those who aren't 

familiar with it -sounds like gambling with safety, doesn't it ?  

[erikem]

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.

[PNWRMNM]

Paul_D_North_Jr

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. (1/2*a*t**2).

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. 

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 (70*140+40*33)/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 for details.

We had a real test the other day. From 26 MPH an emergency application in Biloxi MS took 760 feet from application to stop according to the NTSB. That was on presumably flat track. We do not know what this train's TPOB was, but since it was general freight I suspect was not particularly high, say 100-110. Given that an emergency application at lower speed actually took about what Paul calculated for higher speed and less braking effort, I think Paul's estimate of stopping distance is far too short. He is absolutely correct that the grade will have a tremendous impact on stopping distance.

I can not find my air brake books, so will not elaborate further, except to note that train performance models calculate effective brake pipe, brake cyinder, brake shoe pressures to calculate resultant decelleration rate for each and every car, literally second by second.

The other thing to think about is that blocks will NOT be sized based on full service application. The company wants safe, smooth train handling. Any hoghead wants some reserve braking capacity. I suspect each carrier has its own default application assumption for figuring signal spacing. Also, most engineers will use a split reduction if they are making a heavy application, say minimum service, let it settle, then go to 15# reduction. This too will be factored into any practical distance to stop calculation. Do not forget that the initial condition may be descending a grade or slowing for some reason in dynamic brake. Most locos have a DB Interlock that kicks off the dynamics when air applies on loco, and most engineers will bail off the engine brakes to hold the dynamics under normal conditions. If DB kicks off, then engineer has to make stern application with the independent to keep the power snugged up against the train.

It is complicated but men have been doing it by the seat of their pants, and experience, for years.

Mac

[BaltACD]

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 -

CSX Batimore Division Timetable

5. 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. After recharging the air brake system to the required rear
car air pressure, a 6 to 8 pounds brake pipe reduction must
be made. After the brake pipe exhaust ceases, each car will
be visually inspected to determine the brakes are applied,
piston travel is within standards and brake shoes are against
each wheel.
B. As soon as train speed starts to increase, a minimum
reduction of brake pipe pressure will be made and the
dynamic brake applied.
C. Further reductions of the brake pipe pressure and
modulation of the dynamic brake will be used to control train
speed.
5. Eastward Manifest Trains -
A. Eastward Manifest Trains without rear-end helpers will not
exceed 5,000 tons ascending Newburg and Cranberry
grades.
B. Eastward Manifest Trains exceeding 5,000 tons with rearend
helpers operating from Grafton to Piedmont must have a
minimum of 10 loaded cars on the head end of the train and
a minimum of 8 loaded on the rear end of the train. The
loaded cars must weigh 70 tons or greater and must not be
cars 80 feet or longer.
C. Manifest Trains exceeding 7,000 tons must have the
helper cut-in the train at a point where the head end tonnage
does not exceed 7,000 tons. The eight cars preceding the
helper must be loaded cars weighing 70 tons or greater and
must not be cars 80 feet or longer.
6. Westward Trains –
A. Westward Trains other than solid empty hopper and
loaded unit trains ascending the following grades without a
rear end helper must not exceed the following tonnage:
1. Seventeen Mile Grade – 3,500 tons
2. Cheat River Grade – 4,500 tons
B. Westward empty hopper trains and loaded unit trains
ascending the following grades without a rear end helper
must not exceed the following tonnage:
1. Seventeen Mile Grade – 4,500 tons
2. Cheat River Grade – 4,800 tons
C. Westward Manifest Trains ascending Seventeen Mile
Grade that exceed 5,000 tons require a two unit rear end
helper.
Note: One AC unit will be considered the same as a two unit
helper.
D. Westward empty unit trains ascending Seventeen Mile
Grade without a helper must not exceed 130 cars.
E. Westward empty unit trains between 116 and 130 cars
that stall while ascending Seventeen Mile Grade will not
attempt to restart the train without a rear end helper unless
authorized by the Road Foreman of Engines or the
Trainmaster. If instructed to attempt a restart, the engineer
must first review Rule 5651 for proper understanding and
application.
7. Dynamic Brake Requirements
Before descending the following grades, each locomotive
used to meet the equivalent dynamic brake axle shown
below must be tested to ensure the dynamic brakes are
operating.
Trains descending Seventeen Mile, Cranberry, Cheat River
and Newburg Grades at speeds of less than 20 MPH must
have the following minimum number of operating equivalent
dynamic brake axle values for the tonnage listed.
Note: The following Dynamic Brake values are for head end
only consists:
A) Less than 2,500 tons, a min of 4-axles operating in
Dynamic Brake.
B) Between 2,501 and 3,500 tons, a min of 6-axles operating
in Dynamic Brake.
C) Between 3,501 and 6,000 tons, a min 8-axles operating in
Dynamic Brake.
D) Between 6,001 and 8,000 tons, a min of 12-axles
operating in Dynamic Brake.
E) Over 8,001 tons, a min 16-axles operating in Dynamic
Brake.
F. The train may proceed only after being authorized by the
Road Foreman of Engines or the Trainmaster. If needed,
hand brakes may be left on the train to supplement train air
brakes descending the remainder of the grade. To prevent
sliding of wheels, avoid leaving hand brakes on any empty
cars.
Note: Should the train separate, hand brakes must be
applied to each portion of the train to hold each section on
the grade.
G. Stopped on Grades – When recharging the train air brake
system on descending grades of 1% or more, recharge the
brake system for a minimum of 20 minutes.
Note: During temperatures less than 32 degrees or
inclement weather, additional charging time may be required.
Trains must not proceed until the brake pipe is properly
charged.
3. Train Brakes – Engineers are prohibited from making a
running release of the train air brakes on all trains at the
following locations:
BA 207.8 and BA 223.0 - Seventeen Mile Grade
Engineers are prohibited from making a running release of
the train air brakes on unit trains. Mixed manifest trains may
make a running release if the tonnage of the train is less
than 4,800 tons. These restrictions apply when the head end
of the train is between the following locations:
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
4. Descending Seventeen Mile Grade (BA 207.8 – BA
223.0)
A. Engineers of trains over 5,000 tons will reduce power to
permit the train to pass the summit of the grade at BA 223.1
at no more than 10 MPH.

[jeffhergert]

PNWRMNM

 

 

Do not forget that the initial condition may be descending a grade or slowing for some reason in dynamic brake. Most locos have a DB Interlock that kicks off the dynamics when air applies on loco, and most engineers will bail off the engine brakes to hold the dynamics under normal conditions. If DB kicks off, then engineer has to make stern application with the independent to keep the power snugged up against the train.

 

Mac

 

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

[PNWRMNM]

Jeff,

Thank you for the correction.

Mac

[tree68]

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

[Electroliner 1935]

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. 

[BaltACD]

Electroliner 1935

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.

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 dynamic brake action.  Nothing left to do but ride it out - believe 78 of 80 cars derailed and killed one civilian in a house that wasy destroyed by the derailment.

[Ottawan]

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.

[oltmannd]

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.

[oltmannd]

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..

 

[Cotton Belt MP104]

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

[BaltACD]

Cotton Belt MP104

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

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

[Buslist]

Saturnalia

 

 

 

Alas, moving blocks are not being inrocporated into the first generation PTC systems, which is unfortunate because that is probably where most of the savings on the railroad's part would come from, in terms of increased fluidity, and eliminating the need for the majorty of lineside signals, those being the intermediate types. 

 

 

The main problem was that at the time the PTC mandate was passed no North American supplier had demonstrated a reliable moving block system (and sorry Aries didn't fit the bill). The industry decided not to gamble on someone doing so by 2015. They decided to stick with the fixed block system which in itself still needed development efforts. As it was the deadline was missed. BUT there is still considerable interest in moving block to deliver the benefits you discussed. Look for renewed efforts on this front once the current build out is complete.