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41

INTER SIGNAL DISTANCES IN AUTOMATIC SIGNALLING

INTRODUCTION

The "Inter signal Distances in ground based Automatic Signalling territories" has alwaysbeena subject of great interestto the Railwaymentfrom all the departments.Howeverso far nobodyknows for sure, any systematic guidelines in the matter.

On the face of it, it appears that you should provideore signals if you want a better frequencyof service, which is absolutely true. However most people tend to over simplify the matter bydesigning the inter signal spacing by multiplying the distance traveled by a train (at its normalspeed) in a given time, with the time interval at which we want to run the trains one after the other.The novice feels confident in declaring his views, whereas an expert reserves his opinion.

In actual practice, the "Inter Signal Spacing"depends on many factors like maximumpermis-sible speed of trains, normal speed of trains, distance between two stations, permanent speedrestrictions, braking and accelerations characteristics of the rolling stocks, types of rolling stocksrunning on the section etc apart from the desired frequency of service.

Here I've attempted to define a certain number of guidelines for arriving at the best possibleInter Signal Distances, in various situations.

FREQUENCYOF SERVICES

Irrespective of the Inter signal distances the frequency of train services can not be increasedbeyond a certain limit for a given type of rolling stock, train length, track structure, halting time andrequirement of Signal overlap. (Safety margin/adequate distance beyond the next signal).

MINIMUM DISTANCE BETWEEN TWO TRAINS :

When trains are run one after the other on the same line, we will have to keep a minimumdistance between them to run them at their booked speed. This safe minimum distance can bearrived at as follows:-

(We will confine our discussions to multiple aspect Colour Light signaling only as other typesof signaling have no relevance in Automatic signaling)

(Fig :-(1)

.\ sl \

i-U)~l-D) . . .

. . .

.....

--

42

I

,II

,

Fora train to runat its normal speed, (ref fig.1) it shouldsee the approaching signal Green (S-1) andfull braking distance should be available beyond the next signal (S-2) (so that if the next signal (S-2) is yellow or double yellow, the Driver is able to stop the train short of the next train, thus thedistance between the engines of both the trains, will include the length of the first train. Also we willhave to cater for a safety margin which may be called "overlap".

Thus the minimum distance between the trains comes to :-

Dtrains = Distance between a Green Signal and next signal which is yellow/Double yellow (fromwhere the train will start braking)

+Braking Distance

+TrainLength

+Safety margin (Overlap Distance)

or Dtrains = Dg:yy + Dbr + TI + Ov

THE WORST DISTANCETRAVELLED BY A TRAIN :-

Now let us have a look at the worst distancetraveled by any train, we will call that distanceasworst distance "which consumes maximum running time of the train". During the co.urspof its

. . journey, the train will take maximum time in the signalling sections which include halting stations;"Because the train will have to Decelerate, Stop, halt and Accelerate to catch up the full speedagain, in these sections. Thus the distance travelled by th~ train which will consume maximumrunningtime will include the breaking distance,and acceleratingdistance (becausethe train travelsat its normal speed before braking and after accelerating). Let us call the worst case distance as"D worst". Hence

Dworst = Dbr + Dacc

EON. (1)

where

Dbr --Braking distance for stopping a train from its normal speed and

Daac-- Accelerating distance to achieve normal speed after starting

And worst case time taken for travelling the above distance will be :-

T worst = Tbr +Tacc + Th + tr

EON. (2)

Where

Tbr -Braking time

Tacc Accele~ting time to achieve normal speed after starting

Th - Halt time at station

Tr -Reaction time of Driver before starting the train.

-

----

t~

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43

BEST POSSIBLE FREQUENCY OF SERVICE :-

NowifDtrainsisthe distancebetweentworunningtrains,dependinguponthe requiredfreqeuncyof service there can be two situations :-

1) Where D trains> D worst (Normalsituation)

2) Where D trains < D worst (situation where the requirement of frequency of service is so highthat we are not evenable to allow trains to fully acceleratebefore it hasto either stopagain or reducethe speed because it is following another train closely.)

Now let us consider the running time available for a train (Iet.us call it train frequency Le.running time for a given frequency of service) in each of the above cases.

a) When

Dtrains > Dworst

Train frequency =Tworst+ ( Dtrains - Dworst)

Vbo

where Vbo = Booked speed

Because the running time available is more than worst time, and, the train is supposed totravel at booked speed for a distance in which it is neither braking nor accelerating.

b) Similarly when Dtrains < Dworst

Train Frequency = Tworst - (Dworst -Dtrians)

Vbo

=Tworst+ (Dtrains-Dworst)

Vbo*

EQN. (3)

*[Assuming that (Dworst - Dtrains) will be very less because normally Dtrains will be more thanDworst but in extremecases of requirementof very high frequency of service the distance betweenof requirement of very high frequency of service the distance between the trains may be less thenthe bare minimum distance required for braking and acceleration. Thus even if it happens "(Dworst -Detrain)" will be very less and for such a small distance the trains must have either just startedbraking or must be close to achieving full speed on acceleration. Hence, no much error will becaused by assuming that the train will be traveling at Vbo for a distance "Dworst - Dtrains.")

[For example, referenceto Graph I, the distance required for achieving a speed of 65 kmph is880 meters and that for achieving70 kmph is 1389meters,thus the speed for a substantialdistanceof nearly 500 meters in the vicinity of booked speed varies only from 65 Kmph to 70 Kmph.)

Thus we see that in both cases

Tfreq =Tworst+ (Dtrains-OfJorst)

Vbo

44

= Tworst + Dtrains -Dworst--Vbo Vbo

= (Tace+Tbr + Th + Tr) + (Dbr+Dg:yy+Ov+TI) - Dbr+Dacc

Vbo Vbo

EQN (4)

(By substituting values from Eqns. 1 &2 in Eqns 3)

(Dg:yg - The distance between double yellow and green aspects, here applies to a signal which is4th signal in rear of the starter signal.This will become more clear on subsequent discussions.)

From the above it can be seen that the frequency of service that can be achieved will dependbasicallyon the type of rolling stock in usewhichwill governthe accelerating,braking and maximumachievable (Tacc,Tbr, Dbr, Dacc & Vbo) speed of the trains. Secondly it will also depend upon thehalting patterns (Th), the train length (TI), the inter-signal distance and the signal overlap require-ments.

Many a times we tendto presume that whatever be the type of rollingstock we have, by closestacking of signals, any desired frequency of service can be achieved.The above derivationclearlybrings out the limitations of the intersignal distances, in improving the frequency of service.

To illustrate it further let us take an example, based on the field data of Mumbai - Kalyansuburban section. (for a 9 coach EMU) (Ref charts in Annx A&B) .

EXAMPLE :-

Booked speed Vbo = 65 Kmph

Tacc = 78 Sec

Tbr = 52 Sec

Th = 30 Sec

Tr = 05 Sec

(To achieve 65 Kmph Vbo)

(To stop from 65 Kmph)

(At minor stations)

(Reaction time of Driver of 5 Sec is taken)As standard

(to stop from 65 Kmph

(Assumed)

(Standard signal overlap)

(a 9 coach EMU length)

(to achieve 65 Kmph Vbo)

Thus (as per Eqn -4)

Tfreq. =Tacc+ Tbr+ "Fh+Tr + (Dbr+Dg:yy+Ov+ Ti) - (Dbr+Dacc)4

Vbo Vbo

= 78+52+30+5+(4.25+1000+120+200)- (425+880)

65XO.28 65XO.28

.,- -

-

Dbr = 425 Mts.

Dg:yy = 1000

Ov = : i20 mts.".

T1 = 200 mts

Dacc = 800 .rnts

III

45

(Speed conversion factor 65kmph = 0.28m/secto meter/sec.)

= 165 + 1745 -1305

65x 0.28= 165+28= 193 secondsThis is the maximum theoretical frequency of service that can be achievedNow if we reduce the intersignal distance, Dgy:yy to 400 meters then,Tfreq. = 165+ (425+400+120+200)-(425+88)

65XO-28 65XO-38= 165 + 1145 - 1305

65XO-28= 165-10= 155 seconds

It can be seen from the above that even by reducing the Dg :yy to 40% (Le. increasing thenumber of signals by two and a half times) the achievement in the frequency of service is a reduc-tion of only 38 seconds.,(though in 3 aspect signalling it will not be possible to reduce Dg:yy to lessthan Dbr, which in this case is 425 meters.)

By feeding various values of Dg:yy,it can be easilydemonstrated that the score for achievinghigher frequency of services, only by reducing ISD (inter signal distances) is very limited.The realchange will come by changing the rolling stock parameters.

Hencewe see that the above derivationgives the maximumpossible frequency of service fora given type of rolling stock.This will have to be a guiding factor before any exercise for placementof signals is taken in hand.The derivation can also incidentally be used to determine the optimumbooked speed for a given type of rolling stock for minimizing the frequency of service.

A very interesting off-short of this, is a conclusion that, the maximum frequency of servicecan be achieved at a speed, which is much different from the maximum speed. The graph belowplots the frequency of service for various speeds)or a 9 coach EMU (Electrical Multiple Unit) inMumbai-Kalyan section during peak hours (Data from Charts in Annex A&B)

OPTIMUM SPEED CURVE

u 180: 170.5 160~150LL 140

o

M~"Ji"Z'$~"N"";' "''''''''''\lillfl:1I'i,iowt"''''''''''

~~J~;~<~;~1_~J'20 40 60 80 100

Speed in kmph

Note : The meaning of ISO herll is the Inter signal distance in the sections away from the haltingstations. The inter signal distances in the viCinity of halting stations will depend on entirely differentconsiderations, which we will be discussing subsequently. The distance Og:yy will be generally lessthen the ISO of the sections away from the station, because these signals will be comparativelyclo.ser to the stations. Nevertheless Og:yy will be a representative figure of ISO and will vary propor-tionately.

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46

PLACEMENT OF SIGNALS

Having calculated the "maximum possible frequency of service", we can get down to t hescheme of placement of signals for achieving the same.

The "Inter Signal Distance" as brought out earlier will be a uniform distance, applicable inautomatic section, which are away from halting stations. In the vicinity of halting stations, theplacement of signals will have to be decided separately.

Let us consider the following situation,wherethe signals have been named as Home,Outer1,Outer2, Starter, Starter1 and Starter2 etc.

Fig3

: Outer.2 I

~I Outer1 I

f-«*)I Home I

f-«*)I Starter I

I-«:«)

IStarter1 I

~IStarter2 II-«:«)

: STATION:L-__~ -+

Location of each of the above signals will depend on the headway (Headway:- of a signal isdefined as the time, that a train takes to change the aspect of the particular signals from green toRed and again to Green during the course of its run. Through in some cases, Yellowand doubleyellow aspect is considered instead of Green) available for its clearance, depending on the patternof running of trains in the section controlled by them. This will be more clear on going through thefollowing discussion, for the location of each of the above signals.

LOCATION OFTHE STARTER SIGNAL (ST)

This is the only signal whose location does not call for any argument. The starter signal has to belocatedat the end of the Platform ( Howeverin caseswhere the platform is extra long, the starter willbe located at the normal place of stoppage of the train in question.

LOCA"fION OFTHE SIGNAL, NEXTTO STARTER(St1):

St1 should be locate~ at such a distance from ST, that when a train starts from the stations accel-erates past St1 to el,ear the signal overlap ( so as to clear the St to Yellow) ( As per the signallingstandards on Indian Railways, Red signal is preceded by a Yellow signal, which in turn is precededby a double yellow signal which in turn is preceded by a Green Signal). The time taken should beless then or equattoTrainirequency. Or in other words, the Yellow head way of S1<=Tfreq. Thus thedistance between St and St1 ie. Dst: st1' is

Dst: st1 = Dice +Tfreq-Tacc-Tr-Tp)*Vbo-TIOv. .EQU-5

- --- -

47

Where

he Dacc = Distance travelled in accelerating up to booked speed

. Tacc=Timetakenfor above

Tr = Reaction time of the Driver before starting

Tp =Time loss due to permanent speed restriction.

Vbo = Booked speed

TI = Train length

Ov :I:Overlap

Because after accelerating upto booked speed the train will travel at booked speed, and thetrain will have to travel its length and overlap distance for turning the starter St to Yellow.

Let us take an example of train with a booked speed of 65 Kmph a 9 Car rake (200 meterlength) and accelerationand decelerationcharacteristicsas per Annexure A (The date is a resultofactual trials conducted in Mumbai suburban section of Mumbai-Kalyan), We can assume the fre-quency of service required as 3 minutes Le., 180 seconds. Toachie'le a practical headway of 180seconds, it is considered reasonably safe to target a theoretical headway of 150 seconds. Thus:-

Dstst1 =880m (Le. Dacc = Distance for accelerating upto Vbo) + 150-78-5) x 18 - 200 - 120

(78 Sec is the time for accelerating to Vbo, 200m is train length and 120 m is overlap distanceVbo=65 kmph = 18 m/Sec)

(AssumingTp i.e., permanent speed restrictions to be NIL)

or

Dstst1

=880+67x18-320

=880+ 1200-320

=1766 meters

Though the signal St1 can be placed at a maximum distance of 1766 meters from ST. Thepoint to be noted here is that we are considering only" Yellow Headway" of St and not "GreenHeadway", as normally the case should be. This is to take into account the fact that every trainstops at this signal for halting station and restarts after the halt (There may be a train runningthrough also but the scheme has to be designed for a union pattern of halting. Although, as will beclear later in the discussion, that the, scheme will be generally suitable for such occasional runthrough trains also). On starting from a speed of "Zero", the train need not see a double yellow orgreensignal. .

We'll have to defer, the discussion, about placementof other signals for some time as at thispoint, it becomes necessary to discuss some aspects like Headways of various other signals andthe details of Inter signal distances in general. These are brought out as follows:-

--= ==

,

48

HEADWAYS OF VARIOUS SIGNALS

On similar arguments, the headways of various other signals are required to be as follows (Ref tofig2)

Signal Required Headway.

St - Yellow( as the trains has to start at this signals after stopping

Sh - Yellow( as the train has to stop after this signal)

Sol - Double yellow ( as the train has to stop after the next signal Le., SH

S02 - Green (as the train has to stop after the next to next signal)

St1 - Green ( as the train has to catch up speed while approaching / Crossing this signal)

St2 - Green ( as the train has to catch up speed while approaching / Crossing this signal)

INTER SIGNAL DISTANCE (ISD)

As brought out ea~lier,the location of signals in the Automatic block sections in the vicinity ofHalting stations has to be decided seperately for each signal. But the location of signals in Auto-matic Block sections away from halting stations can be at a uniform" Intersignal distances", whichmay be called the ISOfor the entire Scheme. This ISOwill depend upon some more factors, ratherttlan only headway considerations. Let us examine them in detail.

Fie-4

~~

I S04 I

~I S03 I

~~~

~~

~~

~~

..

Fig.4

Refer'to figure3 above(considering a 4 aspect signalling Scheme, the preference of 4 aspectsignalling over 3 aspect or any other number of aspects is discussed in the next section). In thediscussion~nearlier section, the trains under considerationfor the scheme will run at their bookedspeed, ~rily at signal S02 and onwards (S03 & S04) because at St & Sh requirement is only yellowand that at S01 is only double yellow. (The train will be brakingwhile passingthese signals so as tostop at the station, thus it will not be running at its booked speed.)

' ...

-- - -

y .

49

When a train passes S02, it turns it to Red ( in Automatic Signalling territory, when a train passes asignal, the signal turns to Red). The other signals in rear follow the aspects, yellow, double yellowand green respectively Le., S03 turns to yellow S04 Turns to double yellow and S05 turns to Green.Thus the uniform ISO will apply S05 onwards because, for S03 to turn to green Sh will be Red, S01will be 'V" and S02 will be VV, ad since the trains will start retarding at S01, Sh (so as stop, short ofSt) the time taken for S03 to turn to Green will be more, Similarly for S04 to turn to Green, S01 willbe Red, S02 will be "V" and S03 will be "VV" and since the train may start retarding at S01 forstopping at St, which will consume more time for the yellow of S02 to come, it will take more time forthe Green of S04 to come.

Fig 5

~\-8I)

[ill\-8I)

~ ~\-8I) '. ~

~~

~\-8I)

~\-8I)

Let us calculate the locations of such signals (refer figSabove). The distance between S05 to S06to S07 to S08 can be calculated as follows: - .

Os08:s05=Time available for running

For clearing S08 fromGreen to Red, Vellow,Oouble

Veilowand again to Green aftera train passes it at booked speed.

X Booked speed

= (Totaltime available as per - (Time for clearing train X Booked Speed

the required headwayas length + overlap beyond

per freq. Of service) signal S05)

Hence, since the ISO is uniform, the distance between S05 to S06 ( or ISO) will be

Os05:s06= ISO = Os05:s06/3 = (As S05,S06,S07, S08 are equal distant from each other)OR

ISO (Tfreqx Vbo)/3 -Tl+ov/3

Let us consider the example for the~ minutes service. With a theoretical headway requirementof150 seconds, a train length of 270 m ( 12 coach EMU) and an overlap of 120 meters.

ISO=1/3(150x18-(270+120): Speed 65 kmph=18m/sec

= 1/3 (2700-390)

1/3(2310)

I

I

II.

~

.--

---

r

50

ror

ISO = 770 meters

Here it is worth noting that if we don't need Yellow and double yellow signals in between Red andGreen, the ISO can be as high as 2310 meters. If our working conditions are ideal Le, the signalswork to 100% reliability and the running of trains is at exact uniform intervals then achieving both theabove factors is possible. However practically these type of situations can not be ensured, leadingto the use of 4 aspect signalling, necessitating less ISOs).

Similarly for a section 10 minutes service the ISI will be :

(Considering a theoretical headway of 8")

ISO = 1/3 (60x8)x18 -270+120)

= 1/3 (85540-390)

8150/3

2717 Meters

ISD = 2.7 Kms

MAXIMUM ISD

However, keeping the ISO only as per the above consideration, will cause problems of bunching.When a train stops for more time in any section, than it is supposed to, or goes at a slow speed, theOriver of the following trains comes across a Red signal. He passes this Red signal as per rules( After stopping at the signal for 1" during day and 2" during night and at 15 kmph during day and 8kmph during night*) and takes a long time to clear the section, which results in the next trainscoming across a similar situation and so on and on. etc., In the automatic section there will be anumber of occasions in which a.train will have to pass an automatic signal at On (Red), or example,some situations are :-

a) A train ahead in the section

b) An intermittent track circuit failure resulting in signal going to "On" because of its fail safe feature,due to :

* (As per the prevailing General Rules on Indian Railways)

i) Technical fault-ip tract circuiting

ii) Engineering wdrk going on in the tract circuited area resulting in short circuiting of the tract circuit.

iii) Miscreants shorting the tract circuit.

iv) Rail fracture resulting in discontinuity of tract circuit current

c) Fusing of other aspects' bulb of the signal

d) Fusil1g of Red aspect bLftb of next signal etc.

As per the present General and subsidiary Rules of Central Railway, when an automatic signal ispassed at "ON" by a train, it must first stop short of the signal for 1" during day and 2" during night

.and-subseQ.uently proceed at a speed of 15 kmph during day and 8 KMPH during night, upto the nextsignal.

...

- -- --

T"-- --

51

Thus if we cater for the day situation to clear the signal even only to "Yellow"after passage of onetrain ( With signal at ON Red) with above stipulations. The ISO will be calculated as follows: -ISO= (Thw-Td-Ta-Tov)x 15 kmph

Thw -Time as per headway requirement

Td-The difference in time that the train will take to stop at the signal instead of travelling at bookedspeed

Ta - Half of 1" during day.

Tov - Time for clearing the train length and overlap while accelerating at next signal.

Let us take an example of 3" service, with 9 coach EMU

Hence ISO= (150 ( 52-25)-60-42) x 15x 0.28

Where

Thw - 150(Required)

Td = 52-25 (from data from Ann "8")

Ta = 60 Sec

Tov = 42 Sec (From data from Ann "A")

0.28 = conversion factor for 15 kmph

= (150-129)x15xO.28

= 21x15xO.28=64

Or

ISD = 64 Meters

which is not practically possible.

If we take a case of 4" service.

ISO = (60 +150 -129) x 15 x 0.28 = 321

or ISO: 321 meters

Which is again not practic~1lypossible ( Particularly in section awayfrom station. Where the ISOismeant for)

For higher frequencies of services, this ISO will increase, but it will be far below the ISO,which isotherwise required and it will be a great wastage to employ such smalilSOs

Thus it can be concluded that the bunching of trains can not be avoided, without creating a gap Le.,canceling of the trains so as to send to next train'only after twice the normal headway..Thus after creating a gap we will get second train for clearing the section.

Hence ISO = (180+21) x 15xO.28

(From last equation adding 180 sec margin of cancelled train)

=800 meters (3" services)

.. -