THE NUMBER OF TRACKS IN MAIN TRACK GROUPS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000200050015-9
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 14
• Document Creation Date: December 22, 2016
• Document Release Date: April 20, 2012
• Sequence Number: 15
• Publication Date: June 16, 1952
• Content Type: REPORT

Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
The N er of Tracks in Main Trac Gro s
by Gerhart Potthof f , Prof. , Dr-Eng.
Der Verkehr, Vol 10, Oct 51, Mo per,
(German)
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
STAT
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
Prof Gerhart Potthgff
Doctor of Engineering
Dresden Technical College
1. THE PROBLEM
Main tracks, according to the Railway Construction and Oper-
ating Regulations, are those tracks used by trains in regular oper~
ata.on, Sometimes main tracks exist in groups, as for instance the
entrance and exit tracks of a switching yard or the platform tracks
of a passenger station, in which cases the tracks have similar or
identical functions. In the first case (tracks with similar func-
ta. ons) each track has its own particular function: in a group of
platform tracks, for instance, one track may be the through main
track of the lane AB in the direction AB and another track may be
the overtaking track of the same line in the directions AB and BA,
etc. If suitable swatch connections are available, tracks within
the group may substitute for each other. That is to say, a given
track may fulfill not only its own particular function, but may
tical functions) the tracks are so arranged that any track may ful-
normally belonging to them. In the second case (tracks with iden-'
also substitute for neighboring tracks, fulfilling functions
fill the functions pertaining to the group.
The way in which the tracks in an existing group are em-
NU~dBER OF TRACKS IN CAIN
TRACK GROUPS
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20: CIA-RDP82-00039R000200050015-9
out new track facilities, the lowest feasible number of tracks is
toyed is shown graphically in a track utilitiation plan. In laying
p
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
determined by the requirement that the track group be able to ab-
sorb without difficulty the scheduled peak traffic during the part
of the day with the heaviest load. It is, however, also necessary
to consider the possibility of time table changes, lateness of trains
and other irregularities in operations (see item No in bibliogra-'
phy). This makes it necessary to add a margin of safety to the
minimum number of tracks deternt.ned under the track utilization
plan. This margin of safety may be calculated with reference to
the disturbances of traffic which may occur if the extra tracks are
]a eking. The question of the length of the daily period during
which the peak load occurs deserves special consideration.
The method of determining the number of tracks will be il?
lustrated by three examples. These are the entrance tracks of a
switching yard (section 2), the freight train tracks of a medium
. 4\;\ platform tracks
sized Ord (section 3) and a group of passenger p
(section !i.).
2. ENTRANCE TRACKS OF A SWITCHING YARD
21. Processing Time
The utilization of an entry track is calculated as beginning
with the point of time at which the dispatcher assigns the empty
track to an incoming tram'.
The time required for setting up the
passage way for the train varies according to local conditions and
may be determined by adding together the individual times values
'l (items $ and 10 in bibliography. The modai time for the set-
for the operation of signals, as set forth in a so-called ' 6 gna
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
r up of the passage way is approad.mately two minutes. The next
tiny,
occurrence is the entrance of the train, which is reckoned from the
the trains passes a point the visual distance of 200 meters
moment when
ahead of the advance entry signal until the train has stopped in the
entrance track. In a particular case, for inatance, the entrance
of the train consists of 200 meters (visual distance) + 700
path
distance from advance entry signal to main entry signal)
meters
~2a0 meters (distance from entry signal to beginning of first switch
2S0 meters (switch zone) 4 60 meters (length of train ) x 2000
meters altogether. The time required for entrance including an al-
owance for braking should be about Ii. minutes in this case but in
1
,After the train has stopped, the conductor turns over the
manifests of the cars to the dispatcher. rRolling stock mechanics
make a technical inspection of each car. The switching master or
a special switching clerk prepares for the dispersion of the train
by noting each car or group of cars on a switching order. Finally
yard men unfasten the couplings and detach the air brake hoses
between the cars or groups of cars to be separated and make the
train ready for breaking up. The times required for these prepara-
tory steps may take place simultaneously and if so which. The
entire time for preparing to break up the train averages between ).j5
detail by Maier (items 10 and 11 in bibliography), who gives special.
the hump, pushing the ca?s over it. This process is discussed in
accomplished by having a switching locomotive move the train up to
and 60 minutes (item 2 in bibliography). The actual breaking up is
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
consideration to the speed of the huanping operation as affected by
the height and gradient of the hump, wind and weathers type and 1o8c~-
'~ '~~
ing of cars and number of cars handled as a unit for humping purposes.
locomotive has left the entrance track after
Not until the switching
the track available for the next train. The
humping the train is
time elements from the assignment of the track by the dispatdher~
~'~'
until the track again becomes free can be calculated for each oper~
at?ve step according to local conditions. The sum of these times
~
we shall call the processing time, "b".
The train occupies the entrance track at least for the dur-
ation of the processing time.
22. Waiting Time
To the m' nimum time for occupancy of the track we must add
~.
which no progress is made with operations, which
the time during
we will designate as waiting time for "w". The sum of the pro-
"b" and the waiting time is the time during which
cessa.ng time
the train occupies one of the tracks in the group.
221. The dispatcher cannot judge the time for setting up
the passage way so accurately that the incoming train reaches the
point at the visual distance ahead of the advance signal at the
exact moment when this signal moves to "proceed". In order to avoid
stopping the train way in, the dispatcher usually sets up the
; ~n on i
passage way a little earlier, the interval being named "margin of
safety for entrance" by Behr (item 4 bibilography), who has deter-
mined that it averages about 13 seconds at a large passenger station.
14
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
222. Preparatory operations on the entrance track do not
in all cases begin immediately after the entrance of the train, but
are scheduled according to a work plan which keeps the various
workers in the yard busy at all times. The waiting of trains for
inspection after entry, for the writing of switching orders, etc,
must be so regulated by the assignment of sufficient working forces
that it remains within the waiting time hereinafter described and
does not become of itself a factor determining the total load on the
group of tracks.
223. The bottleneck in a switching yard is usually the hump.
The operating speed in humping determines how fast the group of
entrance tracks can be emptied. As soon as trains arrive faster
than they can be humped, waiting time ensues.
2231. Diagram 1, based upon operating records in a switching
yard, shows how the 13 trains arriving during a period of approximate-
ly six hours were humped. The average processing time in the yard
is b 1.S hours. The time spent by the 13 trains on the entrance
tracks varies between 1.~ and 2.S hours, so that the waiting times
vary between wmj . 1. - 1? = O and wmin w 2. - 1. x,1.0 hours.
The median time spent by the trains on the tracks is 2.02 hours, so
that the median waiting time is wm c 2,02 - 1.~ 0.~2 hours. From
the lave connecting the times when humping operations of each train
are completed we may read that every c z 0.43 hours a train is humped.
From the line connecting the time of arrival we may see that fre-
quently the trains arrive only z . 0.2 hours behind each other.
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
2232. In Diagram 2, we make the unfavorable supposition that
the trains in a group follow each other at equal intervals of z hours.
Every C hours a train is humped. Since the group of tracks is supposedly
empty when train number 0 arrives, this train may be humped as soon as
preparatory operations have been completed. Train nurr~ er N has the
longest waiting time, which is wm .(c " z)N. The median waiting
time of all trains in the group is w~ (c - z) N/2 hours. The time
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
line showing time of
humping
n trains
line showing times of
arrival
t hours
Diagram 1
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
required for proc?ssira the entire peak load is N ~ cN. I, fox inw
~. _ o. L3 hours per train and z =0.2 hours per
stance, N ~12, c
.~ ours ~ w w 1? l~ hours and H ~ ~.2 hours.
8 h ~ m
train, txaen wax ~ 2 ?
the simplifications of the lines showing
2233. Instead of
times of arrival and humping given in Diagram 2, it is also possible
to use other curVe..smoothing forms such as, for instance, a parabolic
arrival. In this case too it is possible to
curve for the times of
determine the maximum and median waiting times and the time required
for processing a groupof trains. In the foregoing examples it was
assumed that trains would be humped in the order of their arrival.
In practi fie, departures are made from this order to assure that care
arr oming trains connect with the proper departing trains. arriving on a.nc
This does not change the median waiting time, since the increased
~?
waiting time of one train is equal to the decreased waiting time of
another.
Track Utilization Plan and -n~-r~ Number of Tracks
23.
the sums of the processing times b (section 21) and
Having
-
waiting times w (section 22) of each train, it is possible to f ormu
a track utilization plan, when the niTiber of tracks in the group
late
is fixed. ?sing the same figures one may also determine the rma?nimuan
of tracks necessary. In Diagram 1, for instance, one runs a
number
horizontal cut through the lines indicating track occupancy at all
passible times and counts the number of trains through which the cut
passes. It appears that at most nmax :6 trains are simultaneously
in the track group. Maximum occupancy is reached when the arrival
line runs parallel to the humping line, that is, when the train with
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
The track utilization plan is to be considered for the
period H during which a group of incoming trains is processed. At
the beginning and end of this period the tracks are empt5'br, to be
more specifica the first and last trains of the group may be pro
cessed without delay. Diagrams 1 and 2 were constructed to conform
to these conditions.
We have determined the minimum number of tracks in the
not to be expected. Minor i-regularities and trains delays
ever,
may cause deviations from the norm and will cause disturbances in
the assignment of tracks unless certain track space is aval~iable
to reserve to cove temporary and irregular peaks. The actual
as
of tracks must therefore, and quite apart from the need
number
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
the1.mum waiting time arrives.
In the case of a straight arrival line (Diagram 2) there are
... ~, N .. zN c ~ b~c ~ (c x)N ~ b)/c
upon arrival of the last train nmax
trains in the graup of tracks.
hours per train, z 0.2 hours per train
If N = 12; c ~ 0. .3
and b =1. hours, then nmax = 10 trains.
The greatest number of trains which may be present at any
one time is si ousty the ndnimum necessary number of tracks
multane
entrance group under the supposition that trains would arrive
according to schedule. Rigid adherence to time tables is, how-
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
Consider npw
to a whale number, be greater than fl)nin'
or round g
rin the peak load period H. The N
this expanded group of tracks du g
e tracks for individual times totalling
trains processed occupy th ail-
riod H the railroad has track capacity av
(b 4' wm)N. During the pe
of tracks multiplied by the time, that is mH.
able equal to the number )
The operations cause the tracks to be occupied in the ratio q (b+ wm
N/nH, which we will call median track occupancy. If we assume a
straight humping line (H/N' c) and abbreviate nm ; (b .. wm)/c, then
(sic : probably should be q 4 n1/m17
The probability that a track will be occupied is q?
in tracks will simultaneously be occupied
The probability that all
is, accoxing to the laws of probability qm and the duration of this
simultaneous occupancy of all m tracks is p Hqm. During this
tracks is not able to receive a further train.
time p the group of
A, further flow of trains into the yard wi11 therefore be disturbed'
and we may designate pas ttdisturbance time" (item 12 in bibiio"'
disturbance times are phenomena which we may ob"
gra,phy) , These
serve in actual railroad operation: they are the intervals during
which trains must wait outside a yard.;..since all the tracks in the
yard are filled. The relationships between nm, m and p/H ~ (n~;/m)m
are shown in Diagram 3.
1 we were able to determine that b . 1?~
From Dlagram.
ours; c 0.4.3 hours per train and H .2 hours
hours; wm ,. O. , 2 h ,
312 s This means that nm 4.6 The minimum number
~,nute .
of tracks was -6. For various numbers of tracks m the
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
expected disturbances p have been calculated, as follows:
m
qm
p minutes
In the calculations, Etude's table of exponents (item 6 in
bibliography) has been used. It is in our case indicated that
really disturbance-'free operations can be expected only when m
is set at at least eight tracks.
3.
THE FREIGHT TRAIN TRACKS OF A MEDfM-SIZED YARD
At a junction various lines merge, which are travelled by
through freight trains. These trains stop at thejunction station
for certain operative steps. These include: passing trains going
the other way on single track lines, being overtaken by faster
trains, watering the locomotives, and sometimes changing locomo--
Lives or dropping or picking up groups of cars. All these activities
are determined by the time table and involve an occupancy of tracks,
which with the help of the track? utilization plan may be converted
into a track requirement. The same tracks used for taking care of
the through train are also used for assembling short. stance
freight trains leaving the station in various directions. For this
operation too the occupancy time and track need may be determined.
This problem is different from that presented in subhead 2, since
it was there assumed that all tracks could substitute for each other.
In the case to be examined here, some of the tracks are accessible
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
an that 9/6 -. 1?~ tracks would be ne
direction. This would me
essar'Y in each direction.
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
x'Ma~t~.on, 8 Others ply by
tY~rough tracks in on the e di
the
only from It is thus nec"
~
n
.a
other direct
way of the through 'tracks in the
? each
arate~.y for cb
lan sep
utilization p
set up the track
sary to
es
ecessary re"
y the n
lets separata~.
and to calcu
du
p~
f the gr
t
par oc disturbance .
txaff~
sexye tracks needed each part to e~,iminate
. ~.n tracks
be a f forded when, for instance, .the enter each side, $o that they may be
Some relief may'
may be connected to through nayS On loads
ay be connected to through ways ?n ads
. It may be the case that the peak to
used in either da.rection. is then
s do not Occur at the same time. It
in the two dtirect~.on stitute for each
the two subgroups to sub
i
n
acks
assible for tr p
xp
it the alternation of peaks can be eected
other; but/is doubtful ether e ex
M
at all times. It is advisable to provide at least for possib/
tracks so that peak loads in bot
ansion so as to provide enough
P
s can be handled at the same time.
d?.rectlon
~
gate hoer the total of expected dis-
,An example will illus
assume that in a station the peak
tuxbances Is calculated. Let us
the
load period H is 6 hours and that during this time tracks in
cu ied, a total of 9 hours in each
two directions Ow and NO are oc p
Cr
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
Case A~ There are 3 tracks in each direction, but the
~~
tracks of the two sub-groups cannot substitute for each other.
The probable total disturbance in each sub-group is the p
6(i./3) 3 0.7 hours. The combined total disturbance for both
P 2 ' O.7~ = 1. hours, that is to say, fairly
sub groups is A
high.
Case B:? There are 6 tracks, of which the two outer pairs
can each be used in only one direction, the two center tracks,
however, in either directiono The probability thattwo trains
in one direction are present in the yard is (l.~/2)2
in one direction are present (1.x/3)3 m O.l2
that three trains
and for four trains one direction it is (1.~/4)~ = 0.0198.
in on
The Probability that either 2 OW and WO trains, 3 OW and 3 WO
trains or 4 OW and 2 WO trains are present at one time, thus
occupying all available tracks, is: 0.625' 0.0198 + 0.125' +
~
0.198 ' ?.62 = 0.0379. This means that the total expected
disturbance in this case, PB, is only 0.0379 ? 6 0.23 hours.
In both cases A and B there are six tracks. The possi-
bility of using the center pair of tracks in both directions
reduced the total expected disturbance to about 1/6 what it would
be otherwise.
14. PLATFORM 'RACKS
In addition to operating activities taking place on platform
tracks, such as passing and overtaking, watering or changing loco-
motives, adding or taking off inter-lire cars, there are also tra
ffic activities, that isto say the boarding and alighting of passen-d
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9
and un1oadiTJC of baggage, express and mail.
gars and the loading
The minimum times required for platform stops may be calculated
and must be added to the time required for moving in and out of
the track to determine the total time the track is occupied.
The track occupyncY time of a passenger train is usually much
shorter than those of ttit freight trains considered in the pre"
ceding subheads. For this reason a much more important con-
the case of passenger trains is the waiting time
sideration in
the fact that various possible through passage ways
caused by
clusive? In the case of yards which present
are mutually e
waiting time for a clear passage out
operating difficulties,
of the yard may be many tunes the miramum time the train stops
platform for operating and traffic purposes. A care-
atthep
on between the number of platform tracks and the
ful coordinati
r
development of the yard asa whole is therefore a condition for
W,
achieving a low disturbance factor, and simultaneously the
guarantee for efficient and frictionless operation. The remarks
oncerning the substitution of tracks for each other made in
c
Subhead 3 app1Y equally to the case of platform tracks.
Declassified in Part - Sanitized Copy Approved for Release 2012/04/20 : CIA-RDP82-00039R000200050015-9