DETERMINING THE NEED FOR TRAIN LOCOMOTIVES IN THE CONDITIONS OF TRAINE MOVEMENT IMPAIRMENT

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ABSTRACT

This article presents the methods of determining the need for train locomotives in conditions of imbalance of train
traffic. To check the reliability of the obtained results, as an example, the indicators of use of electric locomotives for
the AV circulation section were analyzed. Also, an algorithm for determining the fleet of electric locomotives needed
to service freight trains has been developed.

KEYWORDS

Indicators of the use of locomotives,turns, equipment, tortuv shoulders, interval between trains.

INTRODUCTION

In the conditions of the market economy and the
reconstruction of railway transport, the use of
effective technology of the transport process, aimed at
improving economic indicators, increasing the quality
of transport, the prestige and attractiveness of railway
transport, and the search for methods of its
implementation, is one of the urgent issues of our time.

The modern needs for the quality of transportation
require the need to increase the regularity, accuracy
and rhythm of operation of all railway lines. At the
same time, reducing freight costs and increasing their
profitability largely depends on the development and
implementation of a number of systems, the
optimization of which affects the improvement of

Research Article

DETERMINING THE NEED FOR TRAIN LOCOMOTIVES IN THE
CONDITIONS OF TRAINE MOVEMENT IMPAIRMENT

Submission Date:

February 18, 2023,

Accepted Date:

February 23, 2023,

Published Date:

February 28, 2023

Crossref doi:

https://doi.org/10.37547/ajast/Volume03Issue02-08

Jumayev Sh.B.

Phd, Associate Professor, Tashkent State Transport University, Uzbekistan

Khudaiberganov Sk

C.T.S., Associate Professor, Tashkent State Transport University, Uzbekistan

Journal

Website:

https://theusajournals.
com/index.php/ajast

Copyright:

Original

content from this work
may be used under the
terms of the creative
commons

attributes

4.0 licence.

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Pages:

72-81

SJIF

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(2022:

5.

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(2023:

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railway transport. One of them is a complex system for
managing the use of locomotives. For this, important
measures aimed at improving the service of the
transportation process by locomotives and locomotive
brigades are being developed. However, determining
the need for train locomotives is recognized as one of
the urgent issues in almost all railways of the world, in
a situation where train traffic is variable.

MAIN PART

When calculating the need for locomotives, it can be
divided into two parts: main and additional.

A basic need- this is the minimum number of
locomotives required to serve a certain number of

freight trains running at a certain frequency under ideal
conditions, that is, to ensure the minimum calculated
locomotive cycle time in the traffic schedule.

Additional need occurs as a result of locomotives
staying longer than the accepted technological time
standards due to waiting for the train at the turning
points.

After calculations, both of these requirements should
be increased, taking into account the uneven
movement caused by the change in the daily train flow.

The basic need for locomotives is calculated by the
following formula:

𝑀

𝑜

= 𝜃

𝑝

∙ 𝑁/24

(1)

here

𝜃

𝑝

−

calculated turnover of locomotives, hours;

𝑁 −

average size of freight traffic, pair of trains

The calculated turnover of locomotives is determined based on the following formula:

𝜃

𝑝

=

2∙𝐿

𝑣

𝑦

+ (

2∙𝐿

𝐿

𝑡𝑒𝑥

− 2) ∙ 𝑡

𝑡𝑒𝑥

+ 𝑡

𝑜

′

+ 𝑡

𝑜

′′

+

2∙𝐿

𝐿

𝑒𝑘

∙ 𝑡

𝑒𝑘

(2)

here

𝐿 −

length of locomotive circuit section, km;

𝑣

𝑦

−

section speed, km/h;

𝑡

𝑡𝑒𝑥

, 𝐿

𝑡𝑒𝑥

–

respectively, the transit train's stopping time at the technical stations without

changing the locomotive and the distance between these stations, km.;

𝑡

𝑜

′

, 𝑡

𝑜

′′

−

minimum technological (calculated) stay time of locomotives at turning points;

𝑡

𝑒𝑘

, 𝐿

𝑒𝑘

−

respectively, the time of equipping the locomotive at the technical stations and

the walking distance between the equipments, km.

The basic need for the locomotive fleet can be determined by the average interval (Isr min.) of freight trains

moving between passenger trains:

M

o

=

θ

p

𝐼

𝑠𝑟

1/60

(3)

In long-distance circulation sections it is equal to-

𝐼

𝑠𝑟

= 1440/𝑁

, and in short-distance sections:

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𝐼

𝑠𝑟

=

1440−[𝜀

𝑝

+1)∙𝐼

𝑝

∙𝑁

𝑝

𝑁

(4)

here

𝜀

𝑝

−

the coefficient of displacement of freight trains by passenger trains;

𝐼

𝑝

−

the interval between passenger trains in the schedule of trains (non-packaged),

min.;

𝑁

𝑝

−

number of passenger trains, train.

With the help of the coefficient of daily imbalance of the flow of cars (y), it is possible to take into account the

increase in the basic need for locomotives caused by the daily imbalance of the flow of cars, that is:

𝑀

𝑜

𝑛

𝑀

𝑜

𝑛

= 𝑀

𝑜

∙ 𝑦

(5)

𝑦

- the fluctuation of the flow of cars, which is equal to the value of the mean square deviation between the

maximum and minimum value of the flow of cars increased by one and a half, i.e.

𝜎

𝑦 =

1,5∙𝜎

𝑢

(6)

In this case:

𝐼

𝑠𝑟

′

=

𝐼

𝑠𝑟

1+𝑦

(7)

here

𝑢 −

the average size of the flow of wagons in the planned period;

𝐼

𝑐𝑝

−

the average interval in the running of freight trains, taking into account the

imbalance.

Total demand for locomotives, taking into account the imbalance

𝑀

𝑜

′

= 𝑀

𝑜

+ 𝑀

𝑜

𝑛

(8)

By substituting the value from formula 1, we get:

𝑀

𝑜

𝑀

𝑜

′

=

𝜃

𝑛

∙𝑁∙(1+𝑦)

24

(9)

The additional need for locomotives consists of two parts:

𝑀

dop

n

𝑀

𝑑𝑜𝑝

𝑜𝑏

−

the need that arises due to the fact that the end time of technological operations does not coincide with

the time interval of the departure of freight trains, as well as the omission of passenger trains and imbalances in the

arrival and departure of freight trains, that is, delays at turning points.

𝑀

𝑑𝑜𝑝

𝑛

−

the need that arises due to the provision of services for the withdrawal of trains from round stations on

a long circuit section in conditions of imbalance of train traffic.

For a plot with several tortuous shoulders:

𝑀

𝑑𝑜𝑝

𝑛

=

∑ 𝑇

𝑑𝑜𝑝

24

+ 0,5 ∙ П

(10)

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here

П −

the number of turning points, including the number of stations delimiting the

turning sections;

∑ 𝑇

𝑑𝑜𝑝

−

total additional delay of locomotives at all turning points;

∑ 𝑇

𝑑𝑜𝑝

=

[24∙𝑘

𝑠

−∑ 𝑡

𝑠𝑡

+2∙𝑁

𝑝

∙(𝑡

𝑜𝑏

+𝜀

𝑖

∙𝐼

𝑝

−𝐼

𝑒𝑟

′

)]

𝐼

𝑠𝑟

′

∙ [(𝜀

𝑝

+ 1) ∙ 𝐼

𝑝

− 𝐼

𝑠𝑟

′

]

(11)

here

𝑘

𝑠

−

the proportionality coefficient of the placement of passenger trains in the

traffic schedule. It is approximately equal to:

𝑘

𝑠

= 0,8 + 0,2 ∙ 𝑁

𝑝

(12)

here

∑ 𝑡

𝑠𝑡

−

stopping time of passenger trains at the turning point of locomotives;

𝜀

𝑖

∙ 𝐼

𝑝

–

time chart of a passenger train on a freight train.

For sections delimiting turning points, half of is taken. The method of analytical determination of

∑ 𝑇

𝑑𝑜𝑝

∑ 𝑇

𝑑𝑜𝑝

An additional number of locomotives is needed to ensure the daily increase in the volume of traffic in conditions

of unbalanced traffic:

𝑀

𝑑𝑜𝑝

𝑜𝑏

=

𝜃

р

∙𝑛

𝑦

24

∙ (

𝜃

𝑝

𝑡

𝑝

− 1)

(13)

here

𝑡

𝑝

−

locomotive work planning period.

The general need for locomotives consists of basic and additional parts:

𝑀 = 𝑀

𝑜

′

+ 𝑀

𝑑𝑜𝑝

𝑜𝑏

+ 𝑀

𝑑𝑜𝑝

𝑛

(14)

If the number of freight trains exceeds a certain critical value, additional delays of locomotives at the turning

points begin to occur:

𝑁

𝑘𝑟

≥

[1440−(𝜀

𝑝

+1)∙𝐼

𝑝

∙𝑁

𝑝

]

[(𝜀

𝑝

+1)∙𝐼

𝑝

]

(15)

ANALYSIS OF FOREIGN AND LOCAL LITERATURE

Engineering and technical staff of the All-Russian
Research Institute of Railway Transport (BRTTITI)
"Railway Operation" Department and "Locomotive
Operation" Department and Technical Department of
the Central Directorate and MPS "Locomotive
Farming" guidelines for calculating the necessary
locomotive fleet have been developed by the General
Administration [1].

Also [2] the scientific work is based on the
systematization and generalization of materials related
to the performance of locomotives, the analysis of
shortcomings in this important branch of railway
transport,

and

recommendations

for

further

improvement of the performance of practically tested
locomotives are given. Analytical formulas for
determining the time of stay of freight locomotives at
the turning point were also recommended. In [3], the
present state of the use of freight locomotives and the
analysis of scientific works were performed. As a

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result, the condition "no train is absolutely waiting for
a locomotive to depart from the station" was used to
calculate the fleet of locomotives in freight traffic. In
most cases, failure to meet this condition was found to
result in increased dwell times of locomotives at
turnpike points, which was addressed by using
modeling to change this indicator in a positive
direction. In [4], the influence of the time of freight
locomotives at the turning point on the locomotive
fleet was studied. As a result, it has been determined
that the waiting time of freight trains at the turning
points of locomotives at the same movement size
varies within a certain interval, and it is scientifically
proven that the accuracy level is not high when
determining this amount of time using analytical
formulas. In [4], the influence of the time of freight
locomotives at the turning point on the locomotive
fleet was studied. As a result, it has been determined
that the waiting time of freight trains at the turning
points of locomotives at the same movement size
varies within a certain interval, and it is scientifically
proven that the accuracy level is not high when
determining this amount of time using analytical
formulas. In [4], the influence of the time of freight
locomotives at the turning point on the locomotive
fleet was studied. As a result, it has been determined
that the waiting time of freight trains at the turning
points of locomotives at the same movement size

varies within a certain interval, and it is scientifically
proven that the accuracy level is not high when
determining this amount of time using analytical
formulas.

[5-10] researched the effect of increasing train
locomotive productivity, automating the process of
calculating the fleet of locomotives, and the effect of
the section speed of trains on the performance
indicators of locomotives.

The main goal of the above research is to achieve the
most benefits with the least cost, to improve the
indicator of the effective use of locomotives [11]

HARMONY OF THEORETICAL AND PRACTICAL
RESEARCH

Below is an example of calculating the required fleet of
electric locomotives, taking into account the imbalance
of train traffic, and these calculations were carried out
using nomograms and calculation tables. The
numerical values of the coefficients of the calculation
formulas are indicated in the instructions for
calculating the locomotive fleet. For the AV circulation
section of electric locomotives (conditional railway
section) (Fig. 1), the following performance indicators
were adopted (Table 1).

A

V

B

320 km

380 km

8

15

p

g

N

N

=

=

10

60

p

g

N

N

=

=

20

g

N

=

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Figure 1. Scheme of locomotive circulation sections and zones

In the research work, the following indicators were
selected as initial data on the conditional railway
section:

- number of thermal trains;N_sb=3 even

- the average number of wagons in the train;m=60
wagons

- mean square deviations of the flow of cars , , car;

〖

σ

〗

_(A-

V)=312σ_(A

-

B)=128σ_(B

-V)=112

- hours of maintenance of locomotives, taking into
account equipment, reception, delivery; clock;t_l-
t_V=t_ob=2,0t_b=0,6

- coefficient of displacement of freight trains by

passenger trains;ε_p=3,0

- coefficient of displacement of freight trains by

thermal trains;ε_sb=4,0

- hours of passenger trains staying at technical
stations;t_pas=0,15

- hours of scheduled operation of electric
locomotives.t=24

- distance between technical stations in km.L_tex=350

- hours of staying at technical stations.t_tex=0,15

A-V it is necessary to determine the fleet of electric
locomotives necessary for the service of freight trains
on the section.

Table 1

Indicators of use of electric locomotives for the A-V circulation section

Indicator name

Pullover shoulder

A-V

A-B

BV

Length L, km.

700

320

380

Number of freight trains, pair of trains

𝑁

𝑔

60

15

20

Number of passenger trains, pair of trains

𝑁

𝑝

10

8

-

Section speed in cargo movement, km/s

𝑣

𝑢

50

50

50

Interval between passenger trains in the package,

hours

𝐼

𝑝

0.166

0.166

-

The algorithm for solving this problem is presented in Figure 2.

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Boshlang ich ma lumotlar

tahlili

Elektrovozlarga bo lgan asosiy

talab ni hisoblash

ning nomutanosibligini

inobatga olgan holda ni

hisoblash

Uchastkalar bo yicha kritik

harakat o lchamini aniqlash

Elektrovozlarning ushlanib

qolish punktlari

(stansiyalari)ni aniqlash

Stansiyalar bo yicha ushlanib

qolish vaqtini aniqlash

( Т

qo sh

)

Elektrovozlarga bo lgan

qo shimcha talab ni

aniqlash

Harakat nomutanosibligi

bo yicha elektrovozga bo lgan

qo shimcha talab ni

hisoblash

Elektrovozlarga bo lgan

umumiy talab ni

hisoblash

ni depolar

bo yicha taqsimlash

Sutkalik nomutanosiblik

ko rsatkichlarini aniqlash

ni aniqlash

Uchastkalar bo yicha

vagonlar oqimini aniqlash

va

ni

taqqoslash

Yo lovchi poyezdlarining

joylashtirish koeffitsientini

aniqlash

(К

с

)

I

o rt

intervalni aniqlash

p



o

M

o

M

y

( )

y

kr

N

kr

N

g

p

N

N

+

'

qo sh

um

M

'

n

qo sh

M

um

M

um

M

Figure 2. Algorithm for determining the fleet of electric locomotives needed to serve freight trains on a

conditional railway section

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We will step by step determine the operating fleet of electric locomotives necessary to serve freight trains on a
conditional railway section:

1. Calculated circulation of electric locomotives on tortuv shoulders A-V, A-B, BV (formula 2):

𝜃

р

А−𝑉

=

2∙700

50

+ (

2∙700

350

− 2) 0,5 + 2 + 2 = 33,0

hours;

𝜃

р

А−𝐵

=

2∙320

50

+ 2 + 0,6 = 15,4

hour;

𝜃

р

𝐵−𝑉

=

2∙380

50

+ 0,6 + 2 = 17,8

hours;

2. According to formula 1, the main need for electric locomotives was determined. The obtained results are
presented in Table 2.M_o

Table 2

The results obtained from the approximate rotation of electric locomotives on the traction shoulders AB, BV

Plots

he

𝜃

𝑝

𝑀

𝑜

М

о

′

М

𝑑𝑜𝑝

𝑜𝑏

М

𝑑𝑜𝑝

𝑛

𝑀

A-V

0.13

33.0

82.5

93.2

22

4

119.2

A-B

0.21

15.4

9.6

11.6

…

…

…

BV

0.14

17.8

14.8

16.9

…

…

…

3. The daily imbalance of the flow of cars (y) leads to an increase in the basic need for locomotives by the value of y+1,
i.e.

𝑀

𝑜

′

= 𝑀

𝑜

∙ (𝑦 + 1)

The coefficient of daily imbalance of the flow of cars:

𝑦 =

1,5 ∙ 𝜎

𝑈

=

1,5 ∙ 𝜎

𝑁 ∙ 𝑚

𝑦

𝐴−𝑉

= 1,5 ∙

312

60 ∙ 60

= 0,13;

𝑦

𝐴−𝐵

= 1,5 ∙

128

15 ∙ 60

= 0,21;

𝑦

𝐵−𝑉

= 1,5 ∙

112

20 ∙ 60

= 0,14.

The values for the given plots are given in Table 2.

М

о

′

4.

Additional

delays

of

electric

trains

appear

at

points

A

and

B

(stations),

due

to

the

volume

of

traffic

approaching

these

stations

above the critical stations calculated by formula 15 and it is equal to a double freight train for section AB and a double
freight train for section B-V. The calculation of the need for electric locomotives for the "AB" and "BV" sections is

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705

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)

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carried out in a similar way to the following calculation for the "AV" section. The results of calculations are presented
in Table 2.

𝑁

𝑔

𝐴−𝐵

= 60 + 15 = 75𝑁

𝑔

𝐵−𝑉

= 60 + 20 = 80

5. Additional delays at points A and B are calculated to calculate according to formula 13. For this, according to formula
12, the coefficient that ensures the placement of passenger trains on sections AB and AV in proportion to the train
schedule, and according to formula 4, the average distance between freight trains moving between passenger trains
interval should be calculated.

𝑀

𝑑𝑜𝑝

𝑜𝑏

∑ 𝑇

𝑑𝑜𝑝

𝑘

𝑠

𝐼

𝑠𝑟

𝐴𝐵

for section A-B;

𝑘

𝑠

А−В

= 0,8 + 0,2 ∙ (10 + 8) = 4,4

𝐼

𝑠𝑟

𝐴𝐵

=

1440 − (3 + 1) ∙ 10 ∙ 18

75 ∙ (1 + 0,21)

= 8 𝑚𝑖𝑛. ≈ 0,133 ℎ𝑜𝑢𝑟.

Section for A-V

𝑘

𝑠

А−𝑉

= 0,8 + 0,2 ∙ 10 = 2,8

𝐼

𝑠𝑟

𝐴𝑉

=

1440 − (3 + 1) ∙ 10 ∙ 10

80 ∙ (1 + 0,13)

= 11,5 𝑚𝑖𝑛. ≈ 0,191 ℎ𝑜𝑢𝑟.

The additional delay at station A is equal to:

∑ 𝑇

𝑑𝑜𝑝

𝐴

=

[24 ∙ 4,4 − 0,15(10 + 8)2 + 2 ∙ (10 + 8092 + 3,0 ∙ 0,166 − 0,133)]

0,133

∙

∙ [(3 + 1) ∙ 0,166 − 0,133]

locomotive clock;

Additional delays at station V are equal to:

∑ 𝑇

𝑑𝑜𝑝

𝑉

=

[24 ∙ 2,8 − 0,15 ∙ 10 + 2 ∙ 10 ∙ (2 + 3,0 ∙ 0,166 − 0,191)]

0,191

∙

∙ [(3 + 1)0,166 − 0,191]

locomotive clock

Average value for both points:

∑ 𝑇

𝑎𝑑𝑖𝑡

𝐴−𝑉

=

740+277

2

= 508,5

locomotive clock

By skipping passenger trains, the additional demand caused by imbalances in the arrival and departure of freight
trains, that is, due to delays at the turning points, is determined as follows (formula 10):

𝑀

𝑑𝑜𝑝

𝑛

=

508,5

24

+ 0,5П ≅ 22

electric locomotive

The calculation cycle of locomotives for the general circuit section AB was 33 hours, that is, 24 hours more than the
planning period, due to which there is a certain complexity of control under unbalanced traffic conditions, which
requires additional electric locomotives and it is calculated according to formula 13 for the AV section:

𝑀

𝑎𝑑𝑖𝑡

об

=

33∙60∙0,13

24

(

33

24

− 1) = 4

electric locomotive

CONCLUSION

In order to determine the operating fleet of
locomotives necessary for the service of freight trains
on the railway section, it is necessary to carry out work

on the distribution of units of torque in the main depot
in proportion to the total circulation of locomotives of
each depot. This will lead to a significant improvement
in locomotive utilization in the future.

Volume 03 Issue 02-2023

81

American Journal Of Applied Science And Technology
(ISSN

–

2771-2745)

VOLUME

03

I

SSUE

02

Pages:

72-81

SJIF

I

MPACT

FACTOR

(2021:

5.

705

)

(2022:

5.

705

)

(2023:

7.063

)

OCLC

–

1121105677

Publisher:

Oscar Publishing Services

Servi

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—

Text: neposredstvennyy //

Molodoy uchenyy.

—

2022.

—

No. 12 (407).

—

S.

23-29.

—

URL:

https://moluch.ru/archive/407/89736/

(data

processing: 14.01.2023)