Train Movement and Environmental Resistance

Gennady Akkerman

and Sergei Akkerman

Ural State University of Railway Transport, Yekaterinburg, Russian Federation

Keywords: Resistance, gravity, train, curves, weather, traffic intensity, acceleration noise, energy-optimal profile, railway

track maintenance.

Abstract: The reason for the appearance of additional resistance to the movement of the train are weather conditions,

the gravitational component of the weight, curved sections of the track, the density of train traffic, the non-

normative track gauge maintenance. Some of these reasons are tied to the conditions of the railways of the

Urals. The possibilities of mitigating these resistances are being considered.

1 INTRODUCTION

When a train moves along a rail track, forces appear

that prevent this movement – the forces of

environmental resistance. According to (JSC Russian

Railways, 2016), these forces are divided into the

main resistance and additional resistances.

The main resistance is the resistance to movement

experienced by the rail crew when moving uniformly

in a straight line on the site at a wind speed of less

than 10 m/sec and an outdoor temperature of more

than -25

The term "additional resistances" combines all

resistances caused by:

− weather conditions other than those of the main

resistance;

− the gravitational component of the weight

when the train is moving on an incline;

− curved sections of the track;

− the density of traffic flow when the speed of the

train changes due to the high traffic intensity

(the train cannot move "under green on green"

traffic lights);

− the non-normative track maintenance

(deviations in the geometry of the track).

The forces acting on 1 ton of train mass are called

specific forces in all literary "transport" sources. In

theoretical mechanics, there is no such concept, since

the force per unit of mass, according to Newton's

second law, is acceleration. Therefore, we should talk

https://orcid.org/0000-0003-1330-1825

https://orcid.org/0000-0001-9237-3637

about the influence of all these factors on the

acceleration (deceleration) of the train.

2 MATERIALS AND METHODS

The parameters characterizing the movement of the

train can be taken as:

− travel time or average speed;

− specific consumption of energy or fuel, specific

consumption is the consumption per 1 tkm;

− a criterion for the quality of movement, which

characterizes the uniformity of movement or

the deviation of individual acceleration values

from the average on the section. It is proposed

to take for this criterion the standard deviation

of acceleration at each moment of time from

the average. Let's call this parameter

"acceleration noise" (Akkerman, 1989; Drew,

1972). The noise of acceleration during the

movement of the train "on the green under the

green", i.e. with the free movement of the train,

we will call the natural noise peculiar to this

section of the road. It can be assumed that such

an acceleration noise is equal to the

acceleration noise on an ideal road with a

coefficient characterizing this segment of the

road.

Akkerman, G. and Akkerman, S.

Train Movement and Environmental Resistance.

DOI: 10.5220/0011580500003527

In Proceedings of the 1st International Scientiﬁc and Practical Conference on Transport: Logistics, Construction, Maintenance, Management (TLC2M 2022), pages 143-146

ISBN: 978-989-758-606-4

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

143

Thus, by improving the geometry of the road, we

bring the conditions of movement of the train along it

to the movement on the ideal road.

3 RESULTS AND DISCUSSION

Weather conditions are determined by the main

meteorological indicators:

− air temperature;

− atmospheric pressure;

− air humidity;

− the strength and direction of the wind.

The influence of these indicators on the

movement of the train is different, but in the end it

comes down to the forceful effect of the air

environment on the moving train. Taking into account

this influence affects even the design of the railway,

for example, the design of the longitudinal profile.

To assess the force effect of the air environment,

an experimental test of the influence of these factors

on the conditions of train traffic on some sections of

one of the Ural railways with electric and diesel

traction was carried out.

The initial data for the study were:

− longitudinal profiles of sections;

− personal accounts of locomotive crews,

according to which the specific energy

consumption (fuel) was determined as a

quotient of the division of energy (fuel) costs

per tkm of work;

− indicators of locomotive speed gauges;

− meteorological indicators at the time of

departure and arrival of trains at the final points

according to weather stations;

− information from weather recorders

(barographs, thermographs, etc.) installed on

locomotives.

The average meteorological indicators along the

route coincided with the data of the recorders

installed on the locomotives, with an accuracy of up

to 10%, except for the readings of barographs on the

transshipment sections.

The studies were conducted separately for the

"even" and "odd" directions of movement. Known

ratios (Turbin, 1989) q=3.1r, kWh/1000tkm, q=0.85r,

kg/1000tkm,

here q is the specific consumption of electricity or

fuel for the traction of trains, adjusted for the

influence of the mass of the train,

r –specific mechanical work of the traction force,

tkm/1000tkm

Since part of the mechanical work of the traction

force went to overcome the additional resistance to

movement, then:

w=q/3.1 or w=q/0.85kg/t or

w=3.29q for electric traction and w=11.5 q, n/t for

diesel traction.

Of all the considered weather and climatic

indicators, according to our research, low outdoor

temperatures have the greatest impact on the

conditions of train movement in the Urals region, see

Table 1.

Table 1: Increased resistance to train movement by the

influence of meteorological factors.

Meteorological factors Increasing resistance,

Atmospheric

precipitation

Icy phenomena

Cold temperatures

Win

0.7

Up to 30

Up to 39

Precipitation "directly" does not affect the

resistance to the movement of the train. However, in

the form of rime or frost on the surface of the rail,

i.e..as ice formations can be associated with a

decrease in the coefficient of adhesion of locomotive

wheels with rails, which for locomotives with limited

traction force on coupling, can lead to a decrease in

traction force and speed on descents due to its

limitation on brakes. A decrease in the coupling

coefficient to 15% (Railway transport: Ref. journal,

1971; Akkerman, 2021) under unsatisfactory weather

conditions can lead to a decrease in the mass of the

train to 15% or its speed on the rise at the same mass

to 30%, which is equivalent to an increase in

resistance by 15% with constant traction. There are

cases when the formation of ice on the rails and the

contact wire generally disrupted the movement of

trains (Railway transport: Ref. journal, 1971;

Akkerman, 2021). The presence of an electric current

contributes to icy formations.

The contact fatigue strength of rails depends on

the coefficient of sliding friction (Skvortsov, 1970),

therefore, a change in this coefficient may affect the

service life of the rail. Icy phenomena are not such a

rare phenomenon: on the territory of Russia: in some

areas up to 200 times a year, between San Petersburg

and Novokuznetsk, ice and frost were observed for

about 40 days per year (Buchinsky, 1960).

With an increase in the specific humidity of the

air, the specific air resistance to the movement of the

train, according to our research, decreases

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144

approximately 1.004-1.012 times compared to dry air.

But we should not forget that the humidity of the air

is associated with icy phenomena.

The air resistance is directly proportional to the

atmospheric pressure (Akkerman, 1992), which

depends on the absolute terrain marks of the region

and on the meteorological conditions at a given time.

An increase in the marks by 500 m. leads to a change

in pressure by approximately 45 mmHg (Baranov,

1981), which reduces air resistance by 6%. In the

middle Urals, the amplitude of atmospheric pressure

fluctuations can exceed 11 mm Hg, which is

equivalent to a change in air resistance by 1-2%

At low atmospheric pressure, the traction force of

the locomotive decreases: in case of non-standard

conditions (air temperature is more than 20 °C and a

pressure less than 760 mmHg) the traction force (F)

will be determined:

𝐹=𝐹



(1 − 𝑘



−𝑘



) (1)

Where Fk is the traction force under standard

meteorological conditions,

k1, k2 are coefficients that take into account the

decrease in diesel power at an air temperature of more

than 20 °C and atmospheric pressure less than 760mm

Hg.

With an increase in the absolute relief marks,

atmospheric pressure decreases, the traction force

decreases, the consequence of this may be a decrease

in weight norms (Astakhov, 1966) or the speed of the

train (Kantor, 1984).

The totality of weather factors can be considered

as a microclimate, i.e. the climate of the local section

of the highway (embankments, recesses, etc.) or a

macroclimate, i.e. the climate of the region. Even at

the neighboring points of the route, the weather

conditions may be different: the wind speed on the

embankment is 15% higher than the wind speed in the

field.

3.1 The Gravitational Component and

the Conditions of Movement of the

Train

It is known that the acceleration from the

gravitational component during the movement of the

train or the specific force from the slope is

proportional to the slope of the longitudinal profile

itself –i

𝑊



= 9,81𝑖 (2)

The force effect of the longitudinal profile in the

balance of forces acting on the train can be very

significant. By combining the slopes and lengths of

the profile elements, it is possible to obtain such a

ratio of forces acting on the train, at which the energy

consumption will be minimal. We will call such a

profile energy-optimal (Akkerman, 2006; Akkerman,

2018). Energy savings when moving a train along an

energy-optimal profile is equal to 15% or more. The

movement of the train along such a profile is more

uniform, the acceleration noise is close to a minimum.

3.2 Resistance to Train Movement on

Curved Sections of Track

Curved sections of the railway, as a rule, are

represented by a circular curve, mated at the ends

with straight transition curves. In this case, the length

of such a section is equal to the sum of the lengths of

the circular lk, and the transition lp, curves. The

resistance from the curve according to (Akkerman,

2008) is inversely proportional to the radius of the

curve, Rcr. For example: wr=6870/Rcr.

Our department proposed to design curved

sections with two transition curves without a circular

curve, the so-called biclottoid projecting. With such

projecting, the average additional resistivity is two

times less.

3.3 The Density of the Traffic Flow and

the Resistance to the Movement of

the Train

The intensity (throughput) of the traffic flow N is

determined by:

𝑁=𝐾𝑉 (4)

Here: -K is flow density,

V is the speed of the traffic flow.

Applying the hydrodynamic analogy for the

traffic flow, we obtain the optimal Kopt density,

where

Kj is the maximum density of the traffic flow.



К





, (5)

the optimal speed, -Vopt, i.e. the speed at which

the throughput is maximum (km/h):

𝑉



=0,33𝑉



(6)

and throughput:

𝑁=𝑉



+𝐾



(7)

Here 𝑉



is the speed in free movement, i.e. "on the

green under the green" without speed limits.

Train Movement and Environmental Resistance

145

Additional exposure to the environment leads to a

decrease in speed 𝑉



According to our data, an increase in resistivity by

9.81 n/t leads to a drop in the speed of free movement

by an average of 7.7%, and hence the throughput by

the same proportion. You can increase the speed 𝑉



appropriate profile design, 9.81

⁄

is the resistivity

at 𝜄=1



∙ 𝜗

3.4 The Non-normative Track

Maintenance

When trains move, deformations accumulate in the

railway track, which is expressed in the appearance of

deviations in the geometry of the track gauge -

irregularities occur. The irregularities vary: by

location, length, amplitude, area and intensity

(quantity per 1 km). Deviations differ in degrees: the

first degree is not taken into account, the second

degree of deviation does not require a reduction in

speed and immediate straightening of the path, the

third requires immediate correction and speed

reduction, at the fourth degree the running line is

closed. Therefore, the deviation of the second degree

was taken into account. According to our data, if the

deviation is within the curve, then the transverse

forces of the wheel-rail increase to 20%, and an

increase in additional resistance in the curve should

be expected by the same amount. In (Shapetko, 2020),

it is concluded that irregularities in the longitudinal

profile can lead to excessive electricity consumption

on each km of track per 1000 tons of train of 0.82

kWh, which is equivalent to 2.64kN per km of

mechanical work of the locomotive traction force or

2.64 n/t of resistivity - this is approximately 0.18 wo.

An example is also given here that on the Trans-

Baikal Railway, additional resistance from

irregularities reached (0.3-0.4) wo. Therefore, it can

be assumed that irregularities lead to an increase in

additional resistance to the movement of the train

within (0.18-0.4) of the main resistance.

4 CONCLUSIONS

1. Adverse weather conditions can increase the

resistance to train movement by up to 39%.

2. The design of an energy-optimal profile allows

you to reduce energy costs on the rise by up to

15% or more. Moreover, the movement of the

train on such a rise is more uniform.

3. The resistance to the movement of the train on

curved sections of the track is reduced by half

when using biclottoid projecting of such

sections.

4. The additional environmental resistance by

9.81 n/t leads to a drop in the speed of free

movement by 7.7%, and hence the throughput

by the same proportion.

5. Unevenness of the track leads to an increase in

additional resistance to the movement of the

train to 0.4 of the main resistance.

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TLC2M 2022 - INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE TLC2M TRANSPORT: LOGISTICS,

CONSTRUCTION, MAINTENANCE, MANAGEMENT

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