
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

73107
10.1038/s41598-024-73107-2
Article
Assessing the risks arising from a trailer connected behind a passenger car
Synák František frantisek.synak@uniza.sk

1
Jakubovičová Lenka 2
1 https://ror.org/031wwwj55 grid.7960.8 0000 0001 0611 4592 Faculty of Operation and Economics of Transport and Communications, Department of Road and Urban Transport, University of Žilina, Univerzitná 1, 010 26 Žilina, Žilina Slovakia
2 https://ror.org/031wwwj55 grid.7960.8 0000 0001 0611 4592 Faculty of Mechanical Engineering, Department of Applied Mechanics, University of Žilina, Univerzitná 1, Žilina, 010 26 Slovakia
20 9 2024
20 9 2024
2024
14 219375 3 2024
13 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Article pays attention to the impact of using the trailer on driving performances of a studied vehicle combination.The research was performed via extensive experimental measurements. A new methodology of determining a technical condition of the trailer’ brakes was proposed and verified, which can be also applied during the regular technical inspection. Various load distributions in the trailer caused the centre of gravity’s position of the vehicle was changed, which may increase the risk of skidding or disconnection of the trailer from the towing vehicle. Also, the vehicle’s ability to accelerate and decelerate decreased considerably due to the loading up. There were assessed the braking characteristics of the combination of vehicles as well, depending on the technical condition of the trailer’s brakes. The importance of this article lies in the quantification of selected factors on road safety in relation to driving with a combination of vehicles.

Keywords

Road safety
Acceleration
Cargo transport
Combination of vehicles
Training for drivers
Traffic accident
Driving performances
Braking
Subject terms

Mechanical engineering
Engineering
issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Road transportation often uses combinations of vehicles composed of a passenger car and a trailer to transport cargo. However, the experimental measurements connected to such a combination of vehicles are poorly covered in scientific journals. Therefore, the main objective of this study is to assess the change in driving performances of a vehicle that tows a trailer bearing in mind various load distributions in the light of road safety based on real experimental measurements. A vehicle that is often used in road traffic was chosen particularly for the measurements, so that the results can be applied to as many vehicles and vehicles as possible. To perform it, a new trailer of which the parameters correspond to the market leading type was purchased, and it is equipped with an inertia brake that can broaden the measurements. The inertia brakes are controlled by the inertia forces of the trailer by a variable length of the drawbar when it is getting closer to the towing vehicle during the deceleration. When the drawbar is shortened, the braking force is applied in the trailer’s brakes via the leverage. The extensive experimental measurements in this article are divided into three parts.

The role of the first part of the measurements is to determine the relation between the control force of the trailer’s inertia brake and its control force applied on the wheel’s perimeter. The measurements will be performed under laboratory conditions according to the innovative measurement methodology proposed for this article. The real dependence will be determined and the result can be used by other authors for the simulations focused on the deceleration of combinations of vehicles composed of the passenger car and trailer. The measurements also clarify the force of the braking trailer applied on the towing vehicle in the horizontal direction. The found values may be used in calculations relating to the energy recuperation of electric vehicles and hybrid electric vehicles. The trailers with a weight to 750 kg are not usually subjected to the technical inspection, and the trailers with a weight above 750 kg are subjected to technical inspection only once every 4 years in the European Union. Such technical inspection of brakes is performed only visually by a driving test with an empty trailer. The objective of the first part of the measurements will be to introduce the measurement methodology under which these parameters could be observed during the technical inspection of the trailers. Therefore, the contribution of the first part of the measurements would be such a methodology of which the results can provide significantly more precise data in comparison with current technical inspection, bearing in mind the measurement applicability for the technical inspection stands.

The second part of the measurements will pay attention to determining the impact of load distribution in the trailer on the change of the centre of gravity’s position of the towing vehicle in the horizontal direction. The real values of the axle load as well as the actual position of the centre of gravity will be determined since all the factors affecting these values will be reflected, such as suspension spring compression, tyre deformation and other factors. Also, the load of a towing vehicle will be determined. The second part of the measurements will provide information on the impact of load distribution on the centre of gravity’s position and will bring new expertise in the area of proper load stowage emphasising the reduction of the risk of the axle load or its excessive reduction of load in relation to the passenger car and the trailer. The values observed will be also used by other authors focusing on the vehicle centre of gravity’s position, vehicle construction, axle load, dynamics of a combination of vehicles, modelling of the vehicle dynamics, modelling of the division of driving and braking moments for each axle, and many other aspects in their research.

The third part of the measurements will focus on the dynamic performance of a combination of vehicles, ability to accelerate and decelerate depending on the load distributed in the trailer. The measurements will be performed without a trailer, with an empty trailer and with a load placed in the front, in the middle and in the rear of the trailer. Since in relation to the inertia brake it leads to its frequent malfunctions, the measurements will be performed with a functional inertia brake, non-functional inertia brake, and when the trailer will be acting as a non-braking, which means that the length of the drawbar will not be able to change. During the measurements of the combination of vehicles’ ability to decelerate, the forces in binding straps to avoid cargo movement in the trailer will be determined as well. A significant contribution of this part of the article lies also in the determination of tensions in the binding straps used in the trailer after the passenger car. The measurement results provide new knowledge in the dynamics of the frequently used combination of vehicles, which can be applied in forensic practice to study car accidents as well as in the scientific field of simulations and the like.

Additionally, the contribution of this study is to complement the scientific and practical knowledge in relation to the combination of vehicles based on the extensive experimental measurements and the result analysis since this issue is under-discussed in scientific journals, especially regarding experimental measurements. Another contribution is visibility for a dangerous phenomenon in road traffic which means using the trailers by drivers that are not supposed to have any experience with the above mentioned facts. Information gained from this study may be, to a large extent, applied to heavier trailers with inertia brakes as well as to caravans. Thus, by knowing the appreciable part of road transportation in more detail, it will be possible to increase the safety on roads and to reduce motor accidents, injuries and deaths.

The article is divided as follows: the introduction is followed by the literary review in which the gaps in recent scientific publications are identified. The part with a description of the measurement methodology is next. In the results, the measurement results are discussed with the other authors’ results accompanied by the comparison of approach to the issue dealt in this article and the article of other authors in the form of a table. The conclusion part pays attention to the assessment of results and indication of further study possibilities.

Literary review

In European Union, a basic driving licence, category B, suffices to drive a combination of vehicles composed of a towing vehicle with a weight to 3500 kg and a trailer with a weight to 750 kg if provided that the maximum permissible mass of the car and trailer does not exceed the value of 3500 kg. However, driving with a trailer is included neither in the theoretical nor in the practical part of the courses or tests1,2. Similarly, in the USA, the basic driving licence suffices to drive a combination of vehicles with a total mass even up to 11,793 kg, and there is not any attention paid to trailers in the driving licence courses3,4. Thus, combining the early age, little driving skills and no experience of driving with a trailer, miscalculation of the braking distance and distance needed for a combination of vehicles to start can substantially increase the risk of motor accidents, as also follows from publications5–7. The level of risk of driving with trailers is also elevated by the fact that the trailers for passenger vehicles are not equipped with electronic stability control, anti-lock braking system, or any other safety systems and assistants which are usual in passenger cars and on which the majority of drivers often rely8–10. It follows from the first part of the literary review that there is a need to pay attention to the issue of differences in driving a passenger car without a trailer as well as the combination of vehicles with various load distributions.

The trailers towed by passenger cars are used for both business and private purposes. For instance, in Finland, there are 806,373 trailers to 750 kg and 120,854 from 750 to 3500 kg registered, and in Germany, there are 3,210,827 trailers to 750 kg and 2,793,324 from 750 kg to 3500 kg registered11. Since the combination of vehicles composed of a passenger car and a trailer forms a significant part of road traffic, it is necessary to focus on it in scientific publications as well. Such a need is supported by the fact that during the random technical inspections in Great Britain performed by the Driver & Vehicle Standards Agency (DVSA), it was found that, in relation to the trailers from 750 kg to 3500 kg, about 50% from those vehicles did not meet the technical requirements or showed any malfunction. To compare it, it was only 20% in relation to the trailers above 3500 kg. Dangerous malfunctions with immediate prohibition of further driving were found in vehicles of O2 category (29%) and of O3 and O4 category (only 5%)12. Vehicle driving performances can be changed substantially due to the attached trailer or by different load distribution in the trailer or its sundry technical conditions, and thus, road safety can be endangered13. Based on data in publications11–13, it may be concluded that it is necessary to pay attention to determine the ability of the combination of vehicles with the trailer to 3500 kg to decelerate when the brakes malfunction.

The authors of the publication14, based on the results from the mathematical model using the root-locus method, say that the driving speed has the largest impact on the operating stability of a combination of vehicles. However, they did not take into consideration various load distributions. Publication15 gives the reason for the reduced stability of the trailer with increasing speed as a reduction of the suspension and dampening. The impact of load distribution in a trailer on road safety is almost exclusively observed by the simulations16,17. Publication18 also focused on such an impact, and the authors, based on the simulations, concluded the optimal load on the hook of about 6% of the total weight of the trailer. In the publication19, driving performances of combinations of vehicles are observed by the simulations with three different ways of the load stowage in a trailer. However, the simulations, besides their advantages, are connected with certain simplifications as well as disadvantages. For instance, publication19 takes into consideration the fact that the friction coefficient between all tyres of a towing vehicle and trailer and the road surface has the same value of 0.75. Based on the research of the other authors, however, the real situation is different since the friction coefficient depends on several factors such as different size, design, pattern and material of the tyres of the towing vehicle and trailer20–22, its diverse load, also depending on the load distribution23, and many other factors mentioned in publications24,25 as well. Therefore, the results of simulations would differ from reality. In publication26, it is considered in the mathematical simulations that the vehicle structure is assumed to be rigid, the vehicle is symmetric about its centreline, the lateral deflection of the suspension is negligible and the reaction forces from the road are applied at the centre of the tyres, which also do not correspond to the real situation. Since it follows from the above-mentioned publications15–26 that the dynamics of vehicles and combination of vehicles are observed almost exclusively by simulations with many simplifications, it is necessary that this publication must fill in the gap by complementing the recent literature with the results achieved by extensive experimental measurement without simplified estimations.

Publication27 focuses on the overview of energy recuperation in electric and fuel cell vehicles, and it may be crucial in the issue of trailers and their deceleration. Therefore, the part of this article will pay attention to determining the dependence between the inertia brake’s control effort, i.e. the force usable for recuperation of energy, and the braking force.

The authors of the European Commission’s study28 recommend implementing a regular technical inspection also for the trailers with a weight to 750 kg in a period of every two years. The authors also state that the braking test must include driving and following braking from the speed of about 30 km.h− 1, and it is necessary to visually monitor the activation of the brakes on each wheel or anomalies. The combination of vehicles with the trailer of 750 kg can usually drive with the speed up to 130 km.h− 129. When decelerating from such a speed, especially on a wet surface or in a curve, it is very important to have a perfect condition of the trailer’s brakes in relation to road safety and a combination of vehicles’ stability30. Besides the ability to apply the braking forces sufficient for blocking the wheels of the empty trailer, the important parameters are also the braking force depending on the steering force, the symmetry of braking performance and its fluctuation as well as the braking ratio, which is the ratio between the sum of maximum braking forces applied on the wheels and the vehicle mass31,32. These parameters are crucial for driving with a combination of vehicles, and it is impossible to observe them33 by neither the current methodology under which the technical inspection is performed nor by the proposed methodology mentioned in28. Therefore, it is necessary to focus also on the proposal and verification of a new methodology according to which more objective data on trailers’ brake conditions would be obtained, as a part of this publication.

The centre of gravity’s position and its following axle load has a direct impact on the dynamics of the combination of vehicles, its ability to accelerate, decelerate, turn, etc., as mentioned in publications34,35 as well. If any axle, or a towing vehicle, is overloaded, the wear and tear of the vehicle parts increases, especially in suspension, dampening, wheel and tyre suspension. There is also an increased risk of their immediate destruction, which can lead to a car accident, as also follows from publication36 in which the authors mention tyre rupture as one of the most frequent causes of fatal accidents. The axle load also increases the road’s wear and tear, and formation of ruts, even though the vehicle has lower total mass since these vehicles, in comparison with articulated vehicles, cover a lower contact area which increases the specific pressure37. What is more, it can increase the production of tyre particulates, which is proved by the research in the publication38. Besides the axle load, when the load is not distributed properly, it may lead to an excessive reduction of the axle load, which can result in the skid or loss of the vehicle’s ability to turn, in relation to the steering axle, or in loss of the vehicle’s or combination of vehicles’ ability to accelerate, in relation to the driving axle39. Publication40 puts the largest emphasis on the vehicle mass and the axle load in the simulations focused on the direction-holding of a vehicle. The axle overload as well as their excessive reduction of load may be sanctioned by police41.

Since the assessment of forces in the binding straps is a part of this article, it has been observed how this issue is being solved in other scientific publications. The authors of the publication42 were focused predominantly on the firmness of binding straps under various situations, such as different humidity and like. Publication43 pays attention to the impact of dynamic load on the ability to fix the load in the heavy goods vehicle through the binding straps, and on the interaction between the heavy goods vehicle and the road in the context of load securing against the movement through the binding straps. The publication focused on the forces in binding straps when carrying cargo in the trailer behind the passenger car was not found. Therefore, this article shall fill in the gap in the specialization of scientific publications to increase road safety since road transport is a significant source of serious injuries, as follows from44–46.

Methodology

The measurements focused on determining the relation between the control force of the inertia brake and the control force of the wheels, determining the centre of gravity’s position of the towing vehicle and the vehicle’s ability to accelerate and decelerate under various conditions, Fig. 1.

Fig. 1 Experimental measurements.

Measurements focused on the determination of the relation between the control force of the inertia brake and the braking force (Fig. 1, blue colour) were performed according to the new methodology proposed for this article. In this way, the dynamometer was used to determine the control force, and the cylinder brake test station was used to determine the trailer’s braking force.

The change in the towing vehicle’s centre of gravity (Fig. 1, purple colour) was determined without the trailer as well as with the trailer at various load distributions. For the calculation of the centre of gravity, the weights applied on each axle were determined by the weighing axle scales.

Dynamic characteristics of the combination of vehicles (Fig. 1, pink colour) were determined in the same way as for the centre of gravity. The vehicle’s ability to accelerate was determined from the speed of 0 km.h− 1 to 20 km.h− 1 in relation to the time and distance. During the vehicle’s deceleration, the mean fully developed deceleration as well as the maximum force in the binding straps was determined in relation to the trailer’s functional brakes, non-functional brakes, and in relation to the unbraked trailer.

All the measurements were performed with the same combination of vehicles, which represents by its parameters a typical combination of vehicles driving mainly on European roads.

Technical parameters of the passenger vehicle used for the measurements are given in Tables 1 and 2 shows the technical parameters of the trailer.

Table 1 Technical parameters of Kia Ceed47.

Vehicle	Kia Ceed, 1.6 CVVT	
Engine	1.6 CVVT	
Engine power, engine type	93 kW, spark-ignition	
Transmission	Automatic, with a torque converter	
External dimensions	4235/1790/1480 mm	
Wheelbase	2650 mm	
Total mass	1710 kg	
Kerb mass	1263 kg	
Load capacity	447 kg	
Maximum front axle load	960 kg	
Maximum rear axle load	920 kg	

The parameters of the trailer used for the measurements are given in Table 2.

Table 2 Technical parameters of the trailer48.

Total mass	750 kg	
Kerb mass	152 kg	
Load capacity	598 kg	
External dimensions	2880 mm x 1600 cm x 780 mm	
Wheels	155/70 R13	
Brake design	Inertia braking	
Fixing loops for binding straps	4 pieces, force 400 daN	

Measurements of the relation between the control force and the braking force.

The first measurement focused on determining the relation between the intensity of the control force of the trailer’s drawbar and the braking force on the wheel perimeter. The measurements were performed under laboratory conditions, on the Motex 75 19 cylinder brake test station with the cylinder peripheral speed of 5 km.h− 1. The measurement deviation according to the manufacturer is a maximum of 2.5% and the braking force range is from 0 N to 5000 N49. The order during the measurements is shown in Fig. 2.

Fig. 2 Determining the dependence between the steering control force and braking force of the trailer.

The trailer (Position 1) was placed on the cylinders of the Motex cylinder test station (Position 5). In order to reduce the risk of the wheel slipping on the cylinders, the trailer was loaded down by a load weighing 600 kg (Position 2). The steering control force on the steering drawbar (Position 3) was applied to the braking mechanism via the chain turnbuckle (Position 4) that is coupled with a fitting tackle inserted in the trailer’s coupling. The intensity of the control steering effort applied on the braking mechanism was determined by dynamometer Load-Cell-619 (Position 6) from which the data were processed via IPRE2 4 S connected to a notebook, and the braking force was displayed via the Motex display. Then, there was a graph drawn on the basis of the measurement results. The measurement deviation of the dynamometer is max. 0.030% from the value measured50. The frequency of recording the value measured is 100 Hz.

Measurements of the change in the centre of gravity’s position.

The second measurement focused on determining the distance of the towing vehicle’s centre of gravity from the front axle. To determine the centre of gravity’s position, it was necessary to obtain the weight applied to the axles under various conditions. The weight applied to each axle was determined by the axle weighing scales – Portable scales PW-10. The maximum permissible load of the scales per one wheel is 10,000 kg, i.e. 20,000 kg per axle and the measurement deviation is 10 kg per wheel when weighing the vehicle in motion, as given by the scale’s manufacturer51. To increase the accuracy of the measurements, they were performed with a stationary vehicle. The accuracy class of static weighing according to EN 45,501 is IV52.

The calculation of the distance of the centre of gravity from the front axle was made according to formula:1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{1}=\:\frac{{m}_{2}.\:L}{m}$$\end{document}

L1 is the distance of the centre of gravity from the front axle [m].

m2 is the mass applied on the rear axle [kg].

L is the axle wheelbase [m].

m is the total vehicle mass [kg]53.

As follows from the relation above, the centre of gravity recedes from the rear axle by the same value as it has when getting closer to the front axle. For this reason, the position of the centre of gravity was determined as a distance from the front axle only.

The measurements focused on determining the distance of the centre of gravity from the front axle were performed:

• With an empty towing vehicle without a trailer,

• With a combination of vehicles composed of a towing vehicle and empty trailer,

• With a combination of vehicles with a load of 500 kg placed in the front of a trailer,

• With a combination of vehicles with a load of 500 kg placed in the middle of a trailer,

• With a combination of vehicles with a load of 500 kg placed in the rear of a trailer.

Measurements of dynamic characteristics of the combination of vehicles.

The third measurement focused on determining the impact of a various arrangement of the combination of vehicles on its ability to accelerate and decelerate. The studied vehicle combination used for the measurements is shown in Fig. 3.

Fig. 3 Studied vehicle combination.

First, the measurements focused on the vehicle’s ability to accelerate under different conditions were performed. The distance and time needed to reach the speed of 20 km.h− 1 from zero speed were determined by XL Meter Pro during the measurements focused on the vehicle’s ability to accelerate. The measurement frequency by XL Meter Pro is 200 Hz, the measuring range is from − 14.0 m.s− 2 up to + 14.0 m.s− 2, the differentiation is 0.002 m.s− 2, and the measurement deviation is ˂3%54. The driver applied the acceleration pedal sharply to the maximum and the vehicle started to accelerate. After reaching the speed of 20 km.h− 1, XL Meter Pro sounded an alarm signal. After that, the measurement was finished and the driver released the acceleration pedal and stopped the vehicle. The intensity of deceleration was important since after reaching the above-mentioned speed, the measurement was automatically stopped. Then, the device could show the distance and time needed to reach the given speed. For better result representativeness, the measurements were 10 times repeated.

The same device, XL Meter Pro, was also used for another measurement, when decelerating from the speed of 20 km.h− 1. To express the impact of the load and its location on a vehicle’s deceleration better, the results include the mean fully developed deceleration (MFDD). MFDD can be calculated according to formula:2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:MFDD=\:\frac{{V}_{b}^{2}-\:{V}_{e}^{2}}{25.92*\:\left({S}_{e}-\:{S}_{b}\right)}$$\end{document}

MFDD is mean fully developed deceleration [m.s− 2].

Vb is the vehicle speed at starting speed of 0.8 V1 [km.h− 1].

Ve is the vehicle speed at starting speed of 0.1 V1 [km.h− 1].

Sb is the distance driven between V1 and Vb [m].

Se is the distance driven between V1 and Ve [m]55.

MFDD is more relevant than the braking distance since it depends substantially higher on the initial speed which can distort the results56. Each measurement was performed 10 times. The temperature during the measurements was about 12 °C. The measurements were performed on a flat asphalt road surface, which was wet.

The measurements focused on determining the vehicle’s ability to accelerate were performed in the same way as for measuring the centre of gravity’s position, i.e. without the trailer, with the empty trailer and with various load distributions.

The measurements focused on the vehicle’s ability to decelerate were performed under the same conditions as the above-mentioned measurements, and besides these, they were performed with:

• With functional brakes of a trailer, without a load and with a load placed in the front, in the middle and in the rear of a trailer,

• With non-functional brakes of a trailer, without a load and with a load placed in the front, in the middle and in the rear of a trailer,

• In a situation in which it could not lead to shortening the trailer’s drawbar, and thus, to the brake activation, without a load and with a load placed in the front, in the middle and in the rear of a trailer.

The functionality of the trailer’s brakes was verified on the cylinder test station during the measurements focused on the relation between the control steering effort and the braking force. Since the mechanism for the braking control was uncoupled, it caused a non-functionality in the brakes. During the deceleration, the trailer got closer to the towing vehicle and the drawbar was shortened, however, the brakes were not activated due to the uncoupled braking control. In order to have a situation when the trailer is not decelerating, which is the most frequently used variant, the drawbar was fixed. It was done so that its length could not be changed to avoid activation of the inertia brake.

During the measurements of braking decelerations, the effort in binding straps that secures the load of 500 kg against the movement was measured by the same dynamometers by which the steering control force of the inertia brake was determined as well. The binding straps were two and they were bound directly. The frequency record of the effort in binding straps was 100 times per second.

Measurement results

Measurement results of the relation between the steering control force and the braking force.

Figure 4 shows the graph displaying the dependence between the steering control force on the trailer’s drawbar and the braking effort on the wheel’s perimeter, determined by the Motex cylinder brake test station. The left axis displays the total braking force measured on the axle’s wheel perimeter. The right axis displays the steering control force applied to the trailer’s drawbar. The braking force is given in Newtons. The steering control force is given in Decanewtons (daN) as being standardly given when the force is applied on the brake pedal during the technical inspection. One daN is approximately 1 kg57.

Fig. 4 Dependence of the braking force on the steering control force of the trailer.

As follows from Fig. 4, it can be concluded the direct proportion between the steering control force and the braking force. Increasing the steering control force (dashed black curve) led to an increase in the braking force (red curve). The maximum steering control force was about 200 daN. Subsequently, the wheels started slipping on the cylinder test station’s cylinders and then they were blocked. Based on the theoretical calculation according to Newton’s first law of Inertia, when the steering control force of 200 daN is applied, the braking force of 3500 N is produced, and this is sufficient to decelerate the trailer, which weighs 750 kg loaded completely, with a value of 4.66 m.s− 258. However, the tests were restricted by the blocked wheels on the cylinder test station’s cylinders. There may be assumed the higher value of friction coefficient on the asphalt surface, and thus, more intensive braking forces59. Since the trailer is not equipped with the ABS system, usually in practice, its wheels are blocked and the trailer decelerates by the skid60. Theoretically, to decelerate the empty trailer of 152 kg (Table 2) with deceleration of 8 m.s− 2, which is an approximate value of deceleration when braking sharply61,62, the braking force of about 1216 N is sufficient, according to Newton’s first law of Inertia. The braking force of 1216 N is 34% of the maximum braking force measured (Fig. 4). The maximum friction force between the tyres of the empty trailer and the asphalt surface with the friction coefficient of 0.75 would be approximately 1118 N, which is lower than the needed 1216 N and, thus, the wheels of the trailer would probably be in a skid63. The inspector during the technical inspection would assess the wheel blocking of the trailer, under certain technical inspection methodology64 and under proposed methodology of28, as function brakes so the vehicle would be regarded as roadworthy65. However, in practice, the function of the brakes may have decreased by about two thirds, as follows from Fig. 4 and from the theoretical calculation according to Newton’s law. During the deceleration, it leads to the reduction of load of the trailer’s axle and to decrease in the value of force applied perpendicularly to the asphalt, and, thus, there would be even lower braking force needed for the trailer’s wheels getting into a skid66,67. Given disadvantages may have been reduced by an obligation to load the trailer during the measurements, for example with a weight that equals to 50% of the vehicle’s load capacity, etc68. However, such a measure would require a certain cargo acquisition, its proper fixation as well as the weighing the vehicle, and it is also related to a risk of damaging the binding points69. The performed and proposed methodology of assessing the trailer’s brakes requires an available test track that is near the technical inspection stand, and the measurement objectiveness is also decreased since the inspector may or may not recognise the wheel blocking correctly70. The wheels may also be blocked at a different braking force depending on the road surface71,72, , the trailer’s tyres, temperature, rain, snow or many other factors, as also mentioned in publications73–76. Inspection cameras are located directly in the technical inspection stands and not in the test tracks, so it also decreases the measurement objectiveness under current and proposed methodology77. By this current and proposed methodology28 it is almost impossible to determine the asymmetry and fluctuation of the trailer’s brakes which are important parameters for deceleration and road safety78, and these parameters may not have been determined by a decelerometer, which is mentioned in the publication79 focusing on comparison of dynamic and static braking test. Given the most used technical solution of the brakes for trailers (drum brakes with brake bars and brake cams), the risk of brake asymmetry and fluctuation of braking performance is substantially higher as in the hydraulic disc brakes of towing vehicles, as also follows from publications80,81. The permissible driving speed of the vehicles of categories O1 and O2 is 130 km.h− 1 at which it may have led to a substantial decrease of driving stability if there were a sharp deceleration and asymmetry, or fluctuation of braking performance82. For the reasons given above, the implementation of the methodology mentioned in the previous part of this publication would bring a significantly higher specification and objectiveness of the results from the assessment of the trailer’s brake condition, and also, in some respects, a reduction of demands for technical inspection equipments since the test track would not be necessary.

The dependence of braking force on the steering control force is not absolutely linear, which may be caused by the nonlinear setting of the inertia brake’s silencer or mechanical losses in the brake mechanism. This fact highlights the need for experimental measurements and also the shortage of simulations since in relation to them, the direct proportional course is considered83,84.

The measurements of the relations between the steering control effort and the braking force and the further result analysis have shown the real dependence between the control and braking force, which is usable in the mathematical simulations of vehicle combination’s dynamics. Verification of the proposed methodology also affirms the usability during the regular technical inspections as well. The analysis of this methodology and the methodology from28 have proved more objective results obtained by the methodology proposed for this article as well as sufficiency of the results obtained by the methodology from28.

The measurement results of the change in the centre of gravity’s position.

Figure 5 displays the weight applied to each axle when the load is placed in the rear, in the middle and in the front of the trailer.

Fig. 5 Mass distribution on the axles for three studied load cases.

As follows from Fig. 5, there was not any axle overload within particular load stowage, neither in the towing vehicle, nor in the trailer. It led to substantial changes in the axle load, mainly in the rear axle of the towing vehicle where the load was decreased, due to transferring the cargo, from 780 kg to 360 kg, i.e. by 54%. However, in the first case, when the load was placed in the front of the trailer, it led to an excessive overload of the towing equipment. The permissible weight applied to the towing equipment is 70 kg and the actual weight measured was 225 kg. Instead of the recommended 6%, as mentioned in the publication18, the load of a coupling device was more than 53% of the weight of the trailer, which may result in a substantial reduction of driving stability. When the load is placed in the front, the number of binding straps is reduced since the load is leaning against the front face of the trailer, and thus, this way of stowage is quite often used85. On the other hand, the towing vehicle may be damaged since, in this case, the weight applied to the towing equipment was exceeded multiply, which may have negative effects on the safety of the vehicle86. There is also a risk of penalties from the police and prohibition to continue driving without having the load transferred87. On the other hand, it is exceptional in practice that police commands to disconnect the towing vehicle and to weigh the mass applied to the towing vehicle. Therefore, the load is placed in the front part of the trailer, also due to avoidance of its overload, when keeping the maximum permissible weight applied to the rear axle of the towing vehicle as well as the minimum front axle load. As follows from Fig. 5, when the load of 500 kg is placed in the trailer’s front part, which weighs 152 kg, only 420 kg apply to the trailer’s axle. The weight of the trailer of 152 kg with a load of 500 kg was 652 kg, which is 87% of the maximum permissible weight of the trailer, but the axle load was 420 kg, which is only 56% of the maximum permissible weight applied to the axle, respectively from the overall permissible weight of the vehicle determined by weighing the load applied on the axle88. If it was a vehicle with a longer rear overhang, for example with an estate car body type, there would have been a risk of extensive reduction of the load of the front axle, which is the steering axle at the same time. Therefore, there would be an increasing risk that the front axle does not give sufficient effort on the road surface, and thus, the vehicle may go straight in the bend. Due to the excessive reduction of load or overload, the suspension characteristics are changed. For the same reason, the risk of insufficient vehicle’s ability to accelerate increases as well89. In this case, the trailer’s axle transfers the lowest weight, and thus, the wheels are at risk of being blocked during the deceleration90.

When the load is placed in the middle of the trailer, above its axle, it does not lead to exceeding the weight on the towing equipment, and the theoretical mass distribution is optimal91. However, this stowage requires enhanced securing of the load against motion by the binding straps since the load is not blocked against the motion forward by leaning against the front face of the trailer and, also, it is not blocked even rearwards.

When the load was in the rear of the trailer, there was a reduction of the load in the rear axle of the towing vehicle, and this can increase the risk of an oversteer skid and bending the studied vehicle combination into the shape of number 1 while braking in the bend92. It leads to an excessive reduction of load of the towing equipment, the drawbar acts on it upwards which substantially increases the risk of detachment of the trailer from the towing vehicle while driving. When the load is placed in the rear of the trailer, the load can be easily handled since there is no need to transfer it through the load area, and the loading and unloading is clearly the simplest of the three tested variants. Not only the total mass of the load transported, but also its stowage has a significant impact on the load of each axle and road safety. It is also evident from Fig. 5 that the axle load changes significantly due to various load distributions, which is necessary to take into consideration when modelling the vehicle dynamics93, distributing the power from the engine to axles94, or dimensioning the adaptive suspension95. Neglecting the impact of load stowage on the axle load, when modelling, would lead to inaccurate and misleading results. Thus, data from Fig. 4 can be used as input data or data for further comparison.

The distance of the centre of gravity from the front axle under different conditions is given in Table 3. The distance of the centre of gravity from the rear axle is not given since the change in position of centre of gravity’s distance from the rear axle is always the same but with an opposite sign as the change in centre of gravity’s distance from the front axle. For better visualisation, the third column of Table 3 shows the change in the centre of gravity’s position given metres and percentages in comparison with the empty vehicle.

Table 3 Distance of the centre of gravity from the front axle with different variants.

Variant	Distance of the centre of gravity from the front axle [m]	Difference in comparison with the empty vehicle
[m]/%	
Empty vehicle	0.98	–	
Combination of vehicles, empty trailer	0.98	0.00/0.00	
Load of 500 kg in the front	1.38	0.40/40.82	
Load of 500 kg in the middle	1.12	0.14/14.29	
Load of 500 kg in the rear	0.81	0.17/17.35	

The change in the load position caused a change in the position of the towing vehicle’s centre of gravity in the longitudinal direction. When the load was in the front of the trailer, the centre of gravity moved up to 0.40 m, which can substantially affect the driving vehicle performances96. Concerning the empty trailer, the centre of gravity’s position did not change. When the load was placed in the middle of the trailer, there would have been a theoretical assumption that the towing vehicle’s centre of gravity does not change. However, the weighing showed that the centre of gravity changed even though there was an effort to place the load directly on the axle. There was grit in the pallet (Fig. 2), and thus, the presumption was that the load’s centre of gravity of the pallet was in its centre. The measurements have shown that due to the inertia during the brake tests, the part of the grit moved to the front part of the pallet, thus, the pallet’s centre of gravity was not directly above the axle of the trailer, but it was moved towards the towing vehicle, and so the trailer applied a certain weight on the towing equipment of the towing vehicle. Also in this case, the substantiation of performing the experimental measurements was shown in comparison with the simulations. The authors in publication97 paid attention to similar situations, i.e. when the force of -1118 N is applied on the towing equipment in static condition, so the force is applied upwards from the towing equipment as well as when the force of + 1746 N is applied on the towing equipment. Then, the control ability and stability of the combination of vehicles were determined by a driving test. They97 concluded substantial changes in them depending on the towing equipment load during an avoidance manoeuvre. The results from Fig. 4; Table 3 may also be considered in the context of driving schools since there is no attention paid to the issue of proper load distribution in the driving licence courses, for example in Bulgaria, Czechia, Denmark, Finland, Netherlands, Croatia, Lithuania, Latvia, Germany, Poland, Slovakia, Slovenia, Sweden and other countries, as also follows from publication98 focused on the analysis of education system in driving schools. This issue is observed only in the training of lorry drivers99. However, regarding the combination of vehicles, the load stowage has a great impact on driving safety100.

Measurement results of dynamic characteristics of the combination of vehicles.

As also mentioned in the “methodology” part, each measurement was performed ten times. Since it is difficult to display all the values measured, only the average values and standard deviations of particular measurements are shown. Table 4 displays the variant of measurement in its first column, the average time needed to reach the speed of 20 km.h− 1 from zero speed with a different load variant followed by the value of standard deviation in brackets in its second column. The second column also contains the distance needed to reach the speed of 20 km.h− 1 from zero speed followed by the value of standard deviation in brackets. The last third column shows the difference in time in seconds (before the slash) and in percentages (after the slash) needed to reach the speed of 20 km.h− 1 in comparison with the empty vehicle.

Table 4 Time and distance needed to reach the speed of 20 km.h−1.

Variant	Time [s] (Standard deviation)
/Distance [m] (Standard deviation)	Difference in comparison with the empty vehicle
[s]/%	
Empty vehicle	1.39 (0.01) /3.78 (0.01)	–	
Combination of vehicles, empty trailer	1.52 (0.01) / 4.18 (0.01)	+ 0.13/+9.35	
Load of 500 kg in the front	2.12 (0.02) / 6.19 (0.02)	+ 0.73/+52.52	
Load of 500 kg in the middle	2.13 (0.01) / 6.18 (0.01)	+ 0.74/+53.24	
Load of 500 kg in the rear	2.20 (0.01) / 36.20 (0.01)	+ 0,81/+58.27	

The impact of load on the vehicle’s ability to accelerate is also given in the form of a graph for better display (Fig. 6). The left vertical axis displays the time needed for acceleration from 0 to 20 km.h− 1, and the right vertical axis displays the trajectory.

Fig. 6 Time and distance needed to reach the speed of 20 km.h−1.

The time needed to reach the speed of 20 km.h− 1 on the flat road surface, between the empty vehicle without the trailer and the studied vehicle combination loaded in the front of the trailer, increased by 58%, i.e. from 1.39 s to 2.20 s, as follows from Fig. 6. Such a significant increase must be taken into consideration either in modelling the vehicle dynamics101 or, as follows from data in publication102, in calculations of sight triangles at railway crossings. The authors of the publication103 propose using the system of radars to avoid side collisions via enforced deceleration or acceleration of the vehicle in a junction, which must have also included the knowledge of the vehicle’s or studied vehicle combination ability to accelerate depending on their actual weight and the weight applied to the driving axle. If the measurements were not performed on the flat road surface but in a gradient, the differences in the time and distance needed for acceleration would have been increasing (Fig. 4)104. It can also be assumed that the differences will increase at the higher end speed since there would be a lower driving force on the wheels available at the second and any subsequent gear105.

The experimental measurements focused on the vehicle combination’s ability to accelerate have made real data usable in forensic practice in the area of car accidents as well as within the calculations in the area of autonomous vehicles.

Table 5 shows the variant of measurement in its first and fourth columns. The second and the fifth columns display the average value of the mean fully developed deceleration and the standard deviation in brackets. The third and the last columns display the comparison with the empty vehicle containing the absolute value and the percentage.

Table 5 Mean fully developed deceleration under different conditions.

Variant	Average [m.s− 2] (Standard deviation)	Difference in comparison with the empty vehicle
[m.s− 2]/%	Variant	Average [m.s− 2] (Standard deviation)	Difference in comparison with the empty vehicle
[m]/%	
Empty towing vehicle	9.08 (0.01)	–	Middle, brakes OK	5.75 (0.01)	− 3.33/-36.67	
Towing trailer, brakes OK	9.01 (0.01)	− 0.07/-0.77	Middle, brakes failure	5.15 (0.01)	− 3.93/− 43.28	
Towing trailer, brakes failure	7.02 (0.01)	− 2.06/-22.69	Middle, not brakes	5.57 (0.01)	− 3.51/− 38.66	
Towing trailer, not brakes	7.52 (0.01)	1.56/− 17.18	Front, brakes OK	5.65 (0.01)	− 3.43/− 37.77	
Rear, brakes OK	5.80 (0.01)	-3.28/− 36.12	Front, brakes failure	4.97 (0.01)	− 4.11/− 45.26	
Rear, brakes failure	4.79 (0.01)	− 4.29/− 47.25	Front, not brakes	5.42 (0.01)	− 3.66/− 40,31	
Rear, not brakes	5.66 (0.01)	− 3.42/− 37.67				

For better display, Fig. 7 shows the results of the average measured MFDD during deceleration from the speed of 20 km.h− 1 under different driving conditions. The red colour displays the results of deceleration with functional brakes of the trailer, and the black colour displays the results with non-functional brakes of the trailer, which means that the drawbar was shortened and the brakes were not activated. The green colour displays the results measured with the trailer which was modified to be unbraked. It means that the drawbar could not be shortened, and thus the brakes could not be activated. The results are given for the load of 500 kg placed in the rear, in the middle and in the front of the trailer.

Fig. 7 Mean fully developed deceleration under different conditions.

The ability of the studied vehicle combination to decelerate was to a large extent affected by the load, its stowage as well as the functionality of brakes. Loading the load of 500 kg on the trailer with functional brakes caused a considerable reduction of MFDD. The differences are substantially higher than in vehicle acceleration (Fig. 7). The lowest MFDD was when the brakes were non-functional and the load was in the rear. This is probably due to the fact that when the brakes were non-functional, the drawbar was shortened, and when the braking forces were not applied, it led to the towing equipment’s thrust. Thus, the towing vehicle started to decelerate and the trailer continued even with the unchanged speed until the limit position in the braking mechanism was achieved, and then, it led to the thrust on the towing vehicle. Such a thrust of the trailer’s drawbar is a risk mainly when braking in a bend, when there it could lead to a skid of the rear axle or the towing vehicle’s overturning106,107.

When the load was placed in the rear, from all ways of stowage, the largest mass was applied to the trailer’s axle, as also given in Fig. 4, and the lowest mass was applied to the towing vehicle which derived the braking forces. MFDD was lower without the load and when the brakes were non-functional than with functional brakes and the trailer loaded. Thus, the non-functional brakes, when the drawbar is shortened and the thrust is evident, pose a direct threat to road safety. In practice, it relatively often leads to the inertia brakes non-functionality, respectively to their weaker effect due to a wrong adjustment on the cables and rods108. The thrusts cause damage in the towing equipment as well as the coupling equipment, and the trailer is at risk of being uncoupled from the towing vehicle109. The measurements of the vehicle’s ability to accelerate and decelerate depending on the vehicle load are also given in the publication110 in which the towing vehicle with a load in the form of three passenger vehicles was discussed. Increasing gearing engaged meant that the towing vehicle’s ability to accelerate was reduced due to the load. The authors of the publication110 reached the same conclusions that can be also deduced from the data in Figure and Fig. 7, i.e. that the increase of vehicle weight results in the increase of inertia and it has an influence on acceleration and braking processes. On the basis of investigation analysis of total deceleration, we can notice the falling tendency of the value MFDD for increasing the cargo mass. In this study, the ability to accelerate was observed with the first gear engaged. Thus, there are strong indications that with the higher gear engaged, the difference in the values measured would be greater. Concerning the first gear, the main limiting factor was probably an adhesion between the tyres and the asphalt surface. Relating to the higher gears, it would probably be the engine power111. At the same initial speed, the length of braking distance is inversely proportional to the value of MFDD. The lower the MFDD value, the longer the braking distance. The results given in Fig. 7 would be also useful for students in driving schools, as mentioned in the publication112 in which the braking distance was estimated via software simulations.

Table 6 shows the variant of the maximum forces in the binding straps measured in its first column. The second column displays the average maximum force together with the standard deviation in brackets. The last column shows the difference in comparison with the empty vehicle including the percentage.

Table 6 Maximum force in the binding straps during the deceleration.

Variant	Average [daN] (Standard deviation)	Difference in comparison with
The empty vehicle [daN]/%	
Rear, brakes OK	421 (7.25)	− 	
Rear, brakes failure	509 (9.47)	+ 88/+20.90	
Rear, not brakes	382 (7.12)	− 39/− 9.20	
Middle, brakes OK	319 (11.47)	− 102/− 24.22	
Middle, brakes failure	580 (12.89)	+ 159/+38.09	
Middle, not brakes	262 (11.56)	− 159/− 37.76	
Front, brakes OK	291 (8.16)	− 130/− 30.87	
Front, brakes failure	418 (10.24)	3/− 0.71	
Front, not brakes	252 (8.44)	− 169/− 40.14	

During the decelerations shown in Fig. 7, the force in the binding straps that prevent the load moving forwards was measured as well. For better clarity, these values are given in the form of a graph (Fig. 7). The left axis displays the force measured in the binding straps. The binding capacity of the straps and fastening lugs is usually given in daN, therefore, Fig. 8 shows the same unit.

Fig. 8 Maximum force in the binding straps during the deceleration.

The force in each binding strap was approximately from 50 daN to 60 daN before the deceleration. The forces shown in Fig. 8 are achieved during the deceleration. The largest forces in the binding straps securing the load movement were applied when decelerating with the non-functional brakes of the trailer (Fig. 8). The reason is that within the non-functional brakes of the trailer, it led to a large thrust of the trailer on the towing vehicle. Despite the fact that MFDD was the lowest when the brakes were non-functional, the force in the binding straps was the largest. When the load is in the middle of the trailer, the increase in forces between the functional brakes and non-functional brakes is by 262daN, i.e. by 81%, to the value of 580 daN. The fixing points are usually dimensioned to 400 daN. In this case, it led only to the damage of the binding eye and not to its total destruction. It was probably due to the fact that it is a completely new trailer, not yet used. Besides the risk of the lowest MFDD (Fig. 7), there is a risk of changing the load position (Fig. 8) or destruction of the binding strap or binding point as well. After such destruction, the cargo is at risk of falling out onto the road or against an oncoming vehicle. The increased risk of the destruction of binding straps or fixing points would thus be also when observing the condition of the brakes during the technical inspection via a driving test with cargo in the trailer, when there is an attempt to reach the highest possible braking deceleration. The highest risk of destruction during deceleration also follows from the conclusion of the authors113 who focused on the comparison of securing the load in several vehicles bearing in mind the braking deceleration. The risk would be higher mainly with non-functional brakes, or with brakes of decreased performance (Fig. 8), however, also with functional brakes, it could lead to the destruction of the binding straps or points, and it may increase the value of inertia forces, as also mentioned in publication114. The value of maximum force reached in the binding straps also depends on the load stowage, since when the load is placed in the front, the pallet is leaning against the front face of the trailer. Nonetheless, the force in the straps increased during the deceleration in this case too.

The selection from the course of forces during deceleration is shown in Fig. 9.

Fig. 9 The course of forces in the binding straps during deceleration.

The course of forces in the binding straps with functional brakes was different than with non-functional brakes and an unbraked trailer. The likely explanation is a combination of several factors, such as gradual, continuous deceleration of the trailer and the wheel skid while braking. As follows from Fig. 9, the maximum force is in the binding straps in all cases, and in the binding points, it is reached always at the beginning of deceleration and then the pressure slightly decreases. If the binding strap or point were destructed, it would be probably at the maximum force, i.e. at the beginning of deceleration, and then, the inertia force, applying to the cargo during the deceleration, would have made the cargo move. Therefore, it is suitable to check the brake condition statically on the cylinder brake test stand in order to increase safety during the technical inspection, as also mentioned in this study.

For a better comparison of the approach to the issue in this and in other publications, Table 7 displays the investigation part in its first column, the approach of this article in its second column, and the approaches of other authors in its two last columns.

Table 7 Comparison of approaches to the areas of investigation.

Investigation	This article	Publication28	Publications115,116	Publication117	
Control force and braking force, inspection without a trailer	The entire course was recorded via experimental measurements under laboratory conditions.	The wheel blocking was determined by visual check, with a risk of subjective error, and the control force could not be determined.	Method of extrapolation of the values measured, with a risk that the results could be influenced by a different load.	Activation of the inertia brake’s control force caused a rapid reversing of the cylinders on the cylinder brake test station, and the control force could not be determined.	
	This article	Publication118	Publication119	Publication120	
Determination of the centre of gravity’s position	Experimental weighing, different load distribution in the trailer.	Estimation by using a combination of Huber Extended Kalman Filter and Extended Kalman Filter, without the trailer.	Proposed algorithm based only on longitudinal motion of the vehicle, excluding excessive lateral, yaw and roll movements of the vehicle, without the trailer.	Estimation based on the improved square-root unscented Kalman filter algorithm, without the trailer.	
	This article	Publications120–122	Publication19	Publication123,124	
Determination of dynamic characteristics of vehicle combination	Experimental measurements, acceleration and deceleration, including the force in the binding straps.	Computer simulations of deceleration and acceleration with different axle load distribution, without the trailer.	Investigation of driving stability of a vehicle–trailer combination depending on the load’s position within the trailer based on simulation computations performed in the commercial multi-body software, with many simplifications.	A simulation method was applied for the analysis, which used a relatively simple, quasi-static, model of the tractor-semitrailer set’s rectilinear motion and models of the braking system and the longitudinal forces in the tyre-road surface contact.	

As follows from Table 7, the experimental measurements are used minimally for the issue mentioned in this article. Majority of the authors have chosen the simulation methods, however they are with various simplifications and estimated input values that can affect the result accuracy.

Conclusion

The experimental measurements mentioned in this study were divided into three investigations, i.e. determining the relation between the steering control force and the braking force, determining the position of the centre of gravity, and the studied vehicle combination’s ability to accelerate and decelerate under different conditions.

Based on the first measurement mentioned in this study it may be concluded relatively low forces in the horizontal direction from the trailer on the towing vehicle in relation to the functional brakes. The proposed and verified methodology enabled to determine important parameters of the trailer’s brakes with an inertia brake during the technical inspection. The measurements provided also data on the change in the axle load and on the change in the centre of gravity’s position due to different load distribution in the trailer. There were identified risk load distributions in the trailer which can cause an excessive overload or reduction of load of any axles or coupling devices. The variants, when the load was in the rear part of the trailer and also in the front part of the trailer, were identified as risky. When the load was in the rear, it led to an excessive reduction of load on the rear axle of the towing vehicle and also there was a risk of its disconnection from the trailer. When the load was in the front, it led to a multiple exceeding the permissible load on the towing vehicle as well as to an excessive reduction of load on the driving axle. All this happened despite not using the trailer’s maximum load capacity.

The measurements focused on the vehicle and studied vehicle combination ability to accelerate and decelerate provided the data important for further survey in the field. In road traffic, there are predominantly used unbraked trailers weighing up to 750 kg due to their lower price in comparison with the braked trailers. As observed by the measurements, using the trailer with the inertia brake under the same conditions considerably increases MFDD and reduces the braking distance. On the other hand, decelerating trailers are connected with a risk of shortening the drawbar and the thrust effect on the tow vehicle if the brakes do not work. The effect of non-functional inertia brakes would be considerably higher relating to the trailer with a higher weight, for instance 3500 kg. Thus, the trailer’s brakes enhance road safety significantly, however, only under their proper technical condition. Thus, implementing the technical inspection of brakes according to the methodology from this article would increase the road safety since it would reduce the occurrence of trailers with non-functional brakes or poorly functional brakes.

The analysis of the results obtained by the experimental measurements has evinced significant differences depending on using the trailer, its technical condition, transport and distribution of a cargo, which may affect road safety, predominantly when neglecting the education of drivers.

The experimental measurements and the result analysis have pointed to the need for their performance and contribution in the practical and scientific field, even when considering their demands in time, material and financial spheres. The disadvantage of experimental measurements, in comparison with simulations, is that they are time, material and money-demanding. On the other hand, this article has proven that it is necessary for particular areas to perform experimental measurements, despite their complexity, in order to obtain the highest accuracy of results possible. The results may be used by the other authors as input for the vehicle dynamics’ modelling, or as the values for comparison, since based on the literary review it may be concluded that there is a shortage of the results obtained by experimental measurement.

Although the measurements were performed only with one passenger vehicle and one trailer, the results can be applied to the other vehicles and combination of vehicles as well. The passenger car and the trailer used in this article represent the most common type of vehicle used in road traffic, mainly in European countries and parts of Asia. The substantial factors such as size, weight, tyre and technical design of the studied vehicle combination, which have a crucial impact on the relation between the steering control force and the braking force, the centre of gravity’s position and the ability to accelerate and decelerate, are very similar to the most common used vehicle combinations composed of a passenger car and a trailer. A limiting factor is that the towing vehicles used in the US are generally heavier. However, even trailers tend to be heavier, so the results in this article can also be applied to the measured vehicle pair in the USA after modifications.

Recommendations for future work are to observe the area of braking from higher speeds or braking in the beds via modelling since the limitation of experimental measurements is the safety aspect as well. A limiting factor of experimental measurements is also their difficulty, however, as shown in this article, in many cases experimental measurements are necessary.

Author contributions

F.S. - wrote the main manuscript text , L.J. - prepared figures, L.J. - formal, F.S. - measurement, F.S. - methodology, L.J.: prepared tables.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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