Impact assessment of the transported load mass on the lateral dynamics of a light delivery vehicles

Abstract

This study addresses the broadly defined safety of cargo in light commercial vehicles. The practical goal was to verify whether costly accelerators used for bench testing of palletized cargo units could be effectively replaced by experimental tests using typical motor vehicles. Road tests were conducted using a standard Fiat Ducato van equipped with two acceleration sensors positioned at different heights within the cargo area. This configuration also allowed for a comparison of the lateral accelerations to which goods transported are exerted at different heights of vehicle body. The tests included multiple drives along a route chosen due to numerous tight curves, and the vehicle’s lateral dynamics were examined under four different load conditions. The experimental measurements demonstrated that the tested light delivery vehicle could reach lateral accelerations up to 0.8 g, with exceedances of 0.6 g occurring across all loading configurations. Moreover, lighter vehicle configurations showed 10 – 25% higher maximum and mean lateral accelerations compared with the heaviest configuration, confirming that reduced gross mass significantly increases lateral dynamic response. These results confirm that light commercial vehicles and their loads can be subjected to very high lateral accelerations. Furthermore, higher maximum accelerations were recorded in the upper zone of the cargo area. To assess the vehicle load limits at which the risk of rollover becomes critical during intense turning maneuvers, further analytical calculations were performed using a simplified vehicle model. The analytical assessment further indicated that rollover risk becomes critical when the vehicle’s center of gravity exceeds approximately 1.12 m, providing a quantifiable threshold for evaluating the safe testing of pallet units with higher center of gravity.

Introduction

This research focuses on examining the effects of load weight on the cargo securing and transport stability of load units in the delivery vehicle category with a total weight of up to 3.5 tonnes. These vehicles are significantly more dynamic than heavy goods vehicles (HGVs) with a gross mass more than 3.5 tons. This research aims to use practical tests to determine the impact of load weight on lateral acceleration in delivery vehicles of up to 3.5 tonnes, and whether it is possible to achieve the design acceleration used for securing loads and pallet stability for individual vehicle weight categories. Practical tests were carried out using a delivery vehicle carrying variants (of the same) load with different masses. To determine the effect of load weight, the same delivery vehicle was used with the same driver on the same test route while changing the load weight. In other studies, such as¹ and², different vehicles, routes and drivers were used, which makes the results difficult to compare.

Analytical methods can also be used to determine the maximum height of a vehicle’s gravity center above the ground, at which its lateral stability is maintained under given road conditions. The experiments conducted may allow for the development of a method for determining the maximum height of the center of gravity of vehicles with the expected vehicle stability – lateral acceleration g. Even a simplified theoretical model allows for determining the limiting state at which a vehicle traveling along a curve with a high turn intensity begins to rollover. Using other well-known formalisms, it’s also possible to calculate the maximum height of uniform load units in delivery vehicles with typical parameters to prevent their loss of stability on the road. Such theoretical methods were also used in this research.

Although many studies investigate vehicle dynamics, there is limited real-road data on long-duration lateral accelerations affecting pallet stability in light commercial vehicles. The study additional aims to compare accelerations at two sensor heights, determine exceedances of design accelerations and analytically estimate rollover-critical center of gravity heights.

Despite extensive research on vehicle dynamics, previous studies have rarely examined lateral acceleration in light delivery vehicles under real operating conditions with systematically varied load masses. Existing works typically focus on passenger cars or generic models, use different vehicles and drivers, or rely solely on simulations, making their results unsuitable for evaluating cargo securing requirements. The novelty of this study lies in conducting controlled, repeatable road measurements on a single N1 category delivery vehicle while varying only the transported load mass and using dual-position accelerometers to quantify lateral accelerations at different heights of the vehicle body. This approach enables, for the first time, a direct assessment of how load mass influences achievable lateral acceleration relevant for both cargo securing and pallet stability, and whether real-vehicle tests can reproduce the design accelerations (0.5 – 0.7 g). In addition to experimental measurements, a simplified analytical model is used to evaluate rollover limits and to estimate safe load-unit heights for future tests on cargo with a higher center of gravity. The main goal of this work, as mentioned earlier, is to determine the effect of transported load mass on the lateral dynamics of a light delivery vehicle and to evaluate the feasibility of replacing costly laboratory acceleration platforms with road-based vehicle tests for assessing cargo stability.

Literature review

Vehicle dynamics is an important parameter that influences driving safety. Testing vehicle dynamics in real-life tests is an important part of the research on this issue. That is why Antonios et al.³ focused on investigating vehicle dynamics related to driving safety. Authors recorded lateral acceleration for various interchanges and curves and then analysed the effects of on-ramp speed and curve geometry. Data collection avoids heavy traffic, focusing on free flow conditions. Results show that higher speeds correlate with in-creased lateral acceleration. Small-radius curves exceed comfort and safety limits, contrasting with larger-radius curves. Speed increases with curve radius, particularly pronounced in smaller-radius curves. The authors Frej et al.⁴ discussed in their research the significance of a vehicle’s longitudinal acceleration in determining motion dynamics and evaluating driver behaviour and passenger comfort, presenting test results from city buses and coaches during rapid acceleration and braking manoeuvres, revealing significant impacts of road conditions on longitudinal acceleration. Additionally, it presents longitudinal acceleration values during regular operation, indicating that maximum deceleration in real traffic conditions is lower than during sudden braking, suggesting drivers rarely use sudden braking, and maximum positive acceleration during acceleration manoeuvres slightly exceeds values from rapid acceleration tests on the track. When measuring vehicle dynamics, it is important to have the right measuring equipment. For this reason, the authors Ahmed et al.⁵ examined MEMS accelerometers’ effectiveness in measuring vehicle vibrations in various locations, revealing frequencies and amplitudes and their potential applications in vehicle diagnostics and safety enhancements. Modern vehicle development increasingly uses objective measurements, often with steering robots, to streamline data processing and improve vehicle dynamics measurement quality. This technology was investigated by Pfeffer et al.⁶. Measurement of dynamics was also addressed by Tsanov and Mladenov⁷. Their article presents a method using MEMS sensors to measure car accelerations on Sofia’s (Bulgaria) streets, analysing driving styles and road conditions. A different approach to measuring vehicle dynamics was taken by Wallace et al.⁸ who focused on obtaining acceleration data from GPS and OBDII unit. Authors validated vehicle acceleration/deceleration signals derived from 1Hz GPS and OBDII velocity sensors by comparing them to 40Hz accelerometer measurements, crucial for assessing driving habits without requiring dedicated accelerometer installations. Results show strong correlations between GPS and accelerometers (0.810) and between OBDII and accelerometers (0.808). . Investigating safety in real tests is also a very important area of research. This is precisely the issue addressed by Stanojčić et al.⁹, whose paper discusses conducting severe lane-change manoeuvre tests, which is crucial for assessing vehicle stability and safety. Authors used a BMW 650i 2014 vehicle as an example. Results were compared under various conditions as per ISO standards. Driving safety in terms of dynamics has also been investigated by Kumar et al.¹⁰. Their paper focuses on testing methods for Advanced Driver Assistance Systems (ADAS), particularly the Autonomous Emergency Braking System (AEBS), emphasizing factors like test environments, traffic scenarios, and validation methodologies. The combination of simulation and real tests is an option to ensure the most accurate results of the proposed simulation models. It is not always possible to validate simulation models with real-life tests. Papers dealing only with simulations and modelling are equally important when investigating vehicle dynamics. Just such research has been published by Li et al.¹¹. Their paper pro-poses an adaptive STKF to enhance TRFC estimation for vehicle control and safety. It im-proves accuracy by incorporating a vehicle dynamics model and adjusting fading and ex-citation factors. Experimental results show significant improvements in TRFC estimation stability and accuracy compared to the benchmark method. The simulation for the purpose of testing the Electronic Stability Program (ESP) was carried out by the team of authors Sun et al.¹². To improve ESP testing, a simulation device mimicking lateral acceleration and yaw is designed. It combines centrifugal acceleration principles to replicate dynamic signals. The device structure includes key components like power devices and actuators, ensuring accurate signal transmission to ESP for real-time vehicle response, enhancing electrical performance testing. The modelling of dynamics was addressed by the authors Wei et al. in two studies. In the first research¹³, the authors focused on da-ta-driven method for accurately modelling nonlinear lateral vehicle dynamics, requiring minimal data and no training. In the second research¹⁴, the authors presented a recursive IPDB algorithm for online modelling of lateral vehicle dynamics, offering accuracy with improved computational efficiency compared to conventional methods. Neural networks are also often used in modelling. Nie et al.¹⁵ proposed to use them for real-time prediction of autonomous vehicle dynamics, offering improved accuracy and efficiency over traditional multibody models like ADAMS. The authors Pan et al.¹⁶ also proposed to use deep neural networks to model vehicle dynamics, for real-time autonomous vehicle control. For simulations, equipment can be used that allows real tests to be carried out under laboratory conditions. This procedure was used by Kurz et al.¹⁷ who verified new test procedures on vehicle test benches for ADAS and AD functions, emphasizing Vehicle in the Loop testing. It introduces a validated model approach, providing insights into vehicle pitch motion during testing. Laboratory equipment for dynamics testing has also been addressed by Unni et al.¹⁸ who developed a test bed to analyse electric vehicle motor performance through simulation and emulation. It uses a PMDC generator and a special chopper circuit to emulate load torque under various driving conditions. User-input parameters calculate load torque based on vehicle simulation models. The system’s effectiveness is validated using MATLAB/Simulink with a coupled DC motor drive. In simulations, it is also possible to investigate phenomena that are very difficult to test in real tests. Such phenomena include rollover, which Li et al.¹⁹ investigated using simulation methods. Their study conducts comparative analysis and simulation verification on two calculation methods for the critical safety speed of vehicle roll during extreme turns, with and without considering suspension effects. It systematically analyses the factors influencing vehicle roll during extreme turns, including driver operation, vehicle structure parameters, and road conditions²⁰. Using a specific truck as the subject, TruckSim software is employed to simulate and verify the analysis results. Advanced simulation methods have also been used by Xun-Xiao and San-Hua²¹ to investigate the issue. They established a vehicle dynamics model using root locus analysis to evaluate vehicle roll stability. A four-degree-of-freedom vehicle system equation is formulated based on vehicle theory and dynamic analysis principles. Using Matlab, simulations are conducted to study turning characteristics at fixed speeds and varying steering wheel angles, yaw rates, and roll angles. Root locus analysis proves effective in analysing and evaluating vehicle roll stability, demonstrating its utility for vehicle dynamics research. A dynamic model that tests SUV rollover risks in cornering scenarios was conducted by Bao²². His simulations analysed steering, rotation speed, and suspension stiffness effects to identifying the main rollover factor. Cong et al.²³ analysed vehicle roll stability. Their findings suggest measures to enhance stability, informing vehicle design and manoeuvrability improvements. When examining vehicle dynamics, it is also necessary to know the distribution of the load and the associated centre of gravity (COG) of the vehicle, which can negatively affect driving safety. Such research has been undertaken by Synák et al.²⁴ who, in their paper, address how varying load distribution affects the position of a vehicle’s centre of gravity, impacting both driving performance and its surroundings. Experimental measurements on three vehicle types - a passenger car, van, and truck - reveal insights into this relationship, highlighting how load distribution can lead to axle overloading even without fully utilizing the vehicle’s load capacity. Furthermore, the study provides a database for future research and modelling endeavours. The centre of gravity of the vehicle has also been addressed in the research of Skrúcany et al.²⁵ where he describes how cargo weight and distribution affect braking in small trucks or vans. The paper focuses on the impact of cargo mass and position on axle load and braking performance, using a decelerometer to measure vehicle deceleration directly. In their other research, Skrúcaný et al.²⁶ described the importance of the vehicle’s centre of gravity and its influence on safety and dynamics. This research presents a method for measuring the centre of gravity and examines how it shifts with varying passenger and luggage loads, providing insights into its impact on vehicle handling. An interesting topic in relation to this issue was also addressed by Triananda et al.²⁷ who investigated how converting vehicles to electric power affects their stability, focusing on changes in centre of gravity and total mass. An accurate calculation of the vehicle’s centre of gravity is essential for further investigation of this issue. This is why Win et al.²⁸ have compiled a methodology for calculating the vehicle centre of gravity. Their study emphasizes the importance of accurately determining a vehicle’s centre of gravity for assessing its stability and dynamic behaviour. It introduces a new method for calculating the centre of gravity position and load distribution on axles, aiming to improve accuracy and reduce reliance on laboratory-based measurements. Park and Choi²⁹ proposed an integrated observer for real-time vehicle centre of gravity height estimation, enhancing safety control systems by monitoring rollover risk effectively across various driving scenarios. Vehicle rollover in relation to centre of gravity position has been the subject of research by Yang et al.³⁰, who applied adaptive adjustment technology to loaders, enhancing rollover protection based on centre of gravity position. This study develops a dynamic rollover stability index and proposes an adaptive attitude adjustment system based on electro-hydraulic control. Experimental validation confirms its effectiveness in improving vehicle safety. Statistical investigation of the location of the centre of gravity was undertaken by Grakovski et al.³¹. Their research addresses vehicle load balancing, proposing a solution based on a multi-span continuous beam model. Numerical methods are compared with computer modelling to assess accuracy, with examples of cargo weight distribution provided³².

Unlike other authors, our research focused on vehicle dynamics from the perspective of cargo securing and pallet stability which required to simulate and analyze long duration lateral acceleration events. The main objective was to assess whether costly acceleration platforms used for bench testing of palletized loading units could be effectively replaced by experimental tests using typical motor vehicles. We chose a practical experiment with a load that has a low center of gravity in order to develop the highest possible lateral acceleration with the light delivery vehicle and to verify whether it is possible to achieve the design acceleration for securing the load in the lateral direction of 0.5 – 0.7 g with different loads in the vehicle and how the load weight affects the lateral acceleration achieved. This level of lateral acceleration is unlikely with heavy goods vehicles, which typically experience lower lateral accelerations. We used manual and automatic event selection as well as a simplified model to verify whether such measurements would also be possible for load units with a higher center of gravity.

Many researchers use passenger cars or generic vehicle models instead of light delivery vehicles for cargo transportation. There are few studies that provide specific, measurable data under real-road conditions that can be used for securing cargo or pallet stability.

Although many studies address vehicle dynamics, acceleration measurement methods, or rollover behaviour, most of this research focuses on passenger cars, heavy trucks, or simulation models rather than on light delivery vehicles operating under real transport conditions. The reviewed literature therefore highlights a clear gap. There is limited experimental evidence describing the lateral accelerations experienced by N1 category vehicles with different transported load masses, even though these vehicles represent a significant portion of urban and regional freight transport. This gap directly motivates the present study, which aims to provide measurable and repeatable data on how load mass affects the lateral dynamics of a light delivery vehicle in real operation.

Materials and methods

To obtain the vehicle acceleration data, it was necessary to carry out test runs on an N1³³ test vehicle, which were conducted in an urban environment. Two sensors were used to record the data, with each sensor containing an accelerometer and a GNNS sensor.

Test vehicle

A Fiat Ducato delivery van was used for testing. The vehicle parameters can be found in Table 1. and in Figure 1. Figure 1 illustrates the geometric configuration of the test vehicle and the placement of the two accelerometer units. Sensor S1, positioned on the vehicle roof, is located farther from the roll axis and therefore captures additionally peripheral accelerations caused by angular vibrations of the vehicle. Sensor S2, mounted lower on vehicle body, measures accelerations near to the vehicle mass centre (according (ISO 8855) and is not very sensitive by angular motion. This difference in sensor positioning is fundamental for interpreting the measurement discrepancies between S1 and S2 presented later in the paper.

Table 1.

Test vehicle.

Model	Model year	Max. power (kw)	Tyres	Wheel track (mm)	Lenght (mm)	Width (mm)	Height (mm)	Tare vehicle mass (kg)	Loading area length (mm)	Loading area width (mm)
Fiat ducato 250	2022	103	Continental van contact eco 215/75 R16 C	1790	6363	2050	2522	2420	3700	1860

Fig. 1.

Test vehicle dimensions and sensor positions.

Before the measurements, the technical condition of the Fiat Ducato test vehicle was verified to ensure that no mechanical irregularities could influence the results. The vehicle’s curb mass and axle loads were measured on a calibrated weighbridge. These procedures ensured that the test object was in proper technical condition and suitable for reliable lateral-dynamics measurements.

Test runs with different load weight were carried out to see how the mass of the load with the low center of gravity affects the vehicle lateral accelerations. Metal box pallets were used to load the vehicle, where each pallet weighed 400 kg. A total of four test scenarios were performed, which are denoted as V1 (vehicle 1), V2, V3 and V4. The total weights and load distributions are shown in Table 2 and Figure 2.

Table 2.

Test load and cargo securing.

Test scenario	Test pallets	Cargo securing
	(1 pallet = 400 kg)	Friction force increase	Forward	Backwards and sideways
V1	1200 kg	anti-slip mats	headboard and empty pallets	lashing straps
V2	800 kg	anti-slip mats	headboard and empty pallets	lashing straps
V3	400 kg	anti-slip mats	lashing straps	lashing straps
V4	0 kg	-	-	-

Fig. 2.

Load distribution of metal pallets for each test scenario.

The Figure 2 demonstrates that while the total mass changes significantly between variants, the longitudinal location of the pallets remains controlled and repeatable. This allows isolating the effect of load mass on lateral acceleration without introducing additional variability from shifting the centre of gravity along the vehicle length.

The metal pallets were secured in such a way that they did not move during the test runs. The pallets were placed on anti-slip mats which increased the friction force. In the forward direction, in V1 and V2, the load was blocked by headboard to prevent the forward movement in the event of braking. To secure the load sideways, 50 mm lashing straps were used. In most cases, the load was secured by diagonal cross lashings and in one case the load was additionally secured by a top-over lashing to prevent lateral movement. The same driver drove the vehicle in all test scenarios.

In this study, all load variants (V1–V4) were intentionally positioned within the central region of the loading area to ensure repeatability of lateral-acceleration measurements and to isolate the effect of total load mass on vehicle dynamics. Variants simulating cargo placed predominantly over the rear axle or extending into the rear overhang were not included, although such configurations could exist in practical operation. These loading patterns substantially alter axle load distribution, the longitudinal position of the center of gravity, and potentially the vehicle’s lateral-dynamics response. It lightens the front axle, which has a negative impact on the safe steering of the vehicle. Their omission was deliberate to avoid introducing additional variables that could obscure the specific influence of load mass.

The V4 scenario (0 kg load) was intentionally included as a baseline condition to distinguish the influence of vehicle loading from that of inherent vehicle dynamics. Empty-vehicle tests are commonly used in dynamic studies to isolate the effect of load mass on lateral acceleration, as they represent the most responsive and least inertially damped state of a light commercial vehicle. Testing the unloaded configuration enables identification of the upper boundary of lateral acceleration achievable with the vehicle, provides the reference for comparing V1–V3, and reflects real-world situations in which delivery vehicles often travel without cargo for portions of their routes.

The center of gravity of the load in the longitudinal direction from the front of the loading area is calculated according to the following equation:

1

Legend:

X_T - center of gravity of the load in the longitudinal direction from the front of the loading area

x_i - distance of the load unit center of gravity from the front of the loading area

m_i – load unit weight

The following applies to the vehicle’s center of gravity in the longitudinal direction from the front axle:

2

Legend:

X_VL - center of gravity of the vehicle in the longitudinal direction from the front axle

m_RAVE – rear axle weight of empty vehicle

d_WB – distance between the front and rear axle (wheel base)

m_L – load mass

d_FAHB – distance of front axle to the front of the loading area

m_VL – vehicle mass

The weights of the load and vehicle, axle loads, and are listed in Table 3 for all test scenarios.

Table 3.

Axle weights and center of gravity of load and vehicle for each test scenario.

Test scenario	Load mass [Kg]	Vehicle mass [Kg]	Front axle mass [Kg]	Rear axle mass [Kg]	Distance of cog of load from the headboard [M]	Distance of cog of vehicle from the front axle [M]
V1	1240	3660	1860	1800	1.47	1.984
V2	900	3320	1790	1530	1.34	1.862
V3	400	2820	1610	1210	1.47	1.732
V4	0	2420	1490	930	-	1.550

Research²⁴ was focused on longitudinal position of center of gravity where light delivery vehicle Citroen Jumper was studied with a test load of 1000 kg placed in the front, middle and rear part of loading platform. Vehicle V2 is like this situation. Research also used simulated load of 1260 kg like our vehicle V1. Tests and simulations studied also axles overloading when load was placed in front or rear part of loading platform. In all of our test vehicles axles were not overloaded.

Sensors

Two sensors were used to measure vehicle dynamics and the associated lateral acceleration, speed and position on the map. Each sensor contained an accelerometer and a GNNS sensor.

The N1 FIAT Ducato vehicle was fitted with two MEMS sensors, comprising an accelerometer, a gyroscope and a GNSS sensor. Sensor S1 was mounted on the roof and Sensor S2 was mounted on the body of the vehicle. Sensor S2 was located close to the vehicle’s center of mass, in accordance with the requirements for experimental vehicle dynamics studies (see, for example, ISO 8855). Mounted much higher, sensor S1 enabled the measurement of actual lateral accelerations that can occur in the upper layers of the cargo space, located just below the roof of the cargo area. In this case, when angular vehicle vibrations occur (e.g., due to different road surface profiles under the left and right wheels), additional peripheral acceleration occurs, often with a large amplitude. A sensor installed according to ISO recommendations cannot record such a component, but the one designated here as S1 definitely can.

Lateral acceleration data were evaluated on the y-axis at an evaluation time of 1000 ms. The method for determining the evaluation times is described in³.

A description of Sensor S1, an industrial-grade dual-antenna GNSS/INS sensor providing higher position and velocity accuracy (Vectornav VN-300 from Vectornav, Dallas, United States of America), is given in³⁶. A description of the low-cost Sensor 2 (BOSCH BHA250 + UBlox UBX-M8030-CT from Bosch and UBlox) can be found in³. Sensor S2 produced acceleration results comparable to those of sensor 1 at an evaluation time of 1000 ms.

Test route

The test drive took place around the city of Žilina. Test route included roundabouts and curves to obtain lateral acceleration data. The test runs were carried out at night between 22:00 and 04:00 due to low traffic, with permission for the measurements being secured from the road operator. The route averaged 17 km in length and was driven four times for each test scenario (see Figure 2), for a total of sixteen test runs. The test route is shown in Figure 3 containing repeated roundabouts, curved segments, and U-turns. These features produce lateral accelerations of varying magnitude, enabling repeated measurement of similar maneuvers under controlled conditions. Because the vehicle was driven multiple times on the same route, the figure provides a spatial reference for comparing the consistency of acceleration peaks associated with specific Test Route Events (TREs), as later shown in Figures 5 and 8.

Fig. 3.

Test route map. The map was created by the authors using QGIS (version 3.34.10; https://www.qgis.org) with OpenStreetMap basemap data © OpenStreetMap contributors, licensed under the Open Database License (ODbL). Available at: https://www.openstreetmap.org.

Fig. 5.

Maximum acceleration in individual testing scenarios for sensor S1.

Fig. 8.

Mean speed and mean lateral acceleration from all tested vehicles and sensor S1 for individual TREs.

The order of identified test route events (TRE) on test route is as follows START (S) 1, 4, 5, 7, 10, 11, 12, 13, 14, 6, 2, 3, 19, 20, 21, 22, 23, 24, 3, END (E). Events 1-6 presents small roundabouts and 10-14 large elliptical roundabouts. Events 20-24 present U-turns. The same vehicle with different load weights was used for all test scenarios, and the vehicle was always driven by the same driver. For each vehicle load tested, the route was driven four times to obtain more data and statistically evaluate the impact of load weight. The fourth run usually achieved the highest average speed for each TRE, as well as the maximum lateral acceleration, reflecting the driver’s greater experience with the route and control of the vehicle with a certain load weight.

Evaluation of data

Manual and automated labeling is used to evaluate specific acceleration events numbered in Figure 4.

Fig. 4.

Automatic and manual selection of lateral acceleration event.

To compare data between sensors and subsequently demonstrate the effect of cargo mass on lateral accelerations, we chose a time of 1000 ms because of the most used in cargo securing tests as per EN12642:2017³⁴. Comparison of manual and automatic selection is given in Figure 4.

Automatic selection is based on selection of events higher than 0.05 g in time window , where median and maximum lateral acceleration are evaluated using MATLAB® R2025a. In the case of research³⁵, a threshold of 0.1 g was used for the automatic identification of acceleration events for transport by significantly different heavy goods vehicles on motorways. However, the research did not compare events with manual selection, as it focused only on identifying the maximum accelerations of individual acceleration events.

Manual selection is based on manual labeling of main lateral acceleration in curve from acceleration profile in MATLAB® R2025a and is significantly time consuming. Maximum and mean lateral acceleration from time window are later evaluated. Maximum lateral acceleration of event from automatic and manual selection is the same, therefore the automatic selection is more suitable to identify maximum lateral accelerations for large amount of acceleration events.

In addition to defining the manual and automatic selection procedures, it is important to highlight the implications of these methods for the accuracy and comparability of the extracted lateral acceleration values. The manual selection enables precise identification of the dominant acceleration peak within each curve, but it is time-intensive and subject to human judgement when applied to large datasets. Conversely, the automatic selection algorithm identifies all events exceeding a predefined threshold of 0.05 g and evaluates them over a standardized 1000 ms time window, ensuring consistent event detection across the entire dataset. This threshold was chosen to remain sensitive to lateral acceleration patterns typical for urban roundabouts and U-turns, which exhibited long-duration load effects in our measurements. The comparison between both methods demonstrated that maximum accelerations identified automatically corresponded closely to manually selected values, while the median values from automatic selection showed only a small deviation from the manually derived mean values. This confirms that the automated approach is sufficiently robust for large-scale event extraction and allows objective statistical comparison between test scenarios. Furthermore, applying uniform time windows and event identification criteria ensures that differences in measured accelerations can be attributed primarily to vehicle loading conditions rather than methodological inconsistencies.

The data from time windows were then analyzed for each TRE, with the following parameters evaluated:

3

4

5

6

7

8

Legend:

– the number of data in time window

– the mean vehicle speed in time window

ayst_min – the minimum value of average lateral acceleration in 1000 ms in for left-turn events

ayst_max – the maximum value of average lateral acceleration in 1000 ms in for right-turn events

– absolute value of or

– absolute value of mean lateral acceleration

Linear regression is then used to compare the sensors with each other using the values of ayst_min, ayst_max and as well as statistical tests to identify the influence of the load mass using .

Results and discussion

Maximum lateral accelerations

Table 4 shows the highest measured lateral accelerations cy1000 for individual TREs and both sensors S1 and S2. The highest measured lateral accelerations are mainly for the empty vehicle V4 and sensor S1 located on the roof. The maximum measured accelerations already indicate the influence of vehicle weight on the lateral accelerations achieved for individual TREs.

Table 4.

Maximum acceleration in individual testing scenarios for sensors S1 and S2.

	V1		V2		V3		V4
TRE	S1	S2	S1	S2	S1	S2	S1	S2
1	0.62	0.57	0.60	0.56	0.60	0.56	0.68	0.61
2	0.51	0.47	0.60	0.54	0.57	0.52	0.66	0.60
3	0.63	0.57	0.70	0.63	0.74	0.67	0.68	0.61
4	0.64	0.57	0.71	0.64	0.72	0.65	0.76	0.68
5	0.58	0.54	0.57	0.53	0.69	0.63	0.70	0.64
6	0.65	0.58	0.65	0.59	0.73	0.66	0.81	0.72
7	0.47	0.49	0.45	0.47	0.55	0.57	0.69	0.72
10	0.40	0.38	0.45	0.44	0.40	0.39	0.53	0.51
11	0.45	0.43	0.50	0.48	0.45	0.42	0.57	0.56
12	0.40	0.39	0.44	0.43	0.37	0.36	0.61	0.59
13	0.48	0.47	0.48	0.47	0.46	0.45	0.64	0.62
14	0.44	0.43	0.45	0.44	0.37	0.36	0.61	0.60
19	0.51	0.47	0.55	0.51	0.54	0.50	0.61	0.56
20	0.55	0.51	0.63	0.56	0.58	0.51	0.59	0.53
21	0.60	0.55	0.60	0.55	0.64	0.58	0.66	0.60
22	0.59	0.52	0.57	0.52	0.62	0.56	0.56	0.51
23	0.61	0.55	0.65	0.59	0.68	0.62	0.68	0.62
24	0.55	0.49	0.61	0.54	0.61	0.54	0.62	0.55
Maximum	0.65	0.58	0.71	0.64	0.74	0.67	0.81	0.72

Figure 5 shows the maximum lateral accelerations measured by sensor S1 for individual TREs and testing scenarios. The highest accelerations are visible in almost all cases for empty vehicle V4 and in the case of TRE3 (roundabout) and TRE22 (U-turn) for vehicle V3 and for TRE20 (U-turn) for vehicle V2.

Lighter vehicles (V3 and especially V4) consistently reach higher acceleration levels, reflecting reduced inertia and greater susceptibility to rapid directional changes. TREs with tighter radii (e.g., small roundabouts such as TRE3, TRE4, and TRE6) generate the highest peaks, consistent with the relationship between radius, speed, and centripetal force.

Table 5 shows the number of exceedances of design accelerations with limits of 0.5 g, 0.6 g, and 0.7 g, which are the design accelerations for cargo securing and transport stability of load units according to VDI 2700-16 and EN12195-1:2010.

Table 5.

Number of exceedances offor cargo securing and transport stability of unit loads for individual tested vehicles and sensors.

	Design acceleration	V1S1	V1S2	V2S1	V2S2	V3S1	V3S2	V4S1	V4S2
		mVL=3660 kg		mVL=3320 kg		mVL=2820 kg		mVL=2420 kg
EN 12195-1:2010	0.5 G	26	13	21	16	45	30	40	30
VDI 2700 - 16	0.6 G	7	0	9	2	15	9	19	10
VDI 2700 - 16	0.7 G	0	0	2	0	5	0	3	2

The heaviest vehicle, V1, in the weight category above 3.5 tons exceeded the design acceleration of 0.5 g 26 times in S1 and 13 times in S2. It even exceeded the higher design acceleration of 0.6 g 7 times in S1. Vehicles V2 - V4 in the weight category above 2.0 tons to 3.5 tons exceeded the design acceleration of 0.6 g more times in S1 than in S2, and even exceeded the design acceleration of 0.7 g used for the weight category up to 2.0 tons, mainly in S1. The empty vehicle V4 exceeded the design acceleration of 0.7 g three times at S1, while the heavier vehicle V3 exceeded this limit up to five times. The inertial properties of the empty vehicle and the driver’s driving technique may have an influence here (see also 3.2).

Table 6 contains the values of all TREs that exceeded an acceleration level of 0.7 g. The data are sorted from the highest to the lowest. We would like to point out that with V2, V3, and V4 vehicles, which are heavier than 2 tons, it was possible to achieve such high lateral acceleration, which has an impact on the design of cargo securing as well as the stability of load unit packaging (requiring more durable and expensive packaging, as we assume that most pallet units have a stability of 0.3 to 0.5 g, which is significantly lower than the long duration lateral acceleration we measured). Table 6 shows that the highest lateral accelerations occurred almost exclusively on small roundabouts, mainly TRE6 and TRE4, with vehicles V4 and V3 traveling at an average speed of 25-30 km/h, which is significantly lower than the 50 km/h speed limit permitted by regulations in built-up areas in several countries ³⁶.

Table 6.

The highest lateral accelerations cy1000 above 0.7g.

TRE	Test vehicle	Test route repetition	Sensor	Average speed [km/h]	[G]
6	V4	4	S1	29.7	0.808
4	V4	4	S1	29.1	0.755
3	V3	4	S1	31.7	0.738
6	V3	4	S1	28.4	0.726
4	V3	3	S1	26.2	0.723
6	V3	3	S1	28.1	0.721
7	V4	4	S2	52	0.720
4	V3	4	S1	28.2	0.718
6	V4	4	S2	25.7	0.716
4	V2	3	S1	27.1	0.714
5	V4	4	S1	30.7	0.701
3	V2	3	S1	30.8	0.700

All accelerations of 0.7 g occurred during the third or fourth run. This is consistent with other research, where driver experience has an impact on vehicle speed³⁷.

The highest lateral acceleration cy1000 measured during the entire test, 0.808 g, was at the small roundabout TRE6 (radius ≈ 10 m) with an empty vehicle V4 and sensor S1 at an average speed of 29.7 km/h during the last of four runs. This is a very high lateral acceleration, which is too sudden for most people³⁷.

The results presented in this section clearly demonstrate that vehicle loading has a substantial influence on the magnitude of lateral accelerations achieved during real-world turning maneuvers. The highest accelerations consistently occurred in the lighter vehicle configurations, particularly in the empty (V4) and lightly loaded (V3) scenarios, confirming that reduced mass allows the vehicle to reach higher dynamic responses on identical curves. The exceedances of design acceleration limits (0.5 g, 0.6 g, and 0.7 g) across all configurations further indicate that light delivery vehicles can subject cargo units to lateral loads significantly exceeding standard design assumptions, even at moderate speeds. Notably, the highest recorded acceleration of 0.808 g occurred on a small roundabout at speeds below 30 km/h, illustrating that relatively low-speed urban maneuvers can produce severe and long-duration lateral loading conditions. These trends underline the need for robust cargo-securing systems and support the relevance of using real vehicle tests to assess the stability of palletized units.

Influence of sensor position

In the case of maximum lateral acceleration, we found (see Table 4) that sensor S1 always achieved higher lateral acceleration than sensor S2 for individual TREs. This was likely due to vehicle angular vibrations. Sensor S1, mounted at a much greater distance from the body roll axis, recorded a signal augmented by the peripheral accelerations of a point located on the car roof. For sensor S2, such interference, if any, was significantly smaller. However, to examine the entire data sample, we used the non-parametric Kruskal-Wallis test to determine the effect of the sensor position on all measured values of lateral acceleration cy1000, as the data sample under investigation does not have a normal distribution, which was confirmed by the Kolmogorov-Smirnov test in Matlab (kstest).

Figure 6 compares lateral accelerations measured by S1 and S2 using box plots and Kruskal–Wallis test p-values. The distributions show systematically higher values for S1, confirming the expected amplification of accelerations detected at the roof due to body angular vibration. The statistically significant differences (p < 0.05) indicate that sensor position has a quantifiable effect on both peak and mean acceleration values. This underscores the need for careful sensor placement when interpreting lateral-dynamics data for cargo-securing applications.

Fig. 6.

Influence of sensor position for (left) and (right) for individual TREs.

Both tests had p<0.05, which shows significant differences between the sensors. One test was performed for the values from both sensors, and the second test was performed for the values of manual selection from all TREs for both sensors.

In most cases, sensor S2 measured lower values than sensor S1, because it didn’t detect the additional high peripheral accelerations resulting from angular vibrations of the vehicle body. This is consistent with the results of³⁵, where the authors found a 5% difference in average acceleration values and a 7.5% difference in maximum acceleration values between the values of the sensor located on the body and roof of a 2840 kg van, which is a vehicle similar to our tested vehicle V3. In our case, we obtained similar results from the data of all vehicles, where the average values of manual selection of TREs of sensor S2 were 5% to 6% lower than those of sensor S1 in 95% of cases.

In the case of the maximum measured lateral accelerations of individual TREs, the values for sensor S2 were 7% to 8% lower than sensor S1 in 95% of cases (see Figure 7).

Fig. 7.

Linear regression of and (left) and (right) of acceleration events from sensors S1 and S2.

Figure 7 provides linear regression analyses comparing minimum, maximum, and mean lateral accelerations recorded by the two sensors. The strong linear correlations demonstrate that although S1 produces consistently higher values, both sensors capture the same dynamic behavior.

A more detailed examination of the sensor placement reveals why the measured lateral accelerations differed systematically between S1 and S2. Sensor S1 was mounted on the vehicle roof, at a considerably greater height above the roll axis of the vehicle body. As the vehicle enters a curve, the suspension and tires deform, generating body roll. This roll motion produces additionally peripheral accelerations at locations farther from the roll axis. Because S1 is positioned at the top of the vehicle, the lateral acceleration it records is the vector sum of the translational acceleration of the vehicle and the rotational (peripheral) acceleration resulting from body angular vibration. Sensor S2, mounted on the body structure closer to the vehicle’s center of gravity, is exposed to much lower peripheral acceleration effects and therefore measures values more representative of the true lateral acceleration acting on the cargo area.

Influence of load weight for maximum and mean lateral acceleration

Lateral acceleration at a similar turning radius is significantly dependent on vehicle speed³⁹, as confirmed by Figure 8 which shows the relationship between mean vehicle speed and mean lateral acceleration for each TRE. The pattern confirms the expected physical dependency: higher mean speeds on comparable curvature sections produce higher mean lateral acceleration. Importantly, lighter vehicles (V3 and V4) operate at higher average speeds during repeated runs, partly due to driver adaptation and partly due to reduced inertia, which leads to higher mean lateral accelerations. This figure contextualizes how speed, load mass, and curve geometry jointly influence vehicle lateral dynamics.

We can say that the highest mean speed and the highest mean lateral acceleration from manual selection for all TREs comes from lighter vehicles V3 and V4, and especially V4, which is at least partially due to also Newton’s second law of motion. In Figure 9 we can observe the maximum lateral acceleration (left) and mean lateral acceleration (right) for vehicles V1 to V4 for sensors S1 (top) and S2 (bottom). Figure 9 summarizes maximum and mean lateral accelerations for all load scenarios and both sensors. The box plots clearly differentiate two behaviour groups: heavier vehicles (V1, V2) and lighter vehicles (V3, V4). Lighter variants exhibit higher peak values and larger variability, consistent with reduced stabilizing mass and higher attainable speeds. The broader spread of data for S1 again reflects its sensitivity to peripheral acceleration caused by angular vibration. This figure provides direct experimental evidence that load mass significantly affects lateral dynamics, supporting the study’s key conclusion.

Fig. 9.

Maximum lateral acceleration (left) and mean lateral acceleration (right) for vehicles V1 to V4 for sensors S1 (top) and S2 (bottom).

Based on Kruskal-Wallis at a 5% significance level, we can say that there is a statistically significant difference between vehicles V1 to V4, which is confirmed by the maximum measured values of from automatic and manual selection as well as the mean values of manual selection of the examined TREs and both sensors. In terms of the similarity of the recorded accelerations, we can divide the vehicles into two groups, namely V1, V2 and vehicles V3, V4. The lighter vehicles V3 and V4 achieved higher mean lateral accelerations than the heavier vehicles V1 and V2.

We can confirm that the mass of the load has an impact on the lateral acceleration achieved by a delivery vehicle. Fig. 9 also confirms the previous observations regarding the presence of significant angular vibrations of the vehicle body, which, as peripheral accelerations, could be detected to a much greater extent by the roof-mounted sensor than by the one located inside the vehicle. This is clearly visible in the box plot as the significantly larger range of values recorded by the S1 sensor compared to the S2 sensor. Furthermore, this range generally decreases with increasing vehicle load, which is clearly consistent with Newton’s second law of motion.

In research³⁹, the authors do not specify what vehicle was used to take the measurements, how this vehicle was loaded, where the sensor was located on the vehicle, or how the data was filtered. Furthermore, a small-scale test on a model may not be representative of actual loads and actual vehicles, whereas we have experience measuring friction coefficients for actual loads rather than low-weight model samples. This means that even though the authors mainly examined vertical accelerations, these are also dependent on the weight of the vehicle. Our measurements were carried out under real driving conditions.

During the measurements, we achieved comparable maximum lateral accelerations as in the research³⁸, where similar Renault Master vehicles weighing 3350 kg with a maximum lateral acceleration of 0.64 g and weighing 3330 kg with a maximum lateral acceleration of 0.53 g were used. Our similar V2 vehicle achieved a maximum lateral acceleration of 0.71 g for S1 and 0.64 g for S2.

Authors of research⁴⁰ used a similar Ford Transit vehicle weighing 3050 kg (with a total weight between our V2 and V3 vehicles) to perform a double lane test on a dry asphalt test surface and achieved maximum lateral acceleration values of 0.512 g, without reaching the design acceleration 0.6 g for securing cargo for such a vehicle. We achieved accelerations above 0.6 g with both the lighter V3 vehicle and the heavier V2 vehicle, with the V2 vehicle and S2 sensor achieving a maximum lateral acceleration of 0.64 g, which represents a difference of 25% compared to this research.

With all tested vehicles, we achieved the design acceleration for securing cargo and transport stability of palletized units.

The authors of⁴¹ measured maximum lateral accelerations of 0.4 to 0.5 g for heavier vehicles; however, they do not specify the gross mass of the truck and trailer, which is significantly larger than that of our test vehicles. Additionally, they employed different sensors and data evaluation methods but we can approximately compare the results and state that heavier vehicles generally experience lower lateral accelerations than lighter ones⁴².

Manual and automatic selection of events

The following linear regression shown in Figure 10 illustrates the dependence between the median of automatic selection from time window and the mean of manual selection from time window of individual TREs (see Figure 4). Figure 10 shows a tight linear relationship between manually derived mean accelerations and automatically obtained medians. The proximity of the regression line to the identity line confirms that median values from automatic selection provide a reliable estimate of manually analysed events. The small, consistent offset quantifies the methodological difference and supports using automatic selection for large data sets without loss of fidelity.

Fig. 10.

Relationship between the median of automatic selection in time window and the mean of the manual selection in time window of TREs for sensor S1 and all tested vehicles.

We can say that the median of automatic selection is very similar to the mean of manual selection, where the mean of manual selection being 2.2 to 3.5% higher than the median of automatic selection in 95% of cases based on the measured data for sensor S1 and all tested vehicles. Median of automatic selection can be used to estimate mean lateral acceleration of certain type of TRE’s as small roundabouts.

These findings demonstrate important practical implications for the evaluation of lateral acceleration data. First, the strong linear relationship between the manual and automatic methods confirms that automatic event selection provides a reliable and objective alternative for analyzing large datasets, while still capturing the essential characteristics of each turning event. This is particularly valuable in studies involving thousands of acceleration samples, where manual annotation would be prohibitively time-consuming and susceptible to subjective bias. Second, the small differences observed between the manual mean values and the automatic medians (typically 2.2–3.5%) indicate that both methods are sensitive to the same dominant acceleration phenomena, meaning that the automated procedure does not lose critical information. Third, the fact that both methods yielded identical maximum values for each event shows that the automatic method is robust enough to detect peak loads—which are most relevant for cargo securing and pallet stability assessments.

Overall, the close correspondence between methods suggests that manual selection may be reserved only for validation or special cases, while automatic identification can reliably serve as the primary tool for comprehensive lateral acceleration analysis. This also implies that future studies could adopt automated selection to achieve repeatability and consistency, especially when comparing different vehicle load states, sensor positions, or test routes. Such consistency strengthens the interpretability of the results and enhances the applicability of real-vehicle measurements in replacing laboratory-based acceleration platforms.

Analytical assessment of vehicle rollover resistance using a simplified method

A simplified model (Fig. 11) can be used to determine the maximum height of a vehicle’s mass centre above the ground at which there is a risk of rollover under given road conditions. This model shows the system of forces acting on a vehicle while traveling along a curve without inclination under steady-state conditions. Tire and suspension deformations, as well as the resulting body roll under the influence of force "Y" were neglected. The influence of this roll on the calculated values was assumed to be small. The vehicle’s centre of mass was assumed to lie on its longitudinal plane of symmetry.

Fig. 11.

Simplified diagram of the forces acting on the vehicle when moving along a curve (left turn).

Legend:

Z_L – sum of the normal reactions of the left wheels of the vehicle;

Z_R – sum of the normal reactions of the right wheels of the vehicle;

b – wheel track;

Y_L – sum of the lateral forces of the left wheels of the vehicle;

Y_R – sum of the lateral forces of the right wheels of the vehicle;

GC – vehicle gravity center;

m – vehicle mass;

g – gravity acceleration;

Y – lateral force;

h_GC – height of gravity center of vehicle.

The sum of forces moments acting on the vehicle, calculated with respect to point "A", is:

9

The phenomenon of a vehicle rolling over under the influence of force "Y" is signaled by the value of force Z_L approaching zero on the inner wheels relative to the center of the road curve (in a similar situation, when turning right, Z_R → 0 appears). When the vehicle begins to rollover, its entire weight rests on the outer wheels. It can then be written that:

10

Replacing "Y" with the formula for centrifugal force, we get:

11

where:

v – vehicle speed;

R – radius of the road curve;

a_L – lateral acceleration.

The maximum height of vehicle gravity centre above the ground as a function of the maximum relative lateral acceleration is therefore described by the following relationship:

12

where:

a_LRmax – maximum relative lateral acceleration;

µ – traction coefficient.

For the considered Fiat Ducato vehicle with a wheel track of b = 1.79 m, this relationship is graphically presented in Fig. 12. The realistic range of variation for both quantities was considered here. As expected, the characteristic is nonlinear. Initially, as the turn intensity increases, the maximum values of the vehicle’s gravity centre height (due to the risk of rollover) decrease quite rapidly. At higher lateral vehicle accelerations, the changes in the analysed parameter are smaller. It can be assumed that on surfaces with moderate traction coefficient values (up to about 0.5 – wet tarmac), the risk of vehicle rollover does not occur, and this is true for all realistic vehicle load cases. Even with very good wheel-to-ground contact properties (e.g., for dry tarmac and a traction coefficient of about 0.8), the risk of vehicle rollover is not significant. Under steady-state driving conditions, such an event can occur if the vehicle’s gravity centre is at a height of 1.12 m or greater.

Fig. 12.

Maximum heights of gravity centre of the Fiat Ducato car as a function of the maximum relative lateral acceleration.

The problem of static stability for delivery vehicles can also be presented somewhat differently. A common question is what the maximum height of uniform load units of known mass can be to, at least theoretically, prevent the vehicle rollover on a curve under steady-state conditions, with high turning intensity.

To answer this question, it should be assumed that, in the unfavourable scenario, the parameters of light D-segment delivery vehicles may be as follows:

• unladen vehicle weight (including driver), m_VL = 1750 kg;

• vehicle payload (after subtracting the driver’s weight), m_Lmax = 1750 kg;

• height of the vehicle’s gravity center (including driver), h_{GC_0} = 0.9 m;

• vehicle track, b = 1.8 m;

• load platform height, H_LP = 0.67 m.

With such assumptions, the maximum height of the gravity center of pallet load units (homogeneous) depending on their mass can be determined by transforming the following relationship:

13

14

where: h_L – height of the load units gravity center above the ground (road).

To calculate the maximum stacking height of a pallet with a standard height of H_EP = 0.144 m, the following formula can be used:

15

By performing calculations for high turning intensities (a_LRmax = 0.8g and a_LRmax = 0.7g), e.g. on a dry tarmac surface with a traction coefficient µ = 0.8 and µ = 0.7 and previously assumed typical parameters of light D-segment delivery vehicles, the curves were obtained as in Fig. 13. For comparison, the results for the Fiat Ducato vehicle are also presented here, with a_LRmax = 0.8g.

Fig. 13.

Maximum stacking heights of loads on pallets as a function of the total weight of these load units transported by delivery vehicles.

The curves in Fig. 13 are generally non-linear and qualitatively similar to those in Fig. 12. However, the results ​​obtained in this case are easier to apply to various delivery vehicles. Quantitatively analysing the worst-case scenario considered here (chart for light D-segment delivery vehicles with a_LRmax = 0.8g), it is easy to conclude that bulky loads with a total weight of up to 500 kg can be stacked on pallets up to a height of approximately 2.2 m, fully utilizing the cargo space height. For loads with a total weight of approximately 1,000 kg, their height should not exceed 1.41 m. When transporting goods with a total weight of 1,500 kg in such vehicles, the stacking height of cargo units should be limited to approximately 1.15 m. An even slightly lower value (H_Lmax = 1.07 m) will be required when using the full vehicle capacity (assumed here 1,750 kg). Due to its higher netto weight (m_VL = 2420 kg), the Fiat Ducato can carry cargo units approximately 25% higher for the same weight. The situation is even better if the vehicle’s maximum lateral acceleration is limited, even slightly (e.g., a_LRmax = 0.7g). Even relatively light D-segment delivery vehicles can then carry heavy loads weighing, for example, 1750 kg, stacking them to a height of approximately 1.7 m, completely using the cargo space.

At this point, it should be noted once again that the analytical method presented here is very simplified and applies to vehicle movement under steady conditions, on a road without inclination. It does not take into account the susceptibility of the suspension and tires, and, as a result, also the roll of the body and the lateral displacement of the body gravity center relative to the wheels.

In real road conditions, however, there are numerous disturbances in vehicle movement that result in various types of vibrations. In this case, the most important are angular vibrations, which cause rapid changes in the vehicle’s roll. These can be caused by both steering wheel excitations and road irregularities – different for the left and right wheels. Ignoring this type of phenomenon results in theoretical results that are more optimistic than those obtained under experimental conditions.

Conclusions

The Table 7 consolidates the primary measured outcomes and analytical findings, highlighting the quantitative relationships between load mass, sensor placement, vehicle dynamics, and rollover risk. These results provide a structured basis for understanding the operational limits of light delivery vehicles and the implications for cargo securing and pallet stability.

Table 7.

Selected parameters influencing operational limits of light delivery vehicles.

Parameter	Quantified finding	Interpretation
Maximum lateral acceleration measured	Up to 0.808 g (V4, S1)	Light delivery vehicles can experience very high lateral acceleration even at moderate speeds, exceeding assumptions commonly used in cargo-securing design.
Exceedance of design thresholds (0.5 g / 0.6 g / 0.7 g)	All vehicles exceeded 0.5 g and 0.6 g; V2–V4 exceeded 0.7 g multiple times	Standard design accelerations (VDI 2700 / EN 12195-1) can be surpassed under real driving, indicating requirements for stronger cargo-securing methods and package stability.
Influence of load mass (V1–V4)	Lighter vehicles (V3, V4) produced 10–25% higher maximum lateral accelerations than heavier vehicles (V1, V2)	Reduced mass decreases inertia, greater sensitivity to curvature, higher lateral acceleration acting on cargo.
Sensor position effect (roof S1 vs. body S2)	S2 measured 5–6% lower mean and 7–8% lower maximum accelerations in 95% of events	Roof-mounted sensors capture additional peripheral accelerations from body angular vibrations; cargo-area sensors provide more realistic values for load stability analysis.
Event identification methods	Manual mean values were only 2.2–3.5% higher than automatic medians; peaks identical	Automatic selection is sufficiently accurate for large datasets and replicable across scenarios. Manual selection is mainly needed for validation.
Highest accelerations by TRE type	Speeds of only 26–32 km/h on small roundabouts produced 0.70 – 0.81 g	Even low-speed urban maneuvers can impose severe lateral loads on palletized cargo.
Rollover analytical limit	Rollover risk becomes critical at hGC ≥ 1.12 m for µ ≈ 0.8	Safe testing of high-COG pallet units requires ensuring the combined COG height of vehicle + load does not exceed this threshold.
Maximum pallet stacking height (analytical)	For typical distribution van, allowable pallet unit height decreases from 2.2 m (500 kg load) to ~1.15 m (1500 kg load)	Heavier loads require substantially lower stacking heights to maintain rollover stability.

This study makes a novel contribution by experimentally demonstrating how transported load mass influences the lateral acceleration of a light delivery vehicle under controlled, repeatable real-road conditions. By using a single vehicle, identical route, constant driver, and systematically varied gross vehicle masses, the research isolates the effect of load mass more effectively than previous studies.

The main research question was to study the impact of transported load mass on the lateral acceleration of light delivery vehicle for cargo securing and transport stability of load units. Extensive experimental measurements were performed in real vehicle test runs with four different vehicle gross mass. Based on this research, we can say that the mass of the load has a significant impact on the lateral acceleration of a delivery vehicle up to 3.5 tons. The lighter the vehicle, the higher the average and maximum lateral acceleration. Therefore, lighter unit loads are on average exposed to higher lateral acceleration than heavier unit loads. During testing, we exceeded the design lateral acceleration of 0.5 g, 0.6 g, and 0.7 g with all tested vehicles, where 0.7 g is specified for vehicles with a . However, we also achieved this acceleration in V2, V3, and V4 vehicles with .

During testing, pallet units with a low center of gravity were used to achieve high lateral acceleration. When testing other pallet units with a higher center of gravity, it is necessary to know the limiting acceleration for vehicle rollover, as pallet units with a high center of gravity pose a risk of vehicle rollover. Therefore, among other things, simplified analytical calculations were performed here for the maximum values of the vehicle’s gravity center height, at which, at least theoretically, it will not rollover on a curve under steady-state conditions with high turning intensities. A similar method was also used to determine the maximum heights of homogeneous pallet units, depending on their total mass, to ensure stable movement of typical delivery vehicles. Further research is needed to determine the safe weight and height limits for testing the stability of pallet units with a high center of gravity using light delivery vehicles, considering vehicle roll angle. Such testing is significantly cheaper than using various acceleration platforms because light delivery vehicles are broadly available and simulate real transport conditions. Authors of [44] states that the long duration events poses challenges for laboratory space and equipment, making it impractical to replicate long time events while preserving the necessary speed and acceleration.

Future work should expand the experimental design in several directions as different load distributions, load units with higher centers of gravity to refine safe weight and height limits for palletized cargo. Additional vehicles of different weight classes and suspension characteristics should be evaluated to generalize the findings. The integration of vehicle lateral tilt, road cant, and transient maneuvers would allow the development of more advanced models linking real road dynamics to cargo stability requirements.

Author contributions

ConceptualisationConceptualization, J.J. and J.K..; editing of the manuscript, J.J and J.K., realisation, J.J., J.K. and P.Z.; introduction J.J.., J.K., P.Z. and S.T.; literature review, J.K, ; materials and methods, J.J., P.Z.; data curation, J.J., P.Z..; results, J.J. and P.Z.; writing-original draft, J.J., J.K.,P.Z. and S.T.; visualization, J.J., J.K.,P.Z. and S.T.; final revision, J.J., J.K., P.Z., S.T.. All authors have read and agreed to the published version of the manuscript.

Data availability

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author upon reasonable request.

Declarations

Competing interest

The authors declare no competing interests.