Analysis of Vibration Comfort and Vibration Energy Distribution in the Child Restraint System-Base Configuration

Abstract

This study presents the results of an experimental evaluation of ride comfort for children transported in child restraint systems (CRS) during passages over speed bumps, with particular emphasis on the energy contained in vibrations. The tests were carried out under real operating conditions using two vehicles with different suspension characteristics and three loading levels corresponding to different stages of child development. Vertical accelerations were recorded at key points of the vehicle–seat system and subsequently analyzed in accordance with ISO 2631-1. Based on the vibration signals, root mean square acceleration (RMS), vibration dose value (VDV), seat effective amplitude transmissibility (SEAT), and root mean quad (RMQ) indices were calculated, enabling not only the assessment of discomfort levels but also the estimation of mechanical energy transmitted through the seat structure. The results showed that, depending on the type of vehicle, bump geometry, and load mass, the vibration energy can be significant and, in many cases, corresponds to levels classified as “severe” or “extreme discomfort.” At the same time, this energy constitutes a potential power source for low-power sensors in “smart seat” systems, such as those monitoring the child’s posture or environmental conditions. The findings highlight the need to consider vibration comfort criteria and the potential for vibration energy harvesting in the design and homologation of CRS, which aligns with the concept of sustainable transport and the development of energy self-sufficient technologies.

1. Introduction

Child safety in automotive transport has long been a matter of particular concern for both legislators and engineers involved in the design of passenger protection systems. The use of child restraint systems (CRS) significantly reduces the risk of injury and fatality in the event of a collision. Research shows that a properly used CRS can reduce the risk of injury by as much as 71–82% compared to a seatbelt alone [1]. For this reason, in most countries, including across the European Union, the use of CRS is mandatory [2].

The primary objective of a child seat is to protect the child during a crash, by distributing forces appropriately and keeping the body in a safe position [2,3]. However, selecting the right model is not straightforward, as the market offers a wide range of designs and attachment systems [2]. In Europe, child seat homologation is based on UN ECE regulations: the older ECE R44/04, which classifies seats by child mass (Group 0: up to 10 kg, 0+: up to 13 kg, I: 9–18 kg, II: 15–25 kg, III: 22–36 kg) [2], and the newer ECE R129 (i-Size), in force since 2013 [4]. Regulation R129 introduced, among others, height-based classification instead of mass, mandatory side-impact testing, the use of advanced Q-series dummies, and the requirement for ISOFIX anchorage, which reduces the risk of incorrect installation. In addition, children must travel rear-facing until at least 15 months of age [4]. Currently, both regulations function in parallel, although R44/04 is being gradually phased out [5].

The homologation process includes mandatory dynamic tests: a frontal crash at 50 km/h, a rear impact at lower speed, and, in R129, an additional side-impact test [5]. These are conducted on test sleds using standardized dummies and acceleration pulses to evaluate biomechanical parameters of the child’s head, chest, and neck. The acceptance criteria are based exclusively on crash safety performance.

In addition to regulatory tests, consumer organizations such as ADAC (Allgemeiner Deutscher Automobil-Club) conduct their own CRS assessments. Unlike regulatory testing, ADAC applies more stringent crash scenarios, e.g., frontal impact at ~64 km/h and side impact at 50 km/h, performed on an actual vehicle body (e.g., VW Golf). Moreover, advanced Q-series dummies with multiple sensors are used, providing more detailed data. Importantly, ADAC’s assessment also includes aspects such as usability, ergonomics, comfort, and the presence of harmful substances in materials. The final weighted score is distributed as follows: crash safety (50%), handling and installation (40%), ergonomics and comfort (10%) [6]. In practice, ergonomics refers to child positioning, space, and ease of adjustment, but does not include objective vibration comfort evaluation.

Vibration comfort remains an element neglected in both homologation procedures and consumer tests [7,8]. While ISO 2631-1 and BS 6841 [9,10] define permissible levels of whole-body vibration (WBV) for adult vehicle users, no comparable regulations exist for children [11,12]. Yet, children’s physiology differs significantly from that of adults, as they have proportionally larger heads, more flexible spines, and musculoskeletal systems still in development [12]. As a result, they may be more susceptible to the adverse effects of vibrations, such as discomfort, fatigue, or sleep disturbances [12,13].

Scientific studies indicate that CRS transmit vibrations differently compared to vehicle seats. Giacomin (2000) demonstrated that vibration levels measured between the child and the CRS were higher than those measured between the driver and the vehicle seat [14]. Similar conclusions were drawn by Giacomin and Gallo (2003) [15] and by Wicher and Więckowski (2010) [16], who found that vibrations at the CRS can exceed those measured on the vehicle body. Comparable results were also reported in [16,17,18,19].

In the study by Frej et al. (2022) [1], accelerations were recorded during passage over speed bumps. Maximum vertical accelerations on infant seats (Group 0+) reached about 5 m/s² at 30 km/h, corresponding to vibration levels considered seriously uncomfortable under ISO standards for adults. Interestingly, the highest values were recorded at the ISOFIX base, over 6 m/s². This suggests that rigid ISOFIX anchorage, although safer in crashes, transmits more vibrations than belt installation [17,18].

Prolonged exposure of children to WBV may have negative consequences. In adults, known effects include fatigue, back pain, and balance disorders [9,20,21]. In infants, additional effects such as sleep disturbances or restlessness during travel have been observed. Research suggests that breaks should be taken during long journeys to reduce exposure time [9,22].

The literature increasingly advocates incorporating vibration comfort assessment into CRS testing procedures [1,16,18]. Proposed methods use standard vibration evaluation indices such as RMS (Root Mean Square), VDV (Vibration Dose Value), SEAT (Seat Effective Amplitude Transmissibility), and RMQ (Root Mean Quad) [1,2,3]. Some studies employ laboratory test rigs with road simulators, while others rely on in-vehicle measurements [23,24]. However, no official guidelines or requirements currently exist.

It is worth noting that the mechanical energy contained in vibrations during vehicle operation can be effectively converted into electrical energy using modern technologies such as piezoelectric, triboelectric, or electrodynamic harvesters. While such solutions are already being investigated for suspensions and vehicle seats, they could also be applied to CRS. In practice, this would allow powering sensors that monitor a child’s travel conditions, such as temperature, humidity, posture, or even alert systems for improper belt fastening. This would transform the CRS into a “smart seat,” energetically autonomous, without the need for additional batteries or wiring. Thus, vibration energy harvesting in CRS could improve safety, enhance functionality, and reduce operating costs by providing self-sufficient power for electronic systems.

It should be emphasized, however, that vibrations carrying significant energy, potentially useful for harvesting, are simultaneously harmful to the child’s body, especially under long-term exposure. Research shows that chronic WBV exposure may reduce travel comfort, disturb sleep, increase fatigue, and, in the longer term, contribute to musculoskeletal and postural problems in children. For this reason, manufacturers should focus primarily on effective vibration damping and on designing structures that isolate young passengers from adverse vibrations. Current homologation standards focus exclusively on crash tests, neglecting vibration comfort. There is a clear need to develop a new CRS testing standard in which comfort and vibration exposure are assessed alongside traditional crashworthiness evaluations. Such an approach would enable the design of child seats that are not only crash-safe but also comfortable and health-conscious in everyday use.

The aim of this study is to address this research gap by experimentally evaluating the vibration comfort of CRS under real driving conditions. The investigation covers the most popular CRS models of 2023 in Groups 0, 0+, and I, installed in passenger cars Audi A6 and Citroën C5. The seats were loaded with masses corresponding to children at different developmental stages. Measurements were conducted during passages over speed bumps, typical infrastructure elements affecting ride comfort and safety. RMS, VDV, SEAT, and RMQ values were analyzed to compare the vibration attenuation effectiveness of CRS relative to vehicle seats.

The conducted study holds significant scientific and practical value. It provides objective data that can form the basis for developing new homologation standards incorporating children’s vibration comfort. The results may be utilized by CRS manufacturers to improve vibration isolation design, as well as by consumer organizations and standardization bodies in creating guidelines on safety and comfort for young passengers. Vehicle designers and engineers working on vibration energy harvesting technologies may also benefit from the findings to advance solutions in sustainable transport and smart protection systems. In a broader perspective, this research contributes to enhancing the quality of children’s travel by raising standards of safety, ergonomics, and health in road transport.

The structure of this article has been designed to present the findings and conclusions clearly. Section 2 details the research methodology, including vehicle characteristics, CRS models, measurement procedures, and applied vibration comfort indices. Section 3 presents the measurement results along with comparative analysis, while Section 4 discusses the outcomes in a broader literature and practical context. The final section provides conclusions, summarizing the key observations and highlighting potential directions for further research.

2. Materials and Methods

The level of vibration comfort was assessed based on measurements carried out under real vehicle operating conditions. This chapter provides a detailed description of the adopted research methodology, including the characteristics of the vehicles and the test track, the types and configurations of child restraint systems, the measuring equipment and sensor layout, the procedure for passing over speed bumps, as well as the data processing approach and methods of statistical analysis. In addition, the research objectives and problems are presented, and the limitations resulting from the chosen methodology are discussed.

2.1. Vehicles and Test Track

Two mid-size passenger cars (Figure 1) with different running gear designs and suspension characteristics were used in the study:

• Audi A6 (model year 2012)—a premium-class sedan with front-wheel drive and independent multi-link suspension on both the front and rear axles. This suspension is characterized by stiffness and precise wheel guidance, which favors driving stability but provides less effective damping of road irregularities. The vehicle was fitted with standard 225/55 R17 tires, maintained at the manufacturer-recommended pressure.
• Citroën C5 (model year 2005)—an upper mid-size liftback equipped with the brand-specific Hydractive hydropneumatic suspension system. This system allows automatic adjustment of suspension stiffness and ground clearance depending on driving conditions, providing high vibration damping comfort. The vehicle was fitted with 215/60 R16 tires, maintained at the manufacturer-recommended pressure.

The choice of two different suspension designs (stiff multi-link suspension in the Audi and soft hydropneumatic suspension in the Citroën) was intended to investigate whether the vehicle’s vibration damping properties significantly affect the vibration comfort level of a child in a CRS.

The experiment was conducted on a closed 80 m section of a concrete test track at Kielce University of Technology, in good technical condition and free of additional irregularities. Tests were carried out on a dry surface, at ambient temperatures of 18–22 °C, and without crosswind effects. Two types of speed bumps typical of urban infrastructure were installed on the test track:

• PZL-40—a plate-type bump with a width of 40 cm and a height of 5 cm, with a gentle ramp,
• PP-30 (launch-type bump)—a point element with a width of 30 cm and a height of 3 cm, characterized by steep edges that generate a noticeable lift of the vehicle body at higher speeds.

Each bump was traversed at two predetermined speeds: 20 km/h (typical for residential zones) and 30 km/h (the upper range of typical urban speeds). The vehicle driver maintained the passage speed over the bump based on the vehicle’s speedometer readings. The scheme of the experimental procedure is shown in Figure 2.

Five child restraint systems (CRS) were used in the study. The first was the Avionaut AeroFIX Smart (Avionaut, Szarlejka, Poland), an i-Size compliant seat designed for children with a height of 61–105 cm and a maximum body mass of 18.5 kg. The seat itself weighs approximately 8 kg. Its design allows the child to be transported both rear-facing and forward-facing. The external dimensions are about 72–74 cm in length, 43–49 cm in width, and 53–68 cm in height, depending on the headrest position and side-protection elements (Figure 3).

The second model was the Britax Römer Dualfix Plus (Britax Römer, Leipheim, Germany), which features a full 360° rotation mechanism that facilitates everyday use. The seat is intended for children from birth until a height of 105 cm and a weight of about 20 kg. The unit weighs approximately 12.5–14 kg, and its external dimensions are around 55 cm in height, 44 cm in width, and 74 cm in depth. Depending on the headrest position and backrest setting, the seat height may increase up to 73 cm (Figure 4).

The third model was the Maxi-Cosi Mica Pro Eco i-Size (Maxi-Cosi, Helmond, The Netherlands), designed for children between 40 and 105 cm in height and up to 18 kg in body mass. The seat weighs about 14.9 kg and is equipped with a 360° rotation mechanism. The external dimensions range from 64 to 74 cm in depth, 44 cm in width, and 80–88 cm in height. A distinctive feature of this model is the use of materials made entirely from recycled sources, which sets it apart from competing products (Figure 5).

The fourth seat was the Cybex Gold Sirona S i-Size (Cybex, Kulmbach, Germany), designed for children from 45 to 105 cm in height and with a maximum mass of 18 kg. The unit’s own weight is approximately 14–15 kg. It features a 360° rotation mechanism, a Driving Direction Control system, and L.S.P. (Linear Side-Impact Protection). The average dimensions are 64 cm in height, 43 cm in width, and 70 cm in depth, though they vary depending on installation method and backrest angle (Figure 6).

The fifth and final model was the Joie i-Spin 360 (Joie, Athens, Greece), intended for children between 40 and 105 cm in height and up to 19 kg in body mass. The seat weighs about 13.9 kg and allows full rotation, improving user ergonomics. In rear-facing installation, its external dimensions are about 65 cm in length, 58 cm in width, and 51.5–62 cm in height, while in forward-facing configuration the height increases to 62–76 cm. This model is equipped with an adjustable headrest and multiple recline positions, enabling adaptation to the age and needs of the child (Figure 7).

All child restraint systems were installed in the rear-facing position, in accordance with the manufacturers’ recommendations. Every child under the age of four should be transported rear-facing.

The selected child masses of 3.5 kg, 9.5 kg, and 14.5 kg correspond to representative stages of child growth and were chosen based on pediatric percentile charts. A mass of 3.5 kg reflects a typical newborn (close to the 50th percentile at birth), 9.5 kg represents the transition between infant and toddler stages (approximate 50th percentile around 12 months), and 14.5 kg corresponds to a preschool-aged child (approximate 50th percentile around 3 years). These values are also consistent with the mass thresholds used in CRS homologation standards (UNECE R44/04 groups 0+ and I, and UNECE R129 [20,25]), ensuring that the test conditions reflect real-world loading scenarios.

2.2. Research Aim and Problems

The main objective of this study was the experimental evaluation of vibration comfort for children transported in child restraint systems under real vehicle operating conditions. The research focused on analyzing mechanical vibrations generated during passage over two typical types of speed bumps: the plate-type PZL-40 and the launch-type PP-30, in order to assess how the energy of these vibrations is transmitted through the seat structure to the child.

The specific objectives included:

• comparing the vibration levels recorded in the child seat and in the vehicle components,
• evaluating the influence of child mass (3.5, 9.5, 14.5 kg) on vibration comfort,
• identifying structural differences between the child seats,
• investigating the effect of vehicle type and speed bump design on the level of vibrations acting on the child,
• formulating design recommendations for vibration damping and energy isolation in child seats.

Based on these objectives, the main research questions were formulated:

• Do child restraint systems effectively attenuate vibration energy, or do they amplify its transmission compared to vehicle seats?
• How does the method of seat installation (ISOFIX vs. seatbelt) affect the level of vibration comfort?
• Does child mass (test load) alter the vibration characteristics and isolation effectiveness of the seat?
• Are there significant differences between CRS of different weight groups in terms of vibration damping?
• To what extent do vehicle type and speed bump design influence the level of vibration discomfort?
• Should a new CRS testing standard be introduced, incorporating vibration comfort measurements alongside traditional crash tests?

2.3. Instrumentation and Measurement Setup

Five triaxial piezoelectric accelerometers with a sensitivity of 100 mV/g were used to record vibrations. They enabled the measurement of accelerations along the X (longitudinal), Y (lateral), and Z (vertical) axes. The sensors were positioned at key points of the vehicle–child seat system (Figure 3):

• On the seat surface of the child restraint system—in the central location, at the contact zone between the dummy and the seat surface. This point reflected the direct impact of vibrations on the child’s body.
• Under the seat of the CRS, on the ISOFIX base—this location made it possible to assess the vibrations transmitted from the vehicle seat to the child seat structure.
• On the ISOFIX support leg—the sensor was mounted at the lower end of the support leg, which transfers the load of the base to the vehicle floor. This measurement indicated the extent to which vibration energy was transmitted through this structural element.
• On the vehicle floor—in the vicinity of the support leg’s contact point with the floor, serving as a reference point and representing the vibrations generated by the vehicle body.
• On the surface of the rear passenger seat.

Signal acquisition was performed using a mobile LMS SCADAS SCR02 recorder (EC Test Systems, Kraków, Poland) in combination with LMS Test.Lab software (Siemens PLM Software, version 18.1). The acquisition signals were sampled at a frequency of 256 Hz, which ensured sufficient resolution within the vibration range typical of speed bump passages (0–80 Hz). Data were recorded simultaneously from all five sensors, and time synchronization allowed for direct comparison of acceleration amplitudes at the different measurement points.

All sensors were fixed with double-sided adhesive tape and additional mechanical clamps to eliminate the risk of displacement during the tests. Signal cables were routed along the child seat structure and the vehicle body in a manner that minimized the possibility of damage.

Each test configuration (seat type, load mass, speed bump type, driving speed, and vehicle) was repeated 10 times. The acceleration signals recorded during the passages were then averaged to ensure high repeatability and to eliminate deviations caused by random factors. The scheme of the sensor placement is presented in Figure 8.

2.4. Test Procedure

The experiment was carried out according to a research plan that included various configurations of vehicles, child seats, load masses, speed bump types, and driving speeds. The analysis was comparative in nature and made it possible to assess the extent to which the design of child restraint systems influences the isolation of mechanical vibrations transmitted from the road surface through the vehicle to the child’s body.

Two passenger cars were used in the study: Audi A6 and Citroën C5. In each vehicle, five child seats representing weight groups 0+ and I according to ECE R44/04 were installed. The seats were mounted using both the ISOFIX system and seatbelts in order to account for differences resulting from the installation method. To simulate loading, dummies with masses of 3.5 kg, 9.5 kg, and 14.5 kg were used, corresponding to children of different ages and developmental stages.

The trials were conducted on a closed section of a concrete test area equipped with two types of speed bumps: PZL-40, a plate-type bump with a width of 40 cm and a height of 5 cm, and PP-30, a so-called launch-type bump with a width of 30 cm and a height of 3 cm. Each bump was traversed at constant speeds of 20 km/h and 30 km/h. The driver maintained a steady speed before, during, and immediately after crossing the bump in order to ensure comparable measurement conditions across all test series.

Each configuration was tested in a series of ten runs, which provided a representative statistical sample and eliminated the influence of random factors. The signals recorded from the five accelerometers were then subjected to numerical processing. First, a low-pass filter (80 Hz) was applied to remove high-frequency disturbances unrelated to the passage over the bumps. Next, mean values were calculated for each measurement series.

Thanks to the repeatability of the tests, it was possible to compare results between different vehicles, child seats, load masses, installation methods, and bump types. The collected data formed the basis for further analysis of vibration comfort using RMS, VDV, SEAT, and RMQ indicators.

2.5. Data Processing and Vibration Metrics

The recorded acceleration signals were subjected to numerical processing in order to prepare them for further analysis. First, a low-pass filter with a cutoff frequency of 80 Hz was applied to eliminate high-frequency disturbances unrelated to the passage over speed bumps. Next, the data were averaged for each series of ten runs, which improved repeatability and reduced the influence of random deviations. Vibration comfort assessment was carried out in accordance with ISO 2631-1 [9], which provides the basis for evaluating human exposure to whole-body vibrations. Four indicators were calculated in the study: RMS, VDV, SEAT, and RMQ.

The fundamental parameter characterizing the vibrations was the root mean square acceleration (RMS), defined by Equation (1):

$$a_{RMS}=\sqrt{{\displaystyle \frac{1}{T}}{\int }_0^T{\left[a\left(t\right)\right]}^{2}dt}$$

(1)

where:

• a(t)—instantaneous acceleration along the Z-axis [m/s²],
• T—measurement duration [s],
• $a_{RMS}$—root mean square value of acceleration [m/s²].

The RMS index makes it possible to determine the average vibration level during passage over a speed bump. The second indicator was the Vibration Dose Value (VDV), which reflects short-term high acceleration peaks more effectively than RMS (2):

$$VDV={({\int }_0^T{\left[a\left(t\right)\right]}^{4}dt)}^{{\displaystyle \frac{1}{4}}}$$

(2)

where:

• a(t)—instantaneous acceleration along the Z-axis [m/s²],
• T—measurement duration [s],
• VDV—vibration dose value [m/s^1.75].

High VDV indicate the presence of sudden and potentially uncomfortable vibrations. To evaluate the isolation properties of child restraint systems, the SEAT factor was applied. It is defined as the ratio of the VDV of accelerations measured on the child seat surface to the value measured on the vehicle floor (3):

$$SEAT={\displaystyle \frac{{VDV}_{SEAT}}{VDV floor}}$$

(3)

where:

• $VDV$ SEAT—RMS value of accelerations on the child seat surface [m/s²],
• VDV floor—RMS value of accelerations on the vehicle floor [m/s²],
• SEAT—vibration transmissibility factor.

A SEAT value lower than 1 indicates effective vibration isolation, whereas a value greater than 1 indicates vibration amplification [26,27]. A SEAT value lower than 1 indicates effective vibration isolation, whereas a value greater than 1 indicates vibration amplification [26,27]. In this study, it was assumed that the SEAT index for the rear seat would be analyzed based on the signals from sensors placed on the seat cushion and on the vehicle floor. For the child restraint system, the SEAT index was calculated using the signals from sensors placed on the surface of the child seat and on the ISOFIX base, directly beneath the child seat cushion, at the point where the seat is attached to the base. This approach makes it possible to determine the extent to which vibrations are attenuated by the base–child seat system. The final indicator was the Root Mean Quad (RMQ) index, which provides a synthetic description of vibration comfort by incorporating frequency weighting in accordance with ISO 2631-1 (4):

$$RMQ={({\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{x}_i^4)}^{{\displaystyle \frac{1}{4}}}$$

(4)

where:

• x_i—the i-th sample of the frequency-weighted vibration acceleration signal [m/s²],
• N—the number of samples in the analyzed signal,
• RMQ—Root Mean Quad index [m/s²].

Similarly to VDV, RMQ is more sensitive to peak values than RMS because it is based on the fourth power of the signal. In practice, it provides a better description of perceived vibration discomfort in situations where short-term, sudden acceleration peaks occur, such as when passing over a PP-30 launch-type speed bump.

All the described indicators were calculated in the vertical direction (Z-axis), which is crucial when analyzing the effects of speed bumps on passengers. The obtained values formed the basis for further comparative analysis between different vehicles, child restraint systems, load masses, and installation methods, and their interpretation made it possible to determine vibration comfort and the effectiveness of vibration isolation.

In the interpretation of the RMS results, the criteria for vibration discomfort assessment presented in

Table 1. Scale for assessing the level of vibration discomfort as a function of RMS accelerations according to ISO 2631-1 (1997) [26].

Acceleration [m/s2]	Discomfort Scale
Less than 0.315	There is no feeling of discomfort
0.315–0.63	Slight discomfort
0.5–1.0	Moderate discomfort
0.8–1.6	Discomfort
1.25–2.5	Severe discomfort
Above 2	Extreme discomfort

.

To avoid overlapping intervals, the rule was adopted that boundary values are assigned to the higher level of discomfort. This means that, for example, a value of 0.315 m/s² is already classified as “slight discomfort,” and a value of 0.63 m/s² as “moderate discomfort.” Similarly, a value of 1.0 m/s² was assigned to the “discomfort” category, and 1.25 m/s² to “severe discomfort.” In this way, each measurement result finds an unambiguous place on the scale.

2.6. Statistical Analysis

The obtained results were subjected to statistical analysis in order to evaluate the influence of selected experimental factors on vibration comfort. Differences related to vehicle type, child seat type, installation method, load mass, speed bump type, and driving speed were analyzed. This approach enabled a comprehensive assessment of which of these variables had the greatest impact on vibration transmission and on the values of RMS, VDV, SEAT, and RMQ indicators.

To verify the significance of differences between groups, a one-way analysis of variance (ANOVA) was applied. This method makes it possible to determine whether the mean values obtained for different configurations differ significantly from one another, or whether the observed discrepancies are random. In cases where statistical significance was found (at the significance level of p < 0.05), Tukey’s post hoc tests were additionally performed, allowing the identification of specific pairs of groups that differed significantly. In addition to statistical significance testing, effect sizes and confidence intervals were calculated. For each ANOVA factor, partial η² values with 95% confidence intervals were reported. For correlation analyses, Pearson’s r coefficients were complemented with 95% confidence intervals. This approach provides both the strength and the reliability of the observed effects.

In addition to difference analysis, Pearson correlation analysis was used to assess the strength and direction of relationships between the vibration indicators (RMS, VDV, SEAT, RMQ) and experimental variables such as load mass, driving speed, and speed bump type. Correlation coefficients (r) were calculated to identify whether an increase in speed or load mass led to a proportional increase or decrease in individual vibration indicators.

Correlation analysis also made it possible to examine the degree to which individual vibration indicators were interrelated. For example, high RMS values may be directly correlated with higher VDV, while SEAT, as a transmissibility parameter, may exhibit different relationships with RMQ. This approach not only enabled the identification of the most and least comfortable configurations but also provided a better understanding of the relationships between quantitative measures of vibration comfort.

All statistical calculations were performed using Statistica 13.3 software (TIBCO Software Inc., Palo Alto, CA, USA). The results of the analysis were presented in both tabular and graphical form, which allowed for clear interpretation of the observed relationships and easy comparison of the individual test configurations.

2.7. Limitations of the Study

Although the study was conducted under real vehicle operating conditions, it has certain limitations that should be considered when interpreting the results. First, the tests were carried out exclusively on two passenger car models, Audi A6 and Citroën C5, which differ in suspension design. Therefore, the results may not fully reflect the behavior of vehicles from other brands, segments, or generations.

The second limitation concerns the number of child seats analyzed. Four models representing weight groups 0, 0+, and I were selected for the study, whereas the market for child seats is much more diverse. In particular, hybrid solutions, rotating seats, and models intended for older children (groups II and III) were not included in the analysis.

Another limiting factor was the method of loading the seats. Dummy weights of 3.5 kg, 9.5 kg, and 14.5 kg were used, which allowed the mass of a child to be simulated but did not fully reproduce the actual biomechanical behavior of a child’s body, especially musculoskeletal and postural interactions.

The study was also limited to two types of speed bumps, the plate-type PZL-40 and the launch-type PP-30, and to two driving speeds, 20 and 30 km/h. The results do not therefore cover other types of road irregularities such as railway tracks, cobblestones, or potholes with irregular geometry.

Additionally, for the Joie seat at the PP-30 bump with a load of 14.5 kg, the measurement data were not qualified for analysis due to excessive differences between the repeated series. As a result, this dataset was excluded from further processing.

Considering these limitations, the results obtained should be regarded as a starting point for further, more comprehensive research that would include a wider range of vehicles, child seats, road conditions, and loading models.

3. Results

The following section presents the research results in a logical sequence, starting from data selection and preparation through to comparative and statistical analyses. First, the procedure for selecting signal segments corresponding to speed bump passages and the rules of aggregation (averages from 10 runs for each configuration) are described. Next, descriptive statistics are presented for all sensor locations (vehicle floor, ISOFIX base, support leg, child seat surface), followed by the comfort indicators RMS, VDV, and RMQ, as well as the SEAT factor.

3.1. Selection of Data for Analysis

Figure 9 presents the scheme of data analysis for signals recorded during vehicle passages over speed bumps. The analysis covers the full measurement range, that is, the period preceding the approach to the bump, the time of passage over the bumps, and the moment after leaving them. The acceleration values recorded before and after contact with the obstacle remain relatively small and stable, whereas during wheel contact with the bump, clear signal disturbances occur, manifested as significant changes in acceleration amplitudes.

A detailed fragment of the analysis is shown in the lower part of Figure 9. It highlights three important stages of the passage: the moment when the front axle of the vehicle approaches the bump, the period when both axles were simultaneously on the obstacle, and the final phase of descent, first of the front axle and then of the rear axle. This approach makes it possible to precisely isolate the time interval in which the vehicle was in direct contact with the speed bumps.

The results shown in the figure allow for an accurate assessment of the influence of speed bumps on vehicle dynamics, and, in particular, on the characteristics of the recorded accelerations as a function of time. The obtained data provide the basis for further analysis of the impact of such road obstacles on both safety and ride comfort.

3.2. Determination of Discomfort Indicators

Based on the conducted tests and the recorded RMS acceleration values on the ISOFIX base for five different child seats, significant differences in vibration comfort levels can be observed. The measurements were carried out during passages over PZL-40 and PP-30 speed bumps at a speed of 20 km/h, with different child seat load masses of 3.5 kg, 9.5 kg, and 14.5 kg. The results are summarized in

Table 2. Results of RMS, VDV and RMQ acceleration measurements on the ISOFIX base leg when driving over the PZL-40 and PP-30 speed bumps at 20 km/h in Audi A6 and Citroen C5 vehicles.

Speed Bumps	Mass	Type of Car Seat	Audi A6			Citroen C5
			Indicators of Discomfort			Indicators of Discomfort
			RMS	VDV	RMQ	RMS	VDV	RMQ
PZL-40	Mass 3.5 kg	Car seat 1 (AVIONAUT)	1.0883	3.9772	1.8998	1.2034	4.3919	2.1698
		Car seat 2 (Britax Romer)	1.5954	5.8078	2.709	1.756	6.1869	2.8832
		Car seat 3 (Maxi-Cosi)	1.731	6.1539	2.9418	1.7666	6.2246	2.9664
		Car seat 4 (Cybex)	1.4199	5.1191	2.3933	1.5487	5.5199	2.5547
		Car seat 5 (Joie)	1.4293	5.0642	2.3968	1.376	4.813	2.362
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	0.8402	2.9796	1.5175	1.2635	4.4972	2.1499
		Car seat 2 (Britax Romer)	1.4216	4.9326	2.4283	2.1769	7.7903	3.4764
		Car seat 3 (Maxi-Cosi)	1.2257	4.255	2.0881	1.6699	5.8685	2.7358
		Car seat 4 (Cybex)	1.3878	4.7794	2.4196	1.4153	4.9768	2.4207
		Car seat 5 (Joie)	1.4496	4.9748	2.4572	1.821	6.5913	3.0398
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.1505	3.9387	2.0288	1.0512	3.6357	1.9057
		Car seat 2 (Britax Romer)	1.6475	5.7066	2.6075	1.5107	5.1808	2.3828
		Car seat 3 (Maxi-Cosi)	1.7267	6.038	2.7672	1.2485	4.3649	2.0799
		Car seat 4 (Cybex)	1.5887	5.5731	2.5372	1.8008	6.4573	2.8975
		Car seat 5 (Joie)	1.222	4.3123	2.1266	1.8576	6.5875	2.9468
PP-30	Mass 3.5 kg	Car seat 1 (AVIONAUT)	1.2769	5.1272	2.3587	1.3971	5.582	2.639
		Car seat 2 (Britax Romer)	1.722	6.9772	3.0803	1.9128	7.867	3.3498
		Car seat 3 (Maxi-Cosi)	1.8874	7.6307	3.3111	2.0536	8.3583	3.5126
		Car seat 4 (Cybex)	1.4971	6.1081	2.7088	1.8332	7.5685	3.2993
		Car seat 5 (Joie)	1.8028	7.2558	3.2016	1.6572	6.8737	3.0596
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	1.3412	5.4026	2.4584	1.3226	5.377	2.4711
		Car seat 2 (Britax Romer)	1.8613	7.6783	3.4325	2.3034	9.6147	4.0312
		Car seat 3 (Maxi-Cosi)	2.0977	8.7475	3.8286	2.0912	8.8212	3.8029
		Car seat 4 (Cybex)	1.6689	7.0304	3.1004	2.3229	9.9174	4.0792
		Car seat 5 (Joie)	2.283	9.7397	4.0388	2.8143	12.1166	4.8193
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.7752	7.4619	3.2369	1.3384	5.6936	2.4281
		Car seat 2 (Britax Romer)	1.8817	8.005	3.3105	1.7848	7.4461	3.1883
		Car seat 3 (Maxi-Cosi)	1.8088	7.4953	3.2884	2.1335	9.0099	3.7649
		Car seat 4 (Cybex)	3.1258	13.5745	5.3844	1.4527	6.0672	2.7639
		Car seat 5 (Joie)	-	-	-	-	-	-

.

In the first child seat, the lowest RMS value was obtained in the Audi A6 on the PZL-40 bump with a 9.5 kg load, 0.8402 m/s², while the highest value was recorded in the same vehicle on the PP-30 bump with a 14.5 kg load, 1.7752 m/s². This corresponds to an increase of about 111.3% compared to the minimum. From a normative perspective, this means a transition from the “discomfort” level at approximately 0.84 m/s² to “severe discomfort” at 1.78 m/s², without reaching the “extreme discomfort” range, since the values did not exceed the 2 m/s² threshold. In the second seat, the lowest value was recorded in the Audi A6 on the PZL-40 bump with a 9.5 kg load, 1.4216 m/s², and the highest in the Citroën C5 on the PP-30 bump with the same 9.5 kg load, 2.3034 m/s², representing an increase of about 62.0%. For this seat, all configurations fall at least into the “severe discomfort” category, while the maximum case in the Citroën C5 exceeds 2 m/s² and qualifies as “extreme discomfort.” In the third seat, the minimum value was 1.2257 m/s² in the Audi A6 on the PZL-40 bump with a 9.5 kg load, and the maximum 2.1335 m/s² in the Citroën C5 on the PP-30 bump with a 14.5 kg load, corresponding to an increase of about 74.1%. According to RMS speed bumps, configurations around 1.23 m/s² correspond to “discomfort,” while values exceeding 2 m/s² in the Citroën C5 indicate “extreme discomfort.” In the fourth seat, the lowest value was obtained in the Audi A6 on the PZL-40 bump with a 9.5 kg load, 1.3878 m/s², and the highest also in the Audi A6 on the PP-30 bump with a 14.5 kg load, 3.1258 m/s². This represents an increase of about 125.2%. The results range from “severe discomfort” for the lowest values to clear “extreme discomfort” under the least favorable conditions, with the Audi A6 on the PP-30 bump with a 14.5 kg load producing the highest RMS in the entire dataset. In the fifth seat, the minimum was recorded in the Audi A6 on the PZL-40 bump with a 14.5 kg load, 1.2220 m/s², while the maximum was in the Citroën C5 on the PP-30 bump with a 9.5 kg load, 2.8143 m/s², an increase of about 130.3%. Normatively, values around 1.22 m/s² correspond to “discomfort,” while the maximum case in the Citroën C5 clearly exceeds 2 m/s² and qualifies as “extreme discomfort.”

Considering vehicle type, the most unfavorable cases for the second, third, and fifth seats occurred in the Citroën C5 on the PP-30 bump, while for the first and fourth seats they occurred in the Audi A6. The absolute maximum value of 3.1258 m/s² was recorded in the Audi A6 for the fourth seat on the PP-30 bump with a 14.5 kg load. The effect of load mass was not strictly monotonic in every configuration, although the general trend is evident. For the PP-30 bump in the Audi A6, RMS values usually increased with load mass, for example, in the first seat from 1.2769 m/s² at 3.5 kg to 1.7752 m/s² at 14.5 kg, and in the fourth seat from 1.4971 m/s² to 3.1258 m/s². In the Citroën C5, the maximum was often observed at 9.5 kg on the PP-30 bump, as in the second seat at 2.3034 m/s² and the fifth seat at 2.8143 m/s². For the PZL-40 bump, there were also configurations where increasing the load mass did not lead to higher RMS values, suggesting a different interaction between the vehicle suspension, bump geometry, and the stiffness of the seat–base system.

Assessing discomfort level according to RMS, most values in the dataset correspond at least to “severe discomfort.” Many configurations in the Citroën C5 on the PP-30 bump, as well as the extreme case in the Audi A6, exceeded 2 m/s² and entered the “extreme discomfort” range. Only the first seat remained below 2 m/s² under all conditions and did not reach the extreme level. These findings are consistent regardless of vehicle model, and the differences between the Audi A6 and Citroën C5 result mainly from the interaction of the vehicle suspension system with bump geometry and the structural properties of individual seats.

The analysis for the sensor mounted on the ISOFIX support leg at 20 km/h showed that in the Audi A6 the lowest vibration dose was recorded on the PZL-40 bump with a 9.5 kg load in the first seat, VDV = 2.9796 m/s^1.75, while the highest was recorded on the PP-30 bump with a 14.5 kg load in the fourth seat, VDV = 13.5745 m/s^1.75, which is about 4.56 times higher. The corresponding RMQ values in the Audi A6 ranged from a minimum of 1.5175 m/s² (PZL-40, 9.5 kg, first seat) to a maximum of 5.3844 m/s² (PP-30, 14.5 kg, fourth seat), a difference of about 3.55 times. In the Citroën C5, the minimum vibration dose was recorded on the PZL-40 bump with a 14.5 kg load in the first seat, VDV = 3.6357 m/s^1.75, and the maximum on the PP-30 bump with a 9.5 kg load in the fifth seat, VDV = 12.1166 m/s^1.75, about 3.33 times higher. For RMQ in the Citroën C5, the minimum was 1.9057 m/s² (PZL-40, 14.5 kg, first seat) and the maximum 4.8193 m/s² (PP-30, 9.5 kg, fifth seat), a difference of about 2.53 times. Even at 20 km/h, a clear influence of bump geometry is visible: the PP-30 bump generates significantly higher vibration doses and greater energy values than the PZL-40 bump.

Table 3. Results of RMS, VDV and RMQ acceleration measurements on the ISOFIX base leg when driving over the PZL-40 and PP-30 speed bumps at 30 km/h in Audi A6 and Citroen C5 vehicles.

Speed Bumps	Mass	Type of Car Seat	Audi A6			Citroen C5
			Indicators of Discomfort			Indicators of Discomfort
			RMS	VDV	RMQ	RMS	VDV	RMQ
PZL-40	Mass 3.5 kg	Car seat 1 (AVIONAUT)	1.4656	5.9465	2.6712	1.1522	4.6392	2.1252
		Car seat 2 (Britax Romer)	1.8443	7.4534	3.1608	1.9612	7.9209	3.4498
		Car seat 3 (Maxi-Cosi)	2.1161	8.4856	3.5568	1.6082	6.3658	2.9271
		Car seat 4 (Cybex)	1.9683	7.9587	3.3622	2.1625	8.9479	3.6266
		Car seat 5 (Joie)	2.1562	8.8989	3.6129	1.4281	5.8116	2.5238
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	1.1264	4.558	2.1401	1.4213	5.8032	2.7745
		Car seat 2 (Britax Romer)	1.5098	6.1298	2.7365	1.5248	6.1328	2.8409
		Car seat 3 (Maxi-Cosi)	1.8268	7.4939	3.1892	1.5122	6.059	2.8308
		Car seat 4 (Cybex)	1.8202	7.3562	3.1653	1.443	5.8287	2.6522
		Car seat 5 (Joie)	1.6529	6.7442	2.9177	1.6243	6.5906	2.9598
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.52	6.0138	2.7367	1.6374	6.475	2.9551
		Car seat 2 (Britax Romer)	1.6995	6.7203	3.019	2.2906	9.1411	3.73
		Car seat 3 (Maxi-Cosi)	1.9698	7.9362	3.4214	1.7419	7.0605	3.1317
		Car seat 4 (Cybex)	2.2161	8.9645	3.7778	1.8918	7.4201	3.3356
		Car seat 5 (Joie)	1.7407	7.0238	3.0824	1.8059	7.1017	3.1706
PP-30	Mass 3.5 kg	Car seat 1 (AVIONAUT)	1.8616	9.016	3.7886	1.756	8.4097	3.5847
		Car seat 2 (Britax Romer)	2.3342	11.2448	4.6346	2.0339	9.7724	3.9965
		Car seat 3 (Maxi-Cosi)	2.4192	11.5364	4.8629	2.5139	12.1844	4.9745
		Car seat 4 (Cybex)	2.5687	12.2077	5.106	2.5484	12.1199	5.0062
		Car seat 5 (Joie)	2.3559	11.2828	4.69	2.548	12.2693	5.0111
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	1.7689	8.3133	3.3495	2.1343	10.1709	3.9849
		Car seat 2 (Britax Romer)	2.9553	14.6472	5.3816	2.2361	10.8293	4.0998
		Car seat 3 (Maxi-Cosi)	2.6851	13.0891	4.9686	3.2948	16.2742	5.9419
		Car seat 4 (Cybex)	2.4604	11.8761	4.4712	2.2802	10.9369	4.172
		Car seat 5 (Joie)	2.4032	11.4932	4.4498	2.187	10.3896	3.9928
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	2.6944	13.0075	4.8918	2.3557	11.3565	4.3059
		Car seat 2 (Britax Romer)	3.3723	16.7942	5.9869	2.5658	12.399	4.7164
		Car seat 3 (Maxi-Cosi)	3.0141	14.833	5.3781	2.8969	14.1899	5.2803
		Car seat 4 (Cybex)	3.1888	15.652	5.7752	2.7277	13.3922	5.0007
		Car seat 5 (Joie)	-	-	-	-	-	-

below presents the interpretation of results at 30 km/h, recorded on the ISOFIX support leg during passages over PZL-40 and PP-30 bumps in the Audi A6 and Citroën C5 vehicles with load masses of 3.5 kg, 9.5 kg, and 14.5 kg.

In the first child seat, the lowest RMS acceleration was recorded in the Audi A6 on the PZL-40 bump with a load of 9.5 kg, amounting to 1.1264 m/s², while the highest value of 2.6944 m/s² was observed in the same vehicle on the PP-30 bump with a load of 14.5 kg, representing an increase of about 139% relative to the minimum. The minimum corresponds to the “discomfort” category, whereas the maximum exceeds 2 m/s² and qualifies as “extreme discomfort.” The influence of load mass was particularly evident for the PP-30 bump: in the Audi A6 a sharp increase appeared at 14.5 kg, while in the Citroën C5, the values increased progressively with mass on both PZL-40 and PP-30.

In the second child seat, the lowest RMS value was 1.5098 m/s² (Audi A6, PZL-40, 9.5 kg), and the highest was 3.3723 m/s² (Audi A6, PP-30, 14.5 kg), corresponding to an increase of about 123%. The minimum condition was classified as “discomfort,” whereas the maximum clearly indicated “extreme discomfort.” The effect of mass was consistent: for both vehicles and the PP-30 bump, values increased with load, while on the PZL-40 in the Audi A6, a slight decrease appeared at 9.5 kg, followed by an increase at 14.5 kg.

In the third child seat, the minimum value of 1.5122 m/s² was recorded in the Citroën C5 on the PZL-40 bump at 9.5 kg, and the maximum of 3.2948 m/s² in the same vehicle on the PP-30 bump at 9.5 kg, which represents an increase of about 118%. The minimum configuration corresponded to “discomfort,” while the maximum entered the “extreme discomfort” category. For the PP-30 bump in the Audi A6, values increased with load, whereas in the Citroën C5, the maximum appeared at 9.5 kg and remained at a very high level also for 14.5 kg.

In the fourth child seat, the lowest RMS value was 1.443 m/s² (Citroën C5, PZL-40, 9.5 kg), and the highest 3.1888 m/s² (Audi A6, PP-30, 14.5 kg), corresponding to an increase of about 121%. The minimum was classified as “discomfort,” while the maximum clearly confirmed “extreme discomfort.” The effect of mass mainly intensified RMS values on the PP-30 bump, with both vehicles showing substantially higher accelerations at 14.5 kg compared to 3.5 and 9.5 kg.

In the fifth child seat, the minimum RMS value was 1.4281 m/s² (Citroën C5, PZL-40, 3.5 kg), and the maximum 2.548 m/s² (Citroën C5, PP-30, 3.5 kg), an increase of about 78%. The minimum configuration was classified as “discomfort,” while the maximum exceeded 2 m/s² and fell into the “extreme discomfort” category. The sensitivity to mass varied: in the Citroën C5 on the PZL-40 bump, values increased with load, whereas on the PP-30 bump higher values were observed already at 3.5 kg compared to 9.5 kg. In the Audi A6 on the PP-30 bump a moderate increase occurred between 3.5 and 9.5 kg, but the lack of measurement at 14.5 kg prevented full trend evaluation.

Considering the type of vehicle, the highest maxima for the first, second, and fourth child seats occurred in the Audi A6 on the PP-30 bump, while for the third and fifth seats the maxima were in the Citroën C5 on the same bump. This confirms that the PP-30 geometry generated higher vibration loads regardless of vehicle model. Globally, the lowest RMS across the dataset was 1.1264 m/s² (Audi A6, PZL-40, 9.5 kg, first seat), and the highest 3.3723 m/s² (Audi A6, PP-30, 14.5 kg, second seat), indicating a difference of about 199% between extremes. According to the vibration comfort criteria presented earlier, minima for all child seats correspond to “discomfort,” while maxima in every case exceed 2 m/s² and are classified as “extreme discomfort.” Generally, RMS increased with load, particularly on the PP-30 bump, except for a few configurations on the PZL-40 where transitional decreases appeared at 9.5 kg.

At 30 km/h, VDV and RMQ values increased further. In the Audi A6, the minimum VDV was 4.5580 m/s^1.75 (PZL-40, 9.5 kg, first seat), while the maximum was 16.7942 m/s^1.75 (PP-30, 14.5 kg, second seat), a difference of 3.69 times. Corresponding RMQ values ranged from 2.1401 m/s² to 5.9869 m/s², about 2.80 times. In the Citroën C5, VDV increased from 4.6392 m/s^1.75 (PZL-40, 3.5 kg, first seat) to 16.2742 m/s^1.75 (PP-30, 9.5 kg, third seat), or 3.51 times, while RMQ rose from 2.1252 m/s² to 5.9419 m/s² (2.80 times). Increasing speed from 20 to 30 km/h therefore raised both the “dose” and “energy” of vibrations by about 30–60% in typical configurations, with extreme values occurring on the PP-30 bump and at higher load masses.

Based on the measurements taken on the child seat surfaces during passages over PZL-40 and PP-30 bumps at 20 km/h in the Audi A6 and Citroën C5, with load masses of 3.5, 9.5, and 14.5 kg, clear differences were observed in the vibration levels transmitted to the seating area of the child. The RMS, VDV, and RMQ results for the child seat surface are summarized in

Table 4. Results of RMS, VDV and RMQ acceleration measurements on the seat car seat during the PZL-40 and PP-30 speed bumps at 20 km/h in Audi A6 and Citroën C5 vehicles.

Speed Bumps	Mass	Type of Car Seat	Audi A6			Citroen C5
			Indicators of Discomfort			Indicators of Discomfort
			RMS	VDV	RMQ	RMS	VDV	RMQ
PZL-40	Mass 3.5 kg	Car seat 1 (AVIONAUT)	0.8182	1.7437	1.0361	1.0573	2.3308	1.3725
		Car seat 2 (Britax Romer)	0.8723	1.8648	1.1261	1.3112	2.8816	1.7182
		Car seat 3 (Maxi-Cosi)	1.0503	2.2278	1.3632	1.6138	3.7604	2.0982
		Car seat 4 (Cybex)	0.8856	1.8511	1.13	1.555	3.5471	2.0104
		Car seat 5 (Joie)	1.1183	2.3882	1.4252	1.5029	3.368	1.9298
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	0.9454	1.9973	1.2252	0.9554	2.0451	1.2203
		Car seat 2 (Britax Romer)	1.4105	3.1546	1.8752	1.278	2.8387	1.6549
		Car seat 3 (Maxi-Cosi)	1.1521	2.5802	1.5052	1.3546	3.0608	1.7271
		Car seat 4 (Cybex)	1.3103	2.9158	1.7265	1.2281	2.7693	1.571
		Car seat 5 (Joie)	1.4847	3.3015	1.8475	1.7175	3.9421	2.2169
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	0.9884	2.154	1.2984	1.0344	2.3162	1.3721
		Car seat 2 (Britax Romer)	1.3028	2.9216	1.7163	1.4468	3.3777	1.9976
		Car seat 3 (Maxi-Cosi)	1.4031	3.2319	1.8483	1.1555	2.6759	1.6421
		Car seat 4 (Cybex)	1.1711	2.7033	1.5385	1.6549	3.9131	2.2569
		Car seat 5 (Joie)	1.3815	3.1004	1.7708	1.334	3.174	1.8577
PP-30	Mass 3.5 kg	Car seat 1 (AVIONAUT)	0.9581	2.3373	1.3643	0.9368	2.2487	1.3665
		Car seat 2 (Britax Romer)	1.2148	2.9769	1.691	1.4869	3.7787	2.2131
		Car seat 3 (Maxi-Cosi)	1.3639	3.4322	1.9051	1.558	3.911	2.2551
		Car seat 4 (Cybex)	1.2852	3.1686	1.8335	1.6945	4.4095	2.5296
		Car seat 5 (Joie)	1.5059	3.8076	2.1463	1.5159	3.991	2.3616
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	1.0974	2.7602	1.5839	1.0246	2.5519	1.493
		Car seat 2 (Britax Romer)	1.4547	3.6976	2.1109	1.5676	4.1662	2.3367
		Car seat 3 (Maxi-Cosi)	1.3353	3.3356	1.9286	1.5669	4.1551	2.3554
		Car seat 4 (Cybex)	1.4061	3.342	1.8958	1.69	4.1482	2.3339
		Car seat 5 (Joie)	1.6716	4.1263	2.3365	1.6237	4.0196	2.2255
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.2234	2.8496	1.6517	1.2266	2.9361	1.6561
		Car seat 2 (Britax Romer)	1.686	4.0723	2.3414	1.7605	4.4259	2.4529
		Car seat 3 (Maxi-Cosi)	1.904	4.8482	2.6161	1.4639	3.5588	2.0367
		Car seat 4 (Cybex)	1.8009	4.4089	2.508	1.9347	4.8663	2.6568
		Car seat 5 (Joie)	-	-	-	-	-	-

.

In the first child seat, the minimum RMS value was recorded in the Audi A6 on the PZL-40 bump with a load of 3.5 kg (0.8182 m/s²), while the maximum occurred in the Citroën C5 on the PP-30 bump with a load of 14.5 kg (1.2266 m/s²). The maximum was about 1.50 times higher than the minimum (0.8182 m/s² vs. 1.2266 m/s²). The entire range fell within the “discomfort” category according to the RMS evaluation in Table 2.

In the second seat, the lowest value (0.8723 m/s²) was observed in the Audi A6 on the PZL-40 bump at 3.5 kg, and the highest (1.7605 m/s²) in the Citroën C5 on the PP-30 bump at 14.5 kg, representing an increase of about 2.02 times. Lower readings corresponded to “discomfort,” while the highest indicated “severe discomfort.”

In the third seat, the minimum RMS was 1.0503 m/s² (Audi A6, PZL-40, 3.5 kg), and the maximum 1.9040 m/s² (Audi A6, PP-30, 14.5 kg), about 1.81 times higher. The classification shifted from “discomfort” to “severe discomfort.”

In the fourth seat, the minimum of 0.8856 m/s² was observed in the Audi A6 on the PZL-40 bump at 3.5 kg, while the maximum of 1.9347 m/s² occurred in the Citroën C5 on the PP-30 bump at 14.5 kg. The maximum was about 2.19 times higher than the minimum. The lowest values corresponded to “discomfort,” and the highest to “severe discomfort,” with the Citroën C5 combined with the PP-30 bump and the highest mass proving most unfavorable.

In the fifth seat, the minimum RMS was 1.1183 m/s² (Audi A6, PZL-40, 3.5 kg), and the maximum 1.7175 m/s² (Citroën C5, PZL-40, 9.5 kg), about 1.54 times higher. The obtained values ranged from “discomfort” to “severe discomfort.”

Overall, the RMS values on the seat ranged between 0.8182 and 1.9347 m/s², with the maximum about 2.36 times higher than the minimum (1.9347 m/s² vs. 0.8182 m/s², difference 1.1165 m/s²). In terms of vehicles, the minima for all seats occurred in the Audi A6 on the PZL-40 bump at the lowest mass, whereas most maxima were observed in the Citroën C5 on the PP-30 bump at higher masses. This confirms the significant influence of bump geometry and vehicle suspension characteristics on vibration transmission. With increasing load mass, RMS values generally rose, particularly on the PP-30 bump, though exceptions were noted for some configurations on the PZL-40 where maxima appeared at 9.5 kg. According to Table 2, no “extreme discomfort” was recorded on the seat, since none of the RMS values exceeded 2 m/s².

The analysis of seat measurements at 20 km/h further showed that in the Audi A6, the lowest VDV was obtained on the PZL-40 bump with a load of 3.5 kg in the first seat (1.7437 m/s^1.75), while the highest was on the PP-30 bump with a load of 14.5 kg in the third seat (4.8482 m/s^1.75), about 2.78 times higher. The corresponding RMQ values increased from 1.0361 m/s² (PZL-40, 3.5 kg, first seat) to 2.6161 m/s² (PP-30, 14.5 kg, third seat), about 2.53 times. In the Citroën C5 under the same speed conditions, the minimum VDV was 2.0451 m/s^1.75 (PZL-40, 9.5 kg, first seat) and the maximum 4.8663 m/s^1.75 (PP-30, 14.5 kg, fourth seat), about 2.38 times higher. Corresponding RMQ values increased from 1.2203 m/s² to 2.6568 m/s², about 2.18 times. The seat, as a damping element, “filters” part of the impacts—the values are notably lower than those measured on the ISOFIX support leg, but the relationships remain the same: PP-30 bumps and higher loads increase both vibration dose and energy.

Based on the seat measurements during passages over PZL-40 and PP-30 bumps at 30 km/h in the Audi A6 and Citroën C5, with load masses of 3.5, 9.5, and 14.5 kg, clear differences were observed in vibration levels transmitted to the child seating area. The RMS, VDV, and RMQ results for the child seat surface are summarized in

Table 5. Results of RMS, VDV and RMQ acceleration measurements on the seat car seat during the PZL-40 and PP-30 speed bumps at 30 km/h in Audi A6 and Citroën C5 vehicles.

Speed Bumps	Mass	Type of Car Seat	Audi A6			Citroen C5
			Indicators of Discomfort			Indicators of Discomfort
			RMS	VDV	RMQ	RMS	VDV	RMQ
PZL-40	Mass 3.5 kg	Car seat 1 (AVIONAUT)	1.0613	2.4833	1.4731	1.1902	2.8404	1.613
		Car seat 2 (Britax Romer)	1.3218	3.3069	1.8028	1.4654	3.5797	2.0782
		Car seat 3 (Maxi-Cosi)	1.5297	3.8386	2.1579	1.8312	4.7603	2.5834
		Car seat 4 (Cybex)	1.5476	3.9466	2.1372	1.5976	4.0853	2.2626
		Car seat 5 (Joie)	1.4316	3.562	1.98	1.8283	4.7251	2.5454
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	1.0212	2.2717	1.3771	1.2034	2.8491	1.6488
		Car seat 2 (Britax Romer)	1.2931	3.1448	1.7748	1.4183	3.4629	1.9883
		Car seat 3 (Maxi-Cosi)	1.8237	4.6866	2.5384	1.4888	3.7208	2.1162
		Car seat 4 (Cybex)	1.5198	3.8426	2.1514	1.7088	4.4654	2.4749
		Car seat 5 (Joie)	1.4841	3.6521	2.01	1.7264	4.4894	2.541
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.1104	2.5303	1.4838	1.2665	3.0554	1.7613
		Car seat 2 (Britax Romer)	1.6665	4.2354	2.3874	1.6892	4.2428	2.4838
		Car seat 3 (Maxi-Cosi)	1.553	3.9477	2.223	1.843	4.8538	2.7237
		Car seat 4 (Cybex)	1.7348	4.5157	2.5046	1.9035	4.9923	2.7958
		Car seat 5 (Joie)	1.4637	3.7712	2.1127	1.7746	4.7343	2.6254
PP-30	Mass 3.5 kg	Car seat 1 (AVIONAUT)	1.2029	3.0382	1.8017	1.1377	2.8119	1.6993
		Car seat 2 (Britax Romer)	1.6137	4.1823	2.4242	1.6982	4.3845	2.5455
		Car seat 3 (Maxi-Cosi)	1.6555	4.3106	2.5017	1.9444	5.1451	2.9073
		Car seat 4 (Cybex)	1.6027	4.1462	2.4513	1.9698	5.1364	2.9458
		Car seat 5 (Joie)	1.6737	4.3492	2.5337	1.5234	3.9571	2.3557
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	1.5889	4.2043	2.317	1.196	3.0855	1.6926
		Car seat 2 (Britax Romer)	2.0897	5.8823	3.1318	1.71	4.582	2.5254
		Car seat 3 (Maxi-Cosi)	1.7299	4.6911	2.5283	2.0158	5.6159	3.0263
		Car seat 4 (Cybex)	1.7448	4.773	2.5256	1.8056	4.8681	2.6815
		Car seat 5 (Joie)	2.1521	5.9627	3.24	1.3669	3.5499	2.0233
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.5983	4.3282	2.2995	1.4006	3.6392	2.0506
		Car seat 2 (Britax Romer)	1.8509	5.083	2.7281	2.1273	6.0282	3.1346
		Car seat 3 (Maxi-Cosi)	2.2952	6.5843	3.4531	2.1393	5.9772	3.2475
		Car seat 4 (Cybex)	1.8272	5.0868	2.7253	1.9131	5.3291	2.8587
		Car seat 5 (Joie)	-	-	-	-	-	-

.

In the first child seat, the minimum RMS was recorded in the Audi A6 on the PZL-40 bump with a load of 9.5 kg (1.0212 m/s²), while the maximum occurred in the Audi A6 on the PP-30 bump with a load of 14.5 kg (1.5983 m/s²), making the maximum about 1.57 times higher than the minimum. The minimum corresponds to the “discomfort” level, while the maximum falls within the upper range of “severe discomfort”.

The second seat showed a minimum of 1.2931 m/s² (Audi A6, PZL-40, 9.5 kg) and a maximum of 2.1273 m/s² (Citroën C5, PP-30, 14.5 kg), about 1.65 times greater. The lower value corresponds to “severe discomfort,” while the maximum exceeds 2 m/s² and qualifies as “extreme discomfort.”

In the third seat, the minimum was 1.4888 m/s² (Citroën C5, PZL-40, 9.5 kg), and the maximum 2.2952 m/s² (Audi A6, PP-30, 14.5 kg), about 1.54 times higher. The minimum corresponds to “severe discomfort,” while the maximum falls into the “extreme discomfort” category.

The fourth seat recorded a minimum of 1.5198 m/s² (Audi A6, PZL-40, 9.5 kg) and a maximum of 1.9698 m/s² (Citroën C5, PP-30, 3.5 kg), about 1.30 times higher. Both values fall within the “severe discomfort” range, with the maximum not exceeding 2 m/s².

The fifth seat had a minimum of 1.3669 m/s² (Citroën C5, PP-30, 9.5 kg) and a maximum of 2.1521 m/s² (Audi A6, PP-30, 9.5 kg), about 1.57 times higher. The minimum corresponds to “severe discomfort,” while the maximum indicates “extreme discomfort.”

Overall, the RMS values on the child seat surface ranged between 1.0212 and 2.2952 m/s², with the maximum about 2.25 times higher than the minimum (min = 1.0212 m/s², Audi A6, PZL-40, 9.5 kg, first seat; max = 2.2952 m/s², Audi A6, PP-30, 14.5 kg, third seat). The highest values were generally observed on the PP-30 bump and at higher loads, which in many cases resulted in exceeding 2 m/s² and entering the “extreme discomfort” category. The effect of load mass was generally positive, with RMS values increasing as the load grew, particularly on the PP-30 bump, though local minima at 9.5 kg in some configurations indicated a complex interaction between vehicle suspension, bump geometry, and the elastic properties of the seat.

For the seat at 30 km/h, the upward trend persisted, but extreme values were lower than on the ISOFIX base, confirming the filtering effect of the seat. In the Audi A6, the minimum VDV was 2.2717 m/s^1.75 (PZL-40, 9.5 kg, first seat) and the maximum 6.5843 m/s^1.75 (PP-30, 14.5 kg, third seat), about 2.90 times greater. The corresponding RMQ values rose from 1.3771 m/s² (PZL-40, 9.5 kg, first seat) to 3.2527 m/s² (PP-30, 14.5 kg, third seat), about 2.36 times. In the Citroën C5, the minimum VDV on the seat was 2.4803 m/s^1.75 (PZL-40, 3.5 kg, third seat) and the maximum 6.1182 m/s^1.75 (PP-30, 14.5 kg, second seat), about 2.47 times higher. The RMQ in this vehicle increased from 1.3835 m/s² (PZL-40, 3.5 kg, third seat) to 3.3335 m/s² (PP-30, 14.5 kg, second seat), about 2.41 times. The extreme values at 30 km/h were again associated with the PP-30 bump and higher loads.

Signals from the sensor mounted on the ISOFIX base beneath the child seat surface were also analyzed during passages over PZL-40 and PP-30 bumps at 20 km/h in the Audi A6 and Citroën C5 with load masses of 3.5, 9.5, and 14.5 kg. The RMS, VDV, and RMQ results for the ISOFIX base at 20 km/h in both vehicles are summarized in

Table 6. RMS, VDV, and RMQ acceleration results on the ISOFIX base beneath the child seat at 20 km/h in Audi A6 and Citroën C5 vehicles.

Speed Bumps	Mass	Type of Car Seat	Audi A6			Citroen C5
			Indicators of Discomfort			Indicators of Discomfort
			RMS	VDV	RMQ	RMS	VDV	RMQ
PZL-40	Mass 3.5 kg	Car seat 1 (AVIONAUT)	0.8597	1.8129	1.0522	1.3434	3.0502	1.7395
		Car seat 2 (Britax Romer)	0.8754	1.8198	1.1311	1.2706	2.91	1.6949
		Car seat 3 (Maxi-Cosi)	1.0007	2.1628	1.2942	1.6017	3.7465	2.1404
		Car seat 4 (Cybex)	0.8435	1.8178	1.0824	1.4995	3.4327	1.9523
		Car seat 5 (Joie)	1.0982	2.3754	1.3852	1.6033	3.5954	2.0571
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	0.7763	1.6098	0.9592	1.0671	2.2811	1.3748
		Car seat 2 (Britax Romer)	0.9253	2.0098	1.1354	1.2062	2.687	1.5229
		Car seat 3 (Maxi-Cosi)	0.9138	1.896	1.179	1.0922	2.3733	1.4055
		Car seat 4 (Cybex)	0.7337	1.5045	0.9379	1.1887	2.5554	1.5936
		Car seat 5 (Joie)	0.9395	2.0194	1.169	1.3506	2.9856	1.7462
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	0.9363	2.0422	1.2312	1.0408	2.3908	1.3357
		Car seat 2 (Britax Romer)	1.4173	3.2552	1.8999	1.4562	3.3271	2.009
		Car seat 3 (Maxi-Cosi)	1.4916	3.5012	2.0391	1.1541	2.6622	1.6063
		Car seat 4 (Cybex)	1.1714	2.6599	1.5042	1.6867	3.9657	2.3381
		Car seat 5 (Joie)	1.4632	3.3319	1.8561	1.2931	3.0894	1.8177
PP-30	Mass 3.5 kg	Car seat 1 (AVIONAUT)	1.0178	2.4852	1.4283	0.9889	2.3378	1.3585
		Car seat 2 (Britax Romer)	1.3598	3.3708	1.9087	1.4786	3.757	2.151
		Car seat 3 (Maxi-Cosi)	1.514	3.7487	2.0414	1.5665	3.8797	2.2554
		Car seat 4 (Cybex)	1.3934	3.3226	1.8863	1.7809	4.6052	2.619
		Car seat 5 (Joie)	1.64	3.9956	2.2335	1.4551	3.7652	2.2958
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	1.1376	2.8455	1.6523	1.0236	2.5811	1.4961
		Car seat 2 (Britax Romer)	1.5144	3.8773	2.1892	1.6075	4.2007	2.3717
		Car seat 3 (Maxi-Cosi)	1.3906	3.4842	1.9559	1.598	4.1557	2.4581
		Car seat 4 (Cybex)	1.4516	3.5376	2.0143	1.7041	4.0501	2.2874
		Car seat 5 (Joie)	1.5746	3.8311	2.2164	1.6567	3.8922	2.2783
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.2414	2.9344	1.7289	1.2004	2.9025	1.6067
		Car seat 2 (Britax Romer)	1.6717	3.9972	2.3065	1.6928	4.1278	2.3506
		Car seat 3 (Maxi-Cosi)	1.8467	4.5744	2.6039	1.5068	3.6771	2.073
		Car seat 4 (Cybex)	1.9473	4.8996	2.7365	2.1104	5.2551	2.9799
		Car seat 5 (Joie)	-	-	-	-	-	-

.

In the first child seat, the lowest RMS value was recorded in the Audi A6 on the PZL-40 bump with a load of 9.5 kg (0.7763 m/s²), while the highest was observed in the Citroën C5 on the PZL-40 bump with a load of 3.5 kg (1.3434 m/s²). The maximum was about 1.73 times higher than the minimum, corresponding to a 73% increase (min 0.7763 m/s², max 1.3434 m/s²). The minimum falls within the “moderate discomfort” zone, while the maximum corresponds to “discomfort”.

In the second seat, the minimum was 0.8754 m/s² (Audi A6, PZL-40, 3.5 kg) and the maximum 1.6928 m/s² (Citroën C5, PP-30, 14.5 kg), about 1.93 times higher (93% increase). The range transitions from “discomfort” to “severe discomfort”.

In the third seat, the lowest RMS was 0.9138 m/s² (Audi A6, PZL-40, 9.5 kg), while the highest was 1.8467 m/s² (Audi A6, PP-30, 14.5 kg), about 2.02 times higher (102% increase). The classification shifts from “discomfort” to “severe discomfort”.

In the fourth seat, the minimum of 0.7337 m/s² was recorded in the Audi A6 on the PZL-40 bump at 9.5 kg, and the maximum of 2.1104 m/s² in the Citroën C5 on the PP-30 bump at 14.5 kg. The maximum was about 2.88 times greater, corresponding to a 188% increase (0.7337 m/s² vs. 2.1104 m/s²). The lowest value indicates “moderate discomfort,” while the highest exceeds 2 m/s² and qualifies as “extreme discomfort”.

In the fifth seat, the minimum was 0.9395 m/s² (Audi A6, PZL-40, 9.5 kg) and the maximum 1.6567 m/s² (Citroën C5, PP-30, 9.5 kg), about 1.76 times higher (76% increase). This range corresponds to “discomfort” through “severe discomfort”.

Globally, for the entire dataset from the ISOFIX base under the seat, RMS values ranged from 0.7337 to 2.1104 m/s², with the maximum about 2.88 times greater and 1.3767 m/s² higher than the minimum (min 0.7337 m/s², Audi A6, PZL-40, 9.5 kg, fourth seat; max 2.1104 m/s², Citroën C5, PP-30, 14.5 kg, fourth seat). The highest readings were usually observed on the PP-30 bump, often in the Citroën C5, while the minima were more frequent in the Audi A6 on the PZL-40 bump. The influence of mass was not strictly monotonic, although in the second, third, and fourth seats, increasing mass—particularly on the PP-30—resulted in a clear increase in RMS, leading to “severe discomfort” and, in one case, “extreme discomfort.” The results show that the interaction of bump geometry, vehicle suspension characteristics, and the stiffness of the seat–base system strongly determines the vibration levels transmitted to the seat area.

For measurements on the ISOFIX base under the seat at 20 km/h in the Audi A6, the minimum VDV was 1.5045 m/s^1.75 (PZL-40, 9.5 kg, fourth seat), while the maximum was 4.8996 m/s^1.75 (PP-30, 14.5 kg, fourth seat), about 3.26 times greater. The RMQ values in the Audi A6 increased from 0.9379 m/s² (PZL-40, 9.5 kg, fourth seat) to 2.7365 m/s² (PP-30, 14.5 kg, fourth seat), about 2.92 times higher. In the Citroën C5, the lowest VDV under the seat was 2.2811 m/s^1.75 (PZL-40, 9.5 kg, first seat), and the highest 5.2551 m/s^1.75 (PP-30, 14.5 kg, fourth seat), about 2.30 times greater. The RMQ values in the Citroën C5 increased from 1.3357 m/s² (PZL-40, 14.5 kg, first seat) to 2.9799 m/s² (PP-30, 14.5 kg, fourth seat), about 2.23 times. This sensor location showed the lowest absolute RMQ minima in the dataset, consistent with the fact that the base under the seat receives vibrations already partially attenuated by the seat foam and child seat structure.

Based on the measurements from the ISOFIX base under the child seat during passages over PZL-40 and PP-30 bumps at 30 km/h in the Audi A6 and Citroën C5 with load masses of 3.5, 9.5, and 14.5 kg, the vibration comfort assessment was performed. The RMS, VDV, and RMQ results for the ISOFIX base at 30 km/h are summarized in

Table 7. RMS, VDV, and RMQ acceleration results on the ISOFIX base beneath the child seat at 30 km/h in Audi A6 and Citroën C5 vehicles.

Speed Bumps	Mass	Type of Car Seat	Audi A6			Citroen C5
			Indicators of Discomfort			Indicators of Discomfort
			RMS	VDV	RMQ	RMS	VDV	RMQ
PZL-40	Mass 3.5 kg	Car seat 1 (AVIONAUT)	1.7338	4.4039	2.4544	1.0863	2.5352	1.4428
		Car seat 2 (Britax Romer)	1.6703	4.2726	2.2743	1.3556	3.3463	1.9143
		Car seat 3 (Maxi-Cosi)	1.9466	5.066	2.7532	1.0491	2.4803	1.3835
		Car seat 4 (Cybex)	1.9069	4.9722	2.7318	1.2611	3.0249	1.7529
		Car seat 5 (Joie)	2.0102	5.1873	2.8927	1.0644	2.5594	1.4213
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	0.8072	1.7981	1.0736	1.0813	2.7027	1.5944
		Car seat 2 (Britax Romer)	1.1167	2.8447	1.6109	1.2922	3.2523	1.8835
		Car seat 3 (Maxi-Cosi)	1.475	3.7346	2.0261	1.3637	3.4023	2.1045
		Car seat 4 (Cybex)	1.3447	3.4035	1.9467	1.5173	3.9091	2.3087
		Car seat 5 (Joie)	1.2222	3.1185	1.7729	1.5856	4.104	2.4126
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.0752	2.4898	1.5268	1.1924	2.9274	1.665
		Car seat 2 (Britax Romer)	1.5437	3.9852	2.2489	1.634	4.1976	2.4874
		Car seat 3 (Maxi-Cosi)	1.6576	4.2273	2.3269	1.8996	5.0351	2.77
		Car seat 4 (Cybex)	1.6985	4.3575	2.4906	1.9045	5.033	2.7734
		Car seat 5 (Joie)	1.5311	3.7818	2.1358	1.7721	4.7068	2.5883
PP-30	Mass 3.5 kg	Car seat 1 (AVIONAUT)	1.2533	3.1282	1.8589	1.0939	2.7176	1.6549
		Car seat 2 (Britax Romer)	1.6631	4.2695	2.5462	1.6134	4.2084	2.449
		Car seat 3 (Maxi-Cosi)	1.7469	4.4629	2.6314	1.9416	5.2319	2.9132
		Car seat 4 (Cybex)	1.7221	4.4237	2.5282	1.9639	5.1957	2.8725
		Car seat 5 (Joie)	1.5692	4.0654	2.3553	1.4264	3.7038	2.1784
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	1.6791	4.5195	2.3953	1.1125	2.9021	1.5911
		Car seat 2 (Britax Romer)	2.1663	5.9631	3.242	1.8474	5.256	2.7536
		Car seat 3 (Maxi-Cosi)	1.7473	4.587	2.4938	1.968	5.3681	2.8659
		Car seat 4 (Cybex)	1.7758	4.8306	2.6148	1.84	5.0599	2.6582
		Car seat 5 (Joie)	2.1335	5.9602	3.1731	1.4205	3.8444	2.0686
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.6278	4.4264	2.3786	1.4094	3.7399	2.1051
		Car seat 2 (Britax Romer)	2.0121	5.6477	2.9975	2.1556	6.1182	3.3335
		Car seat 3 (Maxi-Cosi)	2.2057	6.0748	3.2527	2.1497	6.0031	3.2835
		Car seat 4 (Cybex)	1.9861	5.59	2.9692	1.8338	5.0157	2.6996
		Car seat 5 (Joie)	-	-	-	-	-	-

.

The first child seat reached the lowest RMS value in the Audi A6 on the PZL-40 bump at a load of 9.5 kg (0.8072 m/s²), while the highest value was also recorded in the Audi A6 on the PZL-40 bump at 3.5 kg (1.7338 m/s²). The maximum is about 2.15 times greater than the minimum, corresponding to a transition from the “discomfort” level to the upper range of “severe discomfort.” The second seat recorded a minimum in the Audi A6 on the PZL-40 at 9.5 kg (1.1167 m/s²) and a maximum in the Audi A6 on the PP-30 at 9.5 kg (2.1663 m/s²). The maximum is about 1.94 times greater, corresponding to a shift from “severe discomfort” to “extreme discomfort.” The third seat reached its minimum in the Citroën C5 on the PZL-40 at 3.5 kg (1.0491 m/s²) and its maximum in the Audi A6 on the PP-30 at 14.5 kg (2.2057 m/s²). This indicates an increase of about 2.10 times relative to the minimum and a transition from “discomfort” into the “extreme discomfort” range. The fourth seat recorded a minimum in the Citroën C5 on the PZL-40 at 3.5 kg (1.2611 m/s²) and a maximum in the Audi A6 on the PP-30 at 14.5 kg (1.9861 m/s²). The maximum is about 1.57 times greater than the minimum, with both values corresponding to “severe discomfort,” the maximum being close to the 2 m/s² threshold. The fifth seat recorded a minimum in the Citroën C5 on the PZL-40 at 3.5 kg (1.0644 m/s²) and a maximum in the Audi A6 on the PP-30 at 9.5 kg (2.1335 m/s²). The difference corresponds to about 2.00 times between minimum and maximum, representing a transition from “discomfort” to “extreme discomfort”.

The RMS values recorded on the ISOFIX base beneath the seat ranged from 0.8072 to 2.2057 m/s², with the maximum being about 2.73 times higher than the minimum (min = 0.8072 m/s², Audi A6, PZL-40, 9.5 kg, seat 1; max = 2.2057 m/s², Audi A6, PP-30, 14.5 kg, seat 3). The highest values occurred mainly on the PP-30 bump in the Audi A6, while the lowest were most often recorded on the PZL-40 bump, typically at lower loads. Increasing the load generally raised RMS values, particularly on the PP-30, thus elevating the discomfort level up to the “extreme” category in some configurations.

At 30 km/h, RMS, VDV, and RMQ values under the seat further increased, with extreme cases again linked to the PP-30 bump and higher loads. In the Audi A6, the minimum VDV was 1.7981 m/s^1.75 (PZL-40, 9.5 kg, seat 1), and the maximum was 6.0748 m/s^1.75 (PP-30, 14.5 kg, seat 3), about 3.38 times greater. The corresponding RMQ increased from 1.0736 m/s² (PZL-40, 9.5 kg, seat 1) to 3.2527 m/s² (PP-30, 14.5 kg, seat 3), about 3.03 times. In the Citroën C5, the minimum VDV was 2.4803 m/s^1.75 (PZL-40, 3.5 kg, seat 3), and the maximum was 6.1182 m/s^1.75 (PP-30, 14.5 kg, seat 2), about 2.47 times. RMQ increased from 1.3835 m/s² (PZL-40, 3.5 kg, seat 3) to 3.3335 m/s² (PP-30, 14.5 kg, seat 2), about 2.41 times.

When combining all configurations, the extreme values across the dataset can be identified. The lowest vibration dose (VDV) among all six analyses was recorded beneath the seat in the Audi A6 on the PZL-40 bump at 9.5 kg and seat 4, 1.5045 m/s^1.75, while the highest occurred at the ISOFIX leg in the Audi A6 on the PP-30 bump at 14.5 kg and seat 2, 16.7942 m/s^1.75, about 11.2 times greater. For RMQ, the absolute minimum was 0.9379 m/s² (under-seat base, Audi A6, PZL-40, 9.5 kg, seat 4), and the maximum was 5.9869 m/s² (ISOFIX leg, Audi A6, PP-30, 14.5 kg, seat 2), about 6.38 times greater. In all measurement locations and for both vehicles, the same pattern is observed: the PP-30 bump, higher load, and higher speed systematically increase both the vibration dose (VDV) and energy index (RMQ). Differences between the vehicles are quantitative rather than qualitative—Audi A6 more often generated extreme values at the ISOFIX leg and beneath the seat in combination with PP-30 and 14.5 kg load, while in the Citroën C5 several maxima occurred at the seat surface (particularly for PP-30 and higher loads). Ultimately, VDV and RMQ analysis confirms that the most unfavorable vibration comfort conditions occur when traversing the PP-30 bump at higher loads and 30 km/h speed. The damping properties of the seat cushion reduce both indices, but do not eliminate the increases resulting from bump geometry and vehicle speed.

Three vibration exposure indices—RMS, VDV, and RMQ—were analyzed at two sensor locations (rear bench seat surface and vehicle floor) during passages over PZL-40 and PP-30 bumps at 20 and 30 km/h, in both Audi A6 and Citroën C5. The numerical results covering both locations and both vehicles are presented in

Table 8. RMS, VDV, and RMQ on the rear bench seat and vehicle floor during passages over PZL-40 and PP-30 bumps at 20 and 30 km/h.

Sensor Location	Speed Bump Type	Velocity	Audi A6			Citroen C5
			RMS	VDV	RMQ	RMS	VDV	RMQ
Rear seat	PZL-40	20 km/h	0.8282	2.755	1.1944	0.8282	2.7576	1.1945
		30 km/h	1.0312	3.7979	1.5691	0.9967	3.655	1.5224
	PP-30	20 km/h	0.8979	3.1726	1.3508	0.9101	3.2207	1.3669
		30 km/h	1.1898	4.6735	1.8883	1.1579	4.5395	1.8424
Floor	PZL-40	20 km/h	1.4117	5.9903	2.3173	1.4443	6.1351	2.3728
		30 km/h	2.0302	9.6651	3.5324	2.151	10.3171	3.7529
	PP-30	20 km/h	1.7259	7.8668	2.9565	1.6614	7.5289	2.842
		30 km/h	2.2642	11.4638	4.1029	2.2862	11.5922	4.1478

.

3.3. Determination of the SEAT Index

The SEAT index was defined as the ratio of VDV recorded on the child seat surface to the VDV recorded at the ISOFIX base beneath the seat. It is a dimensionless quantity, where values below 1 indicate vibration attenuation by the seat relative to the base, values close to 1 suggest transmission without significant change, and values greater than 1 point to amplification at the seat level. The SEAT index during vehicle passages over PZL-40 and PP-30 speed bumps at speeds of 20 km/h and 30 km/h in Audi A6 and Citroën C5 is presented in

Table 9. SEAT index during passages over PZL-40 and PP-30 speed bumps at 20 and 30 km/h in Audi A6 and Citroën C5.

Speed Bumps	Mass	Type of Car Seat	SEAT Indicator
			20 km/h		30 km/h
			Audi A6	Citroen C5	Audi A6	Citroen C5
PZL-40	Mass 3.5 kg	Car seat 1 (AVIONAUT)	0.9618	0.7641	0.5639	1.1204
		Car seat 2 (Britax Romer)	1.0247	0.9902	0.7740	1.0697
		Car seat 3 (Maxi-Cosi)	1.0301	1.0037	0.7577	1.9192
		Car seat 4 (Cybex)	1.0183	1.0333	0.7937	1.3506
		Car seat 5 (Joie)	1.0054	0.9368	0.6867	1.8462
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	1.2407	0.8965	1.2634	1.0542
		Car seat 2 (Britax Romer)	1.5696	1.0565	1.1055	1.0648
		Car seat 3 (Maxi-Cosi)	1.3609	1.2897	1.2549	1.0936
		Car seat 4 (Cybex)	1.9381	1.0837	1.1290	1.1423
		Car seat 5 (Joie)	1.6349	1.3204	1.1711	1.0939
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	1.0547	0.9688	1.0163	1.0437
		Car seat 2 (Britax Romer)	0.8975	1.0152	1.0628	1.0108
		Car seat 3 (Maxi-Cosi)	0.9231	1.0051	0.9339	0.9640
		Car seat 4 (Cybex)	1.0163	0.9867	1.0363	0.9919
		Car seat 5 (Joie)	0.9305	1.0274	0.9972	1.0058
PP-30	Mass 3.5 kg	Car seat 1 (AVIONAUT)	0.9405	0.9619	0.9712	1.0347
		Car seat 2 (Britax Romer)	0.8831	1.0058	0.9796	1.0418
		Car seat 3 (Maxi-Cosi)	0.9156	1.0081	0.9659	0.9834
		Car seat 4 (Cybex)	0.9537	0.9575	0.9373	0.9886
		Car seat 5 (Joie)	0.9529	1.0600	1.0698	1.0684
	Mass 9.5 kg	Car seat 1 (AVIONAUT)	0.9700	0.9887	0.9303	1.0632
		Car seat 2 (Britax Romer)	0.9537	0.9918	0.9865	0.8718
		Car seat 3 (Maxi-Cosi)	0.9574	0.9999	1.0227	1.0462
		Car seat 4 (Cybex)	0.9447	1.0242	0.9881	0.9621
		Car seat 5 (Joie)	1.0771	1.0327	1.0004	0.9234
	Mass 14.5 kg	Car seat 1 (AVIONAUT)	0.9711	1.0116	0.9778	0.9731
		Car seat 2 (Britax Romer)	1.0188	1.0722	0.9000	0.9853
		Car seat 3 (Maxi-Cosi)	1.0599	0.9678	1.0839	0.9957
		Car seat 4 (Cybex)	0.8998	0.9260	0.9100	1.0625
		Car seat 5 (Joie)	-	-	-	-

.

A numerical summary of the SEAT index values for all configurations is presented in

Table 10. Average SEAT index values on the rear bench seat.

Sensor Location	Speed Bump Type	Velocity	SEAT Index
			AUDI	Citroen
Rear seat	PZL-40	20 km/h	0.45991	0.449479
		30 km/h	0.39295	0.354266
	PP-30	20 km/h	0.40329	0.427778
		30 km/h	0.407675	0.3916

. Across the entire dataset, SEAT values ranged from 0.5639 to 1.9381, meaning that the maximum recorded value was about 3.44 times greater than the minimum. In interpretative terms, the seat was able to reduce the vibration dose relative to the base by approximately 43.6% (0.5639) in the most favorable case, while in other conditions it nearly doubled the dose (1.9381, ~93.8% increase).

For the PZL-40 bump and the lowest load of 3.5 kg at 20 km/h, the Audi A6 showed a range of 0.9618–1.0301, corresponding to a transition from slight attenuation to minor amplification, while the Citroën C5 ranged between 0.7641 and 1.0333, that is, from strong attenuation to small amplification. After increasing the speed to 30 km/h with the same load, Audi A6 consistently showed attenuation (0.5639–0.7937), whereas Citroën C5 showed clear amplification (1.0697–1.9192), with values approaching doubling of the vibration dose at the seat relative to the base.

For PZL-40, 9.5 kg load at 20 km/h, Audi A6 demonstrated strong amplification (1.2407–1.9381), while Citroën C5 ranged from 0.8965 to 1.3204, i.e., from mild attenuation to moderate amplification. At 30 km/h, values stabilized at an amplification level of 1.1055–1.2634 in Audi A6 and 1.0542–1.1423 in Citroën C5, confirming consistent amplification, though less pronounced than at 20 km/h in the Audi.

For PZL-40, 14.5 kg load, Audi A6 at 20 km/h gave values of 0.8975–1.0547, and Citroën C5 0.9688–1.0274, indicating near-neutral seat behavior. At 30 km/h, Audi A6 showed 0.9339–1.0628, while Citroën C5 recorded 0.9640–1.0437, again with only minor deviations from unity. Thus, for PZL-40, a clear dependence on load is observed: at 3.5 kg, the vehicles behaved in opposite extremes (A6 attenuating, C5 amplifying), an effect further intensified with higher speed, while at 14.5 kg, both vehicles transmitted vibrations nearly unchanged relative to the base.

For the PP-30 bump with 3.5 kg at 20 km/h, Audi A6 consistently attenuated vibrations (0.8831–0.9537), whereas Citroën C5 remained close to unity (0.9575–1.0600). After raising speed to 30 km/h, Audi A6 showed values between 0.9373 and 1.0698, mostly attenuation with occasional slight amplification, while Citroën C5 showed 0.9834–1.0684, mostly mild amplification.

For PP-30, 9.5 kg load at 20 km/h, Audi A6 ranged 0.9447–1.0771 (from mild attenuation to slight amplification), and Citroën C5 0.9887–1.0327 (virtually neutral). At 30 km/h, Audi A6 recorded 0.9303–1.0227, still close to unity with a tendency toward attenuation, while Citroën C5 showed 0.8718–1.0632, indicating greater variability between seats—from noticeable attenuation to moderate amplification; the minimum value 0.8718 represents a reduction of about 12.8% of the dose at the seat relative to the base.

For PP-30, 14.5 kg load at 20 km/h, Audi A6 gave 0.8998–1.0599 and Citroën C5 0.9260–1.0722; at 30 km/h, Audi A6 recorded 0.9000–1.0839, and Citroën C5 0.9731–1.0625. Across the PP-30 subset, SEAT values remained “clustered” near unity (typically 0.90–1.08), suggesting that the sharper bump geometry limited additional attenuation or amplification by the seat and caused vibration transfer at the seat to be very similar to that at the base.

From a vehicle perspective, the most pronounced differences occurred for PZL-40 with 3.5 kg load: in Audi A6 at 30 km/h, the SEAT index dropped to 0.5639 (the strongest attenuation in the dataset), while in Citroën C5, under the same speed and load conditions, it reached as high as 1.9192 (strong amplification). At 9.5 kg and PZL-40, Audi A6 showed the greatest amplification tendency already at 20 km/h (up to 1.9381), while increasing the load to 14.5 kg in both vehicles “stabilized” the system, with SEAT values clustering around unity regardless of speed. For PP-30, regardless of load and speed, values remained close to 1 in both vehicles, with only small deviations toward attenuation or amplification, confirming that the sharper bump profile limits seat influence.

In summary, the SEAT index (VDV_seat / VDV_base) is strongly dependent on the vehicle–bump–load interaction and reveals two typical scenarios. The first is for PZL-40, where seat effects can be extreme: from strong attenuation in Audi A6 with 3.5 kg at 30 km/h (0.5639) to pronounced amplification in Citroën C5 under the same conditions (up to 1.9192) and in Audi A6 with 9.5 kg at 20 km/h (up to 1.9381). The second is for PP-30, where in most configurations the seat behaved as a “transparent” element in vibration transfer, keeping SEAT values close to unity. From a practical standpoint, the most favorable conditions occur when SEAT < 1, meaning the seat effectively attenuates the vibration dose relative to the base, while the most unfavorable cases—SEAT ≫ 1—indicate seat amplification; in the dataset, both situations occurred primarily for PZL-40, while PP-30 was dominated by neutral transmission.

The SEAT index at the rear bench seat was also determined for both vehicles (Audi A6, Citroën C5), two bump types (PZL-40, PP-30), and two travel speeds (20 and 30 km/h). The values presented are means from 10 runs for each configuration: Audi/PZL-40—0.4599 (20 km/h) and 0.3929 (30 km/h); Audi/PP-30—0.4033 and 0.4077; Citroën/PZL-40—0.4495 and 0.3543; Citroën/PP-30—0.4278 and 0.3916. Averaged across all conditions, the Citroën showed a lower SEAT (0.4058) than the Audi (0.4160), indicating slightly more favorable vibration attenuation in the C5 body–seat system under the tested scenarios. The effect of speed clearly depended on bump type (speed × type interaction): for PZL-40, the transition from 20 to 30 km/h significantly reduced SEAT (Audi: −0.0670; −14.6%, Citroën: −0.0952; −21.2%), while for PP-30 the effect was small or moderate (Audi: +0.0044; +1.1%, Citroën: −0.0362; −8.5%). Comparing bump types at constant speed, at 20 km/h PP-30 was more favorable (Audi: −12.3% vs. PZL-40; Citroën: −4.8%), while at 30 km/h PZL-40 had the advantage (Audi: PP-30 worse by +3.8%; Citroën: +10.5%). The lowest, and thus most favorable, value was recorded for Citroën on PZL-40 at 30 km/h (0.3543), while the highest occurred for Audi on PZL-40 at 20 km/h (0.4599). Speed-averaged values confirm that driving at 30 km/h generally resulted in lower SEAT values at the seat (Audi: 0.4003 vs. 0.4316; Citroën: 0.3729 vs. 0.4386), particularly for the PZL-40 geometry.

The SEAT values determined on the rear bench seat (Table 10) were compared with the SEAT values for the child seat cushion (Table 9) in the Audi A6 and Citroën C5 during passages over PZL-40 and PP-30 speed bumps at 20 and 30 km/h. On the rear bench seat, all averages fall within a narrow range of 0.354–0.460, that is, consistently <1, which indicates a constant attenuation of vibration dose relative to the ISOFIX base. The lowest values were obtained for PZL-40 at 30 km/h (e.g., Citroën 0.3543, Audi 0.3929), while the highest were recorded for PZL-40 at 20 km/h (Audi 0.4599, Citroën 0.4495). In contrast, for the child seat cushion, the scatter of SEAT values is much larger, from 0.5639 to 1.9381 (Table 9). This means that, depending on the configuration, the child seat can either attenuate (SEAT < 1) or amplify (SEAT > 1) the transmission of vibrations relative to the base.

Clear differences are visible between bump types. For PP-30, child seat indices are generally close to unity (typically ~0.90–1.08), indicating transmission without significant change. For PZL-40, a much larger variability is observed—from strong attenuation to strong amplification—depending on the vehicle and load mass. For example, at PZL-40, 3.5 kg, 30 km/h, the Audi A6 reached 0.5639 (substantial attenuation), while under similar conditions the Citroën C5 reached as high as 1.9192 (marked amplification). At PZL-40 and 9.5 kg, 20 km/h, the Audi A6 produced the maximum amplification of 1.9381, whereas at the highest load mass of 14.5 kg both vehicles approached SEAT ≈ 1, suggesting a quasi-neutral behavior of the child seat cushion.

Thus, the rear bench seat behaves as a stable isolator (SEAT always <1, narrow range), while the child seat cushion is highly sensitive to the vehicle–bump–mass interaction: for PP-30, transmission is mostly neutral (SEAT ≈ 1), whereas for PZL-40, both favorable attenuation and unfavorable amplification of vibrations relative to the ISOFIX base are possible.

3.4. Data Analysis

Table 11. One-way analysis of variance (ANOVA, Type II) for RMS, VDV, and RMQ indices on the ISOFIX base.

Indicator	Factor	F	df1	df2	p	η2	Request (α = 0.05)
RMS	Vehicle (Audi vs. Citroën)	0.0226	1	106	0.8809	0.0002	Lack of relevance
RMS	Prog type (PZL-40 vs. PP-30)	107.3346	1	106	<0.0001	0.5031	significant, large effect
RMS	Speed (20 vs. 30 km/h)	56.9523	1	106	<0.0001	0.3495	significant, medium-high
RMS	Mass (3.5 vs. 9.5 vs. 14.5 kg)	4.4517	2	106	0.0139	0.0775	Essential, small
RMS	Child seat model (5)	13.0302	4	106	<0.0001	0.3296	significant, medium
VDV	Vehicle	0.0984	1	106	0.7544	0.0009	Lack of relevance
VDV	Threshold Type	192.3206	1	106	<0.0001	0.6447	significant, very large
VDV	Velocity	112.3777	1	106	<0.0001	0.5146	significant, large
VDV	Mass	4.3063	2	106	0.0159	0.0751	Essential, small
VDV	Child seat model	9.9864	4	106	<0.0001	0.2737	significant, medium
RMQ	Vehicle	0.0383	1	106	0.8453	0.0004	Lack of relevance
RMQ	Threshold Type	186.7606	1	106	<0.0001	0.6379	significant, very large
RMQ	Velocity	103.377	1	106	<0.0001	0.4937	significant, large
RMQ	Mass	2.71	2	106	0.0712	0.0486	at the border/irrelevant
RMQ	Child seat model	12.1098	4	106	<0.0001	0.3136	significant, medium

summarizes the results of one-way analyses of variance (ANOVA, Type II) for three vibration measures: RMS, VDV, and RMQ, recorded on the ISOFIX leg/base during passages over PZL-40 and PP-30 speed bumps at speeds of 20 and 30 km/h, for load masses of 3.5/9.5/14.5 kg, five child seat models (Avionaut, Britax Römer, Maxi-Cosi, Cybex, Joie), and two vehicles (Audi A6, Citroën C5). In each analysis, the effect of a single factor was assessed separately: vehicle, bump type, speed, load mass, and child seat model.

The table reports, for each test, the F statistic, degrees of freedom (df1, df2), p-value, and effect size η² (share of variance explained by the factor). The significance threshold was set at α = 0.05. Interpretation of η² follows the conventional guidelines: approximately small effect ≈ 0.01–0.06, medium ≈ 0.06–0.14, large > 0.14.

The table should be read row by row: for each measure (RMS, VDV, RMQ), the ANOVA results are presented for each of the five factors, allowing for a straightforward identification of the variables exerting the strongest influence on the recorded vibration levels.

The analysis of variance (ANOVA) for RMS, VDV, and RMQ recorded on the ISOFIX leg/base showed that the strongest factor was the type of speed bump. For RMS, F(1,106) = 107.33; p < 0.0001; η² = 0.503, for VDV, F(1,106) = 192.32; p < 0.0001; η² = 0.645, and for RMQ, F(1,106) = 186.76; p < 0.0001; η² = 0.638. This means that the difference between PP-30 and PZL-40 accounts for ~50% of RMS variance and ~64% of VDV/RMQ variance. The effect is unidirectional: PP-30 produces higher levels of all three indices compared to PZL-40, consistent with its more impulsive excitation profile. The “dose” measures (VDV, RMQ) are particularly sensitive, hence their larger η² compared to RMS.

Travel speed also showed a large effect. For RMS, F(1,106) = 56.95; p < 0.0001; η² = 0.350, for VDV, F(1,106) = 112.38; p < 0.0001; η² = 0.515, and for RMQ, F(1,106) = 103.38; p < 0.0001; η² = 0.494. The transition from 20 to 30 km/h clearly increases all vibration indices at the ISOFIX base, with a relatively stronger rise for VDV and RMQ. In practice, even a moderate speed increase significantly raises the “dose” of vibrations transmitted to the mounting system.

Load mass had a significant but small effect: RMS (F(2,106) = 4.45; p = 0.0139; η² = 0.078), VDV (F(2,106) = 4.31; p = 0.0159; η² = 0.075), and borderline for RMQ (F(2,106) = 2.71; p = 0.071; η² = 0.049). The dependence was not strictly linear—in many configurations the 9.5 kg load yielded higher values than 3.5 or 14.5 kg, likely related to local resonances of the child seat–ISOFIX system and shifts in load paths.

Child seat model differentiated results to a medium extent: RMS F(4,106) = 13.03; p < 0.0001; η² = 0.330; VDV F(4,106) = 9.99; p < 0.0001; η² = 0.274; RMQ F(4,106) = 12.11; p < 0.0001; η² = 0.314. Structural differences (stiffness, damping, support geometry) are “visible” already at the ISOFIX base, not only at the seat surface, and clearly modulate the injected vibration energy.

Vehicle type (Audi vs. Citroën) showed no significant effect: RMS F = 0.0226; p = 0.8809; η² ≈ 0; VDV F = 0.0984; p = 0.7544; η² ≈ 0; RMQ F = 0.0383; p = 0.8453; η² ≈ 0. The ISOFIX base is dominated by local interactions of bump–wheel–mounting and speed, while global body properties of the tested cars were not decisive.

Practical conclusions are consistent across all three metrics. (1) Bump type and speed are the dominant sources of vibration loading: PP-30 at 30 km/h is the most unfavorable configuration, while lower speeds and the milder PZL-40 geometry substantially reduce VDV/RMQ and moderately reduce RMS. (2) Load mass matters—settings near 9.5 kg tend to be less favorable, while extreme load levels are often better. (3) Seat model choice matters even at the ISOFIX base, with designs offering stronger damping and better support architecture helping to limit RMS/VDV/RMQ regardless of vehicle.

Post hoc Tukey HSD (α = 0.05) was performed for multi-level factors: load mass (3.5/9.5/14.5 kg) and child seat model (AVIONAUT, Britax Römer, Maxi-Cosi, Cybex, Joie), separately for RMS, VDV, and RMQ on the ISOFIX base. Mass: none of the pairwise comparisons reached significance after Tukey correction (all FALSE). For VDV, two contrasts approached significance (3.5 vs. 9.5: p = 0.0511; 9.5 vs. 14.5: p = 0.0586), and for RMQ, 9.5 vs. 14.5 had p = 0.0990. The trend indicates slightly higher values at 9.5 kg, but without statistical support.

Seat model: significant effects appeared only for AVIONAUT compared to others, always with higher values:

• RMS: AVIONAUT > Britax Römer, Cybex, Maxi-Cosi (significant).
• VDV: AVIONAUT > Cybex, Maxi-Cosi (significant).
• RMQ: AVIONAUT > Cybex, Maxi-Cosi (significant).

This shows that structural design (stiffness/damping/supports) significantly modulates vibration levels at the ISOFIX node, with AVIONAUT configurations producing higher values than some competitors (especially Cybex and Maxi-Cosi; for RMS also Britax Römer).

Table 12. Tukey post hoc comparisons (α = 0.05) for pairs of load mass and child seat model levels, mean differences in RMS, VDV, and RMQ indices measured at the ISOFIX base (95% CI, adjusted p, TRUE/FALSE).

Measure	Factor	Level 1	Level 2	Difference in Means	p_adj	CI95_Lower	CI95_Upper	TRUE
RMS	Mass	3.5 kg	9.5 kg	0.0472	0.9139	−0.2301	0.3245	FALSE
RMS	Mass	3.5 kg	14.5 kg	0.1654	0.3555	−0.1195	0.4502	FALSE
RMS	Mass	9.5 kg	14.5 kg	0.1182	0.5877	−0.1667	0.403	FALSE
RMS	Child seat model	AVIONAUT	Britax Romer	0.4983	0.0053	0.1076	0.8891	TRUE
RMS	Child seat model	AVIONAUT	Cybex	0.5165	0.0034	0.1257	0.9072	TRUE
RMS	Child seat model	AVIONAUT	Joie	0.3832	0.0787	−0.0267	0.793	FALSE
RMS	Child seat model	AVIONAUT	Maxi-Cosi	0.5457	0.0017	0.155	0.9365	TRUE
RMS	Child seat model	Britax Romer	Cybex	0.0182	0.9999	−0.3726	0.4089	FALSE
RMS	Child seat model	Britax Romer	Joie	−0.1152	0.9361	−0.525	0.2947	FALSE
RMS	Child seat model	Britax Romer	Maxi-Cosi	0.0474	0.9972	−0.3434	0.4382	FALSE
RMS	Child seat model	Cybex	Joie	−0.1334	0.9075	−0.5432	0.2765	FALSE
RMS	Child seat model	Cybex	Maxi-Cosi	0.0292	0.9998	−0.3616	0.42	FALSE
RMS	Child seat model	Joie	Maxi-Cosi	0.1626	0.7875	−0.2383	0.5634	FALSE
VDV	Mass	3.5 kg	9.5 kg	0.7666	0.0511	−0.0034	1.5366	FALSE
VDV	Mass	3.5 kg	14.5 kg	−0.0114	0.9999	−0.8063	0.7835	FALSE
VDV	Mass	9.5 kg	14.5 kg	−0.778	0.0586	−1.5729	0.0169	FALSE
VDV	Child seat model	AVIONAUT	Britax Romer	1.9957	0.0524	−0.0096	4.001	FALSE
VDV	Child seat model	AVIONAUT	Cybex	2.1815	0.0255	0.1762	4.1868	TRUE
VDV	Child seat model	AVIONAUT	Joie	1.7426	0.1453	−0.2627	3.7479	FALSE
VDV	Child seat model	AVIONAUT	Maxi-Cosi	2.4046	0.007	0.3993	4.4099	TRUE
VDV	Child seat model	Britax Romer	Cybex	0.1858	0.9956	−1.8195	2.1911	FALSE
VDV	Child seat model	Britax Romer	Joie	−0.2531	0.9892	−2.2584	1.7522	FALSE
VDV	Child seat model	Britax Romer	Maxi-Cosi	0.4089	0.9476	−1.5964	2.4142	FALSE
VDV	Child seat model	Cybex	Joie	−0.4389	0.9352	−2.4442	1.5664	FALSE
VDV	Child seat model	Cybex	Maxi-Cosi	0.2231	0.9979	−1.7822	2.2284	FALSE
VDV	Child seat model	Joie	Maxi-Cosi	0.662	0.6284	−1.3433	2.6673	FALSE
RMQ	Mass	3.5 kg	9.5 kg	0.3761	0.1493	−0.1218	0.874	FALSE
RMQ	Mass	3.5 kg	14.5 kg	−0.0576	0.9769	−0.5766	0.4614	FALSE
RMQ	Mass	9.5 kg	14.5 kg	−0.4337	0.099	−0.9527	0.0853	FALSE
RMQ	Child seat model	AVIONAUT	Britax Romer	0.7525	0.0556	−0.0113	1.5164	FALSE
RMQ	Child seat model	AVIONAUT	Cybex	0.8099	0.0319	0.0461	1.5738	TRUE
RMQ	Child seat model	AVIONAUT	Joie	0.5691	0.2874	−0.232	1.3703	FALSE
RMQ	Child seat model	AVIONAUT	Maxi-Cosi	0.8741	0.0164	0.1103	1.638	TRUE
RMQ	Child seat model	Britax Romer	Cybex	0.0574	0.9996	−0.7065	0.8212	FALSE
RMQ	Child seat model	Britax Romer	Joie	−0.1834	0.9691	−0.9845	0.6177	FALSE
RMQ	Child seat model	Britax Romer	Maxi-Cosi	0.1216	0.992	−0.6422	0.8854	FALSE
RMQ	Child seat model	Cybex	Joie	−0.2408	0.9197	−1.0419	0.5604	FALSE
RMQ	Child seat model	Cybex	Maxi-Cosi	0.0642	0.9993	−0.6996	0.8281	FALSE
RMQ	Child seat model	Joie	Maxi-Cosi	0.305	0.8286	−0.4961	1.1061	FALSE

presents the detailed Tukey post hoc comparisons (mean differences, adjusted p, 95% CI, significance TRUE/FALSE) for mass and child seat model.

The largest effect was observed for bump geometry (partial η² = 0.64, 95% CI [0.58–0.70]), followed by speed (partial η² = 0.42, 95% CI [0.35–0.49]). CRS model had a medium effect (partial η² = 0.29, 95% CI [0.23–0.36]), while child mass showed only a small effect (partial η² = 0.07, 95% CI [0.02–0.12]).

The analysis of dependencies was carried out for four measures: RMS, VDV and RMQ (recorded on the ISOFIX leg/base) as well as SEAT (the ratio VDV_seat/VDV_base). The explanatory variables were speed (20 and 30 km/h, treated numerically) and load mass (3.5/9.5/14.5 kg). Correlations were calculated separately for each combination of speed bump type × vehicle (PZL-40/PP-30 × Audi A6/Citroën C5), as well as globally after pooling all observations. For interpretation, standard speed bumps of correlation strength were adopted: |r| ≈ 0.1 weak, ≈0.3 moderate, ≥0.5 strong. Pearson correlations (r) of RMS, VDV, RMQ and SEAT are presented in

Table 13. Pearson correlations (r) of RMS, VDV, RMQ and SEAT indices.

Speed Bump	Vehicle	Measure	n	r_Speed	p_Speed	r_Mass	p_Mass
PP-30	Audi A6	RMQ	28	0.7305	0	0.3277	0.0887
PP-30	Citroën C5	RMQ	28	0.6815	0.0001	0.0561	0.7768
PZL-40	Audi A6	RMQ	30	0.698	0	−0.0610	0.7488
PZL-40	Citroën C5	RMQ	30	0.4368	0.0158	0.0825	0.6647
PP-30	Audi A6	RMS	28	0.6345	0.0003	0.4334	0.0212
PP-30	Citroën C5	RMS	28	0.5681	0.0016	0.1338	0.4974
PZL-40	Audi A6	RMS	30	0.5834	0.0007	−0.0597	0.754
PZL-40	Citroën C5	RMS	30	0.1935	0.3057	0.1145	0.5469
PP-30	Audi A6	VDV	28	0.7423	0	0.3931	0.0385
PP-30	Citroën C5	VDV	28	0.7174	0	0.1439	0.4649
PZL-40	Audi A6	VDV	30	0.7418	0	−0.0853	0.6539
PZL-40	Citroën C5	VDV	30	0.4734	0.0082	0.0789	0.6784
PP-30	Audi A6	SEAT	28	0.1521	0.4397	0.1734	0.3777
PP-30	Citroën C5	SEAT	28	−0.0060	0.9758	−0.1163	0.5557
PZL-40	Audi A6	SEAT	30	−0.3675	0.0457	0.2233	0.2355
PZL-40	Citroën C5	SEAT	30	0.3359	0.0695	−0.3452	0.0617

.

At the ISOFIX level the most regular pattern was the increase in all measures with speed. In the global analysis the results were r = 0.417 for RMS, r = 0.497 for VDV and r = 0.481 for RMQ (all p < 0.001). This confirms that increasing speed from 20 to 30 km/h systematically raises both vibration dose (VDV) and shock intensity (RMQ), and to a slightly lesser extent RMS. The same effect is visible in individual combinations of bump type and vehicle. For example, PP-30/Audi gives r = 0.742 (VDV) and r = 0.731 (RMQ), PP-30/Citroën r = 0.717 (VDV) and r = 0.682 (RMQ), PZL-40/Audi r = 0.742 (VDV) and r = 0.698 (RMQ), PZL-40/Citroën r = 0.473 (VDV) and r = 0.437 (RMQ), all significant (p ≤ 0.016). For RMS the correlations are mostly moderate to strong: PP-30/Audi r = 0.635, PP-30/Citroën r = 0.568, PZL-40/Audi r = 0.583 (p ≤ 0.001). The only exception is PZL-40/Citroën, where the relation with speed was not significant (r = 0.194; p = 0.306). This picture indicates that speed is the most reliable factor for limiting the effects at the ISOFIX base, and that dose and shock indices (VDV, RMQ) are the most sensitive to this parameter.

With respect to load mass, the correlations are predominantly weak and not significant. Globally the results are r = 0.126 (RMS; p = 0.179), r = 0.101 (VDV; p = 0.280) and r = 0.067 (RMQ; p = 0.472). When broken down by vehicle × bump type, significance appears only in the PP-30/Audi scenario, where RMS increases with mass (r = 0.433; p = 0.021) and VDV also increases with mass (r = 0.393; p = 0.039). Other configurations yield r values close to zero (p ≫ 0.05). This suggests that load is not a universal parameter driving RMS, VDV or RMQ. The effects of mass are local and may result from resonances and subtle changes in force transmission paths in the child seat–ISOFIX–body system.

For the SEAT index (seat/base transmission) there is no global linear trend either with speed (r = −0.020; p = 0.833) or with mass (r = −0.011; p = 0.907). This is consistent with the intuition that as a ratio of two VDV measures SEAT largely cancels out common changes in excitation level caused by speed and load. However, a few local relationships appear. In the PZL-40/Audi configuration the index decreases with speed (r = −0.368; p = 0.0457), which means relatively better damping at the seat at 30 km/h compared to 20 km/h. In PZL-40/Citroën, the positive relation is close to significance (r = 0.336; p = 0.070). In both PP-30 combinations, the correlations SEAT–speed and SEAT–mass remain not significant. The cautious conclusion is that seat/base transmission depends mainly on the interaction of seat and mounting construction with the vehicle body dynamics in given conditions, and not on a simple scaling of speed or load.

The correlation data clearly indicate speed as the primary factor influencing vibration levels at the ISOFIX base, with the strongest effects for VDV and RMQ. Load has limited and context-dependent importance, statistically significant only in the PP-30/Audi scenario. The SEAT index remains globally stable with respect to linear changes in speed and load, and the few local effects confirm that its behavior is determined by design details and excitation conditions rather than by these two variables alone. From a practical perspective this means that managing speed, especially on sharper bumps, offers the most predictable improvement, whereas manipulating mass or expecting the seat cushion to compensate for increased excitation does not guarantee consistent benefits across the tested configurations.

Correlations between RMS, VDV, and RMQ indices were statistically significant (r = 0.72–0.88). The inclusion of 95% confidence intervals (e.g., RMS–VDV: r = 0.82, 95% CI [0.76–0.87]) confirms the robustness of these associations.

It should be noted that the descriptive statistics summarize the system behavior for four measures: RMS, VDV and RMQ recorded at the ISOFIX leg/base, as well as SEAT defined as the ratio VDV_seat/VDV_base. For each measure the mean, standard deviation and sample size were calculated at all levels of the factors: vehicle, bump type, speed, mass, and child seat model.

At the ISOFIX level, differences between vehicles are negligible: mean RMS values are 1.8908 (SD 0.5613; n = 58) for the Audi A6 and 1.8822 (SD 0.4846; n = 58) for the Citroën C5, i.e., a difference of less than 0.5%. Similarly, VDV: 8.0090 vs. 7.9206 (≈1.1%), and RMQ: 3.3852 vs. 3.3669 (≈0.5%). This means that the vehicle body type itself is not the main source of variation, and vibration transmission to the ISOFIX base is very similar in both cars.

The geometry of the obstacle has a much stronger effect. For PP-30, mean RMS/VDV/RMQ values are significantly higher than for PZL-40: respectively, 2.1894 vs. 1.6038 (+36.5% for RMS), 9.9685 vs. 6.0947 (+63.6% for VDV) and 4.0313 vs. 2.7646 (+45.8% for RMQ). This consistently indicates that the sharper PP-30 profile generates greater excitation at the ISOFIX node. Speed works in the same direction: increasing from 20 to 30 km/h raises RMS from 1.6696 to 2.1034 (+26.0%), VDV from 6.4698 to 9.4598 (+46.2%) and RMQ from 2.9007 to 3.8515 (+32.8%). From a practical perspective, bump type and speed are therefore the key “levers” controlling vibration levels at the base.

The influence of load mass is weaker and less consistent. Mean RMS for 3.5 and 9.5 kg is almost identical (1.7767 vs. 1.7774), while for 14.5 kg it increases to 2.0820 (≈+17% relative to 9.5 kg). VDV rises from 7.3043 (3.5 kg) through 7.9340 (9.5 kg) to 9.6864 (14.5 kg), and RMQ from 3.1297 through 3.2993 to 3.8665. A rising trend is visible for the highest mass, although it is not as clear as the effects of speed and bump type.

For the child seat model (still at the ISOFIX level), the mean values range from lowest to highest as follows: AVIONAUT (RMS 1.5420; VDV 6.9426; RMQ 3.0127), Maxi-Cosi (1.7857; 7.8411; 3.3116), Britax Romer (1.8891; 8.4060; 3.4130), Joie (1.8709; 8.5731; 3.4732) and Cybex (1.9840; 8.8736; 3.6377). All models fall within similar ranges (SD ~0.5–0.6 for RMS and ~3.0–3.3 for VDV), but the ordering of means suggests that design features of the seats (stiffness, damping, support structure) influence the vibration response at the ISOFIX node to some extent.

The SEAT index clusters close to unity, which means that the child seat most often transmits a vibration dose similar to that at the base, with deviations in both directions depending on conditions. For vehicles the average values were 1.0879 (SD 0.3121; n = 58) for Audi and 1.0178 (SD 0.2095; n = 58) for Citroën, with Audi showing slightly greater variability. The key dependence is on bump type: for PP-30 the mean SEAT = 0.9808 (SD 0.0862; n = 56), while for PZL-40 SEAT = 1.1213 (SD 0.3380; n = 60). This indicates that for the sharper PP-30 the seat tends more often to damp or transmit one-to-one, whereas for PZL-40 amplification (SEAT > 1) and larger scatter are more frequent. The effect of speed is minor: on average 1.0712 (20 km/h) vs. 1.0345 (30 km/h), indicating a small decrease in SEAT at higher speed, but the scale of the difference is small compared with SD. Mass effects are nonlinear (1.0083 for 3.5 kg, 1.1125 for 9.5 kg, 0.9918 for 14.5 kg), which is typical of multi-point vibrating systems where local resonances and damping can alter seat-to-base transmission in a non-uniform way. Across seat models, mean SEAT values were: AVIONAUT 0.9893, Britax Romer 1.0138, Cybex 1.0448, Maxi-Cosi 1.0643, Joie 1.0920, all close to unity, with the highest variability for Joie (SD 0.2541) and the lowest for PP-30 as an excitation (SD 0.0862 at the factor level).

From an application perspective this means that the overall vibration exposure level is primarily determined by bump type and speed, while load mass and seat model modulate the outcome secondarily. At the ISOFIX base, differences between seats are noticeable but smaller than the influence of excitation geometry and speed. For the SEAT index, values mostly remain close to unity, indicating no systematic “decoupling” or “amplification” by the seat itself, except in cases where the bump profile (PZL-40) and seat design details result in greater variability and more frequent values above 1.

Using the method of calculation of potentially obtainable electrical energy proposed in [19], i.e., determining the velocity based on the recorded acceleration waveform, calculating the average kinetic power for the effective leg mass of the ISOFIX base and converting it into power and electricity taking into account the total efficiency of the acquisition and conversion path (η ≈ 0.144), it was estimated that it is possible to obtain an average of about Pel ≈ 8.6 mW. This corresponds to the energy accumulated in one hour of driving equal to Eel ≈ 30.8 J (≈8.56 mWh) at vibration amplitudes corresponding to passing through a speed bump. The study analyzed two types of release thresholds. In the case of “throwing” thresholds, generating higher vibration amplitudes, the electricity obtained will be correspondingly higher compared to thresholds with a milder profile. The stored energy can power simple low-power sensors, e.g., to assess the level of discomfort. For a sensor with an average consumption of Psens = 10 μW, the available energy would allow it to operate continuously for about t ≈ 856 h, which corresponds to approx. 35.6 days. For sensors with higher power consumption, the operating time is proportionally reduced, for example, for Psens = 50 μW it is about 171 h (7.1 days), and for Psens = 100 μW about 85.6 h (3.6 days). The adopted measurement methodology and system layout were presented in detail in [19].

4. Discussion

The results of the study show a consistent pattern of relationships between the excitation geometry, driving parameters, and the construction of the seat–vehicle system and the level of vibration comfort. At the ISOFIX base, the main differentiating factors for RMS, VDV, and RMQ values were driving speed (clear increase at 30 km/h compared to 20 km/h) and bump type (PP-30 clearly “sharper” than PZL-40). The transmission index SEAT, defined as VDV_seat/VDV_base, was most often clustered close to unity, with both damping cases (SEAT < 1) and amplification cases (SEAT > 1), with a maximum of about 1.94 and a minimum of about 0.56. This distribution of values is consistent with numerous observations that child seats are not inherently effective vibration isolators across the full frequency and road condition range. In some scenarios, they may even amplify vibrations relative to the vehicle reference point [1]. Our results add a conditional dimension to this conclusion: whether the seat dampens or amplifies depends on the vehicle–bump–mass interaction and the intrinsic properties of the child seat.

The differences observed between the Audi A6 and Citroën C5 cannot be explained solely by suspension stiffness. Several other design factors likely contribute to the transmissibility of vibrations. First, the geometry of the rear bench mounting determines the effective stiffness and the load path between the floor and the CRS base. Second, the viscoelastic properties of the bench foam influence both damping and the frequency shift in resonance peaks. Third, tire compliance interacts with suspension dynamics and modifies the excitation spectrum reaching the car body. Finally, local body-in-white structural modes may alter vibration propagation and amplify specific frequency bands. These combined effects explain why the same CRS can act as a vibration isolator (SEAT < 1) in one vehicle, while amplifying vibrations (SEAT > 1) in another.

The obtained results are consistent with earlier research on vibration transmission in child restraint systems (CRS). Wicher and Więckowski [16] showed that ISOFIX-mounted seats, while advantageous for crash safety, resulted in higher vertical accelerations compared to belt-mounted seats, with RMS values in the range of 0.6–3.24 m/s². According to ISO 2631 criteria, these levels corresponded to discomfort categories ranging from “uncomfortable” to “extremely uncomfortable”. Giacomin [14,15] and co-workers further demonstrated that children exhibit higher whole-body resonance frequencies (~7.4 Hz) than adults (4–5 Hz), which increases their susceptibility to vibration amplification in the low-frequency range typical of road-induced excitations.

In the present study, RMS values measured at the CRS cushion ranged between 1.0 and 2.3 m/s², confirming the tendency of child seats to amplify vibrations. The observed differences between the Audi A6 and Citroën C5 cannot be attributed solely to suspension stiffness. Additional contributing factors include the geometry of the rear bench mounting, the viscoelastic properties of the seat foam, tire compliance, and local body structural modes. These elements influence the effective stiffness and damping of the system, determining whether a CRS acts as a vibration isolator (SEAT < 1) or as an amplifier (SEAT > 1). This interpretation explains why the same CRS model may attenuate vibrations in one vehicle but intensify them in another.

Comparison with the literature shows agreement on the role of sharp bumps and higher speeds in generating large vibration doses and increased impulsiveness of the signal (VDV, RMQ). Field studies have shown that passing a bump at about 30 km/h leads to acceleration and dose levels classified as highly uncomfortable for passengers [2,3]. In our dataset these dependencies are clear: PP-30 produces significantly higher RMS/VDV/RMQ than PZL-40, and 30 km/h significantly higher than 20 km/h. The conclusion is also consistent that in many measurement scenarios the child seat does not sufficiently decouple vibrations, resulting in SEAT ≈ 1 or >1 [1,2,3]. It is noteworthy, however, that our data also included configurations with clear damping (SEAT < 1), which suggests that new material and structural solutions in certain models can locally improve transmission.

The way the seat is attached to the vehicle is described in the literature as important for vibration transmission. A rigid ISOFIX interface reduces deflections and micro-movements at the connection, which may increase the transmission of short impulsive vibrations, while belt mounting introduces some compliance [2]. Our results obtained at the ISOFIX base and the seat do not contradict this mechanism. The highest vibration doses were recorded for sharp road excitations with short rise times, a situation in which the lack of compliance favors energy transfer to the seat. In practice this indicates a design direction: damping elements in the ISOFIX interface (inserts, elastomers, connectors with controlled compliance) could limit the transmission of high-frequency components without compromising safety.

The effect of load mass proved secondary compared to speed and excitation geometry. In our data, correlations with mass were weak or globally insignificant, with significance appearing only locally in selected configurations. This is consistent with reports where changes in child mass within the typical range did not lead to clear, repeatable increases or decreases in seat accelerations. The mass effect is often masked by other response components and seat construction differences [4]. Mechanistically, this can be explained by the compromise tuning of seats for a wide user weight range. The damping-spring system operates in a “safe” part of its characteristic for most configurations, which limits the response gradient with respect to mass.

Significant differences between child seat models are consistent with earlier findings that construction (shell type, filling materials, seat geometry, presence of base and support leg) significantly modifies transmission [1,3]. In our dataset the range of mean RMS/VDV/RMQ values between models was large enough to result in differences in comfort categories (from “discomfort” to “strong discomfort”) under identical driving conditions. This indicates real room for design optimization with regard to vibration, which is consistent with the proposal that vibration comfort assessment should complement classic safety criteria in homologation regulations [21]. In particular, for sharp road excitations, targeted material and structural solutions could significantly reduce SEAT > 1.

Differences between the vehicles studied are not strictly hierarchical and result from the interaction of suspension–seat–excitation. A more compliant suspension can reduce large amplitude components but may extend decay time, which combined with a small load mass promotes excitation of the seat near its natural frequency. A stiffer suspension transmits a larger part of the impulse but shortens its duration, which can locally lower SEAT. Such interactions, difficult to capture in single-vehicle studies, explain discrepancies observed in the literature and confirm that results should be interpreted as interactions rather than isolated factors [1,2,3].

An important reference point for our results is [19], where vertical vibrations of a child seat on an ISOFIX base (with a support leg) were analyzed in the context of energy harvesting to power a “smart” seat. The author showed that under poor road conditions the vibration amplitudes and doses on the seat structure (seat, ISOFIX base, leg) were sufficient to power sensors in the microwatt range. Specifically, the possibility of maintaining a 10 µW sensor for over 42 days without tapping into the vehicle’s power supply was estimated. This observation aligns with our dataset: the RMS/VDV levels recorded at the ISOFIX base and leg in the harshest scenarios (PP-30, 30 km/h) reached values that, according to electromechanical transducer mechanics, provide a real power budget for low-power electronics (presence, temperature, posture monitoring). In other words, the vibration levels recorded in our study have not only comfort implications but also energetic ones: they constitute a usable source of dispersed energy, potentially harvested at the level of several to a dozen µW using piezoelectric or electromagnetic transducers in the base or leg of the seat. In practice, this is supported by the fact that the strongest excitations accumulate locally in the ISOFIX interface and support leg, where integration of miniature harvesters is technically simplest and does not interfere with the child’s contact area. These findings fit within the broader trend of combining comfort improvement (reduction of impulsive components through proper tuning and damping) with energy harvesting for autonomous safety and monitoring functions, a direction highlighted in the literature as aligned with sustainable mobility and onboard energy strategies.

The experimental findings can also be interpreted using a simplified lumped-parameter dynamic model, where the vehicle suspension, rear bench, CRS base, and child dummy are represented as successive mass–spring–damper elements. In such a framework, the strong influence of bump type and speed reflects the excitation of lightly damped modes, while the relatively small effect of dummy mass corresponds to limited resonance shifts under stiff ISOFIX support. This perspective is consistent with recent dynamic modeling approaches used for seated occupants [28] and reinforces that vibration transmission is governed mainly by interface stiffness and damping rather than child load alone.

In the latest literature, the number of papers analyzing vibration comfort and frequency transfer in other means of transport is increasing. For example, ref. [29] investigated the vertical vibrations and frequency spectrum transmitted to electric scooter users on different urban surfaces, using spectral analysis and comfort assessment for potential health implications. These results confirm the importance of proper frequency weighting and assessment of WBV exposure under real-world conditions, but at the same time highlight the lack of the latest direct studies on child seats (CRS). In this paper, we fill this gap from the automotive side, shifting the emphasis from micromobility to the vehicle-couch-CRS-child system and showing that the arousal profile (threshold geometry, speed) and the design of the interface (couch, ISOFIX base, CRS cushion) determine the child’s exposure and comfort sensations.

There is a lack of dedicated standards and literature addressing vibration discomfort in children. For this reason, the present study applied the ISO 2631-1 frequency weighting, which was originally developed for adults. While this approach does not capture all physiological differences between children and adults, it provides a consistent and internationally recognized framework for evaluating vibration exposure. The absence of child-specific criteria highlights the need for further research in this area and supports the relevance of the present work as one of the few attempts to characterize CRS-related vibration from the comfort perspective.

The principle of vibration energy harvesting has been previously described in detail by the author in [19]. In brief, the methodology assumes determining the instantaneous velocity from the recorded acceleration waveform, followed by calculating the average kinetic power for the effective vibrating mass of the ISOFIX base support leg. This kinetic power is then converted into electrical energy using piezoelectric elements, while accounting for the efficiency of each stage of the acquisition and conversion path (η ≈ 0.16). The study showed that, depending on road conditions, the harvested energy can supply low-power sensors (10–50 μW) for periods ranging from several tens of hours up to more than 40 days, confirming the practical feasibility of using seat vibrations as a power source for smart safety features.

Bringing the dataset together with findings from reviews and experimental studies gives a consistent picture of the main mechanisms. Sharp excitations and speed dominate, SEAT often remains ≈1 or >1, and the ISOFIX interface favors transmission of short impulses. At the same time the evidence shows that optimization of child seat construction and adaptation to operating conditions can meaningfully change exposure levels [1,2,3,4,5]. From a practical perspective this supports two parallel directions: design (child seat and interface construction with damping elements) and operational (speed management and avoidance of sharp bumps in infrastructure planning).

5. Conclusions

In the tested system, the level of exposure was primarily determined by the driving speed and the geometry of the threshold. Going from 20 to 30 km/h and approaching a sharper threshold, the PP-30 consistently raised the RMS, VDV and RMQ values, dominating over other variables. SEAT’s transmission index was most often close to unity, with both damping (SEAT < 1) and amplification (SEAT > 1) in the range of 0.56–1.94. The differences between the seat models were practically significant, and the so-called “vehicle effect” resulted from the interaction of suspension, seat and enforcement, without a simple hierarchy of one car “better” in all conditions. The load weight in the tested range of 3.5–14.5 kg had a secondary and unsystematic effect. The recorded vibration levels in the ISOFIX base nodes and the leg were so high that, in addition to the comfort significance, they allow micro-energy to be obtained to power low-power electronics (≈30.8 J/h on the thresholds, this is enough to power a 10 μW sensor for about 35 days).

From an application point of view, the most effective lever for reducing exposure is speed management and avoiding sharp thresholds. On the product side, it is advisable to integrate damping elements in the ISOFIX interface and in the seat itself, as well as design that limits impulse components. The results justify the inclusion of vibration comfort criteria in the evaluation and homologation and the consideration of micro-harvesters in the ISOFIX base or leg for autonomous sensor power supply and communication.

The interpretation of the results is limited by the experiment matrix (two speeds and two types of thresholds, two vehicles, selected CRS models), the focus on the vertical axis and time metrics, and the use of constant mass loads (without reproducing biodynamic reactions). Environmental conditions may have further influenced the system’s response.

Further work should expand the road stimuli and vehicle pool and CRS, supplement the analysis with spectral transmittance and lateral directions, as well as verify compact damping inserts, with the possibility of co-integration of thin energy harvesters, while maintaining mounting stability and ergonomics.