Energy-Absorbing Countermeasures for Subway-to-Pedestrian Collisions: A Combined Experimental and Multibody Modelling Approach

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Utilizing both impact testing and computational modelling methods to evaluate the effect of energy-absorbing countermeasures on subway-to-pedestrian fatality risk.

Abstract

Epidemiological analysis has revealed key insights into the frequency, severity, and circumstances surrounding subway-to-pedestrian incidents; however, there remains a lack of available impact test data specific to this impact type that can be used in modelling and countermeasure design studies. To address this gap, nine controlled impact tests were conducted using a cylindrical headform to derive force–penetration relationships for foam, as well as foam encased in 1 mm aluminium or 3 mm ABS shells. These relationships were validated in MADYMO multibody simulations. Building on a previous multibody computational study of subway-to-pedestrian collisions this research evaluates three passive countermeasure designs using a reduced simulation test matrix: three impact velocities (8, 10, and 12 m/s) and a trough depth of 0.75 m. In subway collisions, due to the essential rigidity of a subway front relative to a pedestrian, it is the pedestrian stiffness characteristics that primarily dictate the contact dynamics, as opposed to a combined effective stiffness. However, the introduction of energy-absorbing countermeasures alters this interaction. Results indicate that modular energy-absorbing panels attached to the train front significantly reduced the Head Injury Criterion (HIC) (by 90%) in the primary impact and pedestrian-to-wheel contact risk (by 58%), with greater effectiveness when a larger frontal area was covered. However, reducing primary impact severity alone did not substantially lower total fatal injury risk. A rail-guard design, used in combination with frontal panels, reduced secondary impact severity and led to the largest overall reduction in fatal injuries. This improvement came with an expected increase in hospitalisation-level outcomes, such as limb trauma, reflecting a shift from fatal to survivable injuries. These findings demonstrate that meaningful reductions in fatalities are achievable, even with just 0.5 m of available space on the train front. While further development is needed, this study supports the conclusion that subway-to-pedestrian fatalities are preventable.

1. Introduction

According to the International Association of Public Transport, 14 new cities opened a metro system between 2018 and 2020, taking the total number to 193, of which 15 have a length exceeding 250 km [1]. The New York City (NYC) Subway, one of the oldest and largest in the world, transported 5.5 million daily passengers as of 2019. Despite the global increases in metro, subway, and rail transportation use, pedestrian safety measures in this domain have not witnessed the same degree of advancement that can be seen in automotive vehicle design, such as rounded edges, crumple zones, and pop-up hoods [2,3] (Figure 1).

These significant safety advances have been achieved by combining accident data analysis, physical testing, computational modelling, and accident reconstruction. Collisions between subway vehicles and pedestrians, although less frequently addressed in comparison to road vehicle accidents, constitute a significant safety concern within urban settings, with deaths per 1,000,000 train miles increasing from 1.1 to 2.1 in the United States from 2013 to 2023 [4].

Despite decades of technological progress, the front-end design of subway vehicles has seen little evolution with respect to pedestrian safety. This stagnation is reflected in the persistently high subway-to-pedestrian fatality rates, which have shown minimal improvement since 1990 [5,6,7]. Research on subway-to-pedestrian collisions has primarily focused on collision avoidance measures, such as platform screen doors (PSDs). While studies have demonstrated the benefits of PSDs (e.g., [8,9,10]), implementing such large-scale infrastructural investments is often impractical in older subway networks like that of New York City [11]. This gap between complete collision avoidance and passive injury mitigation highlights the critical need for dedicated safety research specific to subway–pedestrian interactions.

Applying existing impact safety methodologies to subway–pedestrian collisions presents several challenges. Epidemiological studies have provided valuable insights into the frequency, severity, and circumstances of these incidents [7], yet there is a notable lack of impact test data specific to subway collisions for computational model validation. While some comparisons can be drawn from studies on Heavy Goods Vehicles (HGVs) with frontal energy-absorbing materials [12,13,14], additional considerations are required to adapt these findings to a subway-specific environment. For instance, a recent baseline computational study showed that secondary-contact head injuries—resulting from impacts with the track or infrastructure—can be more severe than primary-contact injuries, with higher median HIC₁₅ values at velocities up to 12 m/s compared to primary contact [15]. Additionally, the complexity of secondary-impact conditions and run-over risks (pedestrian contact with subway wheels) presents a challenge distinct from tram–pedestrian collisions, where impacts typically occur on flat surfaces. The presence of a third rail and drainage troughs, which have been shown to have an effect on the fatality risk of subway-to-pedestrian collisions, further differentiates this related impact type from those in surface transit systems [15].

From a design perspective, frontal energy-absorbing countermeasures (EACs) must balance impact mitigation with operational constraints. Subway EACs may need to be housed within a protective shell to withstand weather exposure and debris impacts while maintaining energy-absorbing properties [16]. However, the potential effect of this protective shell on head injury risk must be minimised to ensure a net safety benefit.

To address these challenges, this study aims to

• Conduct a series of impactor tests to experimentally derive force–penetration relationships for hard-shelled energy-absorbing materials, which will serve as inputs for computational modelling;
• Use MADYMO V7.8 multibody modelling software to assess the effect of various countermeasure designs on primary and secondary head injury risk compared to a validated baseline model;
• Evaluate how each countermeasure design affects run-over risk, ensuring that new safety features do not introduce unintended hazards.

2. Materials and Methods

2.1. Impactor Test Setup

An instrumented rigid headform with appropriate geometry was developed to support the multibody modelling portion of this study. This custom-manufactured headform comprises a solid aluminium dome with a radius of 0.0825 m and integrated accelerometer mounting points at its base. This dome is connected to a 0.32 m long aluminium cylinder with a wall thickness of 0.02 m. The cylinder serves two primary functions: it stabilises the headform during the acceleration phase with the assistance of small plastic fins and it adjusts the centre of gravity towards the flat side of the dome, positioning it closer to the accelerometer mounting locations to ensure accurate measurements. The overall mass of the headform is 10 kg, which enables the headform to effectively simulate impacts involving body regions with similar geometries, such as the shoulder. Based on a previous NYC Subway epidemiology study, the most common impact velocity is 12 m/s [7]. To accelerate the headform to the desired velocities, a HYGE Dynatest 500 Component Crash Simulation System was used. This system utilises differential gas pressure acting upon two surfaces of a thrust piston within a sealed cylinder.

To identify the suitable foam type for the proposed impact tests, three distinct commercial foam samples were subjected to compression testing with an Instron 3366 up to 80% strain. The examined foam types included firm foam (40 kg/m³), a mixed firm foam with a memory-foam topper (50 kg/m³), and a mixed bound foam (35 kg/m³) with a memory-foam topper. The bound foam exhibited the highest stiffness, making it the most suitable candidate for the intended application. For testing without a hard shell, the foam was held within a rigid mounting box. A total of six hard shells were created using 1 mm aluminium and 3 mm ABS (Figure 2). The material was ordered in sheets, then bent into shape using rolling pins and a heat strip. The side panels of the mounting box were removed when using the hard shells to facilitate lateral flexion of the shell.

Figure 3 outlines the basic instrumentation schematic for the headform impact tests. A Fastec 5G high-speed camera was mounted on the ceiling, facing the top surface of the energy-absorbing countermeasure, and was used to track the position of the headform. The camera’s frame rate was 2500 fps, with the foam illuminated by two spotlights. A MEMS piezoresistive PCB 726ch accelerometer was positioned inside the headform, with its sensitive axis oriented in the direction of motion. The accelerometer’s sample rate (51.2 kHz) was regulated by a 24-bit ADC PCB9234 data acquisition device. The accelerometer was powered by a battery pack housed within a Faraday cage, as the PCB9234 does not provide excitation voltage to piezoresistive accelerometers. Both the camera and accelerometer were activated via an RS PRO Retroreflective Photoelectric Sensor positioned as close as possible to the headform within the Dynatest mount. This arrangement ensured a synchronous start time for both the accelerometer and video footage for each test. The software utilised in this study comprised LABVIEW, Matlab 2024a, and MADYMO, with the raw accelerometer data passing through a 150 Hz Butterworth lowpass filter [17].

2.2. Simulation Test Setup

Three countermeasure design concepts were developed, each targeting a specific area of injury causation. highlighted by [15] primary-contact, secondary-contact, and run-over injuries. These designs are intended to work synergistically to provide a holistic approach to injury mitigation. While their combined use holds the potential for significant safety benefits, their effectiveness remains subject to further evaluation, and practical challenges such as manufacturing feasibility and integration into existing subway systems must also be considered. In this study, the MADYMO software package was used to simulate the effect of each countermeasure design on pedestrian head injury and run-over risk. The simulations used the 50th percentile male ellipsoid model and R160 train geometry developed in [15], as well as a subset of the initial conditions established in that work. Specifically, only the standing and jumping postures were selected, which are based on publicly available video footage (Figure 4).

The Front Panel (FP) countermeasure design features hard-shelled energy-absorbing panels mounted directly on the train front down to but not beyond the anticlimber (see Figure 5). Beyond mitigating head injuries, this design also addresses run-over risks through the strategic geometry of the panels. The panel shape is specifically designed to work in tandem with the drainage trough, leveraging its safety potential to redirect pedestrian kinematics away from hazardous areas such as the third rail. The geometry consists of two circles with radii of 0.15 m and 0.25 m, connected by an arc with a radius of 0.75 m, creating a contour with a minimum depth of 0.3 m and a maximum depth of 0.5 m. By positioning the larger curve at the outer edge of the train front, this configuration is designed to guide pedestrians during the free-fall phase of impact, influencing their trajectory toward the drainage trough and potentially reducing the likelihood of critical run-over injuries. To define contact interactions, three ellipsoids were modelled on each side of the train front to approximate the panel geometry with the experimentally derived contact characteristics of an aluminium-covered EAC. This approach allowed for an evaluation of the panel’s potential effectiveness in altering pedestrian kinematics and mitigating injuries across multiple scenarios.

The second Full Front Guard (FFG) design is aimed at increasing the effective area of the front-panel concept. While the front-panel EAC concept has an effective coverage range extending from the train front to the anticlimber, to ensure standing pedestrians receive the full benefit, this range must be extended further downwards (see Figure 6). While maintaining the same contact characteristics and geometry as the front panel concept, the vertical dimension of the countermeasure was extended such that the panels maintain a clearance of 0.2 m from the rail top (see Figure 5). An additional panel was placed in the centre, covering the coupler while leaving sufficient spacing for the operation of the door. This panel was angled to 45 degrees to further influence pedestrian kinematics toward the drainage trough and away from the third rail. Although more challenging in implementation compared to front panels, the full-frontal-guard concept is expected to have an effect on at least 70% of incidents involving a frontal subway-to-pedestrian collision [7].

The FP and FFG countermeasure design concepts address primary-contact head injury risk and run-over risk, but little benefit is expected from these designs in terms of secondary-contact head injury reduction. To address secondary contact, a rail covering [Track and Front Guard (TG)] was designed (see Figure 7 ). The intention of this rail covering is to provide a softer landing surface while also rounding out edges along the drainage trough and crossties. The geometry of this rail guard is similar to the FP concept and further guides pedestrian kinematics towards the drainage trough. This design concept is intended to be installed over existing rail infrastructure, specifically targeting high-risk areas to minimise financial and operational impact. To keep installation costs and required downtime manageable, coverage could be limited to station zones and extend only 60 m beyond each end of the platform. This approach is based on incident data, which indicates that just 3% of subway-to-pedestrian collisions occur beyond this distance from the platform edge. By implementing the rail-guard system in tandem with the proposed full-frontal train guard, it would be theoretically possible to address 97% of all recorded standing and jumping collisions from 2019 [7]. To evaluate the effect on head injury severity and run-over risk, the rail-guard design was integrated into the multibody simulation model using the FFG on the train front. Therefore, both the primary and secondary contact are affected. In this model, the rail guard is represented as a series of cylindrical elements positioned over the rails and across the crossties. These cylindrical elements use force-deformation characteristics derived from impactor tests with vehicle bonnets [18] to modify the kinematics of a pedestrian during a collision, reducing the likelihood of run-over.

2.3. Simulation Test Matrix and Outputs

The impact velocities tested in the MADYMO simulations (8, 10, and 12 m/s) were selected to match those used in the physical impact tests presented in

Table 1. Impact test matrix.

Foam EAC	3 mm ABS Shell	1 mm Aluminium Shell
7.5 m/s	7.5 m/s	7.5 m/s
10 m/s	10 m/s	10 m/s
11.5 m/s	11.5 m/s	11.5 m/s

. The simulation test matrix shown in

Table 2. Countermeasure design simulation test sample (N = 216).

Countermeasure	Impact Posture	Impact Position	Impact Velocity (m/s)	Total
Baseline	Jumping (x2)	Jumping High (Left Middle Right)	8	54
	Standing (x2)	Jumping Low (Left Middle Right)	10
		Standing (Left Middle Right)	12
Front Panels (FP)	Jumping (x2)	Jumping High (Left Middle Right)	8	54
	Standing (x2)	Jumping Low (Left Middle Right)	10
		Standing (Left Middle Right)	12
Full Front Guard (FFG)	Jumping (x2)	Jumping High (Left Middle Right)	8	54
	Standing (x2)	Jumping Low (Left Middle Right)	10
		Standing (Left Middle Right)	12
Track Guard (TG) with FFG	Jumping (x2)	Jumping High (Left Middle Right)	8	54
	Standing (x2)	Jumping Low (Left Middle Right)	10
		Standing (Left Middle Right)	12

includes variations in posture (standing and jumping), impact position (left, middle, and right), and countermeasure design, resulting in a total of 216 simulations.

Simulation outcomes were categorised as fatal, hospitalised, or survived. Fatal outcomes included the most severe contact events and AIS 6 head injury. Contact involving the head, torso, or third rail are grouped together and classified as fatal. These scenarios include severe outcomes such as decapitation or electrocution, and as such, subsequent metrics like HIC₁₅ score or limb contact are not considered. Simulations without these high-severity contact events are assessed further. HIC₁₅ is used to calculate the risk of AIS 6 and AIS 3+ head injury [19]. AIS6 head injuries are deemed unsurvivable and are categorized as fatalities [20]. Hospitalisation was determined by limb contact with the wheels or AIS 3 to AIS 5 head injury. Previous publications suggest that cases of amputation without other complications rarely lead to fatality. This two-tiered classification allows for a more meaningful interpretation of survivability and treatment severity across the different countermeasure configurations (See Figure 8).

The notches in the resulting box plots represent an approximation of the 95% confidence interval for the median, calculated using an asymptotic normality approximation as described by [21] (Equation (1)). In this study, non-overlapping notches are interpreted as indicating a statistically significant difference in medians at approximately p = 0.05. This visual method was applied to compare simulation outputs across countermeasure configurations, including primary- and secondary-contact HIC₁₅ scores.

$$Notch=Median \pm 1.57x{\displaystyle \frac{IQR}{n^{0.5}}}$$

(1)

3. Results

3.1. Derivation of Experimental Force Penetration Curves

Figure 9 illustrates the acceleration-time histories for all test conditions outlined in Table 1. Notably, the foam EAC exhibited the most prolonged pulse duration across all test velocities in comparison to the covered EAC configurations. At lower velocities (below 10 m/s), the foam EAC generated peak accelerations of approximately 24 G, whereas both covered EACs achieved marginally higher peaks near 27 G. Interestingly, as the impact velocity increases, the relative differences in peak acceleration between the EAC types shift. At 11.5 m/s, the foam EAC produced a larger peak acceleration (53 G) compared to both the aluminium and ABS variants (48 G), thereby reversing the trend previously observed at lower velocities.

To track the penetration of the headform into the EAC, high-speed video footage was analysed frame by frame. A fixed point on the headform was manually tracked in MATLAB by selecting its position in each video frame. These pixel coordinates were then converted into physical distances by utilising known distances and addressing parallax effects based on the camera’s position relative to the headform’s motion. The red points in Figure 10 display the total position change of the tracking point throughout the headform’s penetration during impact into the aluminium-covered EAC at 11.5 m/s. The pixel distance between each of these red points was used to determine the position time history. Figure 11 presents the total measured penetration during the loading phase under all test conditions.

The acceleration time histories (Figure 9) were combined with the mass of the headform and the penetration data captured from the high-speed camera footage (Figure 11) to derive the force–penetration relationships (see Figure 12). For all impact velocities, the covered EACs exhibit an initially high-stiffness region at low penetration, followed by a reduction in stiffness at roughly 0.05 m of penetration, after which another high-stiffness region is observed. This is most evident for the 10 m/s tests. In contrast, the foam EAC demonstrates a more linear response, with lower overall contact stiffness in comparison to the covered EACs.

The experimental impact environment was reconstructed in MADYMO using two rigid bodies, each with an ellipsoid: one representing the EAC and the other representing the headform. The EAC was fixed in place, while the headform was assigned initial velocities as specified in Table 1. The mass, geometry, and centre of gravity of the physical headform were used. Each force–penetration relationship was paired with its corresponding impact velocity. No friction or damping coefficients were applied in the simulation, and neither were the foam’s inertial values, as the effects of these factors were accounted for in the derived force–penetration characteristics.

Unloading curves and hysteresis slopes were manually determined through trial simulations. The results of the simulation are presented in Figure 13 with dashed lines alongside the physical experimental acceleration data. While both hysteresis and the unloading curve had a minimal impact on the overall acceleration profile, hysteresis had a slightly greater effect. However, both variables only influenced the final 15% of the curve.

3.2. Multibody Modelling of Passive Countermeasures

Figure 14 presents the distribution of HIC₁₅ scores for both primary (left) and secondary (right) contacts across all tested countermeasure designs and impact velocities. All countermeasure configurations resulted in a substantial reduction in median primary HIC₁₅ scores compared to the baseline model. The front-panel and full-frontal-guard designs consistently reduced primary head injury risk across all velocities, with the full frontal guard showing the lowest variability and lowest overall scores.

In contrast, the effects on secondary-contact HIC₁₅ were more variable. The track-and-front guard configuration was the only concept to demonstrate a statistically significant reduction in secondary HIC₁₅, as indicated by non-overlapping notches in several velocity conditions. The front panels, on the other hand, showed a slight increase in secondary HIC₁₅ scores, potentially due to altered fall trajectories and a higher likelihood of contact with the track area.

In addition to lowering median values, the most effective countermeasures also substantially reduced the spread and upper range of HIC₁₅ outcomes, highlighting their potential to mitigate both typical and extreme injury scenarios.

Figure 15 outlines the effect of each countermeasure design on the risk of contact between the train wheel and pedestrian body region. The risk of contact with the third rail is also shown. The baseline limb-to-wheel contact score of 0.5 (50%) is reduced to 0.35 with front panels. This is further reduced to 0.2 with a full front guard, as the effect is greater for standing pedestrians. Surprisingly, the addition of the track guard increased the limb CS to above the baseline risk.

Figure 16 illustrates the injury risk associated with each countermeasure configuration, grouped into two categories: fatal injuries and hospitalisation-level injuries. Fatal injury risk includes contributions from the head, torso, or third rail contact, as well as AIS 6 head injury. Hospitalisation risk reflects the combined probability of limb-to-wheel contact AIS 3–5 head injuries.

The baseline and front-panel configurations display the highest total risk of fatal injury, driven largely by high AIS 6 head injury risk. The track-and-front guard configuration shows a lower risk of fatal injury but a noticeably higher hospitalisation risk, primarily due to increased limb contact. The full frontal guard presents a balanced profile, with moderate risk across both categories.

In each simulation, the maximum HIC₁₅ value observed between the primary and secondary impacts was used to calculate head injury risk. This approach ensures that the reported risk reflects the most severe head injury outcome in each case, regardless of when the injury occurred.

4. Discussion

4.1. Impact Tests

The results of the impact tests provide key insights into the dynamic response of energy-absorbing countermeasures (EACs) and their influence on headform acceleration. The data presented in Figure 9 demonstrate that the foam EAC exhibits a lower amplitude but a longer-duration acceleration pulse compared to the covered EAC. The peak acceleration of all EACs increases with the impact velocity; however, the rate of increase is most pronounced in the foam EAC. Notably, at an impact velocity of 11 m/s, the foam EAC causes a peak acceleration of the headform that exceeds that of the covered variants. This may be attributed to the increasing stiffness of the foam as deformation increases, as well as the faster initial deceleration caused by the shells.

During quasi-static Instron testing, there was a notable rise in stress beyond 60% strain. However, those tests did not give rise to the viscoelastic effects observed in the dynamic tests. As the headform penetrates into the foam in the latter, air is expelled through the open cell pores within the foam block. It is hypothesised that the rate at which the air is expelled from the foam could alter the contact stiffness. Figure 17 shows how the contact stiffness changes with both penetration and velocity. This effect may explain why, for the 10 m/s tests, the aluminium and ABS shells experience similar acceleration pulses (Figure 9) despite differences in the penetration time history (Figure 11). The total penetration of the headform into the foam EAC during this test reached 0.27 m, equivalent to 90% of the total length, positioning it within a higher stress region from an elastic perspective. However, in contrast, the velocity of the headform within this region is very small, tending towards zero. This places the headform in a lower stiffness region from a viscous perspective. Both the aluminium- and ABS-shelled EACs demonstrated an initially higher stiffness compared to the foam EAC but a lower penetration. This reduced penetration into the foam effectively limits exposure to the foam’s higher stiffness region, thereby providing a protective advantage at higher impact velocities. For lower impact velocities, where both the penetration into the foam and velocity are low, the initial stiffness of the shells creates a higher peak acceleration.

Figure 13 demonstrates that the MADYMO model faithfully replicates the acceleration-time history during both the impact loading and unloading phases using the derived contact characteristics. The loading curve was derived based on the velocity change matching the initial impact velocity, determined via integration. However, due to the strong velocity dependency of the contact stiffness, the simulations were limited to this specific impact speed.

4.2. Head Injury Risk

4.2.1. Primary Contact

Both the median value and range of primary-contact HIC₁₅ scores in the baseline model show a clear velocity dependence. As shown in Figure 14 (left), the median primary-contact HIC₁₅ score increases by a factor of ~10 from an 8 m/s to a 11.5 m/s impact, consistent with trends observed in previous studies [15]. For impacts involving either front panels or a full frontal guard, the median value and magnitude of the velocity dependency are significantly smaller. The front-panel countermeasure results in an 85% reduction in the median HIC₁₅ score at 8 m/s, with a 95% reduction in HIC₁₅ at 11.5 m/s. While not statistically different from front panels, the full front guard further decreases the median HIC₁₅ by 95% of the baseline at 8 m/s. The range of calculated HIC₁₅ scores is also much smaller. This is likely due to the increased effectiveness in protecting standing pedestrians who may not have fully contacted the front panel design. As both concepts use the same contact definitions, the expected HIC₁₅ score is similar; however, the full frontal guard captures more of the simulated pedestrian postures, resulting in a tighter overall range of HIC₁₅ scores. As expected, the rail guard had no effect on primary-contact HIC₁₅ scores.

4.2.2. Secondary Contact

The front panels and full frontal guard show no statistical difference in terms of median HIC₁₅ scores for secondary contact compared to the baseline model, though in some instances, they do increase the overall range of calculated HIC₁₅ scores (Figure 14). This is likely due to the curvature of the countermeasure altering the fall kinematics of the pedestrian. The rail guard is the only countermeasure concept that produced a statistically significant reduction in secondary contact HIC₁₅ score compared to the baseline model. This was expected, as a softer contact stiffness is used for the rail guard compared to ground contact.

4.2.3. Run-Over Risk

Figure 15 shows a baseline limb contact score of 0.5, indicating that 50% of the 54 baseline simulations resulted in at least one limb–wheel contact. This aligns with the baseline score in [15]. Using the front-panel countermeasure reduces the limb contact score by 30% to 0.35, demonstrating that the panel’s geometry alters pedestrian fall kinematics to reduce wheel contact. The full frontal guard enhances this effect further by influencing standing pedestrians. Figure 18 illustrates the altered kinematics leading to avoided wheel contact.

The primary objective of the rail-guard design was to reduce the secondary-contact HIC₁₅ scores, which was successfully achieved, as illustrated in Figure 14. An additional goal was to lower overall contact scores by guiding the pedestrian into the drainage trough following secondary contact. The rail guard’s geometry (Figure 7) was modelled in MADYMO using cylinders positioned over the cross ties, maintaining a 0.1 m clearance. Ideally, the curvature of these cylinders should influence pedestrian kinematics so that if a person fell near the track edges, the curvature would redirect them toward the centre and into the drainage trough. However, Figure 15 reveals this intended effect was not fully realised. Although there was a modest reduction in body and head contact scores compared to the baseline model, the limb and third-rail contact scores were unexpectedly higher. A detailed review of the .kn3 MADYMO animation files suggests that the rounded cross-tie geometry, combined with a narrower trough from the rail guards, caused pedestrians to rebound upward after ground contact, increasing the risk of wheel impact. This is because the pedestrian’s linear velocity remains predominantly horizontal, and the large radius of the rounded cross ties acts like a ramp, propelling the pedestrian upward after contact. An example of this is depicted in Figure 19.

4.3. Overall Safety Effect

Figure 16 presents the overall injury risk associated with each countermeasure configuration, distinguishing between fatal and hospitalisation-level outcomes.

The track-and-front guard configuration demonstrates the lowest total risk of fatal injury among all configurations. While it is associated with a higher level of hospitalisation risk, this increase reflects a favourable shift in injury severity. In many cases, pedestrians who would have sustained unsurvivable head or torso injuries now experience outcomes that, while serious, are survivable [22]. This includes moderate-to-severe head injuries and limb trauma resulting from redirected fall kinematics. Unlike the full frontal guard, which offers moderate reductions in both fatal and hospitalisation risks, the track-and-front guard configuration more decisively reduces the most critical outcomes. From a system safety perspective, the primary objective is not to balance fatal and non-fatal injuries but to minimise fatalities, particularly those that are preventable through passive interventions. In this context, an increase in hospitalisation risk is a desirable trade-off if it results from a reduction in fatal events.

These results suggest that the track-and-front guard configuration, despite its limitations, is the most effective single countermeasure investigated in this study. Future designs could combine its benefits with additional features to mitigate limb contact risk, further improving outcomes without compromising survivability.

4.4. Limitations

The absence of Post-Mortem Human Subject (PMHS) test data necessary for robust model validation limits the analysis to identifying trends rather than interpreting individual simulations. While the use of experimentally derived contact characteristics for countermeasure interactions enhances model reliability, these characteristics were only evaluated at three specific velocities, resulting in a constrained test matrix. This limited scope reduces the strength of comparisons to the epidemiological data [7], which includes only 36 cases within the tested velocity range. Nevertheless, this velocity range does approach the most prevalent impact speed of 12 m/s. Additionally, only jumping and standing impact postures were modelled, with lying conditions excluded due to operational constraints involving moving components near the top of the rail. Consequently, the safety benefits assessed in this study are applicable solely to jumping and standing impacts, which account for 70% of frontal subway train-to-pedestrian collisions reported in [7]. Despite these limitations, this research provides the first multibody assessment of passive pedestrian safety countermeasures, effectively covering 70% of recorded impact scenarios and 55% of impact velocities observed in a study of 2019 NYCT subway incidents.

5. Conclusions

Force–penetration relationships for candidate foams and foam encased in hard shells were presented for application in subway-to-pedestrian safety. While shell coverings altered the acceleration response, they did not consistently increase peak acceleration values, particularly at higher impact velocities.

Two front-mounted countermeasure designs were developed to address primary impact and run-over injury risk. Simulations showed that these configurations, particularly the full frontal guard, significantly reduced primary head injury risk (up to 90 percent) and train wheel contact risk (up to 58 percent). However, reducing primary contact severity alone did not result in a meaningful decrease in total fatal injury risk. Secondary impacts and post-impact pedestrian kinematics remained significant contributors to overall injury severity.

The track guard, when combined with the full frontal guard, produced the largest reduction in total fatal injury risk. While this combination increased the number of hospitalisation-level outcomes, such as limb injuries, these are preferable to the previously fatal head or torso injuries observed in the baseline model. This shift reflects a positive trade-off. The track guard does not prevent all injuries, but it reduces the likelihood of death by altering how and where the pedestrian makes contact during a fall.

Among the tested countermeasures, the track-and-front guard combination was the most effective. These findings show that a carefully designed energy-absorbing system—even one occupying just 0.5 m of frontal space—can substantially reduce the lethality of subway-to-pedestrian collisions.

The aim of this research was to challenge the assumption that improving pedestrian safety in subway environments is unrealistic due to the size and mass of rail vehicles. This work shows that meaningful reductions in fatalities are possible through practical, space-efficient interventions. While limitations remain, this study provides strong evidence that subway-to-pedestrian fatalities are not inevitable.