## 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  
Figure 1: Safety design change in cars and subway trains over a 100-year period [adapted from publicly available data]. 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 HIC\({}_{15}\) 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  
1. 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;
2.