## 3 Results  
### 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  
Figure 9: Experimental acceleration time history: impact velocity of 7.5 m/s (**left**), 10 m/s (**middle**), and 11.5 m/s (**right**), showing different sample designs and the instant of max penetration (point of zero velocity).  
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  
Figure 11: Experimental penetration time history: impact velocity of 7.5 m/s (**left**), 10 m/s (**middle**), and 11.5 m/s (**right**).  
Figure 10: Position of tracking points throughout the loading phase shown as red circles.  
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.  
Figure 12: Experimentally derived force penetration: impact velocity of 7.5 m/s (**left**), 10 m/s (**middle**), and 11.5 m/s (**right**).