## 3 Results  
### The Effect of the Orientation on the Pressure under the Helmet  
In the first part of this research effort, we evaluated the impact of the helmet orientation on the surface pressure distribution under the ACH (Figure 1B). The representative pressure profiles for the blast exposures performed at 70 kPa incident BOP (\(\sim\)10 psi) are presented in Figure 2. The highest peak overpressures are noted for the frontal orientation of the headform in the eye sockets (490 kPa, Figure 2A, inset) and on the forehead (H1 sensor, Figure 2A). On the back of the head, the underpressure region develops, as evidenced by the signals from the H4 and H5 sensors. The surface pressure in these regions is increased above the incident pressure, while the sensor on the top of the head (H3) and all three circumferential sensors (H6, H7, and H10) report pressure levels similar to the incident pressure. Figure 2: The representative overpressure waveforms recorded at a nominal shock wave intensity of 79 kPa (\(\sim\)10 psi, denoted as T5). The headform equipped with the ACH helmet was oriented at (**A**) 0\({}^{\circ}\), (**B**) 90\({}^{\circ}\), (**C**) 180\({}^{\circ}\), and (**D**) 270\({}^{\circ}\) with respect to the direction of the shock wave propagation (see diagram in Figure 1B). The data recorded by the midsagittal (H1–H5) and circumferential (H6–H10, insets) sensors embedded in the headform are presented. A very similar pattern is observed for the other three headform orientations. The highest pressures are observed on the side facing the shock wave and on the opposite side. These trends are corroborated when the four characteristics of the pressure waveforms were quantified (Figure 3). The pressure amplification is seen in sensors directly exposed to the incident shock wave (H1, H8, and H9 at 0\({}^{\circ}\); H1, H8, and H6 at 90\({}^{\circ}\); and H1, H9, and H10 at 270\({}^{\circ}\) orientation). The same is valid for the sensors under the helmet where the underwash effect is observed (e.g., H4 and H5 at 0\({}^{\circ}\) orientation). It is also noteworthy to mention that at 180\({}^{\circ}\), the lowest peak pressures are observed due to shielding of the back face of the helmet preventing the flow of the pressure wave under the helmet. The rise time is a sensitive measure of the shock front dynamics, and at a shorter rise time values, the corresponding loading rates are the highest. The rise time is described often as an \"almost instantaneous\" increase from ambient to peak pressure. Our results demonstrate that for the incident shock wave with 70 kPa nominal intensity, the rise time is 6 \(\upmu\)s. The rise time is reduced to 3 \(\upmu\)s at the flat surface facing the blast (H1, Figure 3B). The rise time values increase to 10.5 \(\upmu\)s and 800 \(\upmu\)s for sensors facing away or under the helmet. The variation of the impulse and duration values are less pronounced since these two parameters describe the entire waveform and not only the shock front. Nonetheless, in all four orientations, we noticed amplification above the incident waveform impulse and duration (Figure 3C,D). The PCA analysis results are presented in Figure 4. All four characteristics (peak overpressure, rise time, impulse, and duration) for all ten pressure sensors were normalized using their corresponding incident waveform counterparts and natural logarithm normalized. As a result, 40-dimensional space was created for all four headform orientations. The first and second principal components (PC1 and PC2, respectively) describe the variability of 76.3% of the data. The individual data points for each orientation represent separate shock wave exposures (n = 6). The data are clustered according to the headform orientation, and clusters are separated by the PCA algorithm and outlined with 95% confidence interval ellipses. These results demonstrate that the exposure conditions at 0\({}^{\circ}\) and 180\({}^{\circ}\)  
Figure 3: The effect of the orientation on pressure distribution under the helmet.