## 4 Numerical Model and Study Conditions  
Different downfall conditions were considered for the design of the safety chairs as already assumed for the design of the shelter structure [5] (Figure 8):  
* Situation 1: Effects of a vertical fall on a deformable ground/debris;
* Situation 2: Effects of a tilted shelter fall when the occupant is seated on a \"raised\" chair (i.e., on the chair more distant to the shelter impact edge) on the same ground/debris;
* Situation 3: Effects of a tilted shelter fall when the occupant is seated on a \"lowered\" chair (i.e., on the chair closer to the shelter impact edge) on the same ground/debris. In the analysis, the occupant was modelled as seated on the cushion with the front of his chest leaning on a pillow (chest pillow), with the lower limbs bent to insert the feet into specific supports (feet restraints, Figure 1), while the upper limbs were bent hugging the \"bridge\" of the chair. In general, the interaction between the human body and the retention devices (cushions) was simulated with rigid (without penetration) and frictionless contact surfaces. Because the effect of the bumpers in preventing the movement of the chair to the outside of the shelter has caused ricocheting of the human body back, an additional pillow was considered for the headrest (Figure 8a), with the same features as the chest pads. This backrest will later be developed through an anatomical study for the retention of head movement and neck stability to avoid the so-called whiplash effect [34]. Two additional kinematic restrictions were also required, one for the feet (Figure 8c) to keep them in their clogs and the other for the arms (Figure 8b), which simulated not only hugging of the chair bridge, but also inlaying against the thighs. For the analysis of the chair, a time series of displacements were imposed in the points where the chair is connected to the columns of the shelter. Those displacements were obtained in the study for the design of the shelter structure [5]. Therefore, the deformable ground characteristics are the same as in [5], namely a Young's modulus--E\({}_{\text{ground}}\)--of 55 MPa and a damping factor--\(\xi_{\text{ground}}\)--of 30%. In all the falls, an impact vertical (yy) velocity of 13.4 m/s was considered. This velocity was imposed on the human body and on the chair itself, and all analyses were 1 s long after the impact. Two-dimensional sagittal analysis was performed, restricting all movements out of that plane. In the former author's study [5], the mass of the chairs and their occupants was represented as a unique lumped mass, obtaining a first estimate of the accelerations that they will be subjected to during the impact of the shelter. An acceleration value around 70 g was then obtained, considering a unique lumped mass for the chair and its occupant. However, the movement of the occupant may differ considerably from that of the chair, particularly in respect to accelerations/inertial forces. Conversely, the limits of occupant survival assumed when designing the structure of the shelter were based mainly on experimental results [35; 36] involving the so-called  
Figure 8: Chair positions for tilted falls considered (at left—“lower” chair; at right—“upper” chair). Hybrid III dummy [37]. This physical model has been shown to be highly reliable for situations involving frontal and lateral impacts of the human body, but it is not that good in impacts involving compressions of the spine [38; 39], a situation that sometimes requires the modification of the test dummy. To limit the maximum occupant's acceleration, the shock-absorber system considered in [5] needed to be redefined. The characteristics of the damper were maintained, while the stiffness of the rubber springs was reduced to ensure survival conditions, particularly regarding spinal compression.