3. Restraint system parameters

In a sensitivity ranking study, restraint system parameters are rarely independent actors. Seat belt geometry determines how the belt engages the occupant; the pretensioner determines how quickly slack is removed; the load limiter determines how much force is allowed to reach the chest; and airbag venting determines how the bag's pressure decays as the occupant loads it. Each parameter shifts the timing and magnitude of occupant loading, and the ranking exercise is fundamentally about separating which of these shifts dominates the injury metrics of interest. This section explains what each parameter physically controls, how it is represented in a typical MADYMO or LS-DYNA occupant model, and how to reason about its influence before running a full sensitivity study.

Seat Belt Geometry

Belt geometry is defined by the anchor positions (D-ring, retractor, buckle, outboard and inboard lap anchors), the routing over the shoulder and pelvis, and the resulting belt angles relative to the occupant. The two angles that matter most are the shoulder belt angle in the frontal plane (typically 30–45° from vertical for a mid-size male) and the lap belt angle relative to the horizontal (commonly 45–60°). These angles control the belt force vector decomposition: a steeper shoulder belt carries more vertical load and less chest compression, while a shallower lap belt increases the risk of submarining because the resultant force has a larger rearward component under the pelvis.

In the model, geometry is usually parameterized through anchor node coordinates rather than angles directly, so a sensitivity study should perturb coordinates and then recompute the effective angles. A practical approach is to define the D-ring position as a design variable with ±30 mm travel in X and Z, and the buckle position with ±20 mm travel, then log the resulting shoulder and lap angles for each run. Geometry changes are geometrically constrained: moving the D-ring outboard reduces the shoulder belt angle but may cause the belt to slip off the shoulder, which shows up as a sudden drop in shoulder belt force and a spike in head lateral excursion.

Pretensioner Force and Timing

The pretensioner removes belt slack in the first 10–30 ms of the crash. Its two key parameters are peak force (or retraction force profile) and firing delay. A pyrotechnic retractor pretensioner might be modeled with a force profile rising to 2–4 kN over 5–10 ms and decaying over 20–30 ms, while a buckle pretensioner pulls the buckle down by 60–80 mm. The influence on occupant response is strongly non-linear: too little pretension leaves slack that delays belt engagement and increases forward excursion, while excessive pretension can pull the occupant into an overly upright posture and raise chest deflection early in the event.

For sensitivity ranking, pretensioner force is best treated as a profile scaling factor (e.g., 0.7×, 1.0×, 1.3× of the baseline curve) combined with a firing delay variable (0, 5, 10 ms). The observable outputs are belt force at the shoulder, chest deflection, and head forward excursion at 80–120 ms. A useful diagnostic is the time at which shoulder belt force first exceeds 1 kN: earlier engagement generally reduces head excursion but may increase chest loading, so the ranking depends on whether the target metric is head or chest injury.

Load Limiter

The load limiter caps the belt force transmitted to the chest, typically through a torsion bar in the retractor or a deformable element in the buckle. Its characteristic is a force plateau: once belt force reaches the limit threshold (commonly 3–6 kN for frontal occupants), the belt pays out additional webbing at roughly constant force. The two parameters are the limit force level and the pay-out length (available stroke, often 100–150 mm).

Load limiter force is one of the most influential parameters for chest injury metrics such as chest deflection and VC, and it trades directly against head excursion: lowering the limit from 5 kN to 3.5 kN typically reduces chest deflection by 15–25% in a 50 km/h frontal pulse but increases head forward excursion by 20–40 mm unless compensated by pretensioner or airbag tuning. In the model, the limiter is represented as a force-displacement curve on the retractor element; sensitivity runs should scale the plateau force while holding pay-out length constant, then repeat with pay-out length varied to expose the interaction.

Airbag Venting

Venting controls how the frontal airbag deflates under occupant load. It is defined by vent hole area, vent location, and the venting coefficient in the bag's gas dynamics model. Larger vent area produces a softer bag with lower peak pressure and earlier pressure decay; smaller vent area produces a stiffer bag that absorbs more energy but rebounds the occupant more aggressively. Typical driver airbag vent areas are 2,000–4,000 mm² total, and a sensitivity study might vary this by ±30%.

The observable outputs are bag pressure history, occupant chest acceleration, and head rebound velocity. Venting interacts strongly with load limiter force: a soft bag paired with a high load limit can allow excessive chest deflection, while a stiff bag with a low load limit can produce head rebound. This interaction is exactly why single-parameter ranking must be followed by interaction screening.

Building the Parameter Set for Ranking

A defensible sensitivity ranking requires a parameter table with baseline values, perturbation ranges, and the output metrics that will be compared. The table below is an illustrative example for a 50th-percentile male driver in a 50 km/h frontal sled model; the values are representative teaching assumptions, not measured results.

Run each perturbation as a one-at-a-time (OAT) case first, recording the peak value and the time of peak for every output. Normalize the change in each output by the baseline value to obtain a relative sensitivity index, then rank parameters by the magnitude of that index for the metric of interest. For example, if reducing the load limiter from 4.5 kN to 3.5 kN lowers chest deflection from 32 mm to 26 mm, the relative sensitivity is (32−26)/32 ≈ 0.19, or 19% per 1 kN reduction. Compare that against the vent area change, which might shift chest deflection by only 5–8% over the same relative perturbation, and the ranking becomes clear.

Interpreting the Results

The output of this stage is not a single ordered list but a metric-specific ranking. Load limiter force typically ranks first for chest deflection and VC, pretensioner timing ranks first for head excursion in the early phase, belt geometry ranks first for submarining and lap belt migration, and venting ranks high for head rebound and neck metrics. When the study's objective is a composite injury criterion, the ranking must be recomputed against that composite rather than averaged from the individual metrics. Document the baseline, the perturbation magnitude, the observed output change, and the interaction checks for every parameter so the ranking can be reproduced and defended in a design review.