2. Occupant safety fundamentals

Restraint tuning is only meaningful when it is anchored to measurable injury outcomes. An airbag or seatbelt calibration that "looks good" in a simulation is worthless unless it reduces a validated injury metric below a regulatory or consumer threshold. This chapter establishes the vocabulary and measurement framework that every subsequent DOE exercise depends on: what the injury criteria actually compute, how the regulatory and consumer test protocols differ, and — most importantly — which restraint parameters physically influence each criterion and in which direction.

The Three Primary Injury Criteria

Head Injury Criterion (HIC). HIC is a time-integrated measure of linear head acceleration, defined as:

HIC = max over [t1, t2] of  (t2 - t1) · [ (1/(t2-t1)) · ∫ a(t) dt ]^2.5

where a(t) is the resultant translational acceleration at the head center of gravity in g, and the integration window t2 - t1 is capped at 15 ms (HIC15) or 36 ms (HIC36). The 2.5 exponent makes HIC extremely sensitive to short, high-amplitude acceleration spikes — a 10% peak increase can raise HIC by roughly 27%. This is why airbag venting and tether design, which shape the deceleration pulse, dominate HIC performance. Typical limits are HIC15 ≤ 700 for FMVSS 208 and HIC36 ≤ 1000 for older protocols; Euro NCAP uses HIC15 ≤ 700 as a four-star threshold and applies a stricter 650 for five stars in some assessment years.

Chest deflection. Chest injury is governed by the compression of the rib cage, measured as the peak deflection (in mm) at a specified sternal or rib location, or as a percentage of the half-chest depth. The standard limit is 63 mm for the Hybrid III 50th percentile male in FMVSS 208, with Euro NCAP applying a graded scale (e.g., ≤ 22 mm for full points, 50 mm for zero points on the 50th male). Deflection is a displacement criterion, not an acceleration criterion, so it responds directly to belt force limiting and load-limiter characteristics rather than to airbag pressure alone.

Neck injury criteria. Two metrics are used in combination: Nij (the normalized neck injury criterion), which combines axial force and bending moment in four modes (tension-extension, tension-flexion, compression-extension, compression-flexion), and Nkm, which captures the bending moment and shear force relationship. Nij is computed as:

Nij = (Fz / Fzc) + (My / Myc)

where Fz and My are the measured axial force and bending moment, and the denominators are the corresponding critical values (e.g., Fzc = 6.8 kN tension, Myc = 310 N·m extension for the 50th male). A value of Nij ≤ 1.0 is the pass threshold. Neck criteria are particularly sensitive to airbag deployment timing and to the interaction between the belt's shoulder path and the head's trajectory.

Regulatory vs. Consumer Protocols

The two protocol families serve different purposes and impose different constraints on tuning. FMVSS 208 (US) is a pass/fail regulation: it specifies rigid barrier and offset deformable barrier tests at 25 mph and 35 mph, with unbelted and belted occupant configurations, and sets hard limits (HIC15 ≤ 700, chest deflection ≤ 63 mm, Nij ≤ 1.0). Compliance is binary — there is no credit for margin. Euro NCAP and IIHS are consumer rating programs that use a points-based scoring system across multiple crash modes (frontal offset, side impact, pole, whiplash) and reward margin above the regulatory floor. This distinction matters for DOE: a regulatory-only optimization drives parameters to the constraint boundary, while a consumer-rating optimization seeks a robust interior optimum that scores well across all modes simultaneously.

A practical consequence is that the same restraint system must satisfy both. A load limiter tuned to minimize chest deflection in FMVSS 208 may increase head excursion in Euro NCAP's offset test, raising HIC. This is precisely the kind of trade-off that a well-designed DOE captures through interaction terms rather than one-factor-at-a-time sweeps.

Linking Parameters to Criteria: A Worked Example

Consider a driver-side frontal airbag with three tunable factors: vent diameter (Factor A, 25–40 mm), tether length (Factor B, 80–120 mm), and load limiter force (Factor C, 3.0–4.5 kN). A 2³ full-factorial DOE with center points yields eight runs plus replicates. For each run, the simulation or sled test outputs HIC15, peak chest deflection, and Nij. A representative response surface (illustrative values, not measured data) might show:

Reading the main effects: increasing vent diameter from 25 to 40 mm reduces HIC15 by roughly 80–90 counts (better venting lowers peak bag pressure), while increasing tether length raises HIC by about 60 counts (a longer tether allows more bag excursion and a later, sharper head contact). Increasing load limiter force from 3.0 to 4.5 kN raises chest deflection by about 10 mm — a direct, near-linear relationship — but has almost no effect on HIC. The interaction between vent and tether is visible in the non-parallel response: the HIC penalty of a long tether is partially offset by a larger vent.

What This Means for the DOE That Follows

Every factor you will select in later chapters must be justified by a plausible causal path to at least one injury criterion. A factor that cannot be linked to HIC, chest deflection, or Nij through a defensible mechanism is a candidate for exclusion during screening. Conversely, criteria that are coupled — as Nij is to both belt and airbag parameters — must be modeled jointly, because optimizing them independently will produce a design that passes one threshold and fails another. The influence map above is the reference you will return to when interpreting main effects and interaction plots: it tells you which arrows to expect to be strong, which to be weak, and where a surprising result likely indicates a modeling error rather than a genuine physical effect.