📚 Course ContentsChapter 2 Occupant injury criteria

2. Occupant injury criteria

Before any sensitivity ranking can be trusted, the response quantities being ranked must be defined precisely. A sensitivity study answers the question "which restraint parameter most strongly influences occupant injury?" — but that question is only meaningful once each injury metric has a fixed mathematical definition, a fixed sign and coordinate convention, and a fixed set of thresholds against which the response is judged. This section establishes those foundations for the five criteria most commonly used in frontal and side impact restraint optimization: HIC, chest deflection, Nij, femur force, and the supplementary metrics that frequently appear alongside them.

Head injury: HIC15 and HIC36

The Head Injury Criterion is defined as the maximum over all time windows of length t₂ − t₁ of the expression

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

where a(t) is the resultant translational acceleration at the head centre of gravity, expressed in g (multiples of 9.81 m/s²), and the integration runs between t₁ and t₂. The window length is fixed by convention: HIC₁₅ uses a 15 ms window and is the standard for FMVSS 208 and Euro NCAP frontal assessment; HIC₃₆ uses 36 ms and appears in older regulations and in some side-impact protocols. Because the exponent is 2.5, HIC is highly sensitive to short, high-amplitude acceleration spikes — a property that matters directly in sensitivity work, since a small change in airbag venting or belt load limiter force can shift the peak acceleration and produce a disproportionate change in HIC.

Thresholds in common use: HIC₁₅ = 700 corresponds approximately to a 22% risk of AIS 3+ head injury and is the FMVSS 208 limit for the 50th percentile male; Euro NCAP awards full points below 650 and zero above 1000. For sensitivity ranking, HIC should always be computed from the resultant acceleration, not from a single axis, and the time window must be reported alongside the value — a HIC of 690 over 15 ms and a HIC of 690 over 36 ms imply very different kinematics.

Chest deflection and the viscous criterion

Thoracic injury in belt-restrained occupants is dominated by compression rather than acceleration. Chest deflection is the peak inward displacement of the sternum relative to the spine, measured in millimetres by a chest band or IR-TRACC (Infra-Red Telescoping Rod for Assessment of Chest Compression) in the dummy. Two conventions must be fixed before any comparison: whether the value is absolute deflection (mm) or normalized compression C = deflection / chest depth (dimensionless), and which rib the measurement comes from. FMVSS 208 uses absolute deflection with a limit of 63 mm for the 50th percentile Hybrid III male; Euro NCAP uses normalized compression with a 42% limit for the same dummy and 35% for the small female. Mixing the two conventions is one of the most common errors in restraint sensitivity studies, because a parameter that reduces absolute deflection on a large chest may leave normalized compression unchanged.

The viscous criterion VC = max[ v(t) · C(t) ], where v is the instantaneous rate of chest deformation in m/s, captures the rate-dependent component of soft-tissue injury and is limited to 1.0 m/s in FMVSS 208. VC is particularly informative in sensitivity studies of load-limiter force and pretensioner timing, because those parameters change the rate of belt pay-out without necessarily changing peak deflection.

Neck injury: Nij and its four modes

The Neck Injury Criterion combines axial force and bending moment into a single normalized index:

Nij = Fz / Fzc + My / Myc

where F_z is the axial force (tension positive) and M_y is the flexion/extension moment at the occipital condyles. The critical values F_zc and M_yc differ by mode: tension–extension (N_te), tension–flexion (N_tf), compression–extension (N_ce), and compression–flexion (N_cf). For the Hybrid III 50th male, representative intercepts are 6806 N tension, 6160 N compression, 310 N·m extension and 300 N·m flexion, giving four separate Nij values; the reported Nij is the maximum of the four, and the limit is 1.0. The sign convention is critical: extension moment is positive in the N_te and N_ce modes, and a sign error silently swaps the flexion and extension denominators, producing a plausible but wrong ranking.

Femur force and supplementary metrics

Femur force is the axial compressive load measured by load cells in the dummy's femoral shafts, limited to 10 kN per leg in FMVSS 208 (roughly 9.07 kN in Euro NCAP for the 50th male). It is the primary discriminator for knee-bolster stiffness, seat-pan geometry, and the interaction between the lap belt and the thigh. In sensitivity studies it frequently trades off against chest deflection: a stiffer knee bolster reduces femur force by arresting the pelvis earlier but can increase chest loading by changing the occupant's forward rotation.

Other metrics that commonly enter the ranking include the Brain Injury Criterion (BrIC, based on rotational head velocity, limit 0.68 in Euro NCAP), the Abbreviated Injury Scale probability curves used to convert physical measures into injury risk, and pelvis force for side impact. Each has its own threshold and its own sensitivity to restraint parameters, which is why a single "injury score" is rarely sufficient — the ranking must be performed per criterion and then aggregated deliberately.

Using the criteria in a sensitivity study

With definitions fixed, the sensitivity workflow becomes concrete. Consider a frontal sled model with six restraint parameters — load limiter force, pretensioner firing time, airbag vent area, knee bolster stiffness, seat-pan angle, and outboard belt anchor height — each varied over a plausible range. For every run, the post-processor extracts the six criteria above and normalizes each against its threshold, producing a dimensionless utilization ratio u_i = criterion_i / limit_i. A value of 0.85 means the occupant uses 85% of the allowable head budget; values above 1.0 indicate a failed configuration.

The sensitivity coefficient for parameter p and criterion i is then the partial derivative of u_i with respect to p, estimated from the design-of-experiments sample by a linear regression or by a variance-based Sobol index. Two practical cautions follow directly from the definitions above. First, HIC and Nij are non-smooth functions of their inputs — the max operator and the 2.5 exponent create kinks — so a linear regression over a wide range can misrank parameters that only matter near the threshold. Second, chest deflection and femur force often respond in opposite directions to the same parameter, so the ranking must be reported per criterion rather than collapsed into a single score without stating the weighting.

When reporting a sensitivity ranking, always state the criterion definition (HIC₁₅ vs HIC₃₆, absolute vs normalized chest deflection), the dummy and percentile, the sign convention for Nij, and the parameter range over which the derivative was estimated. A ranking without these four pieces of context is not reproducible.

Do not compare HIC values computed over different window lengths, or chest deflections measured on different rib levels, as if they were the same quantity. In a multi-criterion ranking this error can invert the apparent importance of the load limiter and the airbag vent, because the two criteria respond to those parameters on different time scales.

The criteria defined here are the dependent variables of every subsequent sensitivity analysis in this course. Once each is expressed as a utilization ratio against a stated threshold, parameters with different physical units — newtons, milliseconds, millimetres — become directly comparable, and the ranking of restraint parameters can be interpreted as "which knob buys the most injury-budget reduction per unit of design change."