2. Occupant injury metrics and criteria

In occupant injury sensitivity analysis, the response quantities we rank are almost never raw accelerations or displacements. They are injury metrics: scalar functions of the time-history that compress a complex physical response into a number that can be compared against a regulatory or biomechanical threshold. The choice of metric determines what the sensitivity study can reveal. A parameter that strongly influences peak chest acceleration may barely move HIC; a parameter that shifts head impact timing by 5 ms can change HIC by 30%. This chapter defines the four most common occupant injury metrics, explains how each is computed from simulation or test output, and shows how each behaves under parameter perturbation — which is precisely what makes them suitable or awkward as ranking objectives.

HIC: Head Injury Criterion

HIC is defined over the resultant translational acceleration at the head centre of gravity, measured in g:

HIC = max over t1,t2 of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt from t1 to t2 )^2.5 ]
subject to t2 - t1 ≤ 15 ms

In practice the integral is evaluated on the sampled acceleration trace, and the maximisation is a sliding-window search over all window lengths up to 15 ms. The 2.5 exponent makes HIC strongly nonlinear: doubling the average acceleration in the window multiplies HIC by about 5.7. This nonlinearity is the single most important fact for sensitivity work. HIC is dominated by the highest-amplitude, best-aligned 10–15 ms segment of the pulse, so parameters that change pulse shape near the peak matter far more than parameters that change the overall duration or the low-amplitude tail.

A typical frontal restraint simulation might report HIC = 620 against a 700 limit. If a sensitivity run shows HIC rising to 810 when the seat-belt load limiter force is raised from 3.5 kN to 4.5 kN, that parameter is a high-leverage factor for the head metric — but the same change may leave chest deflection almost unchanged. Ranking must therefore be done per metric, not on a single composite score, unless a weighted objective is explicitly defined.

Chest Deflection and the Chest Criteria

Thoracic injury is assessed primarily through chest deflection — the sternum-to-spine compression — usually reported as an absolute value in millimetres and as a percentage of the initial chest depth. Two derived criteria are common: the peak deflection itself, and VC (viscous criterion), the product of the instantaneous deflection velocity and the instantaneous compression, expressed in m/s:

VC = max over t of [ dD(t)/dt * D(t)/D0 ]
where D(t) = deflection, D0 = initial chest depth

Deflection is a displacement metric, so it responds to belt geometry, pretensioner timing, and load-limiter force in a comparatively smooth, monotonic way. This makes it well behaved for sensitivity ranking: response surfaces are usually single-peaked and gradients are stable. VC, by contrast, is a product of two time derivatives and is far noisier — small changes in contact stiffness or belt slack can flip the peak location. When you rank parameters against VC, expect more run-to-run scatter and consider averaging over a small perturbation ensemble rather than relying on a single one-at-a-time (OAT) sweep.

Femur Force

Femur load is measured as the axial compressive force along the femoral shaft, typically at the knee-thigh-hip load path, and is compared against limits in the 7–10 kN range depending on the regulatory regime and occupant size. Unlike HIC, femur force is a quasi-static quantity: it tracks the restraint force transmitted through the lap belt and knee bolster, and it is largely insensitive to high-frequency content. In sensitivity studies, femur force is the metric most directly tied to restraint stiffness and to knee-bolster contact geometry, and it is often the cleanest signal for ranking those parameters. Its weakness is that it can be nearly flat with respect to parameters that dominate head and chest metrics, so it should not be dropped from the ranking set merely because its sensitivity is low — a low-sensitivity metric is itself informative.

Neck Injury Criteria: Nij and Nkm

Neck injury is assessed with the Nij criterion, which normalises the four load components — axial tension, axial compression, flexion moment, extension moment — against their respective critical values:

Nij = Fz/Fzc + My/Myc
evaluated for each of the four load/moment sign combinations,
with Fzc and Myc taken from the appropriate intercept table

Nij is a combined-load criterion: it is a sum of normalised components, so it is sensitive to the phase relationship between force and moment. A parameter that shifts the timing of peak neck moment relative to peak axial force can change Nij substantially even when neither component's peak magnitude changes. This makes Nij the most phase-sensitive of the four metrics and the one most likely to produce non-monotonic sensitivity behaviour. The related Nkm criterion uses a similar normalisation with a moment-dependent weighting and is preferred in some European assessments.

How the Metrics Behave Under Perturbation

The figure below maps the four metrics against the physical response they extract and the parameter classes that most strongly influence each. It is a working reference for choosing ranking objectives, not a substitute for the actual sweep.

Injury Metrics: Extracted Response Feature and Dominant Parameter Class Metric Response feature extracted Dominant parameter class Sensitivity behaviour HIC 15 ms window Peak 10–15 ms average of resultant head acceleration, raised to power 2.5 Airbag venting, belt load limiter, head–restraint contact timing Highly nonlinear; pulse-shape sensitive Chest deflection and VC Peak sternum–spine compression; VC adds deflection velocity Belt geometry, pretensioner timing, load-limiter force, padding stiffness Smooth, near-monotonic; VC noisier than peak D Femur force axial compression Peak axial load along femoral shaft, knee–thigh– hip load path Lap-belt stiffness, knee- bolster contact geometry, seat pan angle Quasi-static; clean gradients, low HF content Nij / Nkm combined load Normalised sum of axial force and bending moment, four sign combinations Head–restraint contact angle, airbag force vector, seat-back recline Phase-sensitive; non-monotonic possible Ranking must be performed per metric; a parameter that dominates one column may be inert in another.

Practical Consequences for Parameter Ranking

Three working rules follow from the metric definitions. First, normalise before ranking. A 0.4 kN change in femur force and a 0.4 change in Nij are not comparable in engineering significance; divide each metric's response by its own limit (or by its baseline value) so that sensitivity indices are dimensionless and comparable across metrics. Second, respect the nonlinearity. For HIC, a one-at-a-time sweep around a baseline that sits on the steep part of the response surface will overstate sensitivity relative to a sweep around a flat region; report the baseline and the perturbation range alongside every sensitivity index. Third, check phase-sensitive metrics separately. For Nij, run a small ensemble of timing perturbations (for example, airbag trigger ±2 ms) rather than a single OAT point, because the peak of the combined criterion can migrate between load cases.

When building the ranking table, record for each parameter–metric pair: baseline value, perturbation range, resulting metric range, normalised sensitivity index, and a note on monotonicity. The monotonicity note is what distinguishes a robust ranking from an artefact of a single unlucky sample point.
Do not rank parameters using a single composite injury score unless the weighting is explicitly justified and documented. Composite scores can mask a parameter that is critical for one body region — for example, a knee-bolster stiffness change that barely affects the weighted total but pushes femur force close to its limit.

With these four metrics defined and their perturbation behaviour characterised, the next step in a sensitivity study is to select the parameter set and sampling strategy that will exercise them. The metric definitions above determine which outputs must be logged at every run: head resultant acceleration at the CG, chest deflection and its derivative, femoral axial force, and the four neck load components with their timestamps. Logging timestamps alongside peaks is not optional — without them, phase-sensitive effects such as the Nij migration described above cannot be diagnosed after the sweep.

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