3. Occupant injury criteria and targets

Frontal restraint calibration is fundamentally a multi-objective optimization problem disguised as a compliance exercise. The restraint system — airbag, seat belt, pretensioner, load limiter, knee bolster, and steering column — must keep every measured injury metric below its regulatory or consumer-rating threshold, and it must do so across a family of load cases that pull the design in conflicting directions. Before any calibration decision can be made, the engineer needs a precise working model of what each criterion measures, how it is computed, and where its sensitivities lie.

Head Injury Criterion (HIC)

HIC is derived from the resultant translational acceleration at the head center of gravity, measured in g, over a sliding time window:

HIC = max over t1,t2 of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt )^2.5 ]
subject to t2 - t1 ≤ 15 ms   (HIC15)
           t2 - t1 ≤ 36 ms   (HIC36, legacy FMVSS 208)

The 2.5 exponent makes HIC strongly nonlinear: a 20% increase in the average acceleration over the window raises HIC by roughly 58%. This is why HIC is dominated by short, high-amplitude spikes rather than by the overall pulse shape. In practice, calibration work focuses on the first 30–50 ms of head contact with the airbag, where the acceleration peak occurs. Typical targets are HIC15 ≤ 700 for FMVSS 208 compliance and HIC15 ≤ 650–700 for Euro NCAP five-star performance, with US NCAP and IIHS evaluating related head metrics under their own protocols.

Two practical sensitivities matter. First, HIC is computed on the resultant of three orthogonal accelerometers, so a head that rotates while translating can produce a resultant that understates focal brain loading — HIC does not capture rotational injury, which is why brain injury criteria (BrIC) are increasingly evaluated alongside it. Second, HIC is extremely sensitive to the airbag's venting and to the timing of head-to-bag contact: an airbag that is still deploying when the head arrives produces a sharp spike, while an over-vented bag lets the head bottom out against the steering wheel hub.

Chest Deflection and the Compression Criterion

Chest injury is assessed primarily through sternal deflection relative to the spine, measured by a chest band or IR-TRACC (Infra-Red Telescoping Rod for Assessment of Chest Compression) in the Hybrid III and THOR dummies. The metric is usually expressed as an absolute deflection in millimeters and as a normalized compression C = deflection / chest depth. FMVSS 208 limits chest deflection to 63 mm for the Hybrid III 50th percentile male; Euro NCAP applies a sliding scale where lower deflection earns more points, with roughly 22 mm representing best-case performance and 50 mm the zero-point boundary.

The chest is the restraint system's most direct victim of over-aggressive loading. A stiff airbag or a high-tension belt without a load limiter will drive deflection up rapidly, and the deflection rate (mm/ms) is itself predictive of rib fracture risk. Calibration levers here are the belt load limiter force level, the pretensioner payout profile, and airbag pressure/venting. A typical calibration sequence reduces load limiter force until chest deflection approaches the target, then re-checks head excursion and HIC, because a softer belt lets the head travel further forward.

Femur Loads and Lower-Extremity Metrics

Femur axial compressive force is measured by load cells in the dummy's upper legs. FMVSS 208 sets a 10 kN limit per femur; Euro NCAP uses a graduated scale with roughly 3.8 kN as the best-performance threshold and 9.07 kN as the zero-point. Femur load is driven almost entirely by knee-to-knee-bolster contact and by the belt's lap-portion geometry: a lap belt routed too high rides over the iliac crest and loads the abdomen, while a lap belt routed correctly transfers load into the pelvis. Knee bolster stiffness and the steering column's collapse force are the primary tuning parameters. A column that collapses too easily lets the knee travel into the bolster at high velocity; one that is too stiff transmits the full femur load.

Neck Injury Metrics

Neck injury is evaluated through axial force (tension and compression), shear force, and bending moment at the occipital condyle or upper neck load cell. Nij is a normalized combined criterion:

Nij = (Fz / Fzc) + (My / Myc)
where Fzc, Myc are the critical intercept values
for tension or compression, and My is the flexion/extension moment.

FMVSS 208 requires Nij ≤ 1.0. Neck metrics are most sensitive in cases where the head is arrested by the airbag while the torso continues forward — the resulting differential motion produces extension moment. They are also the metric most affected by airbag deployment timing: an early-deploying bag that catches the head before the torso has loaded the belt can produce a sharp extension moment, while a late bag lets the head pitch forward into flexion.

The Trade-off Structure Across Load Cases

The core difficulty is that the load cases are not independent. Consider the standard frontal family: 56 km/h full frontal rigid barrier (FMVSS 208), 64 km/h 40% offset deformable barrier (Euro NCAP/IIHS), 50 km/h full frontal with unbelted occupants (FMVSS 208), and low-speed 16 km/h rigid barrier (bumper/airbag deployment threshold). Each stresses a different metric.

The unbelted case is the classic antagonist. An unbelted occupant has no belt load limiter to absorb energy, so the airbag must be larger, stiffer, and later-venting to arrest the torso and head. But that same bag, applied to a belted occupant whose torso is already decelerating against the belt, produces excessive chest deflection and a HIC spike. The standard resolution is a dual-stage inflator with a belt-status sensor: stage-one-only deployment for belted occupants, both stages for unbelted. The calibration task is then to tune the stage-one output so that belted HIC and chest deflection stay under target while the unbelted case still passes with both stages.

Reading the Trade-off Graph

The SVG below maps the four principal metrics against the two dominant calibration levers — belt load limiter force and airbag vent area — and shows the direction of conflict for each load case. The key insight is that no single lever moves all metrics in the same direction: increasing load limiter force reduces head excursion and HIC in the unbelted case but raises chest deflection in the belted case; increasing vent area reduces chest deflection but raises HIC by letting the head travel further.

Reading the graph: the HIC curve for the belted full-frontal case rises steeply as load limiter force increases, because a stiffer belt lets the torso decelerate earlier and the head arrives at the airbag with more relative velocity. The chest deflection curve falls with increasing force, since a stiffer belt shares more of the deceleration. The two curves cross the target line at different force levels, and the feasible window is the overlap where both remain below 1.0. Femur load is comparatively insensitive to load limiter force in the offset case, which is why knee bolster stiffness is tuned separately. Neck Nij in the unbelted case rises with load limiter force because the belt (when present) and the airbag together produce a differential head-torso motion; in the pure unbelted case the belt is absent and Nij is driven almost entirely by airbag timing.

Practical Calibration Sequence

A defensible sequence for a new frontal restraint calibration is: (1) establish the belt geometry and anchor positions, since these set the baseline chest and femur loading and are expensive to change later; (2) sweep the load limiter force against the belted full-frontal and offset cases to find the feasible window shown above; (3) tune airbag venting and inflator output against the unbelted case, re-checking belted HIC and chest after each change; (4) adjust knee bolster stiffness and steering column collapse force to bring femur loads under target without disturbing chest deflection; (5) verify neck Nij across all cases, paying particular attention to deployment timing relative to head arrival. Each step should be documented with the metric values at the chosen setpoint and at the window boundaries, so that later hardware changes can be assessed against a known baseline rather than re-derived from scratch.

The metrics are not independent objectives to be minimized separately; they are coupled responses to a small set of hardware levers. The engineer's job is to find the lever settings where every metric sits below its applicable target with adequate margin, and to understand which lever to move — and which metric will move with it — when a late-stage hardware change forces a re-calibration.