3. Occupant injury criteria and protection targets

Restraint performance requirements cannot be written in terms of "good protection" or "acceptable injury." They must be expressed as measurable physical responses at specific body regions, compared against validated thresholds. This section establishes the injury criteria that anchor frontal restraint allocation: HIC, BrIC, chest deflection, Nij, and femur loads, plus the combined metrics used when a single number must represent overall occupant risk. The goal is to show how each criterion is computed, what physical mechanism it represents, and how a target value translates into a concrete restraint design requirement.

Head: HIC and BrIC

The Head Injury Criterion integrates resultant head acceleration over the most severe time window:

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

HIC captures linear acceleration and is dominated by hard contact — steering wheel rim, header, A-pillar. A typical frontal target is HIC₁₅ ≤ 700 for the 50th-percentile male in a 56 km/h full-frontal barrier test, with HIC₁₅ ≤ 1000 as the regulatory ceiling. Because HIC scales with the 2.5 power of acceleration, a 20% reduction in peak head acceleration yields roughly a 55% reduction in HIC — which is why airbag venting and steering column collapse are tuned in small increments.

HIC alone misses rotational loading, which drives diffuse axonal injury and subdural hematoma. BrIC addresses this:

BrIC = (ωx / ωxC)^2 + (ωy / ωyC)^2 + (ωz / ωzC)^2
Critical values (rad/s): ωxC = 66.3, ωyC = 53.1, ωzC = 41.5
Injury reference: BrIC = 1.0 corresponds to ~50% AIS 2+ risk

BrIC is a normalized sum of squared angular velocity components, so any single axis exceeding its critical value drives BrIC above 1.0. A practical frontal target is BrIC ≤ 0.7. Translating this into restraint requirements means controlling head rotation: symmetric airbag deployment, avoiding off-center bag contact that induces yaw, and managing belt geometry so the shoulder belt does not pull the head into lateral rotation during forward excursion.

Chest: Deflection and the Nij Analogue

Thoracic injury in frontal impact is dominated by compression. Chest deflection is measured as the maximum sternum-to-spine displacement, usually expressed in millimeters or as a percentage of half-chest depth. For the 50th-percentile male, a common target is ≤ 40 mm (roughly 25–30% of chest depth), with 63 mm as the regulatory limit. Deflection is a direct mechanical readout: it tells you how far the belt and airbag allowed the torso to travel relative to the spine.

For the neck, the Nij criterion combines axial force and bending moment:

Nij = (Fz / Fzc) + (My / Myc)
where Fz is axial force (tension or compression) and My is flexion/extension moment
Nij ≤ 1.0 is the accepted injury threshold

Nij is a linear interaction, so a neck carrying 60% of its critical tension has only 40% of its moment budget left. In frontal restraint design, Nij is most sensitive to airbag force applied to the chin and to belt routing that loads the neck in flexion. A target of Nij ≤ 0.8 leaves margin for the interaction with head rotation.

Femur and Lower Extremity

Femur load is measured as axial compressive force at the femoral shaft, with a target of ≤ 10 kN for the 50th-percentile male (regulatory limit typically 10 kN, with some protocols using 9.07 kN). The mechanism is knee-to-knee-bolster or knee-to-instrument-panel loading during forward excursion. Femur load requirements translate directly into knee bolster stiffness and geometry: the bolster must absorb energy without concentrating force on the patella or shaft.

Combining Criteria into a Single Target

Real restraint systems trade one criterion against another. A stiffer airbag reduces chest deflection but raises HIC and Nij. A softer bag lowers head injury but allows more chest compression. To allocate requirements across crash modes, engineers use combined injury metrics — most commonly a weighted risk score or the "injury probability" approach:

A combined metric such as the "Overall Injury Risk" (OIR) can be formed by mapping each criterion to an AIS 2+ probability via published risk curves and taking a weighted sum or maximum. For requirement allocation, the practical rule is: no single criterion may exceed its target, and the combined risk must stay below the program's occupant protection goal (for example, OIR ≤ 0.35 for a frontal 56 km/h test). This forces the restraint engineer to balance the system rather than optimize one number.

From Targets to Restraint Performance Requirements

Translating a target into a requirement means inverting the physics. If chest deflection must stay ≤ 40 mm, the belt force limiter must cap shoulder belt force at a level where torso excursion stays within that envelope — typically 3.5–4.5 kN for a 50th-percentile male with a pretensioned belt. If HIC must stay ≤ 700, the airbag must vent such that peak head acceleration stays below roughly 80–90 g for the contact duration. These are not arbitrary numbers; they come from sled and component tests where the restraint parameter is swept and the injury response recorded.

The diagram above makes the allocation logic explicit: each body region has a governing criterion, each criterion has a primary restraint lever, and all of them feed a combined risk target that must be satisfied simultaneously. When a program changes one lever — say, increasing belt force limiter from 4.0 kN to 4.5 kN to reduce chest deflection — the engineer must re-check HIC and Nij, because the stiffer belt path changes torso kinematics and head excursion. The combined metric is the guardrail that prevents local optimization from degrading overall protection.

Finally, targets are occupant-size dependent. The 5th-percentile female typically governs chest deflection and Nij because her smaller chest depth and shorter neck produce higher normalized loading; the 95th-percentile male governs femur load and airbag contact because of greater mass and longer excursion. A complete requirement set therefore specifies the target matrix across occupant sizes and crash modes, not a single nominal value. That matrix is the input to the restraint allocation work in the chapters that follow.