3. Injury biomechanics primer

Restraint performance cannot be evaluated by "how the dummy looks" after a test. It must be quantified against injury criteria — physically interpretable metrics computed from measured dummy or human-body responses, each compared with a tolerance limit derived from biomechanical research. This chapter establishes the four criteria that dominate frontal and side restraint assessment — HIC, BrIC, chest deflection, and Nij — together with the AIS scale used to translate physical response into clinical injury severity. The goal is practical: given a set of channel data from a sled or crash test, you should know which metric to compute, how to compute it, what limit applies, and how the result maps to an AIS-coded outcome.

HIC: Head Injury Criterion

HIC estimates the risk of skull fracture and severe brain injury from translational head acceleration. It is defined over a time window:

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 CG,
expressed in g, and (t2 - t1) ≤ 15 ms (HIC15) or ≤ 36 ms (HIC36).

In practice, the integral is evaluated numerically on the filtered acceleration signal. The standard workflow is: sample the head-CG resultant acceleration at ≥ 10 kHz, apply the channel filter class specified by the test protocol (commonly CFC 1000 for head acceleration), then sweep all candidate windows up to the chosen duration and retain the maximum. A frequent implementation error is computing HIC on unfiltered data or on a single-axis channel; both inflate or distort the result. The resultant must be formed from the three orthogonal accelerations before the window search.

Typical tolerance values used in restraint development are HIC15 = 700 for the 50th-percentile adult male (Hybrid III) in frontal certification tests, with HIC36 = 1000 as the classical reference. These are not universal constants: they depend on occupant size, test mode, and the regulatory or consumer protocol being applied. Always state the window duration alongside the value — "HIC = 650" is ambiguous, "HIC15 = 650" is not.

BrIC: Brain Injury Criterion

HIC captures linear acceleration but not rotational loading, which dominates diffuse axonal injury. BrIC addresses this using angular velocity components about the head's anatomical axes:

BrIC = max over time of [ ( |ωx| / ωxC )^2 + ( |ωy| / ωyC )^2 + ( |ωz| / ωzC )^2 ]

with critical angular velocities (rad/s):
  ωxC = 66.25   (about the A-P / x axis)
  ωyC = 56.45   (about the lateral / y axis)
  ωzC = 42.87   (about the superior-inferior / z axis)

BrIC is dimensionless; a value of 1.0 corresponds to the reference tolerance. In restraint work, BrIC is most relevant to side impacts and to occupants whose heads interact with side curtains or pillars, where angular velocity can be high even when translational HIC is moderate. Computing BrIC requires head angular velocity channels, which many legacy dummies do not provide — this is a data-availability constraint worth checking before committing to a BrIC-based assessment.

Chest Deflection and Nij

Chest deflection measures the sternum-to-spine compression and is the primary thoracic injury metric for belt-restrained occupants. It is reported as an absolute deflection (mm) and, more usefully, as a normalized deflection ratio relative to chest depth. For the Hybrid III 50th male, commonly cited limits are approximately 63 mm absolute and 0.33 normalized for the 50th percentile, with lower limits for smaller occupants. Deflection is highly sensitive to belt routing and pretensioner/load-limiter tuning, making it the metric that most directly reflects restraint system design choices.

Nij is the normalized neck injury criterion, combining axial compression/tension and bending moment:

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

where Fz is the axial force (compression positive in the standard formulation),
My is the flexion/extension moment, and Fzc, Myc are critical values
that depend on the force-moment combination and occupant size.

Nij is evaluated at each time step and the peak reported; values above 1.0 indicate exceedance of the reference tolerance. It matters most in frontal impacts with airbag interaction and in rear impacts, where neck loading can be the limiting factor even when head and chest metrics are acceptable.

Criteria are not interchangeable. A restraint that passes HIC can still fail on chest deflection if the load limiter is too aggressive, and a system that passes both can fail on Nij if the airbag is over-powered. Evaluate all applicable criteria together, and report the governing (worst-margin) criterion.

AIS Coding: From Response to Clinical Severity

The Abbreviated Injury Scale (AIS) ranks injury severity from 1 (minor) to 6 (currently untreatable), with 9 used for unknown. It is an anatomical, not a physiological, scale: it describes the injury, not the response metric. The bridge between the two is the injury risk curve — a statistical function mapping a criterion value to the probability of a given AIS level. For example, a chest deflection of 63 mm might correspond to roughly a 50% risk of AIS 3+ thoracic injury for a mid-size male, but the exact curve depends on the source study and occupant population.

In restraint analytics, AIS enters in two places. First, test protocols define pass/fail in terms of AIS-equivalent risk thresholds (e.g., "AIS 3+ head injury probability ≤ 10%"). Second, field or simulation data are coded to AIS so that restraint performance can be compared against real-world outcomes. When you report a criterion value, always pair it with the AIS level and risk curve it is being assessed against — a bare number without its reference is not actionable.

Measured Channels Head CG accel (ax, ay, az) CFC 1000, ≥10 kHz Head angular velocity ωx, ωy, ωz Chest deflection sternum–spine, mm Neck load cell Fz, My Criterion Computation HIC15 max window ≤ 15 ms BrIC Σ (ωi/ωiC)², peak Chest deflection peak mm / normalized Nij Fz/Fzc + My/Myc Tolerance Check HIC15 ≤ 700 50th male, frontal BrIC ≤ 1.0 dimensionless Defl ≤ 63 mm ≈ 0.33 normalized Nij ≤ 1.0 peak over time AIS Risk Risk curve criterion → P(AIS level) AIS 1 minor AIS 2 moderate AIS 3 serious AIS 4 severe AIS 5 critical AIS 6 fatal Report governing (worst-margin) metric Worked example (illustrative values, not measured data) HIC15 = 612 → margin 88 below 700 → governing? no BrIC = 0.71 → margin 0.29 below 1.0 → governing? no Chest deflection = 58 mm → margin 5 mm below 63 mm → governing? YES Nij = 0.83 → margin 0.17 below 1.0 → governing? no Action: tune load limiter / belt routing to reduce chest deflection; re-run and re-check all four criteria.

Putting the Criteria to Work

The figure above shows the complete assessment chain: measured channels feed criterion computations, each criterion is compared against its tolerance, and the result is mapped through an injury risk curve to an AIS level. The worked example at the bottom illustrates the key analytical habit — compute all applicable criteria, identify the governing one by margin, and direct design effort there. In the example, chest deflection is the limiting metric even though HIC and BrIC have comfortable margins; optimizing the airbag further would be wasted effort until the chest deflection margin is improved.

Two practical cautions apply. First, tolerance limits are occupant- and protocol-specific. The values quoted here are reference points for a mid-size adult male in a frontal setting; a small female or a child occupant requires scaled limits, and side-impact protocols use different reference values entirely. Second, AIS risk curves are statistical, not deterministic. A criterion value below its tolerance does not guarantee no injury, and a value above it does not guarantee injury — it shifts probability. Report risk, not certainty, and always state the curve source.

Do not compare criterion values across different filter classes, window durations, or occupant sizes. A HIC36 computed on CFC 180 data is not comparable to a HIC15 computed on CFC 1000 data. Normalize the computation method before comparing results, and document the method alongside every reported value.

With these four criteria and the AIS mapping in hand, the next analytical step is to connect them to the restraint hardware that governs each one: belt geometry and load limiters for chest deflection, airbag venting and tethering for HIC and Nij, and curtain coverage for BrIC in side events. That connection — criterion to hardware to design change — is where injury analytics becomes restraint engineering.

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