2. Injury criteria fundamentals

Injury criteria are the numerical bridge between a physical measurement recorded during a crash test and a judgment about whether an occupant would have been injured. Every criterion in this chapter follows the same logical pattern: a measured signal (acceleration, force, deflection, moment) is filtered, transformed, and reduced to a scalar value, which is then compared against a threshold. The threshold itself is derived from biomechanical research — typically from cadaver, animal, or volunteer testing — and is codified either in a regulation (FMVSS, ECE) or in a consumer rating protocol (Euro NCAP, US NCAP, C-IASI). Understanding the transformation is essential, because the same raw accelerometer trace can produce very different numbers depending on the filter class, the time window, and the integration limits applied.

Head injury: HIC and its variants

The Head Injury Criterion (HIC) is the most widely used head metric. It is computed from the resultant translational acceleration at the head centre of gravity, expressed in multiples of gravitational acceleration g:

HIC = max over (t1, t2) of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt )^2.5 ]

subject to:  t2 - t1 ≤ 36 ms  (HIC36)  or  ≤ 15 ms  (HIC15)
             a(t) in g, filtered per the applicable standard

Two practical details dominate the result. First, the filter: FMVSS 208 and ECE R94 specify a channel frequency class (CFC) 1000 low-pass filter for the head accelerometer, while some consumer protocols apply CFC 600 or a different anti-aliasing chain. Applying the wrong filter shifts HIC by several percent. Second, the window: HIC36 is the regulatory default in many markets, but HIC15 is more sensitive to short, high-amplitude spikes and is used in several consumer protocols and in pedestrian head-impact assessment. A typical passenger-car frontal test might report HIC15 in the range of 300–700; the FMVSS 208 limit for the driver is HIC15 ≤ 700, while Euro NCAP awards full points below roughly 650 and applies a sliding penalty above that.

For head rotation, the Brain Injury Criterion (BrIC) has entered consumer protocols. BrIC combines peak angular velocity about three anatomical axes, normalised by axis-specific critical values, and takes the maximum of the three ratios. It is reported alongside HIC rather than replacing it, because the two capture different injury mechanisms — translational acceleration versus rotational strain.

Neck injury: NIC and Nij

The Neck Injury Criterion (NIC) was developed for rear-impact whiplash and is defined from the relative horizontal acceleration and velocity between the head and the top of the neck:

NIC = 0.2 * a_rel + v_rel^2

where a_rel = relative horizontal acceleration (m/s²)
      v_rel = relative horizontal velocity (m/s)
      0.2   = a regression constant with units s

NIC is evaluated in the first ~150 ms after impact and is compared against a threshold of about 15 m²/s² for a low whiplash-injury probability. Note that NIC is not a general neck criterion for frontal impact; for frontal loading the relevant metric is Nij, the neck injury criterion based on axial force and bending moment:

Nij = Fz / F_int + My / M_int

where Fz  = axial force (tension positive, compression negative)
      My  = bending moment at the occipital condyles
      F_int, M_int = intercept values from the regulation
      Nij is evaluated for each of four modes:
      tension-extension, tension-flexion,
      compression-extension, compression-flexion

FMVSS 208 requires Nij ≤ 1.0 for each mode. The intercept values differ between tension and compression, so the same force produces a different Nij depending on sign — a detail that frequently causes errors when the sign convention of the load cell is not aligned with the regulation's definition.

Chest injury: deflection and the compression criterion

Chest deflection is measured with a chest band or an internal deflection sensor and is reported as absolute deflection in millimetres, or normalised as a percentage of the half-chest depth. The two dominant criteria are:

  • Chest deflection (absolute): peak deflection, typically limited to 50–63 mm depending on the protocol and occupant size.
  • Chest compression criterion (ThCC): a viscous-style combination of deflection and deflection rate, capturing the rate-dependent soft-tissue response.

For the Hybrid III 50th percentile male, FMVSS 208 sets a chest deflection limit of 63 mm; Euro NCAP uses a sliding scale with full points below roughly 22 mm and zero points above roughly 50 mm for the same dummy. The large spread between regulatory and consumer thresholds is a recurring theme: regulations define the legal minimum, consumer protocols push well beyond it.

Femur force and lower extremity

Femur force is measured by load cells in the dummy's upper legs and is reported as the peak axial compressive force. FMVSS 208 limits each femur to 10 kN, with a duration-dependent curve for some configurations. The measurement is sensitive to load-cell zeroing and to the pre-crash positioning of the leg; a few millimetres of knee-bolster contact can change the peak by more than a kilonewton. Lower-leg metrics (tibia index, tibia force) follow the same pattern: a force or moment normalised by an intercept value, compared against a limit.

How the criteria fit together

The figure below shows the measurement chain from sensor to pass/fail decision, and how the same chain is reused across regulatory and consumer evaluations. The key insight is that the sensor and filter stage is shared, while the criterion and threshold stage differs by protocol.

From Sensor Signal to Pass/Fail: Shared Chain, Protocol-Specific Thresholds 1. Transducers Head accelerometer Neck load cell Chest band / IR-TRACC Femur load cells 2. Conditioning Zero / offset check CFC 1000 low-pass (head, neck) CFC 600 (chest, femur) 3. Criterion Computation HIC15 / HIC36, BrIC NIC, Nij (4 modes) Chest deflection, ThCC Femur force, tibia index 4a. Regulatory limits FMVSS 208 / ECE R94 4b. Consumer ratings Euro NCAP / US NCAP / C-IASI Pass / Fail per criterion value ≤ limit ? Aggregate result all criteria must pass Rating / score points per body region Illustrative example — Hybrid III 50th male, frontal 56 km/h (values are teaching examples, not measured results) HIC15 = 520 → FMVSS 208 limit 700: PASS | Euro NCAP full-point band ≈ ≤650: PASS Nij (tension-extension) = 0.72 → limit 1.0: PASS Chest deflection = 41 mm → FMVSS 208 limit 63 mm: PASS | Euro NCAP sliding scale: partial points Femur force (left) = 8.4 kN → limit 10 kN: PASS Overall: regulatory PASS; consumer score reduced by chest deflection — the two verdicts legitimately differ.

Practical implications for automation

When these criteria are automated in Excel, three implementation choices determine whether the workbook is trustworthy. First, the filter must be applied before the criterion, not after; a HIC computed on unfiltered data is not comparable to a published limit. Second, the integration window must be searched exhaustively — HIC is a maximum over all valid (t1, t2) pairs, and a naive fixed-window calculation will under-report. Third, the sign conventions for Nij and femur force must be documented in the workbook itself, because a flipped sign silently converts a passing compression case into a failing tension case.

A useful sanity check before trusting any automated criterion: recompute one channel by hand from the filtered trace and compare. If the workbook and the hand calculation disagree by more than a fraction of a percent, the error is almost always in the filter class, the integration limits, or the sign convention — not in the threshold.
Do not mix regulatory and consumer thresholds in a single pass/fail column. A vehicle can legally pass FMVSS 208 while scoring poorly in Euro NCAP; collapsing both into one boolean destroys the information the engineer needs to decide whether a design change is required.

The criteria in this chapter are the vocabulary the rest of the course builds on. Once each metric's input signal, filter, and threshold are understood, the Excel automation becomes a matter of disciplined data handling rather than biomechanical interpretation.

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