2. Injury criteria fundamentals

Before any pass/fail automation can be trusted, the engineer must be fluent in what each injury criterion actually measures, how it is computed from raw channel data, and what magnitude constitutes a regulatory or consumer-test failure. This chapter establishes that vocabulary. Every criterion below is expressed in the coordinate system defined by the test dummy: the head and chest accelerations are measured along the SAE J211 sign convention, where positive X points forward, positive Y points to the dummy's left, and positive Z points upward. All accelerations are filtered to CFC 1000 (channel frequency class) unless a standard specifies otherwise, and all forces and moments are filtered to CFC 600. Keeping these conventions consistent is the single most common source of silent errors in an Excel workbook.

Head injury: HIC, HIC15, and HIC36

The Head Injury Criterion estimates the likelihood of skull fracture and brain injury from the resultant translational acceleration at the head centre of gravity. It is defined as:

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

where a(t) is the resultant acceleration in g and the integration window t2 - t1 is bounded. HIC15 restricts the window to 15 ms and is the value used in FMVSS 208 and most frontal impact regulations; HIC36 allows a 36 ms window and appears in older or alternative standards. The exponent of 2.5 makes HIC highly sensitive to short, high-amplitude spikes, which is why filtering and sample rate matter enormously. A typical FMVSS 208 limit is HIC15 ≤ 700 for the driver and passenger in a 56 km/h frontal barrier test; Euro NCAP applies the same 700 threshold but evaluates it against a different pulse. HIC36 limits are commonly cited at 1000 for legacy assessments. In Excel, HIC is computed by scanning every pair of samples within the window, integrating the resultant acceleration with the trapezoidal rule, and taking the maximum — a nested loop that is best implemented with helper columns rather than a single array formula.

Chest injury: deflection and acceleration

Chest injury is assessed through two independent channels. Chest deflection measures the compression of the rib cage in millimetres, derived from the chest potentiometer or IR-TRACC (Infra-Red Telescoping Rod for Assessment of Chest Compression) and reported as an absolute value or as a percentage of the initial chest depth. FMVSS 208 sets a deflection limit of 63 mm for the Hybrid III 50th percentile male; Euro NCAP uses a more demanding 42 mm for a five-star rating. Chest acceleration, expressed in g, captures the inertial loading of the thorax and is limited to 60 g in FMVSS 208, typically evaluated as a 3 ms clip. Both channels must pass independently; a compliant deflection does not excuse an excessive acceleration.

The 3 ms clip (a3ms)

The 3 ms clip is the maximum acceleration that can be sustained for a continuous 3 ms interval without exceeding the limit. It is computed by sliding a 3 ms window across the filtered acceleration trace and recording the highest average value within any such window. For chest acceleration the limit is 60 g; for head acceleration in some standards it is 80 g. The metric is deliberately less spike-sensitive than a raw peak, because a single-sample transient that lasts microseconds is physiologically less meaningful than a sustained 3 ms plateau. In Excel, a3ms is implemented with a moving average over a window of 0.003 × sample_rate samples, followed by a MAX over the resulting column.

Neck injury: Nij and Nkm

Neck injury criteria combine axial force and bending moment into a single dimensionless number. The Nij (Neck Injury Criterion) is defined as:

Nij = Fz / Fzc + My / Myc

where Fz is the axial force in Newtons (tension positive, compression negative), My is the bending moment in Newton-metres, and Fzc and Myc are the corresponding critical values, which differ for tension, compression, flexion, and extension. A common FMVSS 208 limit is Nij ≤ 1.0, evaluated at four combinations (tension-flexion, tension-extension, compression-flexion, compression-extension). The Nkm (Neck Injury Criterion for the KTH metric) is a related formulation that uses a weighted combination of shear force, axial force, and moment, and is expressed as a dimensionless value with a typical limit of Nkm ≤ 1.0. Both criteria require careful sign handling: a compression force with an extension moment produces a different Nij than the same magnitudes with flexion, and the critical values are not symmetric.

Femur force and tibia index

Femur force is the axial compressive load transmitted through the femur, measured in kilonewtons. FMVSS 208 limits it to 10 kN per leg for the 50th percentile male; the value scales with occupant size in other standards. Tibia index (TI) combines axial compression and bending moment at the tibia and is defined as:

TI = Fz / Fc + Mx / Mc

where Fz is the axial force in kN, Mx is the bending moment in Nm, and Fc and Mc are critical values (typically 35.9 kN and 225 Nm for the 50th percentile male). The limit is TI ≤ 1.0. As with Nij, the index is dimensionless and must be evaluated at the correct sign combination.

From raw channels to a pass/fail decision

Consider a worked example using a synthetic dataset. Suppose the head resultant acceleration channel is sampled at 10 kHz and the filtered trace contains a peak of 85 g sustained for 12 ms. To compute HIC15, the workbook scans every start sample t1, integrates forward for up to 150 samples (15 ms), and records the maximum of (t2-t1) × (mean_accel)^2.5. If the resulting HIC15 is 680, the criterion passes against the 700 limit; if it is 720, it fails. The same trace might yield a 3 ms clip of 78 g, which would fail the 80 g head limit if that limit applies. The engineer must therefore evaluate each criterion independently and report the governing (worst) result.

A practical Excel implementation uses a helper column for the running integral, a second helper column for the window mean, and a third for the HIC contribution, then takes =MAX() over the third column. For Nij, the workbook needs four separate evaluations — one per sign combination — because the critical values differ. A common mistake is to compute Fz/Fzc + My/Myc using a single pair of critical values and then take the absolute value; this under-reports the true Nij whenever the sign combination is not the one the critical values were calibrated for.

Typical limit summary

These values are the reference points that the automation workbook will compare against. The next step is to translate each definition into a reproducible Excel formula, validate it against a known reference trace, and only then wire the results into a pass/fail dashboard. Getting the units, sign conventions, and filtering order right at this stage prevents every downstream error.