3. Dynamic performance metrics

In a frontal crash, the restraint system must accomplish two competing objectives: couple the occupant to the vehicle early enough to prevent ejection and excessive excursion, yet manage the deceleration energy slowly enough that internal tissues are not injured. The metrics used to evaluate this balance fall into two families — restraint-system metrics (force limits, elongation, energy absorption) that describe how the belt and its anchorages behave, and occupant-injury metrics (HIC, chest deflection, femur load) that describe what the human body experiences. This chapter explains what each metric physically represents, how it is computed, and how the two families are linked through the belt force–deflection path.

Force Limits and Load-Limiting Behavior

A seatbelt transmits load through the webbing, retractor, buckle, and anchorages. The peak force in the shoulder belt, F_shoulder, is the primary driver of chest loading. Modern systems use a load limiter — a torsion bar in the retractor or a deformable webbing loop — that yields at a calibrated threshold, typically 3–5 kN for a 50th-percentile male in a 56 km/h frontal barrier test. Once the limiter yields, force plateaus while the occupant continues to move forward, converting kinetic energy into plastic deformation rather than into chest compression.

The plateau force is not arbitrary. It is bounded below by the need to keep the occupant from striking the steering wheel or instrument panel, and bounded above by chest tolerance. A useful design rule is that the shoulder-belt force should stay below roughly 4 kN for a 50th-percentile occupant, with pretensioner firing within the first 10–15 ms to remove slack before the force plateau begins.

Elongation and Energy Absorption

Elongation is the strain of the webbing under load, expressed as a percentage of original length. Standard polyester webbing elongates about 7–12% at 10 kN. Elongation matters because it determines how far the occupant travels before the belt becomes fully effective; excessive elongation delays coupling, while too little elongation transmits force too abruptly.

Energy absorption is the area under the force–displacement curve of the restraint system. For a load-limited belt, this is approximately the plateau force multiplied by the occupant's forward excursion during the plateau phase. If a 50th-percentile occupant (78 kg) decelerates from 56 km/h (15.6 m/s) and the belt absorbs 60% of the kinetic energy, the absorbed energy is:

E_k = 0.5 × m × v²
    = 0.5 × 78 kg × (15.6 m/s)²
    ≈ 9.5 kJ
E_belt ≈ 0.6 × 9.5 kJ ≈ 5.7 kJ

With a 4 kN plateau, the corresponding excursion is about 1.4 m of belt payout — which is why pretensioners and load limiters must be tuned together, not independently.

Injury Criteria: HIC, Chest Deflection, Femur Load

The Head Injury Criterion (HIC) integrates resultant head acceleration over the most severe 15 ms window:

HIC = max[ (1/(t2−t1)) ∫ a(t) dt ]^2.5 × (t2−t1)
      where t2−t1 ≤ 15 ms, a in g

The FMVSS 208 / Euro NCAP threshold is HIC₁₅ ≤ 700 for a 50th-percentile male. HIC is dominated by the deceleration pulse shape: a sharp spike produces a high HIC even if the average acceleration is modest.

Chest deflection is measured by a chest band or potentiometer on the Hybrid III dummy, reported in millimeters. The threshold is typically ≤ 50 mm for the 50th-percentile male and ≤ 40 mm for the 5th-percentile female. Deflection correlates directly with shoulder-belt force and with the rate of loading; a 4 kN plateau held for 40 ms produces less deflection than a 6 kN spike held for 20 ms.

Femur load is measured axially in the thigh, with a threshold of ≤ 10 kN per leg. In frontal impacts, femur load is driven by knee-bolster contact and by lap-belt geometry; a lap belt routed too high (over the abdomen) increases femur load and risks submarining.

Key linkage: Shoulder-belt force → chest deflection → HIC. Reducing the force plateau lowers chest deflection but increases forward excursion, which raises the risk of head contact. The design problem is a constrained optimization, not a single-metric minimization.

Reading the Metrics Together: A Worked Example

Consider a 56 km/h frontal barrier test with a 50th-percentile male dummy. The measured shoulder-belt force peaks at 4.2 kN at 55 ms, chest deflection reaches 42 mm at 70 ms, HIC₁₅ computes to 620, and peak femur load is 7.8 kN. All four metrics pass their thresholds, but the margin on chest deflection is thin. A practical diagnostic sequence:

  1. If HIC is high but chest deflection is low, inspect the head path — the head may be striking the A-pillar or airbag seam rather than the bag center.
  2. If chest deflection is high but HIC is low, the load limiter plateau is too high or too long; reduce the plateau force or shorten its duration.
  3. If femur load is high, check lap-belt routing and knee-bolster stiffness; a lap belt sitting above the iliac crest will drive femur load up.
  4. If all metrics are marginal, the pretensioner timing may be late — verify firing at 10–15 ms and confirm slack removal before the force plateau.
When comparing runs, always normalize by impact speed and occupant mass. A 4 kN plateau at 56 km/h with a 78 kg dummy is not equivalent to the same plateau at 64 km/h with a 95th-percentile dummy; the energy scales with v² and the tolerance scales with occupant size.

Metric Interaction and Design Trade-offs

The four metrics are not independent. Increasing load-limiter plateau force raises chest deflection and HIC but reduces forward excursion and femur load. Increasing pretensioner force reduces excursion and HIC but can raise chest deflection if the force spike is sharp. Increasing webbing elongation reduces peak force but delays coupling and can raise HIC if the head reaches the airbag late. The practical tuning workflow is to fix the pretensioner timing first, then sweep the load-limiter plateau, then adjust lap-belt routing and knee-bolster stiffness to bring femur load into range.

Frontal Impact: Restraint Metrics → Occupant Injury Metrics Restraint-System Metrics Shoulder-Belt Force Plateau 3–5 kN Peak ≤ 4 kN (50th %ile) Webbing Elongation 7–12% at 10 kN Affects coupling time Energy Absorption Area under F–x curve ≈ 5.7 kJ (example) Pretensioner Timing Fire at 10–15 ms Removes slack Load Path Belt → chest Belt → pelvis Belt → femur Excursion ↔ force trade-off Occupant-Injury Metrics HIC₁₅ Integral of head accel over 15 ms window Threshold ≤ 700 (50th %ile male) Example: 620 → PASS Chest Deflection Measured by chest band / potentiometer Threshold ≤ 50 mm (male), ≤ 40 mm (female) Example: 42 mm → PASS (thin margin) Femur Load Axial load in thigh, per leg Threshold ≤ 10 kN Example: 7.8 kN → PASS Design trade-off: lower plateau force → lower chest deflection & HIC, but higher excursion & femur load. Tune pretensioner timing first, then plateau, then lap-belt routing.

Practical Verification Checklist

When reviewing a frontal impact test report, verify the following before accepting the result:

  • Force plateau stability: Confirm the shoulder-belt force stays within ±10% of the target plateau for at least 30 ms. A rising plateau indicates the load limiter is bottoming out.
  • Pretensioner timing: Check that the pretensioner fires between 10 and 15 ms and that belt slack is removed before the force plateau begins.
  • Chest deflection rate: Compute the deflection rate (mm/ms); values above 1.5 mm/ms correlate with rib fracture risk even when peak deflection is below threshold.
  • Femur load symmetry: Compare left and right femur loads; a difference above 2 kN suggests asymmetric lap-belt routing or a knee-bolster mismatch.
  • HIC window: Verify the 15 ms window is correctly identified; a misidentified window can under- or over-estimate HIC by 20–30%.
Do not evaluate metrics in isolation. A run that passes HIC but fails chest deflection is not a partial success — it indicates the load limiter is mis-tuned and the occupant would likely sustain rib fractures in a real crash. Always report all four metrics together with the force–displacement curve.

The next step in the workflow is to correlate these dummy-based metrics with real-world injury outcomes using field data, which is covered in the following chapter on crash reconstruction and injury probability curves.

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