1. Establish HIC Baseline for a Driver Airbag Deployment

Why a Baseline HIC Must Be Computed, Not Assumed

Head Injury Criterion (HIC) is the regulatory and development metric that condenses a head acceleration time-history into a single injury-risk number. For a driver airbag deployment, the baseline HIC is the reference value against which every later change — bag pressure, vent size, tether length, clock-spring routing, seat position — is judged. If the baseline is computed inconsistently (wrong filter class, wrong window, wrong sign convention), every downstream comparison inherits that error. This case establishes a defensible baseline from a supplied acceleration record and documents both HIC15 and HIC36 so later cases can compare like with like.

The governing definition is:

HIC = max over t₁, t₂ of [ (1/(t₂ − t₁)) ∫t₁t₂ a(t) dt ]2.5 × (t₂ − t₁)

where a(t) is the resultant head center-of-gravity acceleration expressed in g, and the window length (t₂ − t₁) is bounded by the criterion being reported: 15 ms for HIC15, 36 ms for HIC36. The resultant is taken from the three orthogonal accelerometers as √(ax² + ay² + az²) after each channel is filtered per the applicable standard (commonly SAE J211 / ISO 6487 Channel Frequency Class 600 for head acceleration, i.e., a low-pass at 1000 Hz with −3 dB at 1650 Hz). The exponent 2.5 and the linear window term mean HIC is dominated by the average acceleration sustained over the window, not by the single peak sample — a distinction that matters when the airbag interaction produces a sharp early spike followed by a longer, lower plateau.

Sign convention: acceleration is treated as magnitude for HIC. If your data logger stores deceleration as negative, rectify before integration, or the integral will cancel and produce a falsely low HIC. Confirm the polarity of each channel against a known event (e.g., the deployment trigger) before computing.

Worked Baseline from the Supplied Record

The record below is a teaching example: a 120 ms head acceleration trace sampled at 10 kHz, already resultant-combined and CFC 600 filtered, representing a driver airbag deployment at a 25 km/h sled pulse. Values are illustrative, not measured test data.

Time (ms)Resultant a (g)Phase
0–20≈ 0–8Pre-contact, belt/seat ramp
20–35rises to 62Bag contact, membrane tension
35–55plateau 58–64Bag venting, sustained loading
55–75decays 60 → 22Rebound, bag deflation
75–120< 15Residual head motion

To compute HIC15, slide a 15 ms window across the trace and, for each start time, evaluate the mean acceleration and the windowed HIC term. The maximum occurs when the window brackets the sustained plateau rather than the isolated early spike. For this example the maximizing window is approximately t₁ = 33 ms, t₂ = 48 ms, with a mean resultant of about 61.5 g:

HIC15 = (61.5)^2.5 × 0.015
      = 61.5^2.5 ≈ 29,600  (61.5^2 = 3782; 3782 × √61.5 ≈ 3782 × 7.84 ≈ 29,650)
      HIC15 ≈ 29,650 × 0.015 ≈ 445

For HIC36 the window widens to 36 ms. The same plateau is captured but now includes the lower-amplitude decay tail, which pulls the mean down. The maximizing 36 ms window is approximately t₁ = 28 ms, t₂ = 64 ms, mean ≈ 52 g:

HIC36 = (52)^2.5 × 0.036
      = 52^2.5 ≈ 19,500  (52^2 = 2704; 2704 × √52 ≈ 2704 × 7.21 ≈ 19,500)
      HIC36 ≈ 19,500 × 0.036 ≈ 702
The two numbers are not interchangeable. HIC15 ≈ 445 and HIC36 ≈ 702 differ because the 36 ms window admits more low-g tail, lowering the mean but lengthening the window; the 2.5 exponent and linear term do not fully offset that. Always state which criterion a baseline refers to, and never compare a HIC15 against a HIC36 limit.

Reading the Window Selection

The SVG below shows the same trace with the two maximizing windows overlaid. The key visual point is that the HIC15 window sits inside the high-g plateau, while the HIC36 window extends into the decay region — this is why the two criteria diverge on the same event and why the baseline must record both.

Time (ms) Resultant a (g) 0 20 40 60 80 0 30 60 90 120 HIC15 33–48 ms HIC36 28–64 ms ≈61.5 g mean HIC15 window HIC36 window

Documenting the Baseline

A baseline is only useful if it is reproducible. Record the following alongside the two numbers so a later engineer can recompute and match them exactly:

  • Source record: file name, sample rate (10 kHz), channel mapping, and the filter applied (CFC 600, resultant of three channels).
  • Polarity check: confirmation that all channels were rectified to magnitude before integration.
  • Maximizing windows: t₁ and t₂ for each criterion (33–48 ms for HIC15; 28–64 ms for HIC36 in this example).
  • Reported values: HIC15 ≈ 445, HIC36 ≈ 702, each tagged with its window length.
  • Event context: sled pulse, seat position, bag configuration, and ambient conditions, so a later change can be attributed correctly.
Baseline record — Driver airbag, 25 km/h sled, CFC 600 resultant, 10 kHz. HIC15 = 445 (window 33–48 ms). HIC36 = 702 (window 28–64 ms). Values are teaching-example computations from the supplied illustrative trace, not measured test results. Any later comparison must use the same filter class, polarity convention, and window definition.

With this baseline fixed, subsequent cases can isolate a single variable — a vent-area change, a tether adjustment, a clock-spring reroute — and attribute any HIC shift to that change rather than to a difference in computation method. The two windows also tell you where to look: if a modification moves the HIC15 window earlier into the contact spike, the bag is loading the head too abruptly; if it stretches the HIC36 window deeper into the decay tail, the bag is venting too slowly. That diagnostic reading is the real payoff of a clean baseline.

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