4. Crash pulse characterization
Raw accelerometer data from a crash test is never the crash pulse. It is a noisy, drifting, gravity-contaminated voltage history that must be conditioned before any injury-relevant metric can be trusted. This chapter walks through the signal chain that turns a raw accelerometer channel into the three quantities that anchor nearly every frontal-impact analysis: delta-v (Δv), peak acceleration, and pulse duration. The emphasis is on the concrete operations — filter selection, bias removal, integration, and metric extraction — and on the judgment calls that separate a defensible pulse from a plausible-looking but wrong one.
Coordinate Convention and Sign Discipline
Before touching the data, fix the reference frame. For a frontal impact we adopt the vehicle body frame with +X forward (direction of travel) and the accelerometer mounted with its sensitive axis aligned to X. A decelerating vehicle therefore produces a negative X acceleration in the body frame. Many labs instead report the pulse as positive deceleration magnitude; both are acceptable, but the choice must be stated once and held for the entire analysis, including every figure and table. A sign flip between filtering and integration is the single most common source of a Δv that is correct in magnitude but wrong in direction.
Step 1 — Conditioning the Raw Channel
Three artifacts dominate raw crash accelerometer data: high-frequency sensor and structural ringing, low-frequency drift from integration of small bias errors, and a DC offset from gravity or amplifier bias. Handle them in this order:
- Bias/offset removal. Estimate the pre-trigger mean over a quiet window (typically 50–100 ms before T0) and subtract it. This removes gravity projection and static offset in one operation.
- Low-pass filtering. Apply a zero-phase (forward-backward) Butterworth filter. For occupant injury work, CFC 60 (channel frequency class, per SAE J211) is the standard: a 4th-order Butterworth with −3 dB cutoff at 100 Hz, applied forward and backward so no phase shift is introduced. For vehicle-level pulse shape work, CFC 180 (cutoff 300 Hz) preserves sharper features.
- Optional high-pass or detrend. A gentle high-pass (e.g., 0.5 Hz) or linear detrend suppresses residual drift before integration; use it sparingly, as aggressive high-pass filtering distorts the pulse tail and biases Δv.
Step 2 — Integration to Velocity (Δv)
Delta-v is the integral of the filtered acceleration over the pulse:
Δv(t) = ∫ a(t) dt from T0 to T_end
v(t) = cumulative trapezoidal integration of a(t)
Δv = v(T_end) − v(T0)In practice, integrate with the trapezoidal rule at the sample interval, then read Δv at the point where the vehicle has returned to rest (acceleration back to zero and staying there). Two practical cautions:
- Integration end point. Integrating past the true end of the pulse accumulates drift and inflates Δv. Define Tend as the last zero crossing of the filtered acceleration, or where |a| stays below a small threshold (e.g., 0.5 g) for a defined window.
- Drift check. After integration, the velocity trace should return to a flat plateau. A monotonically rising velocity tail after the pulse indicates residual bias — revisit the pre-trigger mean or add a mild detrend.
As a sanity anchor, a 50 km/h frontal barrier test typically yields a Δv near 50 km/h (≈13.9 m/s) for a vehicle that comes to rest; a value 10–15% off that expectation usually signals a filtering or end-point error, not a real physical difference.
Step 3 — Extracting Peak Acceleration and Pulse Duration
Peak acceleration is the maximum absolute value of the filtered pulse, reported with its sign convention and its time of occurrence. Report both the raw peak and, where relevant, a short-window average (e.g., 3 ms) because single-sample peaks are sensitive to residual ringing.
Pulse duration is the time from T0 (first sustained departure from zero, e.g., exceeding 1 g) to Tend (return to rest as defined above). Duration is not a single universal number — it depends on the threshold and filter class — so always state the definition alongside the value. A typical frontal pulse runs 80–120 ms; a stiff barrier impact is shorter and higher, a soft offset deformable barrier impact is longer and lower.
Worked Example (Illustrative Parameters)
Consider a synthetic channel sampled at 10 kHz, 200 ms long, with a pre-trigger window of 50 ms. Suppose the conditioned pulse has a peak of −42 g at 38 ms and returns below 0.5 g at 96 ms. Trapezoidal integration of the filtered trace yields a velocity plateau of −13.6 m/s, i.e., Δv ≈ 49 km/h. The derived metrics are therefore: peak acceleration 42 g (deceleration), pulse duration ≈ 96 ms, Δv ≈ 49 km/h. These numbers are illustrative, not measured; the point is the chain of operations and the internal consistency check (Δv close to the impact speed).
Common Failure Modes and How to Recognize Them
| Symptom | Likely cause | Corrective action |
|---|---|---|
| Velocity keeps rising after pulse | Residual bias / drift | Re-estimate pre-trigger mean; add mild detrend |
| Peak shifted late vs. reference | Causal (one-pass) filter | Apply forward-backward filtering |
| Δv 10–15% above impact speed | Integration past Tend | Truncate at last zero crossing |
| Spiky, non-physical peak | Filter class too high | Use CFC 60 for injury metrics |
| Sign of Δv opposite to impact | Frame/sign convention mismatch | Reconcile body-frame sign once, globally |
The discipline of this chapter is simple: condition first, integrate second, extract metrics last, and always cross-check Δv against the known impact speed. When those three numbers — Δv, peak acceleration, and duration — are derived through a documented, reproducible chain, they become a reliable foundation for the offset-impact injury diagnosis that follows.