3. Crash pulse characterization

An airbag Electronic Control Unit (ECU) never "sees" a crash. It sees a digitized accelerometer signal, and every deployment decision is made on a derived, filtered, and integrated version of that signal. Understanding the crash pulse — its acceleration-time history, its velocity change (delta-v), and the filtering that sits between the raw sensor and the decision algorithm — is therefore the foundation for reasoning about deployment timing. This section builds that foundation from the physical signal upward, and shows where filtering choices directly shift the deployment decision.

Sign conventions and the acceleration-time history

Before any number is meaningful, the reference frame must be fixed. In this course we adopt the SAE J211 / ISO 6487 convention for vehicle crash testing: the vehicle's forward direction of travel is +X, and a frontal impact decelerates the vehicle, so the longitudinal accelerometer mounted on the vehicle structure reads a negative acceleration during the crash event. Many ECU signal chains invert this internally so that the "crash pulse" presented to the algorithm is positive-going; whenever a pulse is quoted, the polarity convention must be stated. All figures and equations below use the raw sensor convention: a(t) < 0 during frontal deceleration.

The acceleration-time history a(t) is the primary observable. Its shape is governed by the vehicle's front-end crush behaviour and the barrier or opponent stiffness. A typical 50 km/h full-frontal rigid-barrier pulse rises steeply within 10–20 ms, peaks somewhere between 25 and 45 g, and then decays with a long tail as the crumple zone bottoms out. An offset deformable barrier (ODB) or pole impact produces a lower-amplitude, longer-duration pulse because less structure is engaged. These shape differences are exactly what the deployment algorithm must discriminate: a soft pole hit at 30 km/h and a severe barrier hit at 50 km/h can produce similar peak accelerations but very different delta-v histories.

Delta-v: integrating the pulse

Delta-v is the time integral of acceleration, and it is the single most useful scalar for characterizing crash severity:

Δv(t) = ∫₀ᵗ a(τ) dτ        (with a(τ) in m/s², Δv in m/s)
Δv_kmh = Δv × 3.6

In discrete ECU terms, with sample interval Δt and bias-corrected samples a_k:

v_k = v_(k-1) + a_k · Δt
Δv_k = |v_k - v_0|

Two practical cautions dominate. First, integration accumulates sensor bias: a residual offset of only 0.5 g (≈4.9 m/s²) integrated over 100 ms produces a spurious 0.49 m/s (≈1.8 km/h) of delta-v — enough to matter near a threshold. ECUs therefore apply a pre-crash bias estimate (averaged over the quiet period before the event) and subtract it before integration. Second, integration must start from a defined trigger point; the algorithm typically arms on the first sample exceeding a small g-level (e.g. 2–3 g) and integrates forward from there.

Delta-v is also the natural bridge to occupant kinematics. A 50 km/h frontal crash that reaches 30 km/h of delta-v within 60 ms means the occupant, restrained only by the belt, is still travelling forward at roughly 30 km/h relative to the decelerating cabin at that instant. The airbag must be inflated and in position before that relative motion carries the occupant into the module region — which is why deployment timing is expressed in milliseconds and why the pulse shape, not just the peak, sets the clock.

Filtering: what the decision algorithm actually consumes

Raw accelerometer output contains high-frequency content from structure-borne ringing, sensor resonance, and road/roughness noise. Feeding it directly into a threshold or integration stage causes false triggers and unstable delta-v. The standard remedy is a low-pass filter, and the automotive reference is the ISO 6487 Channel Frequency Class (CFC) family. CFC 60 (≈100 Hz cutoff, −3 dB) is the classic occupant-protection channel; CFC 180 (≈300 Hz) is used where higher-frequency content matters; CFC 1000 is used for component-level work. The ECU's internal anti-alias and decision filters are chosen to preserve the pulse energy that matters for deployment while rejecting the rest.

A second-order Butterworth low-pass is a common implementation. In discrete form, a biquad section is sufficient:

% Second-order low-pass, fc = 100 Hz, fs = 10 kHz (illustrative)
w0 = 2*pi*fc/fs;  alpha = sin(w0)/(2*Q);  Q = 0.7071;
b0 = (1 - cos(w0))/2;  b1 = 1 - cos(w0);  b2 = b0;
a0 = 1 + alpha;  a1 = -2*cos(w0);  a2 = 1 - alpha;
% normalize by a0, then apply:
y[n] = b0*x[n] + b1*x[n-1] + b2*x[n-2] - a1*y[n-1] - a2*y[n-2]

The filter introduces group delay — roughly 1.5–3 ms for a CFC 60-class filter — and this delay is part of the deployment budget. It also attenuates the pulse peak: a sharp 40 g spike lasting 3 ms may be reduced to 30 g after filtering, while a broad 30 g plateau is barely affected. The decision algorithm must therefore be tuned on the filtered signal, not the raw one, and the same filter must be used in simulation, bench testing, and vehicle validation so that thresholds transfer.

From pulse to decision: a worked example

Consider an illustrative frontal pulse sampled at 10 kHz, filtered at CFC 60, with the following idealized segments (values are teaching assumptions, not measured data):

Using Δv_inc = |a|·g·Δt·3.6 with g = 9.81 m/s², the pulse crosses a 25 km/h delta-v threshold at about 30 ms and a 40 km/h threshold at about 50 ms. A typical frontal algorithm might require, for example, 25 km/h of delta-v within 40 ms to fire stage 1, and a higher delta-v rate to fire stage 2. The table shows why the rate of delta-v accumulation — not the peak g alone — separates a severe barrier hit from a softer event: the severe pulse reaches 25 km/h in 30 ms, whereas a pole impact of similar peak might take 55–70 ms.

Practical characterization workflow

When characterizing a pulse for deployment logic, the following sequence keeps the analysis traceable and reproducible:

1. Acquire and document. Record the raw longitudinal channel at the ECU mounting location, note sample rate, sensor range, and polarity convention. Keep the raw file untouched.
2. Bias-correct. Estimate the pre-trigger mean over a quiet window (e.g. 50 ms before the arming threshold) and subtract it. Report the residual bias.
3. Filter. Apply the CFC class used by the target algorithm (CFC 60 for occupant-protection decisions). Verify the filter's −3 dB point and group delay against the standard.
4. Integrate. Compute delta-v from the filtered, bias-corrected signal starting at the defined trigger sample. Report delta-v at fixed time marks (20, 40, 60, 100 ms) rather than only the final value.
5. Compare against decision thresholds. Plot delta-v versus time with the algorithm's thresholds and timing windows overlaid, as in the figure above. The crossing times are the deployment-relevant outputs.
6. Sanity-check. Confirm that the filtered peak and the delta-v at 100 ms are physically consistent with the impact severity class; a mismatch usually indicates a filter or bias error rather than a genuine pulse.

The crash pulse is thus not a single number but a filtered, integrated, time-resolved description of the event. Delta-v tells the algorithm how much velocity has been shed; the acceleration-time history tells it how fast; and the filter determines which parts of the physical event the algorithm is allowed to see. Deployment timing decisions are only as trustworthy as the characterization behind them, so the polarity, bias, filter class, and integration start point must be fixed, documented, and held constant from simulation through vehicle validation.