2. Crash pulse characteristics and sensing requirements

An airbag ECU does not react to a crash as an event; it reacts to a crash pulse — the acceleration-versus-time history measured at a specific mounting point on the vehicle body. Every deployment decision, from the arming threshold to the discrimination window, is ultimately a comparison between features extracted from this pulse and calibrated limits. Understanding how pulses differ across frontal, side, rear, and rollover events is therefore the foundation of restraint control algorithm development.

Coordinate Convention and Pulse Definition

Throughout this course, the vehicle coordinate system follows ISO 8855: the x-axis points forward, the y-axis points to the driver's left, and the z-axis points upward. Accelerometers are mounted with their sensitive axes aligned to this frame. A frontal impact decelerates the vehicle, so the longitudinal accelerometer reports a negative x-acceleration during a frontal crash; a left-side impact produces a positive y-acceleration at a sensor mounted on the struck side. All thresholds, signs, and plots in this chapter follow this convention. If a project adopts the opposite sign convention (some OEMs define positive as rearward), the polarity of every threshold must be flipped consistently — mixing conventions is a classic source of "the algorithm never fires" defects.

Frontal Crash Pulses

Frontal pulses are the best-behaved of the four families because the vehicle structure is designed to absorb energy over a controlled crush distance. A typical 50 km/h full-frontal rigid-barrier pulse rises steeply within 5–15 ms, reaches a first peak of roughly 20–40 g, then shows a characteristic double-peak shape: the first peak corresponds to the engine cradle and front rails loading up, and the second, broader peak (often 25–45 g, arriving 40–70 ms after impact) corresponds to the powertrain and body structure decelerating the occupant cell.

The sensing requirement is driven by the time-to-fire budget. For a belted occupant, the airbag must be fully inflated before the occupant's head would otherwise contact the steering wheel — typically around 60–80 ms after impact for a 50 km/h event. Allowing 20–30 ms for inflator deployment, the ECU must issue the fire command within roughly 30–50 ms. This forces the discrimination algorithm to make a decision using only the first 20–30 ms of data, which is precisely the interval in which a rough-road or curb-strike event can look deceptively similar.

A practical discrimination feature set for frontal sensing includes:

• Velocity change obtained by integrating the filtered acceleration, Δv(t) = ∫a(t)dt, evaluated at 10–20 ms.
• Energy or jerk-based measures that capture how abruptly the pulse rises.
• Crash severity index (e.g., a weighted integral of acceleration over a moving window) compared against a speed-dependent threshold.

Consider a teaching example: a 50 km/h frontal pulse sampled at 1 kHz, low-pass filtered at 300 Hz. Integrating the first 15 ms yields Δv ≈ 4.5 m/s. A rough-road event of comparable peak amplitude (say 15 g) but with a 30 Hz oscillation produces Δv ≈ 0.7 m/s over the same window. A velocity threshold of 2.5 m/s at 15 ms cleanly separates the two. This is why velocity-based rather than amplitude-based discrimination dominates frontal algorithms.

Side Crash Pulses

Side impacts are fundamentally harder. The struck-side door and B-pillar offer only 100–200 mm of crush space before intruding into the occupant compartment, so the pulse is short and violent: rise times of 2–5 ms, peaks of 40–80 g, and total event durations of 30–50 ms. The time-to-fire budget shrinks to 10–20 ms because the occupant's thorax is already adjacent to the door trim.

Two consequences follow. First, side sensors (satellite accelerometers or pressure sensors in the door cavity) must be mounted close to the impact zone and communicate with the central ECU over a fast bus — typically a dedicated current-loop or PSI5 interface with 1–2 ms latency. Second, the algorithm cannot rely on integration alone; it uses peak detection and slope features evaluated within 5–10 ms. A common approach is a two-stage decision: a fast "safing" threshold (e.g., 8 g within 3 ms) that arms the system, followed by a discrimination threshold (e.g., 25 g within 8 ms) that confirms deployment.

Pressure-based side sensing deserves mention: a pressure sensor in the door cavity detects the pressure rise caused by door deformation. Because pressure propagates at the speed of sound in air, the signal rises within 1–3 ms of impact — faster than an accelerometer on the same door. The trade-off is sensitivity to temperature and altitude, which must be compensated in the algorithm.

Rear Crash Pulses

Rear impacts are generally lower severity for restraint purposes because the seat and head restraint absorb much of the energy. The pulse is longer and gentler: rise times of 20–40 ms, peaks of 10–25 g, and durations of 100–150 ms. The primary restraint concern is whiplash, addressed by active head restraints rather than airbags. Consequently, rear sensing requirements are modest: the algorithm must distinguish a genuine rear impact from a forward push (e.g., being nudged in traffic) and from rough-road inputs, but it rarely needs to fire a pyrotechnic device within a tight window. A typical rear algorithm uses a velocity threshold of 3–5 m/s integrated over 30–50 ms.

Rollover Events

Rollover is a different sensing problem entirely. The trigger is not linear deceleration but angular motion: a roll rate sensor (gyroscope) about the x-axis measures roll velocity, and a z-axis accelerometer measures the change in vertical acceleration as the vehicle tips. The classic discrimination criterion is the roll angle obtained by integrating roll rate, combined with a lateral acceleration threshold. A common formulation requires both a roll angle exceeding roughly 50–60° and a roll rate exceeding 100–150 °/s within a defined window.

Timing is less aggressive than frontal or side: the occupant must be restrained before the head contacts the ground, which gives a budget of 100–300 ms. However, the algorithm must reject false positives from severe cornering, potholes, and off-road driving, where roll rates of 30–50 °/s are routine. The integration of roll rate must therefore be reset or leaky to prevent drift accumulation.

Comparative Summary

From Pulse to Requirement

The practical takeaway is that sensing requirements are not arbitrary — they are derived from the pulse. Given a measured or simulated pulse, you can compute the latest possible fire time from occupant kinematics, subtract the inflator deployment time, and obtain the discrimination window. The algorithm must then extract a feature that separates that pulse from the false-positive set within that window. The following diagram summarizes how the four event families map onto the two axes that matter most: available decision time and the feature type that provides robust discrimination.

Read the diagram as a design map. Side events sit in the low-time, high-robustness-demand corner, which is why they use dedicated satellite sensors and peak-based logic. Frontal events occupy the middle ground where integration over 15–20 ms is both feasible and discriminative. Rear events are forgiving enough that a simple velocity threshold suffices. Rollover is unique in that its feature is angular rather than linear, and its budget is an order of magnitude larger. When you begin calibrating a new platform, the first question is always: which corner of this map does the event occupy, and does my feature set match that corner?