3. Crash pulse characterization

An airbag ECU does not "see" a crash; it sees a filtered acceleration signal and integrates it into velocity change. Every deployment decision — threshold crossing, safing confirmation, fire timing — is ultimately a judgment about the character of that crash pulse. Two events with identical delta-v can produce radically different occupant kinematics if their pulse shapes differ, and two events with identical peak acceleration can differ in severity by a factor of two depending on duration. This chapter builds the vocabulary and quantitative intuition needed to read an acceleration–time history the way a calibration engineer does.

Sign Convention and the Acceleration–Time History

Before any analysis, fix the reference frame. In this course, the vehicle coordinate system follows ISO 4130: +X forward, +Y to the left, +Z upward. Crash accelerometers are mounted rigidly to the vehicle structure and report acceleration in vehicle coordinates. During a frontal impact the vehicle decelerates, so a forward-facing accelerometer records a negative X acceleration. Many data acquisition systems and OEM specifications instead plot the magnitude of deceleration as positive ("crash pulse" convention). Both conventions are legitimate, but mixing them silently is one of the most common sources of sign errors in calibration reviews. State the convention explicitly on every plot and keep it consistent through the entire analysis chain.

A raw acceleration–time history from a frontal barrier test typically contains three overlapping components:

• Rigid-body deceleration — the low-frequency component representing the vehicle's bulk velocity change. This is what the occupant restraint system must ultimately manage.
• Structural ringing — high-frequency oscillation (often 80–300 Hz) from bending modes of the front end, engine cradle, and body-in-white. It carries little momentum but can trip peak-detection logic if unfiltered.
• Sensor and mounting artifacts — resonance of the accelerometer block, cable whip, and bracket compliance, usually above 500 Hz.

Airbag ECUs apply a low-pass filter (commonly a 2nd-order Butterworth with a cutoff in the 100–400 Hz range, sometimes specified per FMVSS 208 or OEM internal standards) before threshold comparison. The filtered signal is what drives deployment; the raw signal is retained for diagnostics and post-crash reconstruction. Understanding which signal a given threshold applies to is essential when comparing calibration data across platforms.

Delta-v: The Integral That Defines Severity

Delta-v is the time integral of acceleration over the crash event:

Δv(t) = ∫₀ᵗ a(τ) dτ        (with sign convention applied consistently)

For a frontal barrier impact, the total delta-v at the end of the pulse equals the initial closing velocity (assuming the vehicle comes to rest relative to the barrier). A 56 km/h (35 mph) flat frontal barrier test therefore produces a total delta-v of approximately 15.6 m/s, regardless of how the pulse is shaped. This is the key insight: delta-v sets the energy budget, but the pulse shape determines how that energy is delivered to the occupant.

In practice, delta-v is computed by trapezoidal integration of the filtered acceleration signal, with the integration window bounded by the event trigger and the point where the vehicle velocity returns to zero (or the barrier contact ends). Integration drift from sensor bias must be removed — a 0.5 g bias over 100 ms produces a 0.49 m/s error, which is 3% of a 15.6 m/s event and enough to shift a severity classification. Standard practice is to high-pass filter the acceleration signal (or apply bias correction from a pre-trigger window) before integration.

Pulse Shape: Why Two Crashes with the Same Delta-v Feel Different

Pulse shape is characterized by three parameters that together determine occupant response:

Consider two idealized pulses with identical 15.6 m/s delta-v. A short, high-amplitude pulse (40 g peak, 80 ms duration) delivers its velocity change early; the occupant's torso begins moving forward relative to the vehicle within the first 20–30 ms, and the airbag must be fully inflated by roughly 30–40 ms after trigger to be in position. A long, low-amplitude pulse (20 g peak, 160 ms duration) gives the occupant more time but also allows more forward excursion before the restraint engages, changing the geometry of occupant–airbag contact and increasing the risk of bottoming-out or out-of-position interaction.

The pulse shape also determines the occupant's effective deceleration profile. Because the occupant is coupled to the vehicle through the belt and airbag, the occupant's acceleration is a filtered, delayed version of the vehicle pulse. A sharp pulse front produces a sharp occupant response with high belt forces; a ramped pulse front spreads the loading. This is why restraint engineers speak of "tuning the pulse" — the vehicle structure (crumple zone, engine cradle, subframe) is designed to shape the acceleration–time history so that the occupant restraint can manage it within injury criteria (HIC, chest deflection, Nij).

Reading a Pulse for Deployment Calibration

The following SVG illustrates a representative frontal barrier acceleration–time history with the key features annotated: the trigger point, the filtered pulse envelope, the delta-v integral, and the airbag fire window. Use it as a reference when interpreting test data.

Three features in the figure deserve attention. First, the trigger point occurs on the rising edge, well before peak acceleration — the ECU must decide to fire based on a threshold crossing that happens early in the pulse, because the airbag needs 25–35 ms to inflate. Second, the fire window (shaded) sits between trigger and roughly 20 ms after trigger; the exact fire time within this window is set by the calibration to place the airbag in position just as the occupant's torso arrives. Third, the delta-v at fire is small (a few m/s) compared to total delta-v — this is the quantity that determines whether the occupant is "in position" when the airbag deploys, and it is the parameter most sensitive to pulse shape.

Pulse Shape Effects in Practice: A Calibration Example

Suppose a calibration engineer is comparing two crash modes for the same vehicle: a 56 km/h flat frontal barrier and a 40 km/h offset deformable barrier (ODB, 40% overlap). Both produce similar total delta-v (approximately 15.6 m/s and 11 m/s respectively), but the ODB pulse is typically longer and lower-amplitude because only part of the front structure is engaged. The calibration must satisfy both. A threshold tuned only to the flat barrier may fire too late in the ODB event, allowing excessive occupant forward excursion before the airbag is in position. Conversely, a threshold tuned too low may fire on rough-road inputs or low-speed parking impacts.

The practical resolution is a two-stage threshold strategy: a low-magnitude, long-duration path (safing sensor plus a velocity-based arming criterion) and a high-magnitude, short-duration path (primary crash sensor). The velocity-based arming criterion integrates the filtered acceleration and requires a minimum delta-v (e.g., 2–4 m/s) within a defined window before the primary threshold can fire. This is precisely a pulse-shape discriminator: it rejects short, high-g events (hammer blows, potholes) that lack sufficient delta-v, while accepting long, low-g events (ODB, pole) that carry real occupant risk.

Practical Checklist for Pulse Analysis

• Confirm the sign convention and filter specification before comparing any two pulses.
• Integrate the filtered signal, with bias correction, to obtain delta-v; verify total delta-v against the known closing velocity.
• Extract peak acceleration, pulse duration, rise time, and delta-v at fire time for each crash mode.
• Plot the fire window against the occupant's forward excursion timeline (from sled or CAE data) to confirm the airbag is in position at contact.
• Check that the safing/arming logic rejects short-duration, low-delta-v events without delaying the fire time in legitimate long-duration crashes.

The acceleration–time history is the primary input to every downstream decision in the restraint system. Reading it correctly — with a consistent sign convention, a known filter, and an explicit delta-v integral — is the foundation for calibrating deployment timing that protects occupants across the full range of real-world crash modes, not just the one test that happens to be in the validation plan.