2. Crash pulse fundamentals for restraint calibration

Every restraint calibration decision ultimately traces back to one signal: the vehicle's acceleration–time history measured at the occupant compartment during a crash event. This signal, commonly called the crash pulse, defines the environment in which airbags, seat belts, pretensioners, and load limiters must operate. Understanding its structure — not just its peak value — is the foundation for setting deployment thresholds, timing, and energy-management characteristics.

Acceleration–Time History and Sign Convention

The crash pulse is a plot of acceleration versus time, typically sampled at 1–10 kHz and filtered per SAE J211 (Channel Frequency Class 60 for vehicle structure, CFC 180 or higher for occupant responses). Before any calibration work, the sign convention must be fixed and documented. In the widely used SAE convention, acceleration is positive in the direction of travel, so a frontal barrier impact produces a large negative acceleration (deceleration) pulse. Some OEMs and CAE teams instead plot deceleration as positive. Mixing conventions between a sled test, a CAE model, and an ECU calibration file is a common and costly source of error, so the convention should be stated explicitly in every pulse dataset and carried consistently into the diagrams and thresholds used downstream.

Delta-v, Duration, and Rise Time

Three scalar descriptors summarize the pulse and drive most restraint timing decisions:

• Delta-v (Δv) — the integral of acceleration over the crash event, i.e., the total velocity change of the vehicle. A 56 km/h frontal barrier test corresponds to Δv ≈ 15.6 m/s. Δv sets the overall severity and is the primary input to occupant energy calculations.
• Pulse duration — the time from impact to the point where the vehicle has essentially reached zero residual velocity relative to the barrier. Frontal pulses typically last 80–150 ms; the exact value depends on vehicle mass, crush stiffness, and structure design.
• Rise time — the interval from impact to the first significant acceleration peak. Short rise times (10–25 ms) indicate a stiff front structure and produce aggressive occupant loading; longer rise times (30–50 ms) indicate a softer, more progressive crush.

These three parameters are not independent. For a given Δv, a shorter duration implies higher average acceleration, and a shorter rise time concentrates that acceleration earlier in the event. The restraint system must therefore be tuned to the specific combination, not to any single number.

How Pulse Shape Drives Occupant Kinematics

Occupant motion is governed by the difference between vehicle deceleration and the forces transmitted through the restraint system. At t = 0, the occupant is moving at the initial vehicle speed while the vehicle begins to decelerate. The occupant continues forward at nearly constant velocity until the belt engages and the airbag inflates. This creates a relative displacement — the ride-down distance — that the restraint system must manage without allowing the occupant to contact stiff interior surfaces.

A pulse with a long, gradual rise allows the belt to engage early and spread the deceleration over a longer time, reducing peak occupant loads. A sharp, early peak forces the restraint system to react within a few milliseconds; if the airbag has not reached full inflation when the occupant arrives, the occupant may "bottom out" against the module or steering column. This is why rise time, not just Δv, determines the required airbag trigger time (time-to-fire, TTF).

Pulse Shape and Restraint Timing

Restraint timing is calibrated against the pulse in three stages. First, the sensing window — the time available for the ECU to detect the crash and decide to fire — is bounded by the rise time. A pulse that reaches its first peak at 15 ms leaves less decision time than one peaking at 35 ms. Second, the airbag inflation time (typically 20–40 ms for a driver frontal airbag) must complete before the occupant's forward excursion reaches the module. Third, the belt force limiter and pretensioner must be staged so that belt load builds in phase with the airbag's cushioning, avoiding a load spike when both act simultaneously.

Consider a representative example. A vehicle is subjected to a 56 km/h frontal barrier test. The measured pulse has Δv = 15.6 m/s, duration = 110 ms, and rise time = 22 ms, with a first peak of −38 g at 22 ms and a second peak of −32 g at 55 ms. The occupant's chest is instrumented with a CFC 180 accelerometer. If the airbag TTF is set to 18 ms and the bag reaches full inflation at 45 ms, the occupant's chest begins loading at approximately 30 ms and peaks at 70 ms. If the chest g exceeds the injury assessment reference value (typically 60 g for a 50th percentile male in a 56 km/h frontal test), the calibration engineer has three levers: advance TTF, increase bag pressure (or vent size), or soften the belt load limiter. Each lever changes the phase relationship between occupant motion and restraint force, and the correct choice depends on where in the pulse the excess load occurs.

Practical Calibration Workflow

In practice, the calibration engineer works from a validated pulse rather than a single test. The workflow typically proceeds as follows:

1. Acquire and filter the pulse. Record the vehicle acceleration at the occupant compartment (or the sled pulse for component tests) at ≥ 10 kHz, apply CFC 60 filtering, and verify that the integrated Δv matches the measured velocity change within ±5%.
2. Extract the descriptors. Compute Δv, duration, rise time, and the time and magnitude of the first and second peaks. These become the calibration targets.
3. Run occupant simulation or sled tests. Apply the pulse to a validated occupant model (e.g., THOR or Hybrid III) with candidate restraint parameters: TTF, bag pressure/vent, belt load limit, pretensioner timing.
4. Evaluate occupant response. Check chest g, chest deflection, head injury criterion (HIC), and femur loads against the relevant injury assessment reference values. Identify the time window where the response exceeds the target.
5. Adjust and iterate. If the excess occurs early (before 40 ms), advance TTF or increase bag inflation rate. If it occurs late (after 60 ms), soften the load limiter or increase bag venting. Re-run and confirm.

Common Pitfalls

Two errors appear repeatedly in restraint calibration programs. The first is treating Δv as the sole severity metric. Two pulses with identical Δv can produce very different occupant responses if their rise times differ by 15 ms. The second is ignoring the second peak. Many frontal pulses exhibit a secondary deceleration peak caused by engine block contact or structural rebound; if the restraint system has already fully vented by that time, the occupant may experience a late load spike that is not captured by early-peak-focused tuning.

Understanding the pulse as a shaped, time-dependent input — not a single number — is what allows the calibration engineer to predict occupant kinematics and set restraint timing with confidence. The next step is to examine how different pulse shapes (barrier, sled, and real-world variants) map onto the same calibration framework.