3. Crash pulse and occupant kinematics fundamentals

Every restraint system design decision ultimately traces back to two coupled physical quantities: the deceleration history the vehicle body experiences during a crash, and the resulting motion of the occupant relative to that body. Engineers call the first the crash pulse (or acceleration–time history, a(t)), and the second occupant kinematics. Understanding how these two interact — and how the restraint system sits between them — is the foundation for airbag timing, seatbelt load-limiter tuning, and pretensioner strategy. This chapter builds that foundation with concrete numbers and a reproducible pulse-analysis workflow.

Reading the acceleration–time history

A crash pulse is recorded by accelerometers rigidly mounted to the vehicle structure (typically the B-pillar base or the tunnel), sampled at 1–10 kHz and filtered per SAE J211 (channel frequency class 60 for vehicle structure, CFC 180 for occupant-relevant signals). The sign convention used throughout this course is: positive acceleration points forward (vehicle direction of travel), so a frontal impact produces a large negative acceleration. All plots and calculations below follow this convention.

Three numbers characterize a pulse for restraint work:

• Peak deceleration — the maximum negative value, e.g. −35 g to −45 g in a 50 km/h rigid-barrier test.
• Pulse duration — the time from impact to the point where deceleration returns near zero, typically 80–120 ms for a frontal barrier event.
• Velocity change (Δv) — the integral of the pulse, which must equal the test Δv (e.g. 13.9 m/s for 50 km/h). This integral is the single most important sanity check on any measured pulse.

Because Δv is the area under a(t), a pulse that is tall and narrow and one that is low and long can produce the same Δv but very different occupant loading. This is why pulse shape, not just peak value, drives restraint calibration.

Ride-down: the concept that couples vehicle and occupant

If the occupant were rigidly attached to the vehicle, they would experience the full pulse. In reality, the restraint system allows the occupant to decelerate over a longer distance and time than the vehicle structure — this is ride-down. The ride-down efficiency is the fraction of the occupant's kinetic energy that is dissipated by the vehicle's controlled deformation rather than by the occupant–restraint interaction.

A useful engineering approximation: for a vehicle that crushes by distance S while the occupant moves forward by distance d relative to the vehicle before being fully restrained, the occupant's effective deceleration is roughly reduced by the ratio of available stopping distance. In practice, restraint engineers quantify this with the occupant load criterion (OLC) and with chest acceleration vs. vehicle acceleration overlays: the gap between the two curves is the ride-down benefit.

Occupant kinematics and restraint coupling

During a frontal impact the occupant continues forward at the pre-crash velocity while the vehicle decelerates. The relative displacement grows until the restraint engages. The sequence is:

1. Free flight (0–15 ms): occupant moves forward at near-constant velocity; belt slack and geometry determine when coupling begins.
2. Belt engagement and pretensioner firing (15–30 ms): pyrotechnic pretensioners remove slack (typically 40–80 mm of belt webbing) and pull the occupant into the seat, improving coupling.
3. Load-limiter phase (30–70 ms): the belt force limiter (e.g. torsion bar yielding at 3–4 kN) allows controlled webbing payout so chest deceleration stays within tolerance while the occupant rides down.
4. Airbag interaction (20–60 ms): the frontal airbag must be fully inflated before the occupant's head reaches the module — typically the head arrives 50–70 ms after impact, so bag deployment must complete by ~40 ms.

The critical coupling insight: restraint timing is referenced to occupant kinematics, not to the pulse alone. A stiffer pulse brings the occupant forward earlier, so airbag trigger thresholds and pretensioner fire times must be calibrated against the measured occupant trajectory, not just the vehicle acceleration.

Worked example: verifying a measured pulse

Suppose a frontal sled test at 50 km/h yields a digitized pulse sampled every 1 ms. Before using it for restraint calibration, verify the Δv integral. A practical procedure:

# Example: trapezoidal integration of a(t), a in g, dt = 1 ms
# Sign convention: negative a = deceleration
# Convert g to m/s^2: multiply by 9.81
# Expected Δv for 50 km/h = 13.89 m/s

import numpy as np
a_g = np.array([...])          # measured pulse, length N
dt  = 1e-3                     # 1 ms
dv  = np.trapz(a_g * 9.81, dx=dt)
print(f"Integrated Δv = {abs(dv):.2f} m/s")   # target 13.89 ± 0.3

If the integrated Δv deviates by more than ~2% from the nominal test speed, suspect accelerometer drift, incorrect CFC filtering, or a missing pre-trigger segment. A common failure symptom is a pulse that looks plausible but integrates to 11–12 m/s — usually because the first 5–10 ms before trigger were clipped. Always retain at least 20 ms of pre-trigger data.

From pulse to restraint decision: a calibration checklist

The following table summarizes how pulse characteristics map to restraint calibration actions. Values are illustrative for a mid-size passenger car in a 50 km/h frontal barrier test.

Practical takeaway

The crash pulse defines the timing budget; occupant kinematics defines when the restraint must act; ride-down defines how much deceleration the occupant can be spared. A restraint engineer's core loop is therefore: measure and validate the pulse (Δv check), extract occupant trajectory (head and chest displacement vs. time), then tune pretensioner, load limiter, and airbag timing so that coupling occurs inside the ride-down window. Get the pulse integral wrong and every downstream calibration inherits the error; get the coupling timing wrong and the best hardware still produces poor occupant metrics.