3. Occupant kinematics in frontal impacts

Frontal restraint design is fundamentally a timing problem. The airbag, seat belt, pretensioner, and load limiter must all act on an occupant whose body is already moving relative to the vehicle at the moment of impact. Before any restraint can be tuned, the engineer must understand two coupled inputs: the vehicle crash pulse (what the vehicle does) and the occupant kinematic response (what the body does in reaction). This chapter establishes the physical framework that every subsequent calibration decision depends on.

3.1 The Crash Pulse as the Forcing Function

The crash pulse is the vehicle body's longitudinal deceleration history measured at a structural point near the occupant compartment — typically the B-pillar base or the seat track cross-member. It is the boundary condition that drives everything downstream. Three characteristics dominate restraint design:

• Pulse shape and duration. A rigid-barrier 50 km/h test produces a roughly 90–120 ms pulse with a peak deceleration of 25–40 g. A softer, more compliant front structure stretches the pulse and lowers the peak; a stiffer structure does the opposite. The area under the pulse (integrated deceleration) equals the velocity change Δv, so shape and duration are not independent.
• Rise time and peak location. A fast rise (short time-to-peak) means the occupant begins loading the restraint early and at high relative velocity. A delayed peak gives the restraint more time to deploy but concentrates the deceleration later in the event.
• Frequency content. Real pulses contain high-frequency structural ringing superimposed on the main envelope. This matters because occupant models and sled pulses must reproduce the low-frequency envelope faithfully while filtering out noise that would not physically reach the occupant.

In practice, engineers work with a sled pulse — a simplified, smoothed deceleration profile that reproduces the vehicle's Δv and principal pulse shape on a deceleration sled. The sled pulse is the controlled input for restraint calibration because it isolates occupant-restraint behavior from body-structure variability. A typical calibration pulse for a mid-size sedan at 50 km/h might be specified as a trapezoidal or half-sine envelope with Δv = 13.9 m/s (50 km/h), peak ≈ 30 g, and duration ≈ 100 ms. These values are illustrative and must be replaced with the actual measured pulse for any real program.

3.2 Occupant Motion Phases

Relative to the vehicle, the occupant continues forward at approximately the pre-impact velocity while the vehicle decelerates beneath them. The resulting relative motion unfolds in four recognizable phases:

1. Free-flight / lash phase (0 to ~30 ms). The occupant is essentially unconstrained; the torso translates forward, the pelvis may submarine slightly, and the head begins to pitch forward. No restraint force has yet developed. This phase sets the initial conditions for everything that follows.
2. Belt engagement and ride-down (~30 to ~70 ms). The belt webbing goes taut, the pretensioner removes slack, and the occupant begins to decelerate with the vehicle. The goal is ride-down: keeping the occupant's deceleration close to the vehicle's so that relative displacement stays small. Load limiter payout controls how much force the belt applies to the chest.
3. Airbag interaction (~40 to ~90 ms). The deploying airbag contacts the chest and head, distributing load over a larger area and arresting forward excursion. Timing here is critical: too early and the bag is still inflating when the occupant arrives (high risk of membrane loading); too late and the occupant has already bottomed out on the belt or steering wheel.
4. Rebound and settle (>90 ms). The occupant is pushed back into the seat by restraint and seat stiffness. Rebound velocity and the resulting head excursion determine secondary-contact risk and out-of-position concerns.

3.3 Restraint Coupling Timing

Coupling timing is the alignment between when the occupant arrives at a restraint and when that restraint is ready to receive them. Three couplings must be managed simultaneously:

• Belt-to-occupant coupling. Pretensioner fire time and webbing slack determine when belt force begins to rise. A pretensioner that fires too late leaves the occupant in free-flight longer, increasing excursion; too early and it may pull the occupant into an unfavorable posture before the pulse develops.
• Airbag-to-occupant coupling. The airbag must be fully inflated and venting before the occupant's chest reaches the module face. The relevant metric is the time-to-contact versus the bag inflation time. If contact occurs before full inflation, the occupant experiences the bag's deployment energy rather than its cushioning.
• Restraint-to-restraint coupling. Belt and airbag must share the load. If the belt is too stiff, the airbag sees little load and the chest takes the belt force; if the belt is too soft, the occupant travels further and the airbag must absorb more energy, raising head and neck loads.

The figure below maps these relationships on a shared timeline, showing how the crash pulse, occupant relative displacement, belt force, and airbag pressure evolve together and where the coupling windows sit.

3.4 Reading the Coupled Timeline

The timeline makes the design logic visible. The belt coupling marker sits where belt force begins its steep rise — this is the pretensioner's effective fire time plus slack removal. The bag contact marker sits where airbag pressure and occupant displacement intersect, i.e., the moment the occupant reaches the module face. Peak excursion occurs after both restraints have loaded the occupant, and rebound follows.

A well-coupled system shows belt force rising before bag contact, so the belt begins ride-down while the bag finishes inflating. If the bag contact marker appears to the left of the belt coupling marker, the occupant is arriving at an inflating bag — a classic mis-timing symptom. If peak excursion occurs before bag contact, the bag is doing no useful work and the belt is carrying the entire load.

3.5 Practical Calibration Workflow

A reproducible calibration loop for a frontal driver restraint system proceeds as follows. Inputs: the measured or target sled pulse (Δv, peak, duration), occupant anthropometry (e.g., Hybrid III 50th percentile), seat position, belt geometry, and airbag module characteristics (inflator output, vent area, bag volume).

1. Establish the baseline. Run the sled simulation or test with nominal pretensioner fire time, load limiter force, and airbag fire time. Record belt force, chest deflection, head acceleration, and relative displacement traces.
2. Locate the coupling markers. From the traces, identify belt-force onset, bag contact time, and peak excursion. Compare against the pulse's rise time.
3. Adjust one parameter at a time. If bag contact precedes full inflation, delay the airbag fire time or increase inflator output; if belt force rises too late, advance the pretensioner. Change only one variable per iteration so the effect is attributable.
4. Verify against injury criteria. Check chest deflection (e.g., ≤ 50 mm for the 50th percentile in a 50 km/h test as a typical target), head injury criterion, and neck loads. Confirm the coupling windows have shifted in the intended direction.

3.6 Common Failure Symptoms and Their Causes

The unifying principle is that restraint performance is not a property of any single component but of the relative timing between the pulse, the occupant's motion, and each restraint's readiness. Mastering the coupled timeline is the prerequisite for every calibration decision in the chapters that follow.