4. Crash pulse and occupant kinematics fundamentals

Every restraint decision — airbag trigger time, seat belt load limiter force, pretensioner stroke, anchor geometry — is ultimately a bet on how the occupant will move relative to the vehicle during a specific crash pulse. Engineers who treat the crash pulse as a single number (peak deceleration, or delta-V) will consistently misjudge restraint timing. The pulse is a time history, and the occupant's motion is the integral of that history filtered through compliance, geometry, and coupling. This section builds the physical intuition needed to read a pulse and predict occupant response before any simulation is run.

Deceleration Profiles: What the Pulse Actually Contains

In a frontal barrier test, the vehicle body decelerates from its initial velocity to zero over roughly 80–120 ms. The deceleration is not constant. A typical full-frontal rigid barrier pulse at 56 km/h (35 mph) rises steeply in the first 15–25 ms as the front structure crushes, peaks somewhere between 30 and 50 g, then falls as the remaining structure and the occupant's own restraint system absorb the residual energy. A pole or offset deformable barrier impact produces a sharper, earlier peak with a shorter duration because less structure participates in the crush.

Two parameters dominate the occupant's fate:

• Delta-V (Δv) — the total velocity change, obtained by integrating the deceleration curve over time. It sets the energy the restraint system must manage. A 56 km/h barrier test corresponds to Δv ≈ 15.6 m/s.
• Pulse shape and rise time — how quickly deceleration builds. A fast-rising pulse (short rise time) gives the restraint system less time to couple with the occupant before the occupant has already moved forward relative to the vehicle.

It is useful to distinguish the vehicle pulse (measured at the B-pillar or tunnel) from the occupant compartment pulse (measured at the seat track or floorpan). They differ because the seat, floor, and body mounts add compliance and filtering. Restraint timing must be referenced to the compartment pulse, not the barrier pulse, because that is the motion the occupant actually experiences.

Ride-Down: The Core Concept

Ride-down is the process by which the occupant's deceleration is spread over a longer time and lower peak than the vehicle's. If the occupant were rigidly bolted to the vehicle, the occupant would experience the full vehicle pulse — a 40 g peak over 60 ms. Instead, the restraint system allows the occupant to travel forward relative to the vehicle while decelerating, converting kinetic energy into belt stretch, load limiter payout, airbag venting, and seat deformation. The result is an occupant deceleration profile with a lower peak and longer duration.

The ride-down efficiency is the ratio of the occupant's peak deceleration to the vehicle's peak deceleration, expressed as a percentage. A well-tuned system might achieve 50–65% ride-down efficiency in a 56 km/h frontal impact. The physical constraint is available stroke: the occupant can only move forward as far as the compartment allows before contacting hard structures. In a typical driver position, the available forward stroke before chest-to-steering-wheel contact is roughly 250–350 mm, depending on seat position and column adjustment.

Restraint Coupling Timing

Coupling timing is the sequence in which each restraint element begins to influence the occupant. The occupant is not a point mass; the pelvis, thorax, and head have different masses, stiffnesses, and distances to their respective restraints. The belt engages the pelvis and thorax almost immediately (within 10–20 ms of impact), while the airbag must inflate and then be contacted by the head and chest. If the airbag is fully inflated too early, it may already be deflating when the head arrives; if too late, the head strikes the wheel or the bag is still deploying.

The design target is often stated as: the airbag should reach full inflation just before the occupant's head would otherwise contact the steering wheel, and the bag should still be pressurized when the head loads it. In practice, this means the airbag trigger time (time-zero to inflator firing) is typically 10–25 ms after impact, with full inflation at 30–50 ms, and head contact at 50–80 ms for an unbelted occupant. For a belted occupant, the belt absorbs much of the early motion, so head contact is later and the airbag timing window shifts.

Three coupling regimes are worth distinguishing:

The critical insight is that these regimes overlap and interact. A load limiter that pays out too aggressively reduces belt force but increases forward excursion, which may push the head into the airbag later and at a worse angle. A pretensioner that fires too late leaves slack in the belt during the early pulse, allowing the occupant to gain velocity relative to the vehicle before the belt engages.

Reading a Pulse and Predicting Occupant Response

Given a compartment deceleration time history a(t), the occupant's relative displacement can be estimated by a simple two-mass model: the vehicle mass moves according to a(t), and the occupant mass is connected to the vehicle through a spring-damper representing the belt and seat. The occupant's absolute deceleration is the sum of the vehicle deceleration and the relative deceleration from the restraint force divided by occupant mass. The relative displacement x_rel(t) is obtained by double integration of the relative acceleration.

In practice, engineers use a sled test or a CAE model to generate this response, but the hand calculation is valuable for sanity checks. For example, if a pulse has a 40 g peak at 35 ms and the belt is modeled as a linear spring with 50 mm of slack, the occupant will free-fly for the first ~15 ms, gaining roughly 5–6 m/s of relative velocity before the belt engages. That velocity must then be absorbed by the belt and load limiter, which determines the peak belt force and the chest deflection.

Worked Example: Timing a Driver Frontal Restraint

Consider a 56 km/h full-frontal rigid barrier test with a 50th percentile male ATD. The compartment pulse is measured as: rise to 35 g at 30 ms, plateau to 45 ms, decay to zero at 95 ms. Δv = 15.6 m/s. The seat is at mid-track, belt slack is 40 mm, pretensioner stroke is 60 mm, load limiter force is 4 kN, and the airbag inflator has a 15 ms trigger delay and 25 ms fill time.

1. Pretensioner timing: Fire at 8–12 ms to remove the 40 mm slack before the occupant gains significant relative velocity. At 10 ms, vehicle velocity loss is small, so the occupant is still nearly at initial velocity.
2. Belt engagement: After pretensioner stroke, the belt engages the pelvis and thorax at roughly 20–25 ms. The load limiter begins paying out at ~3.5–4 kN, allowing controlled forward excursion.
3. Airbag timing: Trigger at 15 ms, full inflation at 40 ms. The occupant's head, restrained by the belt, reaches the airbag at approximately 55–65 ms, when the bag is still pressurized.
4. Ride-down check: The occupant's peak chest deceleration should be below 60 g (the FMVSS 208 limit for the chest is 60 g over 3 ms). If the load limiter is too stiff, chest g exceeds the limit; if too soft, forward excursion causes the head to hit the wheel or the bag to bottom out.

The observable verification criteria are: chest deflection below 75 mm, chest g below 60 g, head injury criterion (HIC) below 700, and no hard contact with the steering wheel or column. If the head contacts the wheel, the airbag is late or the load limiter is too soft. If chest g is too high, the load limiter is too stiff or the pretensioner is too aggressive.

Practical Implications for Restraint Delivery

When specifying a restraint system, the crash pulse is an input, not a given. The body structure team can tune the pulse shape — a longer, flatter pulse is generally easier on the occupant because it provides more ride-down time. The restraint team then tunes the coupling timing to match. The two must be developed together. A common failure mode is a structure that produces a very sharp, high-peak pulse (good for intrusion resistance) combined with a restraint system tuned for a softer pulse — the result is early belt loading, high chest g, and a late airbag that the head reaches after the bag has vented.

The deliverable from this phase of development is a coupling timing table that maps each restraint element to its trigger time, expected engagement time, and the occupant state at that moment. This table becomes the reference for sled test setup and CAE correlation. It should be updated whenever the pulse changes, because a 5 ms shift in pulse rise time can move the optimal airbag trigger by 3–5 ms.

In summary: read the pulse as a time history, not a scalar. Compute the ride-down stroke available from the compartment geometry. Sequence the pretensioner, belt, and airbag so that each element engages when the occupant's mass is in the right position and moving at the right relative velocity. Verify against chest g, chest deflection, and HIC, and treat any hard contact as a timing failure, not a hardware failure.