2. Crash pulse and occupant kinematics

Every restraint decision — airbag vent size, tether length, pretensioner force, load-limiter threshold — is ultimately a response to one input: the vehicle's deceleration pulse. The pulse is the acceleration–time history measured at a structural point (typically the B-pillar base or tunnel) during a barrier impact. It defines how much velocity the occupant must shed, over what time, and therefore how much ride-down distance the restraint system can buy. Understanding the pulse is the prerequisite for understanding why restraint systems are tuned the way they are.

Reading a Deceleration Profile

In a frontal rigid-barrier test at 56 km/h (15.6 m/s), the vehicle must dissipate all of that velocity. The pulse is the derivative of the velocity change, so the area under the deceleration curve equals Δv. A typical passenger-car pulse rises sharply to a first peak of 25–35 g within 15–25 ms as the bumper, rails, and shotgun structure crush, dips as the engine cradle engages, then rises to a second, broader peak of 30–45 g between 40 and 70 ms as the firewall and dash panel resist the remaining energy. Total pulse duration is usually 90–130 ms.

Two parameters dominate restraint design. The first is time to peak: a late, high peak gives the occupant more time to move forward before the vehicle's deceleration field is fully established, which increases the relative displacement the restraint must manage. The second is pulse slope (jerk, in g/ms). A steep leading edge produces a large velocity differential between occupant and vehicle early in the event, which drives the occupant forward into the deploying airbag before the bag has fully inflated.

Pulse shaping is therefore an intentional design activity. Engineers tune crush initiators, rail thickness, and the addition of a "soft" front section to produce a pulse that is aggressive enough to absorb energy in the available crush stroke but gentle enough that the occupant's forward excursion stays within the restraint's working envelope. A common target is to keep the occupant's peak chest deceleration below the vehicle's peak by 10–15 g, which indicates the restraint is providing meaningful ride-down rather than simply transmitting the crash.

Occupant Kinematics and Injury Criteria

Before the belt engages, the occupant is a free mass moving at the pre-crash velocity. The belt locks and the airbag contacts the chest at different times, so the occupant's motion is a sequence of coupled phases: free flight, belt loading, airbag contact, and rebound. The kinematics are governed by the relative velocity between the occupant's center of gravity and the vehicle structure, and by the geometry of the belt path and airbag surface.

Injury criteria translate this motion into pass/fail numbers. The most widely used are:

  • HIC36 / HIC15 — Head Injury Criterion, computed from the resultant head acceleration over the most severe 36 ms or 15 ms window. FMVSS 208 requires HIC36 ≤ 1000 for the 50th-percentile male in a 56 km/h frontal test.
  • Chest deflection — measured by a chest band or IR-TRACC; typically limited to 50–60 mm for the 50th-percentile male, with lower limits for smaller occupants.
  • Chest acceleration (3 ms clip) — peak chest resultant acceleration sustained for 3 ms, usually capped at 60 g.
  • Femur axial force — limited to 10 kN per leg to prevent shaft fracture.
  • Neck injury criteria (Nij) — combines axial force and bending moment; the limit is 1.0.

These criteria are not independent. A restraint that reduces head excursion by increasing belt force may raise chest deflection. A stiffer airbag that reduces chest deflection may increase neck loading. The design problem is a constrained optimization across all criteria simultaneously.

How Pulse Shaping Drives Restraint Design

The pulse determines the timing budget. If the vehicle's first peak arrives at 20 ms, the airbag must be fully inflated by roughly 25–30 ms to be in position before the occupant's chest reaches the module. That constrains inflator output, module volume, and vent area. A vehicle with a later, softer first peak can use a slower inflator and a larger bag, which reduces the risk of out-of-position (OOP) injury.

Pulse shape also sets the required belt load. The belt must absorb the occupant's kinetic energy over the ride-down distance available. If the pulse is short and steep, the ride-down distance is small, so the belt force must be high — which pushes the load limiter toward its upper threshold and increases chest deflection. If the pulse is long and gradual, the same energy can be absorbed with lower belt force, allowing a softer load limiter and lower chest deflection.

This is why restraint tuning is never done in isolation. A change to the front structure that softens the pulse may allow a lower load-limiter threshold, which improves chest scores but may increase head excursion unless the airbag is enlarged or the pretensioner is strengthened. The following diagram shows the coupled relationship between pulse characteristics, occupant response, and the restraint parameters that must be adjusted.

Crash Pulse → Occupant Kinematics → Restraint Parameters Vehicle Deceleration Pulse (56 km/h frontal) Time (ms) Decel (g) 1st peak ~20 ms 2nd peak ~55 ms Occupant Response Phases Free flight 0–25 ms Belt load 25–50 ms Airbag contact 30–70 ms Rebound 70–110 ms Injury Criteria Monitored HIC36 ≤ 1000 Chest defl. ≤ 60 mm Chest accel ≤ 60 g Femur ≤ 10 kN pulse shape sets timing budget kinematics constrain restraint tuning Restraint Parameters Adjusted in Response Inflator output Higher 1st peak → faster fill; risk of OOP injury Load limiter threshold Steep pulse → higher force → more chest deflection Vent / tether geometry Controls bag pressure vs. occupant displacement Pretensioner force Reduces slack; must match pulse onset timing Iterate: pulse change → re-tune restraint → re-evaluate injury criteria

Practical Tuning Workflow

A reproducible restraint tuning exercise starts with a measured or simulated pulse. Suppose the pulse has a first peak of 32 g at 18 ms and a second peak of 40 g at 52 ms, with total duration 110 ms. The occupant's chest reaches the airbag module at approximately 35 ms. The engineer must verify that the bag is fully inflated by 30 ms, which requires an inflator with a fill time under 25 ms at the expected module temperature.

The belt load limiter is then set by working backward from the chest deflection limit. If the available ride-down distance is 120 mm and the occupant mass is 78 kg, the average belt force required to absorb the kinetic energy is roughly:

E = 0.5 * m * v² = 0.5 * 78 * (15.6)² ≈ 9.5 kJ
F_avg = E / d = 9500 / 0.12 ≈ 79 kN  (distributed across belt + airbag)

This is a simplified energy balance; in practice the force is shared between the belt and airbag, and the load limiter is set to a threshold that keeps chest deflection below the limit while allowing enough force to prevent excessive head excursion. A typical starting point is a 4 kN load limiter with a 2 kN pretensioner, then iterate based on sled or CAE results.

Practical check: If the occupant's peak chest acceleration exceeds the vehicle's peak deceleration by more than 15 g, the restraint is not providing adequate ride-down. Check belt slack, pretensioner timing, and airbag venting before increasing the load limiter threshold.
Common failure mode: A pulse with a very early first peak (under 15 ms) can cause the airbag to deploy after the occupant has already moved forward, leading to high HIC and neck injury. In this case, the fix is usually structural — softening the front rail or adding a crush initiator — rather than increasing inflator output, which would worsen OOP risk.

Key Takeaways

  • The deceleration pulse defines the timing budget and energy absorption requirement for every restraint component.
  • Pulse shaping is an intentional design lever: softer, longer pulses allow lower belt forces and reduce injury criteria.
  • Occupant kinematics proceed through free flight, belt loading, airbag contact, and rebound; each phase has different injury mechanisms.
  • Injury criteria (HIC, chest deflection, chest acceleration, femur force, Nij) are coupled and must be optimized together.
  • Restraint tuning is iterative: change the pulse, re-tune the restraint, re-evaluate all criteria.
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