2. Occupant kinematics and injury criteria for side impact and rollover

Curtain airbag (CAB) design is not driven by styling or packaging convenience; it is driven by the occupant's motion and the injury mechanisms that motion produces. Before a single inflator is selected or a bag shape is sketched, the engineer must understand how the occupant moves in a side impact and in a rollover, which body regions are at risk, and what measurable targets the CAB must satisfy. This chapter establishes that foundation: the kinematics of the head and torso, the injury criteria used to quantify risk, and the specific targets — head excursion, ejection mitigation, and coverage — that translate regulatory and consumer-test requirements into CAB design inputs.

Side impact kinematics: the head leads the torso

In a side impact, the striking vehicle or barrier loads the struck vehicle's door and B-pillar. Because the gap between the occupant and the door is small — often only 100–200 mm of trim-to-occupant clearance — the occupant has very little time and distance to react. The pelvis and thorax are loaded first through the door trim, and the head, restrained only by the neck, lags and then whips laterally toward the impact side. This produces a characteristic head-to-torso relative motion in which the head travels outboard and forward relative to the thorax.

The critical consequence is that the head can strike the intruding door, the B-pillar, or the window glass. In a far-side impact, the head can travel across the cabin and strike the opposite-side interior. The CAB's job is to occupy the space between the head and the side structure before the head arrives, and to absorb energy over a controlled stroke rather than letting the head contact rigid trim.

Two reference frames matter and must be kept consistent throughout design and simulation. The vehicle coordinate system is fixed to the vehicle body (typically X forward, Y to the left, Z up, with the origin at the vehicle datum). The occupant coordinate system is fixed to the occupant's anatomy. Head excursion is normally reported as the maximum lateral (Y) displacement of the head center of gravity relative to its initial position, measured in the vehicle frame. When a simulation reports "head excursion," confirm which frame and which reference point are used; mixing them is a common source of design error.

Injury criteria that quantify the risk

Injury criteria convert measured physical quantities — acceleration, force, deflection — into a normalized number that predicts injury probability. For side impact and rollover CAB work, the following are the primary criteria.

HIC is computed from the resultant acceleration at the head center of gravity:

HIC = max over (t1, t2) of [ (1/(t2 - t1)) * ∫ a(t) dt ]^2.5 * (t2 - t1)
where a(t) is the resultant head CG acceleration in g,
and (t2 - t1) is the time interval, capped at 36 ms for HIC36 and 15 ms for HIC15.

The key insight for CAB design is that HIC is dominated by the peak acceleration and the duration over which it acts. A CAB that spreads the head load over a larger area and a longer stroke reduces peak acceleration and therefore HIC, even if total momentum change is unchanged.

Rollover kinematics and ejection mitigation

In a rollover, the vehicle rotates about its longitudinal or lateral axis, and the occupant is subjected to a combination of vertical and lateral accelerations. The occupant's head and upper torso move toward the window opening. If the side window is open or broken, the head can pass through the window plane — this is the ejection mechanism that FMVSS 226 addresses.

FMVSS 226 (Ejection Mitigation) requires that a moving deformable impactor, representing the occupant's head, cannot pass completely through the side window opening during a prescribed test. The CAB must therefore deploy and remain inflated long enough to cover the window opening, and its coverage must extend from the A-pillar to the C-pillar and from the roof rail down to the beltline. The coverage area and inflation duration are the two primary CAB design parameters for ejection mitigation.

From targets to CAB design inputs

The targets above translate into concrete CAB design inputs. Head excursion targets define the required lateral coverage: the bag must extend far enough inboard and outboard to intercept the head before it reaches the door or B-pillar. Ejection mitigation targets define the required vertical coverage and the minimum inflation duration. HIC and rib deflection targets define the required cushioning: the bag must be soft enough to absorb energy but stiff enough to prevent bottoming out against the door structure.

These requirements often conflict. A larger bag covers more area but takes longer to inflate and may be stiffer. A softer bag reduces HIC but may not resist ejection. The engineer must balance these trade-offs, and the balance is evaluated through CAE simulation before any hardware is built.

Practical example: translating a head excursion target into coverage

Consider a mid-size sedan with a driver-side CAB. The CAE team runs a side impact simulation with a moving deformable barrier at 50 km/h. The baseline model, without a CAB, predicts a peak head CG lateral excursion of 320 mm from the initial position, with the head contacting the B-pillar at approximately 45 ms. The HIC36 at that contact is 1450, well above the 1000 threshold.

The design target is to reduce HIC36 below 700 and to keep the head from contacting rigid structure. The engineer adds a CAB with the following initial parameters: a coverage envelope extending 40 mm beyond the window opening in all directions, an inflator with a 25 ms time-to-full-inflation, and a bag depth (inboard reach) of 180 mm at the head contact zone.

After re-running the simulation, the head now contacts the CAB at 38 ms. The bag compresses by 60 mm, and the head CG lateral excursion is limited to 210 mm. The peak head acceleration drops from 180 g to 95 g, and HIC36 falls to 620. The rib deflection on the struck side is 38 mm, within the 42 mm target.

This example illustrates the iterative nature of CAB design: the engineer adjusts coverage, inflation timing, and bag stiffness, then re-runs the simulation until all targets are met. The simulation does not replace physical testing, but it narrows the design space and identifies the parameters that matter most.

Summary

Occupant kinematics in side impact and rollover determine where the head and torso go, and injury criteria quantify the risk of that motion. Head excursion, HIC, TTI, rib deflection, and ejection mitigation are the primary targets that drive CAB design. Translating these targets into coverage envelopes, inflation timing, and cushion stiffness is the core engineering task, and CAE simulation is the tool that makes that translation possible before hardware exists. The next chapter examines how the CAB itself is constructed and how its components — inflator, bag, and mounting — are selected to meet these targets.