2. Far-side crash scenarios and occupant kinematics

In a far-side impact, the occupant sitting opposite the struck side is not directly loaded by the barrier or bullet vehicle. Instead, the occupant is accelerated by the vehicle's own motion — the struck side of the body moves away from the occupant, the restraint system applies asymmetric loading, and the occupant's inertia carries them across the cabin toward the impact side. This indirect loading path is what makes far-side protection fundamentally different from near-side protection, and it is the reason far-side kinematics must be analyzed as a coupled vehicle–occupant problem rather than a simple restraint tuning exercise.

This chapter establishes the loading and kinematic framework that underpins all subsequent far-side restraint design: how near-side and far-side loading differ, how vehicle rotation drives occupant excursion, and which measurable quantities should be tracked when evaluating a far-side event.

Near-Side vs. Far-Side Loading: Two Different Physical Problems

Consider a vehicle struck on the driver's side by a moving deformable barrier (MDB). The driver is the near-side occupant; the front passenger is the far-side occupant. For the driver, the door intrudes, the side airbag and curtain deploy between the occupant and the intruding structure, and the restraint system's job is to distribute a large, early, and highly localized load. The dominant injury mechanisms are thoracic and pelvic loading against the door trim and armrest, plus head contact with the intruding B-pillar or window frame.

For the far-side passenger, no structure intrudes into their seating position. The loading arrives through three coupled channels:

• Belt geometry and asymmetric restraint forces. The outboard-anchored three-point belt loads the inboard shoulder and inboard pelvis preferentially. The diagonal section pulls the torso inboard and forward, while the lap section's outboard anchor produces a yawing moment on the pelvis.
• Vehicle lateral acceleration and rotation. The struck side is pushed away, so in the struck vehicle's reference frame the far-side occupant experiences a lateral acceleration directed toward the impact side, plus a rotational (yaw) component if the impact point is offset from the center of gravity.
• Occupant-to-occupant and occupant-to-interior contact. As the far-side occupant moves inboard, they may contact the center console, the near-side occupant, or the opposite door — a load path that has no near-side equivalent.

The practical consequence is that near-side countermeasures (thicker door trim, side airbags, padding) do nothing for the far-side occupant. Far-side protection must be delivered by the belt, a far-side airbag (typically a center or seat-mounted inboard airbag), seat design, and — critically — by controlling how much the occupant is allowed to move before those devices engage.

Vehicle Rotation and the Occupant Excursion Mechanism

In a far-side event, the impact force is rarely aligned with the vehicle's center of gravity. The offset produces a yaw moment, and the vehicle rotates about its vertical axis while translating laterally. This rotation is the single most important driver of far-side occupant excursion, because the occupant's inertia tends to keep them moving in their original direction while the cabin rotates around them.

Two reference frames must be kept distinct throughout any far-side analysis:

• Ground-fixed (inertial) frame: the occupant's trajectory as seen from outside the vehicle. The occupant continues roughly along the pre-impact velocity vector until restraint forces act.
• Vehicle-fixed frame: the occupant's motion relative to the seat and interior. This is the frame in which excursion, belt slip, and contact with interior surfaces are measured, and it is the frame used for restraint design targets.

In the vehicle frame, a positive yaw rotation of the struck vehicle (struck side rotating away from the occupant) produces an apparent inboard displacement of the far-side occupant. The magnitude of this apparent displacement grows with yaw angle and with the distance from the occupant to the yaw axis. A far-side occupant seated further from the rotation center therefore experiences larger excursion for the same crash pulse — which is why rear-seat far-side occupants often show larger inboard travel than front-seat occupants in the same event.

Reading the Kinematic Chain

The figure below traces the far-side load path from impact to occupant outcome. It separates the vehicle-level response (translation and yaw) from the occupant-level response (belt loading, torso and pelvis motion, head excursion), and shows where the far-side airbag and belt pretensioner intervene.

Quantifying Excursion: A Worked Example

To make the rotation–excursion relationship concrete, consider a simplified rigid-body estimate. Suppose a far-side occupant's head center is located 0.55 m from the vehicle yaw axis in the lateral direction, and the crash pulse produces a peak yaw rate of 25 °/s with a yaw duration of 120 ms. Treating the yaw motion as approximately constant-rate over that window, the yaw angle accumulated is:

ψ ≈ ω · t = 25 °/s × 0.120 s = 3.0°

Apparent inboard head displacement (vehicle frame):
Δy ≈ r · ψ(rad) = 0.55 m × (3.0 × π/180)
   ≈ 0.55 × 0.0524 ≈ 0.029 m ≈ 29 mm

This 29 mm is only the geometric contribution from rotation. Real far-side excursion is substantially larger because the belt's asymmetric loading adds torso rotation and because the occupant's own inertia produces translation relative to the seat. In a representative sled or full-vehicle far-side test, head inboard excursion of 150–250 mm is commonly observed before the far-side airbag is fully engaged — which is precisely why the airbag's deployment timing and coverage envelope matter more than its absolute volume.

What to Observe in a Far-Side Event

When reviewing far-side test data or CAE results, the following sequence is the practical diagnostic order. First, confirm the vehicle yaw history and the lateral acceleration at the occupant's seating position — these define the input to everything downstream. Second, check belt force at the shoulder and lap anchors: an early, steep rise indicates the pretensioner is working, while a plateau indicates the load limiter is controlling chest load. Third, track head inboard excursion against time and compare it with the far-side airbag's coverage window; if the head reaches the airbag's inboard edge before the bag is inflated, the countermeasure is mistimed regardless of its size. Fourth, examine pelvis lateral displacement and torso twist — excessive pelvis yaw often precedes head excursion and is a leading indicator of belt slip.

Typical failure symptoms and their likely causes are worth memorizing. A head that passes in front of the far-side airbag usually points to late deployment or insufficient inboard coverage. A torso that rotates excessively with low belt force suggests the load limiter is too aggressive for the far-side case. A pelvis that slides laterally under the lap belt indicates anchor geometry or pretensioning is inadequate. Each symptom maps back to a specific link in the kinematic chain shown above, which is why the chain — not the individual component — should be the unit of design review.

Design Implications

Three conclusions follow directly from the kinematics. First, far-side protection is a timing problem as much as a force problem: the countermeasure must be present in the occupant's path before excursion develops, which favors early sensing and fast-deploying inboard airbags. Second, belt geometry and pretensioning are primary far-side countermeasures, not secondary ones, because they act earliest in the chain. Third, because excursion scales with distance from the yaw axis, far-side requirements should be derived per seating position rather than applied uniformly across the cabin. These principles carry forward into the restraint sizing and deployment-strategy chapters that follow.