2. Occupant kinematics in oblique crashes

In a purely frontal crash, the occupant's motion is largely planar: the pelvis translates forward, the torso pitches into the belt, and the head rotates about a predominantly lateral axis. In a purely lateral crash, the dominant motion is coronal-plane translation and roll. An oblique crash is not a simple average of the two. Because the restraint system is asymmetric — a three-point belt loads the inboard shoulder and outboard pelvis, while the side structure and far-side airbag act on different surfaces — the occupant's body segments do not move as a rigid unit. They rotate, translate, and decouple from one another in a sequence that depends strongly on the impact angle, the belt geometry, and the timing of airbag deployment.

This section defines the reference conventions used throughout the course, then traces the motion of the head, thorax, and pelvis under combined frontal-lateral loading, and finally shows how to read those motions from a test or simulation so that restraint design decisions can be made.

Reference Frame and Sign Conventions

All kinematic descriptions in this course use the SAE J211 sign convention with the vehicle coordinate system as the primary reference:

• +X — forward, along the vehicle's longitudinal axis.
• +Y — to the occupant's right (lateral).
• +Z — downward, following the right-hand rule for SAE.

Rotations follow the same right-hand rule: pitch about Y, roll about X, and yaw about Z. An oblique impact is characterized by a principal direction of force (PDOF) angle θ measured in the horizontal plane from the +X axis toward +Y. A 30° right-oblique impact therefore has a PDOF of +30°, meaning the resultant force vector points forward and to the occupant's right. This convention is used consistently in the text and in the figure below.

Why Oblique Loading Decouples the Body Segments

The key mechanical reason oblique kinematics differ from frontal kinematics is that the restraint forces and the inertial forces are no longer collinear. In a frontal crash, the belt force and the occupant's inertia vector lie on nearly the same line, so the torso is loaded in compression and forward flexion. In an oblique crash, the inertia vector is rotated by θ, but the belt still pulls along its own path — over the outboard shoulder, across the chest, and down to the outboard buckle. The result is a moment about the vertical axis that yaws the thorax, and a lateral component that rolls the torso toward the impacted side.

Three consequences follow:

1. Thorax yaw and roll. The chest rotates toward the impacted side and simultaneously rolls, so the head is carried laterally before it pitches forward.
2. Pelvis lateral translation. The lap belt anchors the pelvis, but the lateral component of the inertia vector causes the pelvis to slide and rotate under the belt, changing the belt's engagement path.
3. Head–thorax decoupling. Because the neck is a compliant link, the head lags the thorax in yaw and roll, producing relative head rotation that is not present in a frontal crash.

Segment-by-Segment Motion Sequence

The following sequence describes a typical 30° right-oblique sled test with a 50th-percentile male ATD, a three-point belt with a pretensioner and load limiter, and a steering-wheel airbag. The times are illustrative and are intended to show the ordering of events, not to represent a specific validated result.

Two features of this sequence deserve emphasis. First, the pelvis leads the thorax, and the thorax leads the head. This is a direct consequence of the mass distribution and the compliance of the spine and neck. Second, the lateral and yaw motions peak later than the forward motion, which means a restraint that only limits forward excursion will not necessarily limit the lateral excursion that drives head contact with the side interior.

Reading the Motion from Test or Simulation Data

To make design decisions, the kinematics must be quantified. The standard approach is to instrument the ATD or human body model with accelerometers and angular rate sensors at the head CG, thorax CG, and pelvis CG, then integrate to obtain displacement and rotation. The following steps describe a reproducible workflow for a sled test or a validated FE simulation.

1. Define the measurement channels. For each segment, record three linear accelerations (Ax, Ay, Az) and three angular rates (roll, pitch, yaw). For the head, also record the neck force and moment if a neck load cell is available.
2. Filter the signals. Apply a CFC 60 filter for occupant kinematics per SAE J211. Do not filter before integration if you need peak displacement; instead, integrate the filtered acceleration and apply a drift correction using the known initial and final velocities.
3. Compute the relative head–thorax rotation. Subtract the thorax yaw from the head yaw to obtain the relative yaw. This is the parameter most directly linked to neck injury risk in oblique loading.
4. Plot the trajectories in the vehicle frame. Overlay the head, thorax, and pelvis paths on the vehicle plan view. The lateral separation between the head path and the thorax path is a direct indicator of how much the head is moving outboard relative to the torso.
5. Identify the peak timing. Mark the time of peak forward excursion and the time of peak lateral excursion. If the lateral peak occurs more than 20–30 ms after the forward peak, the restraint is not controlling the lateral phase effectively.

Typical Failure Symptoms and Troubleshooting

When reviewing oblique kinematics, three failure patterns appear repeatedly:

• Head slides outboard of the airbag. The head moves laterally before the airbag has deployed, so the airbag contacts the shoulder rather than the head. Remedy: advance the deployment timing or increase the lateral coverage of the airbag.
• Pelvis submarines under the lap belt. The lateral component of the inertia vector rotates the pelvis, allowing it to slide under the belt. Remedy: adjust the lap belt anchor geometry or add a pretensioner with a higher retraction force.
• Excessive relative head–thorax yaw. The head lags the thorax in yaw, producing high neck moments. Remedy: add a far-side airbag or a belt-mounted airbag that engages the inboard shoulder earlier.

Each of these symptoms can be observed directly in the trajectory plots and the relative rotation time histories described above. The design iteration then consists of adjusting the restraint parameters — belt anchor positions, pretensioner timing, airbag venting, and airbag shape — and re-running the test or simulation until the head path remains within the safe envelope and the relative head–thorax rotation stays below the injury threshold.

Summary

Oblique crash occupant kinematics are governed by the misalignment between the inertia vector and the restraint force vector. The pelvis leads, the thorax yaws and rolls, and the head lags and translates laterally. The lateral and yaw motions peak later than the forward motion, so a restraint designed only for frontal loading will not control the full event. By instrumenting the three body segments, filtering and integrating the signals correctly, and plotting the trajectories in the vehicle frame, the engineer can identify whether the restraint is controlling both the forward and lateral phases, and can iterate on belt geometry, pretensioner timing, and airbag design until the occupant's head, thorax, and pelvis remain within safe excursion limits.