4. Injury criteria and biomechanical limits for far-side and oblique loading

Far-side and oblique crashes occupy a distinct corner of the occupant-protection design space. In a far-side impact, the belted occupant is loaded on the side opposite the impact, so the restraint system must manage motion across the vehicle rather than simply absorb energy on the struck side. In an oblique frontal or oblique pole event, the load vector arrives at an angle to the occupant's fore-aft axis, producing combined forward and lateral kinematics. Both cases expose the body to loading directions that the standard frontal and side test matrices were not primarily designed to cover. This chapter establishes the injury criteria and biomechanical limits that analysts and restraint engineers use to judge whether a far-side or oblique loading environment is acceptable, and how those limits are applied in practice.

Why the Standard Criteria Need Reinterpretation

Most regulatory and consumer criteria were derived from loading directions that dominated the historical test matrix: pure frontal (HIC, chest deflection, femur load) and pure lateral (side impact head and chest criteria). Far-side and oblique loading sits between these regimes. The head may strike the far-side interior or the opposite occupant, the neck experiences combined lateral flexion and axial rotation, the thorax is loaded through the belt at an oblique angle, and the pelvis can be pulled out of position by the lap belt as the torso rotates. Applying a frontal HIC threshold to a head path that is largely lateral, or a pure lateral chest criterion to a belt load that is partly diagonal, is defensible only if the criterion's underlying injury mechanism still matches the observed loading. The practical rule is to select the criterion whose injury mechanism corresponds to the actual load path, and to treat the numeric limit as a reference point rather than an absolute pass/fail line.

Head Injury Criteria

For the head, the primary scalar measure remains HIC, computed from the resultant translational acceleration of the head center of gravity over the chosen time window:

HIC = max over t1,t2 of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt )^2.5 ]
      with t2 - t1 ≤ 15 ms, a in g

HIC15 is the usual form for far-side and oblique work because the shorter window is more sensitive to the sharp, short-duration contacts typical of head-to-interior and head-to-occupant strikes. A commonly cited reference limit is HIC15 = 700, with values above roughly 1000 associated with serious head injury in the regulatory literature. In oblique loading, however, the resultant acceleration can be dominated by a lateral component that does not correspond to the same brain-injury mechanism as a frontal impact. Analysts therefore also report the directional components and, where the head rotates, the angular velocity and angular acceleration, because rotational loading is a recognized contributor to diffuse axonal injury and subdural hematoma. A practical check is to compare the peak resultant HIC15 against the limit while separately flagging any head angular velocity above roughly 30–40 rad/s as a rotational-injury concern requiring review, even if HIC15 is below threshold.

Neck Injury Criteria

The neck is the structure most sensitive to the combined loading of far-side and oblique events. Two families of criteria are used. The first is the neck injury criterion Nij, which combines axial force and bending moment:

Nij = (Fz / Fzc) + (My / Myc)
      tension: Fzc = 6.8 kN, Myc = 310 N·m
      compression: Fzc = 6.2 kN, Myc = 310 N·m
      limit: Nij ≤ 1.0

Nij was developed for frontal loading and remains a useful reference, but its force and moment limits assume a predominantly sagittal load path. In oblique and far-side loading the neck also experiences lateral bending and axial rotation, which Nij does not capture. The second family addresses this gap: lateral bending moment limits (on the order of 60–80 N·m for the upper neck, depending on the dummy and the source) and axial rotation limits (roughly 70–80 degrees of rotation before soft-tissue injury thresholds are approached). For far-side analysis, the recommended practice is to report Nij alongside the peak lateral bending moment and the peak axial rotation, and to treat any single exceedance as a flag for detailed review rather than relying on Nij alone.

Thorax Criteria

Thoracic injury in oblique loading is driven by a combination of belt compression, rib bending, and, in far-side events, loading through the far-side interior or the opposite occupant. The standard measures are chest deflection and the viscous criterion:

Chest deflection (absolute):  ≤ 63 mm (reference, 50th percentile)
Chest deflection (normalized): ≤ 0.33 of chest depth
Viscous criterion VC = max( V(t) * C(t) ) ≤ 1.0 m/s

The deflection limit is direction-sensitive: a diagonal belt produces a deflection vector that is not aligned with the pure lateral or pure frontal calibration of the dummy's chest potentiometer. Analysts should record the deflection direction and compare the resultant against the limit, while noting that a diagonal load can produce rib fractures at lower resultant deflection than a pure lateral load because the load is concentrated along the belt path. VC captures the rate-dependent softening of thoracic tissue and is particularly relevant in oblique events where the belt loads the chest rapidly. A VC above 1.0 m/s indicates a high risk of soft-tissue and rib injury even when peak deflection is moderate.

Abdomen and Pelvis Criteria

Abdominal injury in far-side and oblique loading typically arises from belt intrusion into the abdomen and from loading through the far-side door or console. The commonly used measures are abdominal pressure and the abdominal injury criterion:

Abdominal peak pressure: ≤ 200 kPa (reference)
AIC = max( p(t) * v(t) ) ≤ 1.0  (pressure-velocity product)

These limits are less standardized than the head and thorax criteria and should be treated as screening references. For the pelvis, the relevant measures are pelvic force and, in far-side events, the tendency of the lap belt to pull the pelvis into submarining. A practical pelvic limit is an iliac force on the order of 3–5 kN, with the exact value depending on the dummy and loading direction. In oblique loading, the pelvis rotates relative to the torso, and the lap belt can slip below the anterior superior iliac spine; this is a kinematic failure rather than a force exceedance, so it must be checked by inspecting belt position and pelvic rotation, not only by reading force channels.

Applying the Limits in a Far-Side or Oblique Assessment

The criteria above are most useful when applied as a structured screening pass rather than a single-number verdict. A defensible workflow is as follows. First, define the loading direction and the occupant's kinematics from the simulation or test, and confirm which body regions are actually loaded and by what. Second, for each region, select the criterion whose injury mechanism matches the observed load path, and record the peak value together with its time of occurrence and direction. Third, compare each peak against its reference limit, but classify the result into three bands: below limit (acceptable), within roughly 10–20 percent above limit (review, check whether the criterion is direction-appropriate), and clearly above limit (flag for restraint or structure redesign). Fourth, for the neck and pelvis, always add the direction-specific checks (lateral bending, axial rotation, belt position) because the scalar criteria do not capture them.

Worked Screening Example

Consider an oblique pole simulation of a belted 50th-percentile male occupant at 32 km/h with a 30-degree oblique load vector. Suppose the extracted channels give: head resultant HIC15 = 610 with peak head angular velocity 34 rad/s; upper-neck Nij = 0.82 with peak lateral bending moment 72 N·m and axial rotation 58 degrees; chest resultant deflection 58 mm with VC = 0.9 m/s; abdominal peak pressure 165 kPa with AIC = 0.7; iliac force 3.6 kN with the lap belt remaining above the ASIS throughout. The screening result is: head acceptable on HIC15 but flagged for rotational review because angular velocity exceeds the 30 rad/s review threshold; neck acceptable on Nij but the lateral bending moment of 72 N·m sits at the upper end of the 60–80 N·m reference band and warrants a sensitivity check; thorax and abdomen acceptable; pelvis acceptable on both force and kinematics. The actionable output is not "pass" but a prioritized list: investigate head rotation and neck lateral bending first, since those are the two channels closest to their direction-specific limits.

Practical Notes on Channel Selection and Reporting

Three reporting habits make far-side and oblique assessments more reliable. First, always report the direction of each peak, not only its magnitude, because the same scalar value can correspond to different injury mechanisms depending on direction. Second, report the time of peak for each channel so that correlated loading (for example, head rotation coinciding with neck lateral bending) can be identified. Third, for the pelvis, include a kinematic plot of belt position relative to the ASIS over time, since submarining is a position failure that force channels alone will miss. These habits cost little in post-processing and substantially improve the defensibility of the injury assessment.

The criteria and limits in this chapter form the quantitative backbone of far-side and oblique injury analysis. Used with attention to loading direction and injury mechanism, they allow an analyst to move from raw channel data to a prioritized, defensible judgment about occupant protection performance.