3. Occupant injury criteria and biomechanical limits

Load limiter design is not an exercise in minimizing force for its own sake. Every force level chosen at the retractor or buckle anchor translates into a specific deceleration and compression history experienced by the occupant, and that history is judged against biomechanical injury criteria. To optimize a load limiter, the engineer must be able to read a restraint force–time curve and predict, at least qualitatively, how it will move HIC, chest deflection, chest acceleration, and femur loads relative to their limits. This section establishes those criteria, their physical meaning, and the trade-offs that connect them to load limiter force levels.

Head injury criterion (HIC)

HIC is computed from the resultant translational acceleration at the head center of gravity over the crash pulse:

HIC = max over t1,t2 of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt )^2.5 ]
      with (t2 - t1) ≤ 36 ms (HIC36) or 15 ms (HIC15)

The 2.5 exponent heavily penalizes short, high-amplitude spikes, which is why HIC is dominated by peak acceleration rather than by sustained moderate loading. The commonly cited regulatory limit is HIC36 ≤ 1000 (FMVSS 208) and HIC15 ≤ 700 in many consumer and Euro NCAP protocols. For load limiter work, the key insight is that HIC responds to the early portion of the restraint event: if the load limiter force is set too high, the head decelerates abruptly as it contacts the airbag and the restraint stiffens, producing a sharp acceleration peak. If the force is set too low, the head may travel further forward and bottom out on the airbag or strike the steering wheel, producing a late, large peak. HIC therefore has a U-shaped sensitivity to load limiter force, and the optimum is usually found where the head is decelerated smoothly over the longest available stroke.

Chest deflection and chest acceleration

Chest deflection is the measured sternum-to-spine compression, expressed in millimeters, and is the primary predictor of rib fracture and thoracic organ injury. Typical limits are 50–63 mm depending on the protocol and occupant size (for example, 50 mm for the 5th percentile female and up to 63 mm for the 50th percentile male in some rating schemes). Chest acceleration, usually the 3 ms clip of the resultant spinal acceleration, is limited to about 60 g. These two metrics pull in opposite directions with respect to load limiter force:

  • Higher load limiter force restrains the torso earlier and reduces forward excursion, which tends to reduce chest deflection but raises chest acceleration because the deceleration is transmitted more directly through the belt.
  • Lower load limiter force pays out belt progressively, lowering peak chest acceleration but allowing greater forward torso rotation and belt penetration into the chest, which increases deflection.

The chest is therefore the component that most directly constrains the load limiter force window. A force level that satisfies HIC may still violate chest deflection, and the designer must find the force that keeps both metrics inside their limits simultaneously.

Femur loads

Femur load is measured along the femoral axis at the knee-thigh-hip complex, with a typical limit of 10 kN per leg (or 8 kN in some protocols). Femur loading is driven mainly by knee contact with the lower instrument panel and by belt geometry across the pelvis and thighs. Load limiter force affects femur load indirectly: a lower force allows more forward pelvis and knee excursion, which can increase knee-panel contact force, while a higher force holds the pelvis back and can concentrate belt load on the iliac crest. Femur load is usually a secondary constraint in load limiter tuning, but it becomes decisive in vehicles with short lower-instrument-panel clearance or aggressive knee bolster design.

How the criteria map onto the force–time curve

The figure below shows the relationship between a load limiter force plateau and the four injury metrics. The horizontal axis is time; the upper trace is belt force at the retractor, and the lower traces are the normalized injury responses. The shaded band marks the force window in which all four criteria remain below their limits.

Load Limiter Force Plateau and Injury Criteria Response Force / Normalized response Time (ms) 0 20 40 60 80 100 Force plateau (load limiter active) Belt force HIC Chest deflection Chest acceleration Femur load Limit plateau drives chest response

The diagram makes the central design tension visible: the force plateau sits between the early head/chest acceleration peak and the later chest deflection peak. Raising the plateau moves the acceleration curves up and the deflection curve down; lowering it does the reverse. The femur curve is comparatively flat because it is dominated by knee-panel contact rather than by belt force.

Practical tuning procedure

A reproducible way to relate force level to criteria is to run a small parameter sweep in the sled or CAE model, holding all other restraint parameters fixed and varying only the load limiter force. The following example uses illustrative values, not measured results:

  1. Define the baseline model with a 4 kN constant load limiter and record HIC15, chest deflection, 3 ms chest acceleration, and femur load for the 50th percentile male at 56 km/h frontal impact.
  2. Run the same model at 3.0, 3.5, 4.5, and 5.0 kN, changing only the force plateau.
  3. Plot each metric against force and identify the force at which each metric crosses its limit.
  4. Select the force that maximizes margin to the most restrictive criterion, then verify that the other criteria retain at least a 10–15% margin.

In a typical sweep, chest deflection falls monotonically with increasing force while chest acceleration rises; HIC shows a minimum near the middle of the range because both under- and over-restraint produce head peaks. The acceptable window is the intersection of the individual windows, and it is often narrower than expected—sometimes only 0.5–1.0 kN wide. That narrowness is precisely why pretensioner timing and force-limiting strategy must be co-optimized rather than tuned independently.

When the chest deflection and chest acceleration windows do not overlap, the usual remedy is not a single force change but a two-stage load limiter: a higher initial force to control early chest acceleration, switching to a lower force after 20–30 ms to limit deflection. The switch point is tuned so that the force reduction occurs after the head has been captured by the airbag.
Do not compare HIC values computed over different time windows (HIC15 vs. HIC36) or chest accelerations with different filtering (CFC 600 vs. CFC 1000). A criterion is only meaningful together with its window, filter class, and occupant size. Mixing protocols is a common source of false margin in load limiter trade studies.

Reading the result correctly

Once the sweep is complete, the engineer should be able to state, for each criterion, which side of the limit the design sits on and how much force change would consume the remaining margin. A design that passes all four criteria at 4.0 kN but has only 3 mm of chest deflection margin is not robust; a small change in belt geometry or occupant mass will push it over. The practical target is a force level that centers the design in the overlap of the criteria windows, with the pretensioner providing the early restraint that keeps the head and chest from reaching the airbag at high relative velocity. The next step in the optimization is to quantify how pretensioner force and timing shift those windows, which is the subject of the following section.

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