2. Baseline Load Limiter Force–Displacement Setup

Why the Load Limiter Baseline Must Be Defined Before Any Trade-Off

The load limiter is the second half of the restraint system's energy-management story. The pretensioner removes slack and couples the occupant to the belt early; the load limiter then decides how much belt force is allowed to reach the chest as the occupant rides down. In a trade-off study, every later sweep — pretensioner peak force, load limiter level, venting, seat stiffness — is measured against a fixed reference. This case establishes that reference: a baseline load limiter force–displacement characteristic, plus the two derived metrics the rest of the study will track, absorbed energy and maximum chest deflection.

The characteristic is defined in the belt-payout domain. As the occupant moves forward, the belt spools out through the retractor and the load limiter (a torsion bar, a crushable element, or a controlled-slip retractor) pays out webbing at a roughly constant force. Plotting belt force against payout displacement gives the classic plateau curve. The area under that curve is the energy the load limiter absorbs; the plateau level and the available payout together set how far the chest is allowed to travel.

Defining the Baseline Characteristic

Use a 50th-percentile male occupant model consistent with the rest of the study. The baseline load limiter is specified as a piecewise-linear force–displacement curve with three segments: an elastic rise to the plateau, a flat plateau, and a terminal rise once the payout limit is reached (the element bottoms out and force climbs steeply). The parameters below are a teaching baseline, not measured data.

The plateau level of 4.0 kN and the 120 mm usable payout are the two knobs this baseline fixes. Everything downstream — chest deflection, ride-down, head excursion — responds to them.

Computing Absorbed Energy

Absorbed energy is the integral of force over payout displacement. With a piecewise-linear curve, integrate each segment separately and sum. Convert millimetres to metres so the result is in joules.

E = ∫ F(x) dx   over payout x

Segment 1 (elastic rise, 0–20 mm):
  E1 = 0.5 × (0 + 4.0 kN) × 0.020 m = 0.040 kJ = 40 J

Segment 2 (plateau, 20–120 mm):
  E2 = 4.0 kN × 0.100 m = 0.400 kJ = 400 J

Segment 3 (bottom-out, 120–140 mm):
  E3 = 0.5 × (4.0 + 9.0 kN) × 0.020 m = 0.130 kJ = 130 J

Total absorbed energy:
  E_total = 40 + 400 + 130 = 570 J

If the occupant never reaches bottom-out (payout stays below 120 mm), the third segment contributes nothing and the absorbed energy is simply the area up to the actual maximum payout. That is why the baseline must record the achieved payout, not just the available one — the energy actually absorbed depends on how far the belt paid out in that event.

Estimating Maximum Chest Deflection

Chest deflection is not read directly off the load limiter curve; it comes from the occupant model's chest response to the belt force. For a baseline estimate before running the full simulation, use the ride-down energy balance: the energy the chest absorbs is approximately the belt work minus the energy stored in chest stiffness, and deflection follows from a linear chest stiffness assumption. Treat the chest as a spring of stiffness k = 60 N/mm (a teaching value for a 50th-percentile male) and solve for the deflection that stores the net chest energy.

Net chest energy  E_chest ≈ E_total − E_ride_down_loss
Assume E_ride_down_loss = 0.35 × E_total (fraction carried by
  seat/restraint geometry, teaching assumption)
  E_chest = 0.65 × 570 J = 370.5 J

Chest spring energy:  E_chest = 0.5 × k × d²
  d = sqrt(2 × E_chest / k)
    = sqrt(2 × 370.5 J / 60 N/mm)
  Convert: 370.5 J = 370 500 N·mm
    d = sqrt(2 × 370 500 / 60) = sqrt(12 350) ≈ 111 mm

Maximum chest deflection ≈ 111 mm

This is an order-of-magnitude baseline, deliberately simple so the arithmetic is transparent. The full occupant model will return a deflection that differs because it captures belt geometry, chest rate sensitivity, and seat interaction. The point of the baseline is to give a consistent reference number and a sanity check: if the simulation returns 60 mm or 180 mm for this characteristic, something in the setup is wrong before any trade-off conclusion is drawn.

Reading the Characteristic and Its Consequences

The figure below shows the baseline curve with the three segments labelled, the absorbed-energy area shaded, and the two derived metrics called out. The key visual relationship is that the plateau height sets the force the chest sees, while the plateau length sets how much energy is absorbed before bottom-out. Raising the plateau increases force but shortens the payout needed to absorb the same energy; lengthening the payout absorbs more energy at the same force. Those two levers are exactly what the later sweeps will move.

Verification and Common Setup Errors

Before accepting the baseline, check the characteristic against three conditions. First, the plateau must be flat within the tolerance the load limiter element is specified to hold — a drifting plateau means the element model is wrong, not the occupant. Second, the achieved payout in the run must be recorded; if it exceeds 120 mm the bottom-out segment is active and the absorbed energy is higher than the plateau-only estimate. Third, the chest deflection returned by the full model should sit within a reasonable band of the 111 mm hand estimate; a large gap usually points to a belt-routing or seat-interaction error rather than a load limiter problem.

• Plateau too high or low: recheck the force units — kN versus N is the most common slip, and a 1000× error is obvious but a 10× error is not.
• Energy mismatch: confirm the integration used achieved payout, not available payout, when the run did not bottom out.
• Deflection far from estimate: inspect belt anchor geometry and seat cushion stiffness before touching the load limiter curve.

With the baseline fixed at 4.0 kN plateau, 120 mm payout, 570 J absorbed, and a reference chest deflection near 111 mm, the study has a stable origin. Every subsequent sweep changes exactly one of these levers and measures the response against this reference.