4. Submarining Risk Screening in Reclined Posture

Why Submarining Screening Needs Its Own Metric Set

In a reclined posture the pelvis is rotated rearward and the lap belt sits higher on the abdomen than in a nominal upright configuration. Under frontal deceleration the belt can slide over the iliac crest, the pelvis translates forward beneath the belt path, and the occupant "submarines" — the torso ramps down and the belt loads the abdomen instead of the pelvis. Screening for this onset requires two things that a stock restraint model does not provide: a way to measure relative pelvis-to-belt motion, and a way to measure how much belt length has slipped past the pelvis. This case instruments the baseline reclined model with those two metrics, then sweeps belt-to-pelvis friction and lap anchor position to map where submarining onset occurs.

Instrumentation: Pelvis Slip and Belt Slip

Two independent metrics are defined so that a single run can distinguish "pelvis moved" from "belt moved relative to pelvis." Both are computed in the vehicle coordinate frame with +X forward, +Y left, +Z up, origin at the seat reference point (SRP) at t = 0.

  • Pelvis slip, d_pelvis — forward displacement of the pelvis center-of-gravity (H-point marker) relative to the seat cushion reference, measured along +X. Positive values mean the pelvis has migrated forward under the belt.
  • Belt slip, d_belt — cumulative length of lap-belt webbing that has passed the pelvis contact patch, obtained by integrating the relative tangential velocity between the belt segment node nearest the anterior superior iliac spine (ASIS) and the pelvis surface marker. Positive values mean webbing is being pulled through toward the buckle side.

Submarining onset is flagged when the belt has slipped past the iliac crest, i.e. when the belt's vertical position at the pelvis drops below the ASIS marker height while d_belt is still increasing. A practical screening criterion combines both: onset is declared at the first time step where d_belt exceeds 40 mm and the belt-to-ASIS vertical offset becomes negative. The 40 mm threshold is a screening value chosen to sit above normal belt take-up (typically 10–25 mm in a well-coupled pelvis) and below the point where abdominal loading becomes dominant; it should be calibrated against the model's own belt-pretensioner stroke before being used for pass/fail decisions.

Instrument the model once and reuse it across the whole matrix. Adding the two history variables as output requests (not as new constraints) keeps the occupant response unchanged, so differences between runs are attributable to friction and anchor position only.

Building the Screening Matrix

The sweep has two factors. Friction between the lap belt and the pelvis clothing surface is varied over four levels spanning the realistic range for clothing and seat materials; lap anchor position is varied over three fore-aft locations relative to the SRP. That gives a 4 × 3 = 12-run matrix, each run using the same reclined baseline (seat back at 45°, pelvis rotated rearward per the boundary-condition set) so that only the two factors change.

FactorLevelsRationale
Belt–pelvis friction coefficient, μ0.15 / 0.25 / 0.35 / 0.45Low μ approximates slick outerwear; high μ approximates high-grip fabric or a pre-loaded lap belt
Lap anchor X position (mm from SRP)−150 / −50 / +50Rearward anchor pulls the belt down onto the pelvis; forward anchor raises the belt path toward the abdomen

Each run is a frontal deceleration pulse applied to the seat and floor; the occupant is restrained by the lap and shoulder belt with a pretensioner and load limiter active. The two instrumentation channels are logged at 1 kHz alongside the standard chest deflection and head acceleration channels so that a submarining flag can be cross-checked against abdominal belt force if the model includes an abdominal pressure sensor.

Reading the Matrix

The expected pattern — to be confirmed by the actual runs, not assumed — is that onset concentrates in the low-friction, forward-anchor corner of the matrix, where the belt has both the least grip on the pelvis and the highest initial path over the abdomen. The rearward anchor at high friction should keep the belt seated on the iliac crest and produce d_belt that plateaus after pretensioner take-up. The figure below shows how the two metrics are expected to diverge across the matrix and where the onset flag is set.

Submarining Screening Matrix — Belt Slip vs. Pelvis Slip Onset flag: d_belt > 40 mm AND belt-to-ASIS vertical offset < 0 Anchor X = −150 mm Anchor X = −50 mm Anchor X = +50 mm μ = 0.45 μ = 0.35 μ = 0.25 μ = 0.15 d_belt ≈ 18 mm no onset d_belt ≈ 22 mm no onset d_belt ≈ 34 mm marginal d_belt ≈ 24 mm no onset d_belt ≈ 38 mm marginal d_belt ≈ 52 mm onset d_belt ≈ 30 mm no onset d_belt ≈ 47 mm onset d_belt ≈ 61 mm onset d_belt ≈ 39 mm marginal d_belt ≈ 58 mm onset d_belt ≈ 74 mm onset No onset (belt seated on iliac crest) Marginal (near threshold) Onset flagged Increasing forward anchor position → higher belt path over abdomen → greater slip

Interpreting and Acting on the Results

Two failure signatures are worth distinguishing when the matrix is read. First, a run can show large d_pelvis with modest d_belt — the pelvis is translating forward but the belt is staying with it, which is a coupling problem rather than a submarining problem and points to anchor geometry or pretensioner timing. Second, a run can show small d_pelvis but rapidly rising d_belt — the pelvis is held but the belt is being pulled through, which is the classic submarining signature and points to friction or belt routing. The onset flag should only be trusted when the second signature is present, because the first can trigger the 40 mm threshold without the belt actually leaving the iliac crest.

For the screening decision, treat the matrix as a boundary map rather than a pass/fail list. The boundary between "no onset" and "onset" cells identifies the friction–anchor combination below which the restraint loses pelvis coupling. If the boundary falls inside the intended production envelope (for example, if μ = 0.25 with a forward anchor is a realistic combination), the design needs a countermeasure — a lap-belt pretensioner with a shorter stroke, a belt geometry change, or a seat-integrated anti-submarining pan — before the configuration can be released. If the boundary sits outside the envelope, the screening is complete and the configuration can proceed to the detailed injury-metric assessment.

The 40 mm belt-slip threshold and the cell values shown in the figure are screening assumptions for this exercise, not measured results. Before using the matrix for a release decision, calibrate the threshold against a physical sled test or a validated model run at a known non-submarining configuration, and confirm that the belt-slip integration is not contaminated by pretensioner take-up in the first 30 ms.

Reproducible Run Checklist

  1. Load the baseline reclined model (45° seat back, rearward pelvis rotation) and confirm the pre-impact posture matches the boundary-condition set.
  2. Add d_pelvis and d_belt as output history variables; verify they read zero at t = 0 and that d_belt responds to a manual belt-pull test.
  3. Set the lap-belt–pelvis friction coefficient and lap anchor X position for the first matrix cell; run the frontal pulse.
  4. Extract the peak d_belt, the time of the belt-to-ASIS vertical offset zero-crossing, and the peak d_pelvis; record the onset flag.
  5. Repeat for all 12 cells; plot the onset boundary and compare against the intended production envelope.

A run that fails to produce any d_belt response usually indicates the belt-slip sensor node was placed on the wrong side of the buckle or that the contact definition between belt and pelvis is missing; check both before re-running the cell.

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