2. Occupant kinematics in frontal impacts

Submarining is not a single event but the terminal outcome of a kinematic chain that begins the moment the restraint system loads the occupant. To design a seat and belt system that prevents it, you must be able to describe where the pelvis is, how fast it is moving, and what the belt is doing to it at every millisecond of the crash pulse. This section builds that description from the ground up: the reference frames used to measure motion, the mechanics of pelvis excursion, the physical conditions that trigger submarining, and the injury metrics used to judge whether the outcome is acceptable.

Reference Frames and the Belt–Pelvis Interface

All kinematic discussion in this course uses the vehicle coordinate system defined by SAE J670: x positive forward, y positive to the occupant's left, z positive upward, with the origin at the vehicle CG. Occupant motion is reported relative to the seat, not the ground, because the seat is what the belt anchors to. The critical measurement is pelvis excursion: the forward (+x) and downward (−z) displacement of the H-point relative to its pre-impact position, resolved in the seat frame.

Two interfaces govern whether the pelvis stays captured:

• Lap belt–pelvis: the belt must sit on the anterior superior iliac spine (ASIS) and load the pelvis in compression, not ride up onto the soft abdominal tissue.
• Seat cushion–buttocks: the cushion provides a friction and normal-force reaction that resists forward sliding. Once the pelvis slides forward far enough that the lap belt crosses above the ASIS, the geometry becomes unrecoverable.

The lap belt angle relative to horizontal, typically specified between 45° and 65° in FMVSS 208 and ECE R16 seating procedures, is the single most influential geometric parameter. A shallow angle (below roughly 45°) lets the belt slide up the iliac crest under forward load; a steep angle risks abdominal loading. The design window is narrow, and it moves with occupant size.

The Kinematic Sequence of a Frontal Impact

Consider a 50th-percentile male, belted, in a 56 km/h full-frontal rigid-barrier test. The sequence unfolds in roughly 120 ms:

1. 0–20 ms — Pretensioning and take-up: the retractor pretensioner fires, removing 40–80 mm of slack. The lap belt tension rises to 2–4 kN. The occupant has barely moved; this phase sets the initial belt–pelvis contact geometry.
2. 20–60 ms — Coupled deceleration: the pelvis and torso decelerate with the seat and belt. The pelvis rotates forward about the hip joint as the torso loads the shoulder belt. Pelvis excursion is still small, typically under 30 mm.
3. 60–90 ms — Peak loading and the critical decision point: the lap belt reaches its peak force, often 6–10 kN. If the belt is on the ASIS, the pelvis is captured and excursion plateaus. If the belt has migrated above the ASIS, the pelvis slides under it — this is submarining onset.
4. 90–120 ms — Rebound and secondary contact: the occupant rebounds into the seat. If submarining occurred, the pelvis is now forward and low, and the torso may jackknife over the lap belt.

Submarining onset is therefore not defined by a single displacement value but by the rate at which the belt–ASIS engagement is lost. In practice, engineers detect it from high-speed video by tracking the lap belt's position relative to an ASIS marker, and from the belt force signal by a characteristic drop-and-recovery signature as the belt slips off the iliac crest.

Injury Criteria That Quantify the Outcome

Kinematics tells you what happened; injury criteria tell you whether it matters. Four metrics dominate frontal submarining assessment:

These criteria interact. A restraint that keeps pelvis excursion low but loads the abdomen heavily is not a success; a restraint that allows 70 mm of excursion but keeps the belt on the ASIS may still pass. The design objective is to satisfy all four simultaneously, which is why the lap belt angle, seat cushion stiffness, and pretensioner timing must be tuned together rather than independently.

Reading the Signals: A Worked Example

Suppose a sled test at 56 km/h produces the following lap belt force trace (sampled at 1 kHz, values in kN):

t (ms)   F_lap (kN)   Pelvis x (mm)   Belt vs ASIS (mm)
  0        0.0           0              0
 20        2.1           8             -2
 40        5.4          22             -1
 60        8.9          41             +3
 70        9.2          55             +7
 80        7.6          68            +14   <-- onset
 90        6.1          79            +21
100        5.8          84            +24

At t = 80 ms, all three onset conditions are satisfied: the belt is 14 mm above the ASIS, pelvis excursion is 68 mm, and the force dropped 17% from its peak. This is a submarining event. The corrective actions, in order of typical effectiveness, are: increase the lap belt angle toward 60°, stiffen the front edge of the seat cushion to raise the pelvis reaction, advance pretensioner firing by 5–10 ms, and add a lap belt load limiter to reduce peak force without losing capture.

Visualizing the Kinematic Chain

The diagram below maps the causal chain from crash pulse to injury outcome, showing the three onset conditions and the feedback loop between belt geometry and pelvis motion.

The feedback path in the diagram is the engineering reality: submarining is rarely solved by a single change. You adjust lap belt angle, cushion stiffness, and pretensioner timing, re-run the sled, and re-evaluate the same three onset conditions and four injury criteria. The next section moves from kinematics to the seat structure and belt hardware that make these adjustments possible.