4. Occupant kinematics and belt geometry

Belt geometry is not a cosmetic detail of restraint packaging. It is the mechanism through which anchorage coordinates are converted into occupant loading. Once the retractor locks and the belt becomes a load-bearing member, the occupant no longer moves freely; the belt constrains the torso and pelvis along paths determined by where the webbing contacts the body and where the anchorages sit in space. This chapter explains how routing, wrap angle, and anchorage position translate into chest and pelvis loading, and how to reason about them quantitatively during geometry development.

Reference Frame and Sign Conventions

All geometry in this chapter is expressed in the vehicle coordinate system: X positive forward, Y positive to the vehicle's right, Z positive upward, with the origin at the vehicle datum. Occupant motion during a frontal event is therefore predominantly +X relative to the vehicle, and belt forces on the occupant act predominantly −X. Anchorage positions are quoted as (X, Y, Z) triples. This convention is used consistently in the text and in the figure below.

Belt Routing and the Three Contact Regions

A three-point belt contacts the occupant at three distinct regions, and each region governs a different load path:

• Lap belt / pelvis: runs from the buckle stalk across the anterior superior iliac spines (ASIS) to the lap anchor (outboard, near the seat cushion). This segment controls pelvis restraint and is the primary determinant of submarining risk.
• Shoulder belt / chest: runs from the D-ring (upper anchorage) diagonally across the sternum and clavicle to the buckle. This segment controls upper-torso restraint and chest deflection.
• Buckle / junction: the point where lap and shoulder loads are summed and reacted into the seat or floor structure. Its position sets the included angle between the two belt segments.

Routing is the geometric description of these three segments. Two routing parameters dominate occupant loading: the lap belt angle (the angle of the lap segment in the side view, measured from horizontal) and the shoulder belt angle (the angle of the shoulder segment in the side view). Typical target ranges for a mid-size sedan front outboard seat are a lap belt angle of 45°–65° and a shoulder belt angle of 20°–40° from horizontal, but these are starting points, not universal values.

Wrap Angle: Definition and Why It Matters

Wrap angle is the total angle subtended by the webbing as it wraps around the occupant's body at a given cross-section. At the chest, the shoulder belt wraps around the rib cage; at the pelvis, the lap belt wraps around the iliac crest. Wrap angle determines how the belt force is distributed over the body surface.

For a belt tension T wrapping through an angle θ around a body segment, the resultant normal force per unit length on the body is approximately T/R, where R is the local radius of curvature, and the total normal force scales with the wrap angle. A larger wrap angle spreads the same tension over a longer contact arc, reducing peak pressure and chest deflection. A smaller wrap angle concentrates load, increasing local pressure and the risk of rib fracture or soft-tissue injury.

How Anchorage Positions Change the Load Path

Anchorage coordinates set the belt geometry, and belt geometry sets the load path. Three anchorage adjustments produce predictable, and sometimes counterintuitive, changes:

The table shows why anchorage optimization is a coupled problem. Moving the buckle rearward to improve comfort, for example, simultaneously degrades lap belt angle and shoulder belt angle. The engineer must evaluate the combined effect, not each anchorage in isolation.

Worked Example: Lap Belt Angle and Submarining Margin

Consider a front outboard seat with the following initial anchorage coordinates (vehicle frame, millimeters):

Lap anchor (outboard):   X = -180, Y = +340, Z = 180
Buckle (inboard):        X = -120, Y = -180, Z = 200
D-ring (upper):          X = +120, Y = +280, Z = 620
Seat cushion reference:  Z = 200 (top of cushion at H-point)
H-point:                 X = 0, Y = +320, Z = 200

The lap belt angle in side view is computed from the lap anchor to the buckle:

ΔX = -120 - (-180) = +60 mm
ΔZ = 200 - 180 = +20 mm
Lap belt angle = atan(ΔZ / ΔX) = atan(20 / 60) ≈ 18.4°

An 18.4° lap belt angle is far below the typical 45°–65° target. At this angle the lap belt is nearly horizontal and provides little vertical restraint; during a frontal pulse the pelvis can slide forward and downward under the belt, producing submarining. The observable symptom in a sled test would be the lap belt migrating from the iliac crest onto the abdomen, with a corresponding rise in abdominal pressure and a drop in pelvic forward excursion restraint.

To correct this, move the lap anchor forward and upward. A revised position of X = −100, Y = +340, Z = 220 gives:

ΔX = -120 - (-100) = -20 mm  (buckle is now rearward of the anchor)
ΔZ = 200 - 220 = -20 mm
Lap belt angle = atan(-20 / -20) = 45°

The revised geometry achieves a 45° lap belt angle, which places the belt across the iliac crest and provides a downward-and-rearward load path that resists pelvic forward motion. The trade-off is increased pelvic pressure, which must be checked against the pressure injury criterion for the specific occupant population.

Shoulder Belt Wrap and Chest Loading

The shoulder belt's wrap angle around the chest is governed by the D-ring position and the buckle position. Moving the D-ring outboard (+Y) reduces the wrap angle because the belt approaches the chest more tangentially. Moving the D-ring inboard (−Y) increases wrap angle but may cause the belt to cross the neck.

A practical check during geometry development is to measure the shoulder belt wrap angle at the sternum cross-section. For a 50th percentile male, a wrap angle of approximately 60°–90° around the chest is typical for a well-routed three-point belt. Below 60°, chest deflection tends to increase for the same belt tension because the load is concentrated over a narrower contact arc.

Coupling Between Chest and Pelvis Loading

Chest and pelvis loading are not independent. The buckle position couples them: moving the buckle changes both the lap belt angle and the shoulder belt angle simultaneously. A rearward buckle movement reduces lap belt angle (worsening submarining margin) and increases shoulder belt angle (moving the belt lower on the chest, potentially toward the abdomen).

This coupling means that anchorage optimization should be treated as a multi-variable problem. A useful approach is to define a target window for each parameter and then search for anchorage coordinates that satisfy all windows simultaneously. The figure below illustrates the load path from anchorage coordinates through belt routing to occupant loading regions.

Practical Verification During Geometry Development

When evaluating a proposed anchorage layout, the following checks should be performed in order:

1. Compute lap belt angle from the lap anchor to the buckle in side view. Confirm it falls within the target window for the seat position and occupant population.
2. Compute shoulder belt angle from the D-ring to the buckle. Confirm it places the belt across the sternum, not the abdomen or neck.
3. Estimate chest wrap angle at the sternum cross-section using the D-ring and buckle positions and the occupant's chest depth. Confirm it exceeds the minimum for acceptable pressure distribution.
4. Check buckle included angle between lap and shoulder segments. An included angle below approximately 90° tends to concentrate load at the buckle and can cause the lap belt to ride up.
5. Verify with a physical or CAE sled test using the target occupant size. Observe lap belt migration, chest deflection, and pelvic excursion. Compare against the design targets.

Summary

Belt routing, wrap angle, and anchorage position form a coupled system that determines how restraint forces are distributed across the occupant. Lap belt angle controls pelvis capture and submarining margin; shoulder belt angle and chest wrap angle control chest loading and deflection; buckle position couples the two. Anchorage optimization requires evaluating these parameters together, not in isolation, and verifying the final geometry against sled test observations of belt migration, chest deflection, and pelvic excursion.