2. Occupant kinematics fundamentals in frontal impacts

Airbag timing decisions only make sense when you can predict where the occupant will be, and how fast, at every millisecond after bumper contact. This section builds that mental model: how a restrained and an unrestrained occupant move relative to the vehicle in a frontal crash, what "ride-down" actually buys you, and how the three workhorse injury metrics — HIC, chest deflection, and femur load — respond to that motion. Everything here uses a single sign convention: +X points forward (direction of travel), and displacement is measured relative to the vehicle interior unless stated otherwise. Switching to a ground-fixed frame is called out explicitly.

The vehicle pulse is the input, occupant motion is the response

A frontal barrier impact produces a deceleration pulse at the rocker or tunnel — typically 25–40 g peak, 80–120 ms duration for a 50 km/h rigid-barrier test. The occupant, however, is not rigidly attached to that pulse. The occupant is a loosely coupled mass connected through the restraint system: belt geometry, pretensioner, load limiter, seat structure, and — once it fires — the airbag. The occupant's acceleration history is therefore a filtered version of the vehicle pulse, and the phase lag between the two is the entire game.

In the ground-fixed frame, the vehicle decelerates sharply while the occupant continues forward at nearly initial velocity until restraint forces build. The relative displacement that accumulates is the occupant excursion, and it is this quantity — not absolute displacement — that determines whether the occupant meets the airbag in its inflated window, bottoms out the belt, or strikes the steering wheel hub.

Restrained kinematics: belt loading, pretensioning, and load limiting

For a belted occupant, the sequence is roughly:

1. 0–15 ms: Vehicle decelerates; the occupant is still moving at ~50 km/h relative to ground. The belt is slack; the retractor lock and pyrotechnic pretensioner (if fitted) begin removing slack, typically pulling 40–80 mm of webbing within 10–20 ms.
2. 15–40 ms: Belt engages the pelvis and chest. Force rises steeply. The load limiter (torsion bar or stitch pattern) caps shoulder-belt force, commonly 3.5–4.5 kN in modern systems, allowing controlled forward excursion.
3. 40–90 ms: Peak occupant forward excursion, typically 100–180 mm at the chest for a Hybrid III 50th percentile male in a 50 km/h test. The airbag, if timed correctly, is at or near full inflation and the occupant "catches" the bag.
4. 90–150 ms: Rebound and settling as restraint forces decay.

The pretensioner and load limiter are not cosmetic. Without a load limiter, chest acceleration and belt force spike, and chest deflection rises; with too aggressive a limiter, excursion grows and the occupant may contact the airbag late or bottom it out. This trade-off is the reason airbag timing cannot be tuned in isolation from the belt.

Unrestrained kinematics: the free-flight problem

An unbelted occupant follows a very different path. With no belt force until contact with the airbag or interior, the occupant travels forward at essentially constant velocity in the ground frame while the vehicle decelerates beneath them. Relative to the vehicle, the occupant's forward displacement grows almost linearly with time until something stops them. At 50 km/h, that is roughly 14 mm per millisecond — 300 mm in 21 ms. This is why an unbelted occupant reaches the airbag plane far earlier and far faster than a belted one, and why airbag timing tuned only for belted occupants can produce "out-of-position" or late-deployment interactions for unbelted occupants.

The practical consequence: airbag trigger time is usually set so the bag is fully inflated before the unbelted occupant arrives, while still being soft enough for the belted occupant who arrives later. That window is narrow — often 20–40 ms wide — and it is the central constraint of frontal airbag calibration.

Ride-down: what it is and how to quantify it

Ride-down is the process by which the restraint system spreads the occupant's deceleration over a longer time and distance than the vehicle's own crash pulse. The vehicle might stop in 90 ms; a well-restrained occupant's chest may decelerate over 120–150 ms. The benefit is direct: for a given delta-v, longer stopping distance means lower average acceleration, and lower acceleration means lower injury metrics.

A simple energy check makes this concrete. If the occupant's center of mass travels distance s relative to the vehicle while decelerating from velocity v, the average deceleration is approximately a ≈ v²/(2s). For a belted occupant at 13.9 m/s with 0.15 m of chest excursion, that is about 64 g average — already high, which is why load limiting and airbag compliance matter. For an unbelted occupant stopped by the airbag over 0.10 m, the average is ~96 g, and the peak will be substantially higher. Ride-down is the design lever that moves these numbers.

Injury metrics: HIC, chest deflection, femur load

Three metrics dominate frontal occupant assessment, and each maps to a different physical mechanism:

HIC is computed as HIC = max[(t₂−t₁)(1/(t₂−t₁))∫a dt]^2.5 over the window, with a in g. It is dominated by short, high-amplitude acceleration spikes, which is why head-to-airbag contact velocity and bag pressure matter more than the overall pulse. A bag that is too hard at contact produces a sharp HIC spike even if the occupant's overall excursion is fine.

Chest deflection is measured directly by the dummy's chest potentiometer and reflects rib compression. It is the metric most sensitive to belt load limiting: raising the limiter from 3.5 kN to 4.5 kN can add 5–10 mm of deflection in a 50 km/h test. It is also the metric that punishes late airbag contact, because the belt alone must absorb the chest load.

Femur load captures the axial force transmitted through the knee-thigh-hip complex into the knee bolster and lower dash. It rises with occupant forward excursion and with stiff knee bolsters, and it is a useful early indicator of submarining — if the pelvis slides under the lap belt, femur load and pelvis excursion both change character.

Putting the metrics to work: a calibration sanity check

Suppose a 50 km/h frontal calibration shows HIC15 = 620, chest deflection = 58 mm, and femur load = 8.2 kN for the belted 50th percentile. All pass, but the margins are thin on chest deflection. Two levers are available: soften the load limiter (reduces chest deflection but increases excursion and may push HIC up if the head reaches the bag later and harder), or advance the airbag trigger by 5 ms (brings the bag to full inflation earlier, reducing head contact velocity but potentially increasing chest loading if the bag is stiffer at contact). The correct move is to change one variable at a time and re-read all three metrics, because they are coupled through the same excursion history. A useful diagnostic: if chest deflection falls but HIC rises, the occupant is arriving at a harder bag — check trigger timing before touching bag pressure.

The takeaway for airbag timing work: the occupant's excursion history is the shared variable behind every frontal injury metric. Restrained and unrestrained occupants trace different curves on that plot, ride-down determines how much of the crash pulse the occupant actually feels, and HIC, chest deflection, and femur load are three different readings of the same underlying kinematics. Calibration is the act of shaping that curve — through belt hardware, bag pressure, venting, and trigger time — so that all three readings stay inside their limits across the occupant population.