2. Occupant ride-down fundamentals
Ride-down is the controlled deceleration of an occupant over a distance and duration that the body can tolerate. In a crash, the vehicle's front structure crushes and the restraint system pays out webbing, stretches, and vents gas; both processes convert kinetic energy into deformation and heat while stretching the time over which the occupant's velocity change occurs. The central design question is simple to state and hard to satisfy: how much space is available, and how should it be used to keep occupant loads below injury thresholds? This chapter builds the physical picture — crash pulse, occupant kinematics, and the space–injury relationship — that later chapters on energy management will quantify.
The crash pulse as the input
The crash pulse is the vehicle's deceleration history at the occupant compartment, usually expressed as acceleration a(t) in g, or as a velocity change Δv(t). Two pulses can share the same total Δv yet produce very different occupant outcomes. A short, high-amplitude pulse (a stiff barrier impact) delivers its velocity change in tens of milliseconds; a long, low-amplitude pulse (a compliant frontal structure or a moving deformable barrier) spreads the same Δv over 100–150 ms. The occupant's body responds to the pulse through the restraint, so the pulse's shape — peak, rise time, duration, and the presence of a secondary spike — sets the demand the restraint must meet.
For design work, the pulse is often characterized by its peak deceleration, its duration, and the crush distance consumed to produce it. A useful first-order relation links them: for a constant deceleration a bringing a vehicle from impact speed v to rest, the stopping distance is s = v²/(2a). At 50 km/h (13.9 m/s) and a 20 g average deceleration, s ≈ 0.49 m. That number is the front-end crush budget, and it is the same order as the space an occupant must be given to ride down. The pulse and the occupant space are therefore two views of one energy budget.
Occupant kinematics: relative motion is what injures
The occupant does not experience the vehicle's deceleration directly; the occupant experiences the relative motion between the body and the compartment. At t = 0 the occupant is moving with the vehicle at v. As the vehicle decelerates, the unrestrained occupant continues forward at nearly constant velocity until the restraint engages. The relative displacement xrel(t) is the integral of the relative velocity, and it is this displacement that must be absorbed by belt stretch, airbag stroke, and — critically — the free space between the occupant and the interior.
Three phases describe a belted occupant in a frontal crash:
- Free flight / slack phase. The occupant moves forward while belt slack and webbing geometry take up. Duration is typically 10–30 ms; relative displacement is small but sets the initial condition for the next phase.
- Restraint engagement. The belt loads the pelvis and chest; force rises as the webbing stretches and the force limiter (if fitted) pays out. The occupant's deceleration now tracks the restraint force divided by effective mass.
- Ride-down and rebound. The occupant decelerates to the vehicle's post-impact velocity, then rebounds as stored belt energy returns. Head and chest excursions peak near the end of this phase.
The key kinematic quantity is the occupant excursion — how far the head, chest, and pelvis travel forward relative to the compartment. Excursion is what determines whether the head reaches the airbag, the steering wheel, or the A-pillar, and whether the chest loads the belt at a tolerable rate. Excursion is governed by the pulse (how fast the vehicle slows), the restraint (how much force and stroke it provides), and the available space (how far the occupant can move before contact with a hard surface).
Why available space is the injury-mitigation currency
Injury tolerance is usually expressed as a maximum allowable acceleration or force for a given body region and duration. The chest can tolerate roughly 40–60 g of belt loading for a few milliseconds; the head can tolerate on the order of 80 g for 3 ms before the risk of skull fracture rises sharply. These are not arbitrary numbers — they reflect the fact that the body needs distance to stop. If the occupant must be brought from 13.9 m/s to rest, the stopping distance at 40 g is about 0.25 m; at 60 g it is about 0.16 m. The difference between a survivable and an injurious event is often a few centimeters of stroke.
This is why the restraint system is designed as a space budget. Belt webbing stretch, force-limiter payout, airbag stroke, and seat cushion compression all consume space in a controlled way. The airbag, for example, is not a soft pillow; it is a controlled-volume decelerator whose venting and fabric stretch determine how much of the occupant's kinetic energy it absorbs over its stroke. If the occupant reaches the airbag too early (short pulse, stiff structure), the bag may still be inflating; if too late (long pulse, soft structure), the bag may have vented. The timing of peak excursion relative to the pulse is therefore a design variable, not an accident.
Working the numbers: a design example
Consider a frontal impact at 56 km/h (15.6 m/s) into a rigid barrier. Suppose the vehicle's front structure produces an average compartment deceleration of 25 g over a crush distance of 0.48 m. The occupant, belted with a force limiter set to 4 kN and a belt geometry giving an effective chest mass of 30 kg, experiences a restraint-induced deceleration of about 4,000 N / 30 kg ≈ 13.6 g once the belt is fully engaged. The occupant's velocity therefore lags the vehicle's, and the relative excursion grows until the belt force rises enough to bring the occupant's velocity down to the vehicle's.
A first-order estimate of peak excursion uses the relative velocity at engagement and the restraint deceleration: if the occupant is still moving at about 8 m/s relative to the compartment when the belt engages, and the restraint provides 13.6 g (≈133 m/s²), the stopping distance is v²/(2a) ≈ 64/(2×133) ≈ 0.24 m. That 240 mm must be available before the chest reaches the steering wheel or the head reaches the A-pillar. If the measured free space is only 180 mm, the design is short by about 60 mm, and the fix is either a softer pulse (more vehicle crush), a lower force limiter (longer stroke), or more occupant space — each with its own tradeoff against intrusion and compartment packaging.
These numbers are illustrative and assume a simplified single-degree-of-freedom model; real occupant simulation (e.g., a Hybrid III or THOR dummy in a sled or full-vehicle model) resolves the multi-body kinematics, belt geometry, and airbag interaction. But the first-order budget is the right place to start, because it tells you which lever — pulse, restraint, or space — is binding before you invest in detailed modeling.
What to watch in practice
When reviewing a sled or vehicle test, look at three traces together: the compartment pulse, the occupant's chest and head acceleration, and the relative displacement (from high-speed video or a string potentiometer). A well-tuned system shows the occupant's peak excursion occurring near the end of the pulse, with the restraint force rising smoothly and no secondary spike from bottoming out on a hard surface. A system that is short on space shows an early, sharp chest acceleration spike as the belt loads abruptly, followed by a head excursion that exceeds the airbag's coverage. A system that is over-soft shows excessive excursion and a late rebound, with the occupant possibly out of position for a second impact.
The practical takeaway is that ride-down is a space-and-time problem. The crash pulse sets the time; the available space sets the distance; the restraint system is the mechanism that converts one into the other without exceeding injury thresholds. Every later decision about energy management — crush initiators, force limiters, airbag venting, seat design — is a choice about how to spend that budget.