4. Crash pulse and occupant kinematics fundamentals

Restraint performance is not decided by the restraint alone. It is decided by the interaction between the vehicle's deceleration pulse and the occupant's motion inside the compartment. Two vehicles with identical seat belts and airbags can produce very different injury outcomes if their crash pulses differ, because the pulse determines how much time and how much distance the occupant has before contacting the restraint. This section establishes the physical vocabulary — deceleration pulse, occupant excursion, ride-down, and restraint timing — that the rest of the requirements allocation work depends on.

Sign Convention and the Deceleration Pulse

Before any quantitative discussion, fix the reference frame. In this course, the vehicle's forward direction of travel is positive x. During a frontal impact the vehicle decelerates, so its acceleration av(t) is negative. It is conventional in crash engineering to plot the deceleration pulse as positive magnitude, i.e. −av(t), in units of g. All pulses, excursions, and timing values in this course use that convention unless stated otherwise. The occupant, by contrast, continues forward at approximately the pre-impact velocity until a restraint force acts on the body; the occupant's forward displacement relative to the vehicle is the excursion.

A real barrier pulse is not a rectangle. It typically rises steeply within 10–20 ms, holds a plateau, and then decays with a secondary lobe as the engine block, subframe, and other structures crush sequentially. The two parameters that matter most for restraint design are the peak deceleration and the pulse duration (often quoted as the time to zero velocity change, or the interval containing 90% of the velocity change, Δv). A stiff, short pulse — for example, 35 g peak over 60 ms — and a soft, long pulse — 18 g peak over 110 ms — can both produce the same Δv of roughly 50 km/h, yet they demand completely different restraint strategies.

Occupant Excursion and Ride-Down

Excursion is the integral relationship that ties the pulse to the occupant. If the occupant were completely unrestrained, the relative displacement would grow as the double integral of the vehicle deceleration. In practice the restraint applies force early and the occupant "rides down" with the vehicle: the body decelerates over a longer distance and a longer time than the vehicle structure does. Ride-down is precisely this sharing of the deceleration event — the occupant's center of gravity is brought to rest over, say, 250–350 mm of forward travel instead of the 600–800 mm of crush available to the vehicle front end.

The engineering value of ride-down is that occupant deceleration scales inversely with stopping distance. A useful first-order estimate for the occupant's average deceleration is:

a_occ_avg ≈ v_rel² / (2 · s_ride)

where
  v_rel   = occupant velocity relative to vehicle at restraint engagement
  s_ride  = available ride-down distance (occupant excursion budget)

Consider an illustrative example (values chosen for teaching, not measured): a vehicle pulse of 30 g peak, 80 ms duration, Δv = 50 km/h (13.9 m/s). If the restraint engages when the occupant has already moved 60 mm and the total excursion budget to the airbag/knee bolster contact plane is 300 mm, the remaining ride-down distance is 240 mm. The first-order average occupant deceleration is then 13.9² / (2 × 0.24) ≈ 402 m/s² ≈ 41 g. That number is higher than the vehicle peak because the occupant's relative velocity at engagement is still close to the full Δv. This is why early engagement matters: every millimetre of excursion consumed before the belt loads is a millimetre unavailable for ride-down.

The first-order formula ignores belt stretch, load limiting, and airbag compliance. It is a scoping tool for requirement allocation, not a substitute for a sled or CAE simulation. Use it to check whether a proposed timing and excursion budget is physically plausible before committing to detailed modelling.

Coupling to Restraint Timing

Restraint timing is the bridge between the pulse and the occupant. Three timing quantities dominate frontal restraint allocation:

  • Time to fire (TTF) — from impact to the airbag inflator trigger. It must be late enough that the bag is not still deploying when the occupant arrives, and early enough that the bag is fully inflated before occupant contact.
  • Belt load-limiter threshold and onset — the force level at which the retractor or anchor pays out webbing, and the time or displacement at which that payout begins. Load limiting trades chest deflection against excursion.
  • Pretensioner firing time — removes slack and couples the occupant to the vehicle earlier, effectively increasing usable ride-down distance.

The coupling is bidirectional. A long, soft pulse gives the occupant more time, so the airbag can be tuned for a lower internal pressure and the load limiter can be set higher without exceeding excursion limits. A short, stiff pulse compresses the timing window: the pretensioner must fire within a few milliseconds, the bag must be inflated by roughly 30–40 ms after impact, and the load limiter must begin payout early enough to cap chest acceleration while still leaving excursion margin for the airbag and knee bolster. If the pulse is stiff and the load limiter is set too high, the chest sees the full pulse; if it is set too low, the occupant travels further and may bottom out the airbag or contact the steering wheel.

Vehicle deceleration pulse, occupant excursion, and restraint timing coupling Top panel shows a stiff short pulse and a soft long pulse with equal velocity change. Bottom panel shows occupant excursion growing until restraint engagement, then ride-down to rest, with timing markers for pretensioner, airbag fire, and load limiter onset. Deceleration pulse (magnitude, g) g time (ms) 0 40 80 120 160 Stiff: 35 g peak, 60 ms Soft: 18 g peak, 110 ms Both pulses: Δv ≈ 50 km/h Same velocity change, different timing demand Occupant excursion relative to vehicle (mm) mm time (ms) 0 40 80 120 160 Restraint engagement excursion ≈ 60 mm Ride-down distance ≈ 240 mm Pretensioner Airbag fire Load limiter onset Excursion budget (contact plane)

The figure makes the coupling visible. The upper panel shows two pulses with the same Δv but different shapes; the lower panel shows the resulting excursion history for the stiff pulse, with the timing markers overlaid. Note that the excursion curve is steepest before engagement — that is the slack and compliance being consumed — and flattens during ride-down as the belt and airbag share the load. The horizontal dashed line is the excursion budget: the distance from the occupant's initial position to the nearest hard contact (steering wheel rim, knee bolster, or airbag bottoming plane). If the curve crosses that line before the occupant's velocity reaches zero, the restraint has failed to manage the excursion.

Reading the Coupling in Practice

When allocating requirements across crash modes, the pulse and timing data are the inputs that constrain every downstream decision. A practical workflow is to extract, for each crash mode, the pulse's peak, duration, and Δv; compute the excursion budget from the package geometry; estimate the first-order occupant deceleration; and then check whether the proposed TTF, pretensioner time, and load-limiter threshold fit inside the available window. If the estimated occupant deceleration exceeds the chest criterion for the mode, the allocation must shift — either by increasing ride-down distance (earlier engagement, more belt payout), lowering the load-limiter threshold, or revising the pulse itself through structure tuning.

Two failure symptoms recur in this analysis. First, late engagement: the excursion curve consumes most of the budget before the belt loads, and the occupant contacts the airbag at high relative velocity, producing a sharp chest acceleration spike. Second, over-early load limiting: the belt pays out too soon and too much, the occupant travels past the airbag's effective cushion, and the excursion budget is exhausted. Both are timing problems, not hardware problems, and both are diagnosed by comparing the measured excursion history against the pulse and the timing markers — exactly the relationship the figure encodes.

Do not treat the pulse as a single scalar. Peak g alone is misleading: a 30 g pulse lasting 50 ms and a 30 g pulse lasting 100 ms impose very different excursion demands. Always carry peak, duration, and Δv together into the allocation, and verify the pulse shape against the structural crush sequence before committing restraint timing.

With the pulse, excursion, ride-down, and timing relationships established, the next allocation steps can treat these as the governing variables: every restraint requirement in the following chapters is, in effect, a statement about how much excursion is permitted, how early the restraint must engage, and how much deceleration the occupant can be allowed to experience within the available ride-down distance.

← Previous 📖 Contents Next →