2. Crash pulse fundamentals

Every occupant simulation begins with a boundary condition that is deceptively simple to state and surprisingly easy to get wrong: the crash pulse. In a sled or full-vehicle model, the pulse is the prescribed acceleration–time history applied to the vehicle structure, and it is the single most influential input shaping the occupant's relative motion, restraint loading, and injury metrics. This section establishes the four quantities that define a pulse for simulation purposes — the acceleration–time history itself, the velocity change (delta-v), the pulse duration, and the frequency content — and shows how each one propagates into occupant response.

Sign Convention and the Acceleration–Time History

Before any pulse is used, the reference frame and sign convention must be fixed and held constant across the model, the plots, and the reported metrics. The convention used throughout this course is: the vehicle travels in the +X direction, a frontal impact decelerates the vehicle, and the vehicle's longitudinal acceleration is therefore negative during the crash. Many sled facilities and test standards instead publish the pulse as a positive magnitude ("deceleration pulse"). Both are acceptable, but mixing them inside one model inverts the inertial loading on the occupant and produces nonsense results. State the convention explicitly in the model documentation.

The acceleration–time history a(t) is the raw input. In practice it arrives as a sampled table — typically 1 kHz or higher for barrier data, sometimes 10 kHz for accelerometer channels — and must be conditioned before use: bias removal, low-pass filtering per the applicable standard (commonly SAE J211/1 Channel Frequency Class 60 for vehicle structure and CFC 180 or higher for occupant-adjacent measurements), and time-zero alignment to the impact event. Filtering is not cosmetic. An unfiltered channel carries sensor resonance and road noise that, once integrated, corrupts the velocity trace and can inject spurious high-frequency content into the restraint model.

Delta-v: The Integral That Sets Occupant Energy

Delta-v is the area under the acceleration–time curve over the crash event:

Δv = ∫ a(t) dt   (integrated from t0 to the end of the pulse)

For a frontal impact that starts at rest and ends at rest relative to the barrier, delta-v equals the initial travel speed — a 56 km/h (35 mph) frontal test implies roughly 15.6 m/s of delta-v, and the integrated pulse should reproduce that value within a few percent. This integral is the first and most important sanity check on any pulse: if the numerically integrated delta-v does not match the test speed, the pulse has a bias offset, a truncated tail, or a filtering error, and every downstream occupant result is suspect.

Delta-v governs the kinetic energy the restraint system must manage. Two pulses with identical peak acceleration but different delta-v produce very different occupant outcomes: the higher-delta-v case demands more restraint travel and higher belt force to arrest the occupant within the available ride-down distance. In simulation, delta-v is also the quantity most directly comparable across test severities, which is why regulatory and consumer-rating protocols are often specified by delta-v and pulse shape rather than peak g alone.

Pulse Duration and Shape

Duration is the time span over which the vehicle decelerates, typically 80–120 ms for a frontal barrier impact and longer for softer structures or offset configurations. Duration and delta-v together constrain the mean deceleration: a 15.6 m/s delta-v delivered over 100 ms implies an average of about 156 m/s² (≈16 g), so a pulse peaking at 40 g must have a shape that spends much of its time well below the peak. This relationship is why pulse shape matters as much as its scalar descriptors.

Common idealized shapes used as simulation inputs include the half-sine, the trapezoid (rise, plateau, fall), and the equivalent square wave. Each is a deliberate simplification of a measured barrier pulse. The trapezoid is often preferred for restraint tuning because its plateau produces a sustained deceleration that loads the belt and airbag in a controlled way, while the half-sine concentrates loading near its midpoint. When a measured pulse is available, use it directly; when only descriptors are given, reconstruct the shape from peak g, duration, and delta-v and verify the integral.

Frequency Content: Why the Pulse Spectrum Matters

The acceleration–time history can be decomposed into frequency components, and the occupant–restraint system responds selectively to them. The vehicle structure and the occupant's body each have characteristic response bands: the restrained occupant's torso and the belt–airbag system typically respond most strongly in the low-frequency range (roughly 5–20 Hz for whole-body ride-down, with higher-frequency content exciting belt stretch, airbag deployment dynamics, and local tissue response). A pulse whose energy is concentrated near the occupant's principal response frequency will produce larger relative displacement and higher restraint forces than a pulse with the same delta-v but energy spread across a wider band.

In simulation terms, the pulse's frequency content determines how much of the input the occupant model actually "sees." A very sharp leading edge — high-frequency content — can excite numerical stiffness in the restraint model and produce non-physical spikes in belt force; this is one reason pulses are filtered to a defined CFC before being applied. Conversely, over-filtering removes real content and softens the pulse, under-predicting occupant loading. The practical rule is to filter the pulse to the same class used for the measurements it will be compared against, and to document the filter class alongside the pulse.

Putting the Descriptors to Work

Consider a worked example using assumed values. A frontal sled pulse is supplied as a table sampled at 1 kHz, with a stated test speed of 50 km/h (13.9 m/s). The engineer first removes the pre-trigger bias, applies a CFC 60 low-pass filter, and aligns time zero to the first sustained deceleration. Numerical integration of the filtered trace yields 13.6 m/s — about 2% low. That discrepancy is within typical tolerance but worth investigating: the tail of the pulse may have been truncated at the end of the recording window. Extending the integration window and re-checking brings the value to 13.9 m/s, confirming the pulse is complete.

Next, the engineer extracts the peak (assumed 38 g at about 45 ms) and the effective duration (about 95 ms). A quick consistency check using the trapezoid relation with a 15 ms rise time gives an expected delta-v of 38·9.81·(0.095 − 0.015) ≈ 29.8 m/s — clearly inconsistent with 13.9 m/s, which signals that the pulse is far from a full-height trapezoid and that the plateau assumption is invalid for this shape. The lesson is that scalar descriptors must always be checked against the integral; a peak-and-duration pair alone does not define a pulse.

Finally, the engineer inspects the spectrum. If the filtered pulse still shows a pronounced spike near 60–80 Hz, that content is likely structural ringing rather than occupant-relevant deceleration, and it should be attenuated before the pulse is applied to the occupant model — otherwise the belt model will respond to a frequency the real occupant never experiences. The corrected pulse, with documented filter class, verified delta-v, and consistent sign convention, is then applied to the sled model and the resulting belt force and chest deflection traces are compared against the corresponding test channels.

Practical Checklist for Pulse Preparation

• Fix and document the sign convention (vehicle +X, frontal decel negative, or magnitude convention) before any processing.
• Remove bias, apply the specified CFC filter, and align time zero to the impact event.
• Integrate the filtered trace and confirm delta-v matches the test speed within a few percent; investigate truncation and tail behavior if it does not.
• Record peak acceleration, duration, and rise time, and check them against the integral for self-consistency.
• Inspect the spectrum; attenuate structural ringing that lies outside the occupant-relevant band, and document what was removed.
• Store the final pulse table with its filter class, delta-v, and sign convention alongside the occupant model so results remain reproducible.

With a verified pulse in hand, the occupant simulation has a defensible boundary condition. The next step is to understand how that pulse interacts with the restraint system and the occupant's kinematics — the subject of the following sections.