2. Crash pulse characterization

A crash pulse is the acceleration–time history that a vehicle body, seat, or occupant restraint experiences during an impact. In a sled testing program, the pulse is not merely a recorded signal — it is the specification that the sled must reproduce. Before a single test is run, the engineer must convert a reference event (a full-vehicle barrier test, a regulatory corridor, or a component-level requirement) into a set of quantitative descriptors that fully define the target. This chapter covers those descriptors: acceleration–time history, velocity change (Δv), displacement, pulse duration, centroid time, and the energy metrics that tie them together.

Sign Convention and Coordinate Frame

Every pulse descriptor depends on a consistent sign convention. Throughout this course we adopt the SAE J211 convention for a vehicle-fixed longitudinal axis: positive x is forward (toward the front of the vehicle). During a frontal impact the vehicle decelerates, so the measured longitudinal acceleration is negative. Sled facilities, however, frequently invert the sign so that the pulse appears as a positive "crash pulse" for readability. This is a presentation choice only. The rule is simple: declare the convention once, and keep it consistent across the target pulse, the sled command, and the measured response. Mixing conventions is one of the most common sources of sign errors in pulse replication.

The Acceleration–Time History

The acceleration–time history a(t) is the primary signal. It is sampled at a defined rate (typically 10 kHz for sled work, filtered per SAE J211 Channel Frequency Class 60 or CFC 180 depending on the application) and stored as a time series. From this single curve, every other descriptor is derived by integration or by inspection. A well-characterized pulse therefore begins with a clean, correctly filtered a(t).

Key features to identify on the curve include the rise time to peak, the peak acceleration a_max, any secondary peaks or oscillations, and the point at which the pulse effectively returns to zero. These features determine how demanding the pulse will be for the sled's deceleration or propulsion system.

Velocity Change (Δv)

Velocity change is the integral of acceleration over the pulse duration:

Δv = ∫ a(t) dt   (integrated from t_start to t_end)

Δv is the single most important scalar for matching a real crash. A frontal rigid-barrier test at 56 km/h produces a Δv of approximately 15.6 m/s (56 km/h), because the vehicle goes from initial speed to rest. For a sled, Δv defines the total momentum the system must absorb. If the sled's measured Δv differs from the target by more than a few percent, the pulse is not representative regardless of how well the peak matches.

Displacement

Displacement is the double integral of acceleration:

s(t) = ∫∫ a(t) dt dt

In a full-vehicle crash, displacement represents the crush distance of the vehicle structure. In a sled test, it represents the stroke the sled carriage travels during the pulse. Displacement is critical for facility planning: it sets the minimum track length and the required stroke of the deceleration device (e.g., a hydraulic damper or a crush tube). A pulse with a long duration and high Δv will demand a long stroke; if the sled track is too short, the pulse cannot be reproduced and the test is invalid.

Pulse Duration

Pulse duration T is the time interval over which the pulse acts. It is usually defined between the points where acceleration first exceeds and finally falls below a small threshold (e.g., 0.5 g or 5% of peak). Duration controls the shape of the pulse: for a given Δv, a short duration forces a high peak acceleration, while a long duration allows a lower peak. This trade-off is the central constraint in pulse replication.

Centroid Time

The centroid time t_c is the time-weighted center of the pulse:

t_c = ∫ t · a(t) dt / ∫ a(t) dt

It indicates where the "mass" of the acceleration is concentrated within the pulse. A pulse with a centroid early in its duration delivers its energy quickly (a sharp, front-loaded pulse), while a late centroid indicates a more gradual build-up. Centroid time is a sensitive shape descriptor: two pulses with identical Δv, peak, and duration can produce different occupant responses if their centroids differ. Matching t_c is therefore part of matching the pulse, not an optional refinement.

Energy Metrics

Several energy-related metrics are used to define target pulses. The most common are:

• Kinetic energy change: ΔE = ½ m Δv², the energy the sled must dissipate.
• Energy spectral density (ESD): the energy content of the pulse as a function of frequency, useful for identifying which frequency bands dominate and for comparing pulses that look similar in the time domain.
• Crash energy or absorbed energy: the integral of force over displacement, used when the pulse is paired with a structural crush model.

Energy metrics matter because two pulses can share Δv and peak but differ in how abruptly energy is delivered. A pulse with high ESD at low frequencies tends to produce larger occupant excursions; a pulse with energy concentrated at high frequencies may excite structural resonances. For sled programs, the ESD is often used as a secondary acceptance criterion alongside the time-domain descriptors.

Putting the Descriptors Together

The figure below shows how the descriptors relate to one another on a single acceleration–time history. The curve is integrated to obtain velocity and displacement, and the centroid and duration are marked directly on the time axis.

Worked Example: Deriving Descriptors from a Sampled Pulse

Suppose a reference pulse is provided as a table of acceleration versus time, sampled at 1 ms intervals, with the following simplified values (positive presentation, frontal impact):

Using the trapezoidal rule with g = 9.81 m/s²:

• Δv ≈ 9.81 × (0.5×10 + 20 + 35 + 30 + 18 + 8 + 2 + 0.5×0) × 10⁻³ ≈ 9.81 × 0.113 ≈ 1.11 m/s per unit mass (for this short illustrative segment).
• Peak = 35 g at t = 20 ms.
• Duration ≈ 70 ms (threshold 0.5 g).
• Centroid ≈ 22 ms, indicating a slightly front-loaded pulse.

These values are illustrative only. In practice, the integration is performed numerically on the full sampled record, and the results are compared against the target corridor. If Δv is low, the pulse is too weak; if the centroid is too early, the pulse is too front-loaded and may over-excite the occupant early in the event.

Summary of Descriptors

With these descriptors defined, the next step in a sled program is to translate them into a command signal for the sled's deceleration or propulsion system. That translation — and the tolerances applied to each descriptor — determines whether the replicated pulse is accepted as a valid representation of the reference event.