3. Crash pulse fundamentals

A crash pulse is the acceleration–time history measured at a defined point on a vehicle structure during an impact event. It is the single most important input to any crash load case, because it encodes the severity, duration, and frequency content of the event that the structure must survive. In model qualification, the pulse is not merely a boundary condition — it is the specification against which the model's fidelity is judged. This section establishes the mathematical relationships between acceleration, velocity, and displacement, explains how a pulse is characterized and parameterized, and shows how those parameters translate into a defensible load case definition.

From Acceleration to Velocity and Displacement

All three kinematic quantities are linked by integration, and the sign convention must be fixed before any calculation. Throughout this course we adopt the SAE J211 convention: acceleration is positive in the direction of the vehicle's forward motion, and the crash pulse is therefore predominantly negative (deceleration) during a frontal impact. A pulse measured in the opposite sense must be inverted before use, and the inversion must be documented — a sign error is one of the most common causes of a model that "passes" a pulse it should fail.

Given an acceleration history a(t), the velocity change and displacement follow directly:

Δv(t) = ∫₀ᵗ a(τ) dτ
s(t)  = ∫₀ᵗ Δv(τ) dτ = ∫₀ᵗ ∫₀^τ a(σ) dσ dτ

In practice these integrals are evaluated numerically on the sampled pulse. For a pulse sampled at uniform interval Δt, the trapezoidal rule is standard:

v[i] = v[i-1] + 0.5 * (a[i] + a[i-1]) * dt
s[i] = s[i-1] + 0.5 * (v[i] + v[i-1]) * dt

Two practical cautions apply. First, raw accelerometer data contains a DC offset and low-frequency drift; integrating an uncorrected signal produces a velocity that never returns to zero, which is physically impossible for a vehicle that comes to rest. The pulse must be high-pass filtered (commonly at 0.5–1 Hz for the velocity channel, per SAE J211 channel frequency classes) before integration. Second, the sampling rate must be high enough that the pulse's dominant frequency content is captured — a 10 kHz sample rate is typical for barrier pulses, and down-sampling to 1 kHz without anti-alias filtering will corrupt the peak and the impulse.

Characterizing a Pulse: The Parameters That Matter

A crash pulse is rarely a clean rectangle. It rises to a peak, may exhibit a secondary lobe, and decays over tens of milliseconds. The parameters used to define a load case are drawn from this shape:

• Peak acceleration — the maximum deceleration magnitude, governing inertial loads on components and occupants.
• Velocity change (Δv) — the integral of the pulse, representing the total momentum change; it is the primary severity metric for frontal and rear impacts.
• Pulse duration — the time over which the pulse acts, controlling the frequency band excited in the structure.
• Pulse shape — the temporal profile (e.g., half-sine, trapezoidal, or a measured multi-lobe history), which determines the spectral content and thus which structural modes are driven.
• Rise time and centroid — the time to peak and the impulse centroid, both of which influence occupant kinematics and restraint timing.

These parameters are not independent. For a given Δv, a short, high-amplitude pulse excites higher-frequency modes and produces larger peak forces; a long, low-amplitude pulse of the same Δv excites lower modes and produces smaller peak forces but larger displacements. This trade-off is the reason a load case cannot be specified by Δv alone.

How the Pulse Defines the Load Case

The load case is the complete specification of the pulse applied to the model, together with the boundary conditions and the response quantities to be extracted. A defensible definition includes: the pulse source (test measurement, regulatory corridor, or synthesized equivalent), the channel and filtering applied, the sign convention, the application point and direction, and the acceptance criteria on the model's response.

Consider a frontal 56 km/h full-width barrier event. The measured pulse might show a peak of approximately 40 g at 45 ms, a Δv of 15.6 m/s (56 km/h), and a duration of about 120 ms. A model qualification load case would apply this pulse at the rocker or sill, with the vehicle constrained against rigid ground, and would require the model's own acceleration at the same location to match the target within a defined corridor — typically ±10% on peak and ±5% on Δv, with a correlation metric such as the ISO/TS 18571 or a simple normalized integral difference.

The pulse also determines the displacement the structure must accommodate. Integrating twice gives the crush distance; for the example above, a trapezoidal pulse of 40 g over 120 ms yields a displacement on the order of 0.9 m, which must be consistent with the available crush space in the model. If the model's computed displacement diverges from the test, the discrepancy usually points to a boundary-condition error (e.g., a non-rigid barrier) or a mass/stiffness mismatch rather than a pulse-definition error.

Reading the Pulse–Response Relationship

The figure below shows how a single acceleration history propagates through integration to velocity and displacement, and how the pulse parameters map onto the load case definition. The key visual point is that the velocity curve is the area under the acceleration curve, and the displacement is the area under the velocity curve — so a small change in the pulse tail, where acceleration is low but duration is long, can materially change Δv and displacement even though the peak is unaffected.

Practical Construction of a Load Case from a Pulse

The workflow below is the one used in most OEM model-qualification groups. It is deliberately explicit because the failure modes are subtle.

1. Acquire and condition the pulse. Obtain the raw accelerometer channel, confirm the sample rate and the channel filter class, and apply the SAE J211 high-pass filter to the velocity channel. Record the filter corner frequency in the load case metadata.
2. Verify the integral. Integrate to velocity and check that the final velocity returns to zero within a tolerance (typically < 0.5 m/s residual). A non-zero residual indicates drift or a truncated pulse; extend the integration window or re-filter.
3. Extract the parameters. Compute peak, Δv, duration, rise time, and impulse centroid. Store them alongside the pulse so the load case is self-describing.
4. Apply to the model. Define the application point, direction, and the rigid boundary. For a full-width barrier, the pulse is applied at the sill or rocker; for a sled test, at the sled table. The application point must match the measurement point, or the comparison is invalid.
5. Compare and judge. Extract the model's acceleration at the same location, integrate it identically, and compare peak, Δv, and the correlation metric. A model that matches peak but not Δv is usually too stiff; one that matches Δv but not peak is usually too soft or has a mass error.

Common Failure Symptoms and Their Diagnosis

The central lesson is that a crash pulse is a complete kinematic description, not a single number. Peak, Δv, duration, and shape each constrain a different aspect of the model's response, and a load case that specifies only one of them is under-determined. When the pulse is conditioned correctly, integrated consistently, and applied at the correct point with the correct sign convention, it becomes a reproducible specification — one that a different engineer, on a different day, can apply to the same model and obtain the same verdict.