2. Crash test event physics and measurement requirements

A crash test is a short, violent, and highly non-linear event. A full frontal barrier impact at 56 km/h is essentially over in 100–150 ms, yet within that window the vehicle body decelerates at 30–60 g, the occupant compartment deforms by hundreds of millimetres, and the occupant moves forward relative to the vehicle by 300–500 mm before the restraint system arrests the motion. Every specification in a crash test data acquisition system — sample rate, anti-alias filter corner, channel count, sensor range, trigger logic, and data retention window — is ultimately derived from the physics of this event. This chapter builds the chain of reasoning from physical phenomena to DAQ requirements.

Impact Pulse: The Primary Forcing Function

The impact pulse is the acceleration–time history measured on a rigid, non-deforming part of the vehicle structure (typically the sill, tunnel, or rear seat cross-member). It is the primary forcing function that drives everything else: occupant kinematics, restraint deployment timing, and structural deformation. A typical frontal barrier pulse rises from 0 g to a first peak of 25–40 g within 10–20 ms, then oscillates as the crumple zone collapses in stages, and decays to near zero by 120–150 ms.

The frequency content of this pulse dictates the DAQ bandwidth. A pulse with a 10 ms rise time has significant energy up to approximately 1/(π·t_rise) ≈ 32 Hz, but the sharp structural ringing superimposed on the pulse — caused by local panel vibration and sensor mounting resonance — extends to 1–2 kHz. To capture the pulse shape without distortion, the DAQ must have a flat frequency response to at least 1 kHz, which in practice means a sample rate of 10 kHz or higher per channel (5–10× the highest frequency of interest) and an anti-alias filter with a corner frequency of 1–2 kHz. The commonly used SAE J211 standard specifies a channel filter class (CFC 60, CFC 180, CFC 600, CFC 1000) that defines the acceptable frequency response envelope; CFC 600 is typical for structural acceleration, while CFC 180 is used for occupant chest acceleration.

Deformation: Measuring Structural Collapse

Deformation measurement answers a different question: how far did the structure crush, and at what rate? This is measured with displacement sensors (string potentiometers, LVDTs, or optical systems) and with strain gauges on structural members. The deformation signal is typically much lower frequency than the acceleration signal — the crush stroke develops over 50–100 ms, so the fundamental frequency is below 20 Hz. However, the rate of deformation (velocity) and the onset of deformation (when the bumper first contacts the barrier) require higher bandwidth to resolve.

The practical implication is that deformation channels can often be sampled at 1–2 kHz, but they must be time-synchronized with the acceleration channels to within 0.1 ms. This synchronization requirement is what drives the use of a common clock and a hardware trigger across all channels in the DAQ.

Occupant Kinematics: The Human Response

Occupant kinematics are measured with accelerometers and load cells on the ATD (Anthropomorphic Test Device, or crash test dummy). The key signals are:

• Head acceleration — triaxial, CFC 1000, range ±500 g, used to compute HIC (Head Injury Criterion).
• Chest acceleration — triaxial, CFC 180, range ±200 g, used for chest deflection and 3 ms clip.
• Pelvis acceleration — triaxial, CFC 600, range ±200 g.
• Femur load — uniaxial load cell, range 10–20 kN, CFC 600.
• Seat belt load — load cell, range 10–20 kN, CFC 600.

The occupant signals have a different frequency signature than the structural signals. Head acceleration during a hard impact can contain energy up to 1 kHz because the head is a relatively light mass on a stiff neck, and the contact with the airbag or steering wheel produces sharp spikes. Chest acceleration, by contrast, is dominated by the mass–spring behaviour of the rib cage and is typically below 200 Hz. This is why different CFC classes are applied to different channels — a single filter setting for all channels would either over-filter the head or under-filter the chest.

Derived Signals and Their DAQ Implications

Many injury criteria are not measured directly but derived from the raw signals. HIC, for example, is computed from the resultant head acceleration:

HIC = max over t1,t2 of [ (1/(t2-t1)) * ∫ a_resultant dt ]^2.5 * (t2-t1)
where a_resultant is in g, and t2-t1 ≤ 36 ms

This derivation is sensitive to the integration window and to any DC offset or drift in the acceleration signal. A 0.5 g offset in a 50 g signal can shift HIC by 5–10%. Therefore, the DAQ must have excellent DC stability, and the accelerometers must be zeroed immediately before the test. The DAQ must also record a pre-trigger window (typically 100–200 ms) so that the zero-offset can be verified and the integration can start from a known baseline.

Similarly, chest deflection is derived from the difference between chest acceleration and a reference acceleration, or measured directly with a chest deflection sensor. The derivation requires that both channels be sampled simultaneously and have matched filter characteristics. Any phase mismatch between channels introduces error in the derived deflection.

From Physics to DAQ Specification

The following table summarizes how each physical phenomenon maps to a DAQ requirement. This is the core engineering translation that this chapter establishes.

Physical Phenomenon	Typical Frequency Content	Required CFC	Minimum Sample Rate	Typical Sensor Range
Structural impact pulse	DC–600 Hz	CFC 600	10 kHz	±500 g
Structural deformation	DC–20 Hz	CFC 60	1–2 kHz	0–500 mm
Head acceleration	DC–1000 Hz	CFC 1000	20 kHz	±500 g
Chest acceleration	DC–180 Hz	CFC 180	5 kHz	±200 g
Femur load	DC–600 Hz	CFC 600	10 kHz	0–20 kN
Belt load	DC–600 Hz	CFC 600	10 kHz	0–20 kN

Trigger and Timing Requirements

The event trigger is typically derived from a contact switch on the barrier or from a pre-trigger acceleration threshold (e.g., 3 g on the vehicle sill). The trigger must fire the DAQ within 1 ms of the actual impact, and the pre-trigger buffer must retain at least 100 ms of data before the trigger point. This ensures that the zero-offset and the initial rise of the pulse are captured.

All channels must be sampled on a common clock. If different channels use different sample rates, they must be resampled to a common time base before any derived calculation. The time alignment error between any two channels must be less than 0.1 ms, which corresponds to less than 1 sample at 10 kHz. This is achieved by using a single ADC with multiplexed inputs or by using multiple ADCs with a shared sample clock and synchronized start.

Summary of Engineering Translation

The central engineering skill in crash test DAQ is the ability to read a test requirement — "measure head acceleration for HIC" — and translate it into a concrete channel specification: sensor type, range, CFC class, sample rate, filter setting, and trigger configuration. This translation is not arbitrary; it follows directly from the physics of the event. The impact pulse tells you the structural bandwidth. The deformation tells you the low-frequency content. The occupant kinematics tell you the high-frequency content and the DC stability requirement. The derived signals tell you the synchronization and pre-trigger requirements.

In the next chapter, we will apply this framework to the actual selection and configuration of sensors and DAQ hardware, including bridge completion, excitation, and calibration procedures.