3. Rear impact crash pulse characterization

Rear impact protection engineering begins with the crash pulse. The pulse is the acceleration–time history that the struck vehicle experiences at its structure during and immediately after the collision. Everything downstream — seatback rotation, head restraint engagement, neck loading, and the resulting risk of whiplash-associated disorders — is a response to that pulse. Two vehicles with the same closing speed can produce very different occupant outcomes if their pulses differ in shape, duration, or peak level. This chapter defines the pulse parameters that matter, shows how they are derived and measured, and explains how each one propagates into occupant kinematics.

3.1 Delta-v: The Velocity Change Budget

Delta-v (Δv) is the change in velocity of the struck vehicle over the collision, expressed in km/h or m/s. For a rear impact, it is the difference between the vehicle's velocity just before impact and its velocity after the collision has ended and both vehicles have separated or reached a common velocity. Delta-v is the single most cited severity metric in rear impact research because it correlates strongly with occupant injury risk and is relatively easy to reconstruct from vehicle damage or event data recorder (EDR) output.

For a simplified central rear impact where the struck vehicle is initially stationary and the bullet vehicle mass is much larger, the momentum-based estimate is:

Δv_struck = (m_bullet / (m_bullet + m_struck)) × (1 + e) × v_closing

where:
  m_bullet   = mass of striking vehicle (kg)
  m_struck   = mass of struck vehicle (kg)
  e          = coefficient of restitution (0 to 1)
  v_closing  = closing speed at first contact (m/s)

As a worked example, consider a 1,600 kg bullet vehicle striking a stationary 1,400 kg struck vehicle at a closing speed of 30 km/h (8.33 m/s) with a restitution coefficient of 0.2. The struck vehicle's delta-v is approximately (1600 / 3000) × 1.2 × 8.33 ≈ 5.33 m/s, or about 19.2 km/h. This is a moderate-severity rear impact — well within the range where whiplash injuries are commonly reported, even without structural intrusion.

Delta-v alone does not determine injury risk. A 20 km/h delta-v delivered over 80 ms produces different neck loading than the same delta-v delivered over 150 ms. Pulse duration and shape must be considered together with delta-v.

3.2 Acceleration–Time History and Pulse Shape

The acceleration–time history a(t) is the instantaneous longitudinal acceleration measured at a structural point on the struck vehicle, typically the sill, tunnel, or rear crossmember. By convention in rear impact analysis, the struck vehicle is accelerated forward (positive x-direction), so the pulse is predominantly positive. The velocity change is the integral of acceleration over the pulse duration:

Δv = ∫ a(t) dt   (integrated from t = 0 to t = t_end)

Real rear impact pulses are not square waves. They rise rapidly to a peak, then decay with oscillations caused by structural resonance, bumper system behavior, and vehicle pitch. The shape is often characterized by three parameters: peak acceleration (in g), pulse duration (time from first significant acceleration to return to near zero), and the effective or equivalent square wave duration, defined as:

t_eff = Δv / a_peak

A pulse with a high peak and short duration is "sharp"; one with a lower peak and longer duration is "soft." Both can produce the same delta-v, but they load the occupant's neck differently. Sharp pulses tend to produce higher head acceleration peaks and greater relative head-to-torso motion, while soft pulses allow more time for the seat and head restraint to engage and distribute the load.

3.3 Pulse Duration and Its Role

Pulse duration in rear impacts typically ranges from about 60 ms for stiff, high-speed collisions to over 200 ms for low-speed bumper engagements. Duration matters because the occupant's head and torso do not accelerate instantaneously with the vehicle. The seatback pushes the torso forward first; the head, restrained only by the neck, lags behind. This creates relative motion between head and torso — the classic whiplash mechanism.

If the pulse is short relative to the natural response time of the head–neck system (roughly 100–150 ms for the head to reach peak rearward excursion), the head may still be moving rearward relative to the torso when the pulse ends. The subsequent rebound and the timing of head restraint contact determine the peak neck forces and moments. A longer pulse gives the head restraint more time to arrest head motion before the torso begins to rebound, generally reducing peak neck loading.

3.4 From Pulse to Occupant Kinematics

The chain from pulse to injury is a sequence of mechanical events. The figure below shows the signal chain and the key parameters at each stage.

Rear Impact Pulse → Occupant Kinematics Signal Chain Crash Pulse a(t) at struck vehicle Δv, a_peak, t_dur pulse shape rise time, oscillations Seat / Structure Input seatback rotation seat cushion travel head restraint position backset, height Torso Kinematics torso acceleration torso velocity torso displacement seatback deflection Head–Neck relative head motion neck forces neck moments Pulse Parameter Influence on Occupant Response Higher Δv ↑ torso velocity change ↑ head excursion Shorter Duration ↑ peak neck load ↓ time for restraint Higher Peak a ↑ head acceleration ↑ neck shear force Injury Risk: Whiplash-Associated Disorders neck strain, facet joint loading, ligament elongation Key timing: head restraint contact should occur before peak torso rebound to minimize relative head–torso motion. Backset and restraint height determine engagement timing; pulse duration determines whether engagement is early or late.

The chain begins with the crash pulse. The pulse's delta-v sets the total velocity change the torso must undergo. The pulse's duration and shape determine how quickly that velocity change is imposed. The seat and head restraint then transmit the pulse to the torso and head. If the head restraint is positioned correctly and the pulse is long enough, the head is arrested before it reaches extreme rearward excursion. If the pulse is short and sharp, the head may still be accelerating rearward when the torso begins to rebound forward, producing a rapid reversal in neck loading — the condition most strongly associated with soft tissue injury.

3.5 Practical Measurement and Reconstruction

In vehicle testing, the pulse is measured with accelerometers mounted on the struck vehicle's sill or tunnel. The raw signal is filtered per SAE J211 (Channel Frequency Class 60 for vehicle structure, CFC 600 for occupant response) and integrated to obtain velocity. In reconstruction, EDR data or damage-based methods may be used. A typical low-speed rear impact test might yield a pulse with a peak of 8–12 g, a duration of 100–150 ms, and a delta-v of 15–25 km/h.

When comparing pulses, always confirm the filtering class and the mounting location. An unfiltered or differently filtered signal can change the apparent peak by 20–30%, which directly affects any injury-risk assessment or restraint design decision.

3.6 Summary

Delta-v defines the severity budget; acceleration–time history defines how that budget is delivered; pulse duration and shape determine whether the occupant's head and neck can be managed by the seat and head restraint. For rear impact protection engineering, the design target is not merely to reduce delta-v — that is largely set by the collision — but to ensure that the restraint system engages early enough and distributes load over a long enough interval to keep relative head–torso motion and neck loading within tolerable limits. The next chapter examines how seat and head restraint design parameters are tuned to achieve that goal.

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