Accident Reconstruction Physics

When two vehicles collide, the collision interval is so brief (typically 100-200 ms) that road friction on the tires contributes very little impulse compared with the contact force between the vehicles. This lets reconstructionists treat the event as a closed system and apply conservation of linear momentum: the combined momentum vector before impact equals the combined vector after. That equation, coupled with the measured post-impact travel paths, gives the pre-impact speeds.

The momentum method is most reliable when post-impact travel distances and directions are well-documented (tire marks, furrows, final rest positions). It yields the average approach speed rather than the instantaneous speed at any moment. It treats the two-vehicle system as a unit, which is appropriate for a common-direction collinear rear-end or a right-angle intersection collision. For oblique impacts the calculation is done in component form, resolving north-south and east-west momentum separately before recombining.

• Collinear rear-end: one equation, one unknown (the striking vehicle's speed if the struck vehicle's speed is known).
• Right-angle intersection: two component equations yield two unknowns (both pre-impact speeds) if the post-impact departure angle and distance are reliably measured.
• Oblique impact: requires resolving x and y components separately; a combined-mass assumption (perfectly plastic collision) is common unless the vehicles separate at distinct angles.

A skidding tire with wheels fully locked converts kinetic energy into heat through friction. The relationship between speed and skid distance is governed by the kinematics equation: Vf² = Vi² - 2 × a × d. If the vehicle is decelerating on a level surface with all four wheels locked, the deceleration a equals mu × g (the coefficient of friction times gravitational acceleration). Measuring skid-mark length and friction gives the minimum entry speed at the start of the skid.

Friction coefficient measurement is one of the most scrutinised aspects of reconstruction testimony. The preferred method uses a portable drag sled on the accident surface, or an instrumented test vehicle that brakes to a locked-wheel stop. Both must be done under conditions matching those at the accident (surface temperature, presence of sand or wetness, tire compound). The measured value is then tested for sensitivity: reconstructionists typically report a range rather than a single number, showing how speed changes when mu moves within its measured uncertainty band.

Not all deceleration marks are full-lockup skids. Modern vehicles with ABS brake without locking the wheels, leaving no classic dark rubber skid. ABS vehicles may leave scalloped or checkered deceleration scrubs, or no marks at all. In those cases, the reconstructionist must rely on EDR data, vehicle dynamics simulation, or other physical evidence rather than mark length.

Time-distance analysis reconstructs where each vehicle was at each moment leading up to impact. The output is a graphical or tabular sequence: vehicle A at location X at time T, vehicle B at location Y at time T, and the question answered: when did the hazard first become visible, and could a driver who reacted in normal time have avoided the crash?

Perception-reaction time (PRT) is built into every time-distance calculation. The Olson and Farber research, widely cited in US and Commonwealth practice, places the 85th-percentile PRT at 1.5 seconds for alert drivers responding to a simple, expected hazard. The value rises with complexity, surprise, and fatigue. AASHTO uses 2.5 seconds for highway geometric design to accommodate a wider range of the driver population. Expert witnesses routinely face cross-examination over which value is appropriate in a given fact pattern, making the underlying research literature important to know.

1. Identify the hazard-perception point
   Establish the location where a driver exercising reasonable attention would first have been able to see the hazard, accounting for sightlines, obstructions, and posted speed.
2. Apply PRT
   Calculate how far the vehicle travels during the PRT interval at the pre-braking speed. The vehicle is still accelerating or travelling at constant speed during this phase.
3. Add braking or avoidance distance
   Calculate the distance needed to stop or to steer clear given the surface friction and vehicle dynamics.
4. Compare to available stopping distance
   If PRT travel plus braking distance exceeds the hazard-perception distance, a reasonable driver could not have avoided the crash regardless of speed. If it is less, speed or reaction time are candidates for causation.

When a vehicle rounds a curve too fast, the lateral friction demand exceeds available grip and the tires slide sideways. The tires leave a characteristic curved scuff pattern called a critical speed yaw mark. Unlike a straight-line skid, which gives a minimum speed at the start, a yaw mark gives the speed at the time of the slide, and the calculation is simpler because it involves only the radius of curvature and the friction coefficient.

The critical speed formula is v = sqrt(r × g × mu), where r is the radius of curvature of the marks measured in the field, g is gravitational acceleration, and mu is the friction coefficient. Measuring the chord and middle ordinate of the curved mark on the pavement gives r. This method can be highly reliable when the marks are sharp and their geometry can be measured accurately, but it requires careful friction testing and the assumption that the vehicle was at the limit of lateral grip throughout the mark.

When an occupant is ejected from a vehicle, the person becomes a projectile governed by the same two-dimensional kinematics as any object launched at a height and angle. The reconstruction problem is to work backwards from the landing position to establish the ejection speed, which then informs the vehicle speed at the moment of ejection. Ejection analysis is also used to determine seatbelt use: an unbelted occupant leaves through the windshield or roof at approximately the vehicle's speed; a belted occupant stays inside.

The key measurements are the horizontal throw distance (from the likely ejection point on the vehicle to the body's landing position), the ejection height above the ground, and the ejection angle. The horizontal range equation yields the launch speed, which is typically close to the vehicle's speed at the moment of ejection. In rollover cases the ejection speed may be considerably lower than the initial vehicle speed if the vehicle has already decelerated through partial rolling before ejection occurs. SAE technical papers, particularly those in the Accident Reconstruction series, document the range of measured ejection trajectories from staged tests.

SAE International publishes the Collision Reconstruction Methodologies series as the technical framework governing collision reconstruction practice. These volumes cover the mathematical models, the input measurements required, and the sensitivity analyses expected of a competent reconstructionist. The series is not a rigid recipe but a performance framework: it tells practitioners what their analysis must show and what its limitations must acknowledge, rather than prescribing a single method for every situation.

The SAE Dictionary of Vehicle Accident Reconstruction and Automotive Safety provides the shared vocabulary. Terms like delta-V, closing speed, approach speed, departure angle, and rest position all have precise SAE-standardised definitions that reconstructionists and attorneys are expected to use consistently. Departures from standard terminology during testimony are frequently the opening for a Daubert or Frye challenge to the expert's methodology.

• J2980 requires explicit documentation of all input measurements, their sources, and their uncertainty.
• The standard calls for sensitivity analysis: the expert must show how the speed estimate changes as key inputs (mu, rest position) vary within their measurement ranges.
• Results are reported as a range, not a single value, reflecting the combined input uncertainties.
• Peer-reviewed validation of the specific methods used (momentum, crush energy, yaw) must be cited or demonstrated when challenged.