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**Accident Reconstruction Techniques and Accuracy**

- by Brian G. McHenry

©McHenry Software, Inc.

(Originally prepared and presented at an collision reconstruction seminar given at the NHMRC Road Accident Research Unit (RARU), Adelaide, Australia in May 1995 in response to a question by the RARU Director, Dr. A. Jack McLean, as to the accuracy of computerized collision reconstruction techniques)

Also located on McHenry Software website

- Some of the variables are related to the preservation of the Collision Evidence,
- Some are related to limitations in Available Specifications,
- Some are related to the choice of Collision Reconstruction Techniques which fall into two catagories:
- Damage-Based
- Trajectory Analysis

**Accident Evidence**

- The first group of variables related to an collision reconstruction are classified as collision evidence. These are the facts of the particular case and are variables only in that they are unique for a particular case and therefore they should only vary between cases. These items are not under the direct control of a collision reconstructionist except with respect to the reconstructionist's request for their documentation and/or memorialization. These form the basis for the reconstruction.

These items, once preserved, should not vary for a particular case. Many of these items, if not preserved or memorialized in photos or measurements by police or other investigators at the time of the collision, may be forever lost and unavailable to the collision reconstructionist. Their absence detracts from the attainable accuracy of any reconstruction technique.

The items which fall under the category of collision evidence include positions of rest, tire marks, roadway markings, damage to vehicles, and damage to property. The memorialization of these items may vary widely between cases. First the collision investigator (normally the police) must identify the important aspects required to permit a detailed reconstruction. The determination of the requirements of a reconstruction may occur while many more important things are being handled, like life-saving and the restoration of a safe environment to the collision site. The investigator must try to preserve as much of the evidence as possible. The use of photography in conjunction with paint markings to preserve the vehicles positions of rest, impact marking and debris might be the best technique until a sense of order is restored and a more thorough technique can begin. Of course, in many instances photographing a specific item of evidence before putting paint marks on it should be the preferable choice.

There is also a wide variety in techniques used to measure various items at the scene, varying from simple use of sight estimates and pacing of the approximate distances to the more accurate use of tape measures and even possible use of surveying type equipment. The variation in the accuracy of these techniques may detract from the ultimate accuracy of the speed estimates.

The vehicle damage data does not necessarily need to be preserved at the scene. Except for the possible use of extraction devices at the scene to remove the vehicle occupants, and/or additional damage which may occur during transit and/or at the storage facility, normally the vehicle damage will remain unchanged for weeks and/or years at a separate location while either waiting for repair or disposal. This may account for the wide popularity of the use of damage only collision reconstruction techniques by many collision investigators. The use of a damage-only based collision reconstruction should be considered a last resort technique to be used only in the absence of site data. Normal reconstruction techniques should include the consideration of both damage and scene data for a comprehensive reconstruction.

The measurement of the extent of vehicle damage is also subject to some variation. The variation of results of a damage-data based reconstruction is mainly due to differences in the reconstruction and interpretation techniques utilized than to the measurement devices used. The results for a generally competent measurement technique with string, level and measuring tape, compares favorably with those obtained by the use of survey-type measurement equipment applied with similar damage-based reconstruction equations.

It should be noted that many papers have been dedicated to the detailed measurement techniques and guidelines to properly document the damage produced to a vehicle as a result of a collision (e.g., Ref 33). Some of these guidelines are to account for recognized shortcomings of damage-only reconstruction techniques. For example, many reconstructionists include induced damage in their crush measurements in general and/or for narrow object contacts, particularly pole impacts, to compensate for shortcomings in the damage-based techniques. Consistency of measurement techniques is very important, particularly for case studies involving many collisions. Although the results may ultimately fall short of the desired accuracy, use of a consistent measurement protocol will lend itself to later corrective adjustments as more advanced techniques evolve.|

**Available Specifications**

- The next item to consider in the preparation of a reconstruction is the vehicle and other specifications. These form the numbers which go into the equations to permit applications of Newton's Laws for the reconstruction. As a brief review, Newton's Laws of motion are:

Newton's Laws of Motion- Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by some external force to change that state.
- The acceleration of a body is in the direction of, and proportional to, the force that produces it, and is inversely proportional to the mass of the body.
- To every force there is an equal and opposite reaction, or the mutual actions of two bodies are equal and opposite.

Other Specifications required for a reconstruction include approximation for roadway friction coefficients, wheel drag and wheel steer. These are used primarily for trajectory-based analysis where the friction coefficient, drag and steer on the vehicle as it travels from impact to rest are required to permit approximation of the kinetic energy dissipated.|

**Collision reconstruction techniques**

- Now that the investigator has all the items required the investigator must chose which collision reconstruction technique to use. The techniques for collision reconstruction vary widely in levels of sophistication and underlying simplifying assumptions. The choice of any technique will have related strengths and weaknesses. For the collision reconstructionist to obtain the most accurate reconstruction requires a careful evaluation and choice from the techniques available. The two general techniques for collision reconstruction are either damage-based or trajectory-based: |

**Damage-based reconstruction techniques**

- During the late '60's and early '70's, a number of technical papers in the field of highway safety indicated that reasonably accurate estimates of the speed-changes that occur in wide-contact collisions can be obtained through the use of simple linear relationships between the impact speed-change and the extent of residual crush (e.g., References 50-53, 3). While such relationships obviously constitute a gross simplification of complex automobile structures, they were found to be capable of yielding impact speed-change results with approximately a plus or minus 10 percent accuracy when applied to a limited number of staged collisions (e.g., Reference 46). In a more comprehensive evaluation (Reference 54), it was found that the 95 percent confidence limits on individual calculations of delta-V ranged from 9 to 25 percent.

The current state-of-the-art of damage-based only reconstruction techniques are inadequate for individual case reconstructions. The basic premise of damagebased only reconstruction techniques is an assumption of a linear delta-V vs. residual crush "virtual" relationship (e.g., Ref 34, 17, etc.) (The term "virtual" is used to emphasize the fact that the crush energy is dissipated during the dynamic crushing of the vehicles and that equating the residual (restituted or static) crush to the energy dissipated is a "virtual" relationship, i.e., they do not occur simultaneously). Many collision reconstructionists use a single full-scale crash test data point for a given vehicle, combined with an assumption regarding a "nodamage" intercept, to calculate custom-fitted coefficients for use in individual case reconstructions. This must be recognized as a crude "first-approximation" procedure. Any suggestion that the resulting coefficients constitute a reliable definition of the structural crush responses of a given vehicle is misleading and not in keeping with sound engineering practices and principles. Problems associated with the repeatability of full-scale crash test results which produce scatter, limit the reliability and accuracy of a single data point. Minimum scientific principles would require an absolute minimum of at least three data points. In response, some researchers are using techniques involving multiple crash tests on an individual vehicle to create multiple data points for a given vehicle (e.g., Ref 35). The problems associated with the reliability of the crash test procedure, the differences in the crush response characteristics of a pre-damaged vehicle vs. a "fresh" undamaged vehicle and the underlying assumption of the linearity of the "virtual" relationship of delta-V vs. residual crush still classify the damage-based only reconstruction as a crude "first-approximation" technique

For additional information please see our Review of CRASH damage analysis including a discussion of the NHTSA "reformulation" by Prasad and our recent SAE paper 97-0960 - Effects of Restitution in the Application of Crush Coefficients.

- During the late '60's and early '70's, a number of technical papers in the field of highway safety indicated that reasonably accurate estimates of the speed-changes that occur in wide-contact collisions can be obtained through the use of simple linear relationships between the impact speed-change and the extent of residual crush (e.g., References 50-53, 3). While such relationships obviously constitute a gross simplification of complex automobile structures, they were found to be capable of yielding impact speed-change results with approximately a plus or minus 10 percent accuracy when applied to a limited number of staged collisions (e.g., Reference 46). In a more comprehensive evaluation (Reference 54), it was found that the 95 percent confidence limits on individual calculations of delta-V ranged from 9 to 25 percent.

**Trajectory-based reconstruction techniques**

- The generalized concept behind trajectory-based reconstruction is as follows: On the basis of Newton's 2nd and 3rd laws, the total momentum of an isolated system of masses remain constant. This principal, which is referred to as the Conservation of Momentum, serves as the theoretical basis for reconstruction of impact speeds in vehicle-to-vehicle collisions. The principal stipulates that the system momentum preceding a collision and the system momentum after a collision, e.g. at separation, are conserved in the absence of external forces. Therefore, if we can determine the individual speeds and directions of motion that are required for each of the two partners in a collision to travel from separation to rest, then the direction and magnitude of this system momentum can be used to determine the magnitudes and directions of the velocities which must have existed prior to the collision, the impact velocities. (The magnitude of external forces produced by the tires and other possible sources (such as gouging and scraping of vehicle components on the ground) during the collision are normally small when compared to the magnitude of the forces of the collision, however they should not be totally ignored for a comprehensive reconstruction).

When vehicles separate after a collision, they move to rest positions against resistance forces produced primarily by tire-ground friction. Secondary contacts may also occur with roadside obstacles and/or terrain features which sometimes can play significant roles in the dissipation of kinetic energy and can also produce redirection of the spinout trajectories. The task of analyzing the total energy dissipated as the vehicles travel from separation to their positions of rest is essential in preparing a comprehensive trajectory-based reconstruction of the collision.

A trajectory-based analysis directly provides estimates of the impact speed-changes (delta-V) in the form of the differences between impact and separation velocities for each vehicle.

For additional information on trajectory analysis procedures please see our recent SAE paper 97-0949 - CRASH-97 - Refinement of the Trajectory Solution Procedure

- The generalized concept behind trajectory-based reconstruction is as follows: On the basis of Newton's 2nd and 3rd laws, the total momentum of an isolated system of masses remain constant. This principal, which is referred to as the Conservation of Momentum, serves as the theoretical basis for reconstruction of impact speeds in vehicle-to-vehicle collisions. The principal stipulates that the system momentum preceding a collision and the system momentum after a collision, e.g. at separation, are conserved in the absence of external forces. Therefore, if we can determine the individual speeds and directions of motion that are required for each of the two partners in a collision to travel from separation to rest, then the direction and magnitude of this system momentum can be used to determine the magnitudes and directions of the velocities which must have existed prior to the collision, the impact velocities. (The magnitude of external forces produced by the tires and other possible sources (such as gouging and scraping of vehicle components on the ground) during the collision are normally small when compared to the magnitude of the forces of the collision, however they should not be totally ignored for a comprehensive reconstruction).

**Summary**

- In summary, the choice of an collision reconstruction technique should always use all available information, both vehicle damage and scene information. The utilization of a particular technique for convenience and/or due to assumptions of consistently small average errors should be carefully scrutinized. Wherever possible, a technique which includes both scene and vehicle information should be used to perform an collision reconstruction. The process of reconstructing a collision must be seen as first collecting from the scene, police report and photos collision evidence, next obtaining from data sources available specifications, and then choosing an collision reconstruction technique to perform the best possible reconstruction for the data collected and time available.

- SAE paper 97-0949 - CRASH-97 - Refinement of the Trajectory Solution Procedure

SAE paper 97-0960 - Effects of Restitution in the Application of Crush Coefficients