R. Matthew Brach

A review of impact models for vehicle collision

Automobile accident reconstruction and vehicle collision analysis techniques generally separate vehicle collisions into three different phases: pre-impact, impact and post-impact. This paper will concern itself exclusively with the modeling of the impact phase, typically defined as the time the vehicles are in contact. Historically, two different modeling techniques have been applied to the impact of vehicles. Both of these techniques employ the impulse-momentum formulation of Newtons Second Law. The first relies exclusively on this principle coupled with friction and restitution to completely model the impact. The second method combines impulse-momentum with a relationship between crush geometry and energy loss to model the impact. Both methods ultimately produce the change in velocity, delta V, and other pertinent information about a collision. The concepts of impulse-momentum and energy loss as applied to vehicle collisions have been occasionally misrepresented and appear not always to be fully understood. This paper will present the application of these principles to collisions of two bodies in a plane. This relationship between the change in velocity and energy loss is investigated. A review and numerical comparison of several impact models is presented.

Modeling Combined Braking and Steering Tire Forces

The force distributed over the contact patch between a tire and a road surface is typically modeled in component form for dynamic simulations. The two components in the plane of the contact patch are the braking, or traction force, and the steering, or side or cornering force. A third force distributed over the contacts patch is the normal force, perpendicular to the road surface. The two tangential components in the plane of the road are usually modeled separately since they depend primarily on independent parameters, wheel slip and sideslip. Mathematical expressions found in the literature for each component include exponential functions, piecewise linear functions and the Bakker-Nyborg-Pacejka equations, among others. Because braking and steering frequently occur simultaneously and their resultant tangential force is limited by friction, the two components must be properly combined for a full range of the wheel slip and sideslip parameters. This paper examines the way in which these two components are combined for an existing approach known as the Nicolas-Comstock model. First, performance criteria for tire modeling are proposed. Then the Nicolas-Comstock model is examined relative to the criteria. As originally proposed, this model falls short of meeting the criteria over the full range of transverse and longitudinal wheel slip values and sideslip angles. A modified version of the Nicolas-Comstock model is presented that satisfies these performance criteria. Finally, comparisons are made of the Modified Nicolas-Comstock model to other combined tire force models and to existing tire force measurements.

Tire Models for Vehicle Dynamic Simulation and Accident Reconstruction

Various vehicle dynamic simulation software programs have been developed for use in reconstructing accidents. Typically these are used to analyze and reconstruct preimpact and postimpact vehicle motion. These simulation programs range from proprietary programs to commercially available packages. While the basic theory behind these simulations is Newtons laws of motion, some component modeling techniques differ from one program to another. This is particularly true of the modeling of tire force mechanics. Since tire forces control the vehicle motion predicted by a simulation, the tire mechanics model is a critical feature in simulation use, performance and accuracy. This is particularly true for accident reconstruction applications where vehicle motions can occur over wide ranging kinematic wheel conditions. Therefore a thorough understanding of the nature of tire forces is a necessary aspect of the proper formulation and use of a vehicle dynamics program. This paper includes a discussion of tire force terminology, tire force mechanics, the measurement and modeling of tire force components and combined tire force models currently used in simulation software for the reconstruction of accidents. The paper discusses the difference between the idealized tire force ellipse and an actual tire friction ellipse. Equations are presented for five tire force models from three different simulation programs. Each model uses a different method for computing tire forces for combined braking and steering. Some experimentally measured light vehicle tire properties are examined. Some tire force models begin with a specified level of braking force and use the friction ellipse to determine the corresponding steering force; this produces steering forces and a resultant tire force equal in magnitude to full skidding for combined steering and braking. Comparisons are presented of results from simulation programs using different tire models for vehicle motions involving two types of severe yaw. The comparisons in this paper are not of reconstructions where the user seeks initial conditions to match an existing trajectory. The first comparison is a hypothetical postimpact motion with a given initial velocity and initial angular velocity and the other is a sudden steer maneuver. In some cases, the simulations and their tire models predict the vehicle motion closely. In most cases, however, the results differ significantly between simulation programs. The example simulations presented in this paper are not intended to reflect the way vehicle dynamic simulation programs are used typically in accident reconstruction.

Crush Energy and Planar Impact Mechanics for Accident Reconstruction

This paper describes how the algorithm used in the third version of the Calspan Reconstruction of Accident Speeds on the Highway (CRASH3) and planar impact mechanics are both used to calculate energy loss and velocity changes of vehicle collisions. They intentionally solve the vehicle collision problem using completely different approaches, however, they should produce comparable results. One of the differences is that CRASH3 uses a correction factor for estimating the collision energy loss due to tangential effects whereas planar impact mechanics uses a common velocity condition in the tangential direction. In this paper, a comparison is made between how CRASH3 computes the energy loss of a collision and how this same energy loss is determined by planar impact mechanics. The main factors that control energy loss as calculated by CRASH3 are the determination of the PDOF (principal direction of force), definition of a common impact point of the two vehicles, the common normal velocity condition and the tangential correction factor. In the planar impact mechanics solution, the controlling factors are the definition of a crush surface, definition of a common impact point, common velocity conditions and the values of normal and tangential coefficients. Experimental collisions (RICSAC, Research Input for Computer Simulation of Automobile Collisions) are used to provide a basis for comparison. A method is proposed that exploits the features of both methods for vehicle accident reconstructions.

Residual Crush Energy Partitioning, Normal and Tangential Energy Losses

This paper relates the residual damage caused during a collision through the use of crush energy models and impact mechanics directly to the collision energy loss and vehicle velocity changes, DeltaV1 and DeltaV2. The simplest and most popular form of this crush energy relationship is a linear one and has been exploited for the purpose of accident reconstruction in the well known CRASH3 crush energy algorithm. Nonlinear forms of the relationship between residual crush and collision energy also have been developed. Speed reconstruction models that use the CRASH3 algorithm use point mass impact mechanics, a concept of equivalent mass, visual estimation of the Principle Direction of Force (PDOF) and a tangential correction factor to relate total crush energy to the collision DeltaV values. Most algorithms also are based on an assumption of a common velocity at the contact area between the vehicles. The use of point mass mechanics, equivalent mass, a tangential correction factor and zero restitution are unnecessarily restrictive and their use reduces the accuracy of the crush energy methods in crash reconstruction. The paper shows that planar impact mechanics can be adapted to significantly improve the rigor of using residual crush for crash reconstruction. Planar impact mechanics models the impulses and the changes in momentum of vehicles colliding in a plane including restitution of the collision at the inter-vehicular contact surface. Two impact coefficients are used, the (normal) coefficient of restitution and the (tangential) impulse ratio. The work of the normal component and tangential component of the crash impulse vector are individually associated with the crush energy and with the tangential energy loss and to each vehicle’s DeltaV. This work-energy association is referred to as partitioning of the collision energy loss. Partitioning is necessary in order to adapt planar impact mechanics to the CRASH3 measurement protocol. The paper also covers the proper approach to take restitution into account, both as it occurs in the barrier tests to determine each vehicle’s crush stiffness coefficients and as it occurs in the impact between two vehicles. Data from oblique frontal barrier crash tests by Struble-Welsh Engineering are used to assess the use of planar impact mechanics and the partitioning of energy loss into crush energy and tangential energy. The process of using crush energy in reconstructions is also discussed in the paper.

Analysis of High-Speed Sideswipe Collisions Using Data from Small Overlap Tests

Little experimental data have been reported in the crash reconstruction literature regarding high-speed sideswipe collisions. The Insurance Institute for Highway Safety (IIHS) conducted a series of high-speed, small overlap, vehicle-to-barrier and vehicle-to-vehicle crash tests for which the majority resulted in sideswipe collisions. A sideswipe collision is defined in this paper as a crash with non-zero, final relative tangential velocity over the vehicle-to-barrier or vehicle-to-vehicle contact surface; that is, sliding continues throughout the contact duration. Using analysis of video from 50 IIHS small overlap crash tests, each test was modeled using planar impact mechanics to determine which were classified as sideswipes and which were not. The test data were further evaluated to understand the nature of high-speed, small overlap, sideswipe collisions and establish appropriate parameter ranges that can aid in the process of accident reconstruction. An example reconstruction of a small overlap, sideswipe collision using optimization methods based on the planar impact mechanics model is included in the paper. The results of the example reconstruction show that the reconstruction method developed in the paper, using the physical evidence and EDR data, produces useful results. Language: en

Analysis of Collisions Involving Articulated Vehicles

In the vast majority of impacts involving light vehicles, traditional impulse-momentum collision models can be used to analyze the mechanics of two colliding vehicles. However, these models cannot handle the multiple degrees of freedom associated with articulated (pin-connected) vehicles. In addition, collisions involving one or two articulated vehicles may not satisfy the basic assumptions of these traditional collisions models. In particular, the assumption that impulses of external forces (such as tire-road friction) are negligible compared to the impulse developed over the crash surface may not be valid. The large masses, long dimensions, the presence of the pinned joint, or all of these factors, may necessitate special considerations and more flexible model capabilities. This paper lists the assumptions that underlie the application of the principle of impulse and momentum to a planar collision between rigid bodies. The general impact equations involving a pair of pinned rigid bodies are derived and presented. These equations form a set of linear algebraic equations that requires a numerical solution. An example is presented that demonstrates the need to include the capability of modeling the impulses of forces external to the intervehicular contact surface. Results of the model, correlated with data from a controlled experimental collision, follow the presentation of the equations. Another example is then presented that illustrates the application of a velocity constraint to one of the bodies.