Applications of the G-DataΔV™ System of Equations When Determining Total Velocity Change Resulting From Motor Vehicle Collisions
Authors: Ogden Jerry S. , Martonovich Mathew , Engle Courtney N. 
Published: February 2017

Modern methods for analyzing motor vehicle deformation rely upon a force-deflection analysis to determine deformation work energy. Current methods provide acceptable accuracy when calculating the velocity change of vehicles involved in a collision but require significant modification to accommodate oblique and low-velocity collision events. The existing algorythms require vehicle-specific structural stiffness coefficients for each colliding vehicle, determined from full-scale impact testing. The current database of vehicle structural stiffness values is generated mainly through government safety standard compliance testing and is quite extensive for frontal impacts involving passenger cars and many light trucks and SUVs. However, the database is devoid of specific crash testing necessary for deformation analysis of rear and side structures of many vehicles. Additionally, there remains a dearth of structural stiffness coefficients for heavy commercial vehicles, buses, recreational vehicles, heavy equipment and motorcycles, rendering the application of the current force-deflection analysis approach useless for many impacts involving such vehicles.
The research presented, known as the Generalized Deformation and Total Velocity Change System of Equations, or G-DaTAΔV™, develops an accurate, reliable and broadly-applicable system of equations requiring knowledge of the structural stiffness coefficients for only one vehicle, rather than both vehicles involved in a collision event, regardless of the impacted surfaces of the vehicle. The developed methodology is inclusive of non-passenger vehicles such as commercial vehicles and even motorcycles, and it also accommodates impacts with objects and surfaces not supported by the current structural stiffness coefficient database. The G-DaTAΔV™ system of equations incorporates the linear and rotational collision contributions resulting from conservative forces acting during the impact event. The contributions of the G-DaTAΔV™ system of equations are as follows:
1. Consideration of non-conservative contributions from tire-ground forces and inter-vehicular frictional energy dissipation commonly present during non-central collision configurations.
2. Ability to solve for collision energy of a two-vehicle system using a single structural stiffness for only one of the colliding vehicles using work/energy principles.
3. Determination of the total velocity change for a vehicle resulting from a given impact event, which results from conservative and non-conservative force contributions.
4. The ability to predict the time period to reach maximum force application during an impact event, allowing for the determination of the peak acceleration levels acting on each vehicle during an impact.
The results of applying the G-DaTAΔV™ to full-scale impact tests conducted as part of the RICSAC collision research will be presented. Additionally, analysis of real-world collision data obtained through the National Automotive Sampling System demonstrates a close correlation with the collision values recorded by the vehicle event data recorders (EDRs) as part of the supplemental restraint system airbag control moducles (ACM). Compared to other analysis methods currently used, determining the total velocity change of a vehicle due to a collision event is achieved with a higher level of both accuracy and precision when using the G-DaTAΔV™.
The generalized approach of the G-DaTAΔV™ applies to collisions ranging from the simple collinear impact configuration to the most rigorous conditions of offset and oblique impacts. The comprehensive formulation provides greater utility to the researcher or forensic analyst in determining the contributions of the vehicle-roadway-driver environment as it relates to real-world collision events and their effects on vehicle and highway safety.