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This paper presents the various features and operational properties of a two-dimensional mathematical model of crash victim motions. The earliest forms of this model can be traced to the early 1960s. Developmental work on two-dimensional models then continued both within the automotive industry and in independent organizations such as the Highway Safety Research Institute (HSRI). The most recent product of this activity is the MVMA two-dimensional mathematical crash victim simulation developed at HSRI for the Motor Vehicle Manufacturers Association. The features of this model include: 1. An eight mass representation of the human body where contact between the crash victim and the vehicle is represented in terms of independent force-deformation properties of the victim and the vehicle. 2. An extensible multi-joint neck and a realistically flexible shoulder joint. 3. A real-line representation of the vehicle interior or exterior where shape is given as a network of points. 4.

The influence of degraded steering and suspension components on open-loop vehicle performance at the limits of tire-road frictional coupling is examined in this paper. The major conclusion obtained is that, with the exception of the shock absorber in certain maneuvers, the range of limit performance exhibited by new cars, as derived from design differences, is much larger than the in-use changes in limit performance of individual vehicles deriving from degradation of steering and suspension system components. This result should lead to future studies in which: 1. The influence of steering and suspension system degradation in the nonlimit regime of vehicle operation is examined. 2. Equipment for on-the-vehicle evaluation of suspension damping is investigated. 3. Greater emphasis is placed on the degradation of tires and brakes.

This paper describes the development of an improved neck simulation that can be adapted to current anthropometric dummies. The primary goal of the neck design is to provide a reasonable simulation of human motion during impact while maintaining a simple, rugged structure. A synthesis of the current literature on cervical spine mechanics was incorporated with the results of x-ray studies of cervical spine mobility in human volunteers and with the analysis of head-neck motions in human volunteer sled tests to provide a background for the design and evaluation of neck models. Development tests on neck simulations were carried out using a small impact sled. Tests on the final prototype simulation were also performed with a dummy on a large impact sled. Both accelerometers and high-speed movies were used for performance evaluation.

During recent years, the Highway Safety Research Institute (HSRI) has developed and validated two- and three-dimensional models describing the motions and forces acting upon an occupant during a collision. These inexpensive-to-operate models are performing with approximately 90% accuracy in parametric studies of classical crash configurations. In our own validation procedures, contacts with automobile development and design groups, and discussions with federal agencies, certain shortcomings of mathematical modeling procedures have been isolated. These include primarily the inability of the user to determine and input data to the computer programs and also to specify force, motion, velocity, and acceleration output data in a form applicable to the various vehicle design, human tolerance, and compliance tasks for which the models have been developed.

This paper discusses the development of adequate criteria and evaluation methods for seat belt restraint design. These criteria should include the effect of seat belts in abdominal injury as well as head injury. It is concluded that belt load limiters and energy-absorbing devices should limit head-to-vehicle contact, ensure that the lap belt maintains proper contact with the bony pelvic girdle, and limit the belt loads. Studies are made of pulse shape and belt fabrics. Currently available mathematical models are used for the studies included in the paper.

A study has been conducted as an initial step in determining the differences observed between the motions of a living human impact sled test subject and a dummy test subject. The mechanism which is proposed for accomplishing this is the HSRI Two-Dimensional Mathematical Crash Victim Simulator. A series of measurements were taken on human test subjects, including classical and nonclassical anthropometric measurements, range of motion measurements for the joints, and maximum foot force measurements. A series of mathematical expressions has been used to predict body segment weight, centers of gravity, and moments of inertia using the results of the various body measurements. It was then possible to prepare a data set for use with the mathematical model.

Mathematical models of the human body subjected to an impact environment have been developed by many research groups in industry, government, private research organizations, and universities. In most cases, the models have not been verified by or compared with experimental results. The purpose of this paper is to show comparisons between the two- and three-dimensional crash victim simulators, which have been developed at the Highway Safety Research Institute of The University of Michigan, and front and side impact sled test results using anthropometric dummies.

An analysis is made of the influence of tire-mechanics characteristics on the behavior of an automobile undergoing maneuvers requiring the tires to produce combined longitudinal and lateral forces. The mathematical model employed to represent the vehicle incorporates wheel rotational degrees of freedom and relationships expressing the longitudinal and lateral tire shear force components as analytical functions of tire normal load, sideslip and inclination angles, and longitudinal slip. The tire shear force relationships, derived by extrapolating from existing theory for the traction mechanics of a freely rolling tire, agree qualitatively with available experimental data. Analog simulation results are examined to assess the influence on vehicle steering/braking response of variations of three parameters: lateral tire stiffness, longitudinal tire stiffness, and the coefficient of friction at the tire/road interface.

A series of mathematical models of the interaction between an occupant and the interior of a vehicle is presented. The following parameter studies using an eight-mass, two-dimensional model are discussed: belt material properties, belt slack, belt geometric configuration, and comparison of seats with and without headrests in rear impact. In addition, it is demonstrated by example that simple mathematical models can perform a valuable service in laying the groundwork for more sophisticated analytical and experimental work as well as yielding short term results. Finally, three-dimensional models are discussed. It is shown that a three-mass, three-dimensional model is a logical extension of current simulation efforts in order to provide insight into occupant response in oblique and lateral impact as well as nonsymmetric restraint systems.