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Accurate terrain models provide the chassis designer with a powerful tool to make informed design decisions early in the design process. It is beneficial to characterize the terrain as a stochastic process, allowing limitless amounts of synthetic terrain to be created from a small number of parameters. A continuous-state Markov chain is proposed as an alternative to the traditional discrete-state chain currently used in terrain modeling practice. For discrete-state chains, the profile transitions are quantized then characterized by a transition matrix (with many values). In contrast, the transition function of a continuous-state chain represents the probability density of transitioning between any two states in the continuum of terrain heights. The transition function developed in this work uses a location-scale distribution with polynomials modeling the parameters as functions of the current state.

Computationally efficient tire models are needed to meet the timing and accuracy demands of the iterative vehicle design process. Axisymmetric, circumferentially isotropic, planar, discretized models defined by their quasi-static constraint modes have been proposed that are parameterized by a single stiffness parameter and two shape parameters. These models predict the deformed shape independently from the overall tire stiffness and the forces acting on the tire, but the parameterization of these models is not well defined. This work develops an admissible domain of the shape parameters based on the deformation limitations of a physical tire, such that the tire stiffness properties cannot be negative, the deformed shape of the tire under quasi-static loading cannot be dominated by a single harmonic, and the low spatial frequency components must contribute more than higher frequency components to the overall tire shape.