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The objectives of this work are to conduct a comprehensive study of the methods for determining vehicle critical speed based on yaw marks and vehicle performance testing using lane-change maneuvers, then use this information to describe the relationship between critical speed and lane-change kinematics and to develop and validate an optimized emergency lane-change trajectory function, for the purpose of assessing vehicle emergency handling characteristics. The key applications, derivation, basic factors, and common factor measurement methods for the critical speed formula are presented. Yaw marks are defined and techniques for measuring them are described. The assessments of other authorities regarding the applicability and accuracy of the simple approach are presented and explained. Energy methods for determining vehicle speed are included to round out the description of alternative means for determining critical speed based on yaw marks. Background information is presented covering the utility of lane-change maneuvers, lane-change terminology, and known desired open-loop trajectories. Several techniques for assessing vehicle performance against an ideal trajectory are presented. Performance indices such as integral penalty (cost) functions are used for comparing candidate lane-change trajectories. The maximum constant velocity or critical speed is employed as an additional discriminator between the candidate paths. Functional analysis is employed to develop an ideal path for a vehicle undergoing an emergency lane-change maneuver. The problem is formulated using the calculus of variations. The solution technique relies on elliptic functions to achieve a closed-form solution. The concept of critical speed is employed to limit the maximum curvature of any specified lane-change, thereby ensuring that the synthesized trajectory describes a path that can be traversed under realistic road conditions. The analytical solution is confirmed by comparison to a numerical solution. Sensitivity analysis is conducted to analyze the effect of errors in coefficient of friction values on the closed-form optimal lane-change trajectory. The optimal trajectory function is validated by comparing, at two speeds, the optimal lane-change trajectories to trajectories produced by a validated nonlinear 8-DOF vehicle model with lagged tire forces, controlled by a nonlinear continuous-gain-optimized controller based on a 2-DOF linear vehicle model, subject to a step input signal for lateral displacement