Abstract—In Formula Student Automotive Engineering (FSAE) competition, traditional empirical design methods face challenges in quantifying the influence of vehicle geometric parameters on lap times, hindering precise optimization of dynamic performance. This study develops a lap time prediction methodology grounded in optimal control theory by establishing a three-degree-of-freedom (3-DOF) double-track vehicle dynamics model coupled with track constraints and nonlinear programming techniques. The minimum-lap-time optimal control problem is reformulated as a nonlinear programming problem and numerically resolved using the CasADi framework with the IPOPT solver, enabling systematic evaluation of track width, wheelbase, and front-to-rear axle load distribution on figure-eight skid pad performance. Results indicate that the proposed computational approach demonstrates a 10% deviation from empirical performance data yet effectively captures performance trends. A track width of 1,240 mm yields the shortest lap time (4.590 s), achieving a 1.6% improvement over the baseline configuration. Optimal steering agility emerges at a 1,580 mm wheelbase with a lap time of 4.557 s, while a 40% front axle load ratio facilitates the fastest lap (4.547 s) through controlled oversteer strategies. These findings reveal the underlying mechanisms through which dimensional parameters govern figure-eight maneuverability, providing theoretical guidance for parameter optimization in FSAE vehicle design.