Vehicle Braking Distance Model: Analysis and MATLAB Implementation

The vehicle braking distance model serves as a crucial tool for evaluating vehicle braking performance and safety, utilizing mathematical formulations to quantify stopping distances under various conditions. This model typically incorporates factors such as vehicle speed, friction coefficient, road surface conditions, and driver reaction time, facilitating vehicle design optimization and enhancing driving safety awareness.

Core Factor Analysis Initial Velocity: Braking distance is proportional to the square of vehicle speed - higher speeds result in significantly increased stopping distances. Friction Coefficient: The tire-road surface friction coefficient directly affects deceleration efficiency, with reduced coefficients on slippery surfaces leading to extended braking distances. Reaction Time: The delay between hazard recognition and brake application (typically 0.5-2 seconds) adds additional travel distance before braking begins.

Model Construction Approach Based on Newtonian dynamics, the braking process can be divided into two phases: Reaction Phase: Vehicle maintains constant velocity, distance = speed × reaction time. Braking Phase: Uniform deceleration to complete stop, distance = velocity²/(2×friction coefficient×gravitational acceleration). Total braking distance equals the sum of both phases, ultimately demonstrating the nonlinear relationship between speed and friction forces.

MATLAB Implementation Key Points Script development enables dynamic calculation of braking distances under various parameter combinations: Define input variables (e.g., velocity, friction coefficient) using symbolic variables or user input functions. Calculate reaction distance and braking distance segments separately using vectorized operations. Visualize results through plotting functions (e.g., speed-distance curves or 3D parameter impact diagrams) with customized axes labels and legends.

Extended Applications This model can be extended to test emergency braking algorithms in autonomous driving systems, or integrated with real-time data (such as vehicle sensors) for dynamic warning systems, further enhancing road safety. Parameter adjustments also enable simulation of extreme weather conditions or load variations affecting braking performance, using conditional statements and parameter sweeps for comprehensive analysis.