EFFECTS OF COUPLED GEOMETRIC SCALING AND POLYNOMIAL SURFACE CURVATURE ON AERODYNAMIC DRAG AND ENERGY LOSS IN SIMPLIFIED VEHICLE GEOMETRIES

This study investigates the aerodynamic performance and drag-induced energy loss of three-dimensional parabolic vehicle geometries under controlled flow conditions. Four polynomial profiles, represented by y = h - ax², were created in CAD with coupled changes in peak height (h) and curvature coefficient (a), ranging from Model 1 (h = 2.0, a = 0.02) to Model 4 (h = 5.0, a = 0.05). Computational scripts executed in Google Colab were used to evaluate frontal area, drag coefficient (Cd), aerodynamic drag force, and drag-induced energy loss at a constant Reynolds number of approximately 2.3 × 10⁷.
Across the four configurations, increases in geometric scale were accompanied by increases in frontal area and drag coefficient. Model 1, with a frontal area of 12.566 m², produced the lowest Cd of 0.162, drag force of 273.80 N and energy loss of 410.69 kJ. Model 4, with a frontal area of 78.540 m², produced the highest Cd of 0.237, drag force of 2500.01 N and energy loss of 3750.01 kJ.
The results show that steeper and larger parabolic profiles within the tested configuration set were associated with greater aerodynamic resistance and energy demand. Because geometric scale, frontal area, and curvature changed simultaneously, their individual effects cannot be fully separated from the data. The study should therefore be interpreted as a preliminary computational investigation of coupled geometric-scaling effects, providing a baseline for future constant-area curvature studies, validated CFD simulations, and early-stage aerodynamic design of energy-efficient transport geometries.
Investigating the Combined Influence of Geometric Scale and Polynomial Surface Curvature on Aerodynamic Drag and Drag-Induced Energy Loss.
Research Question
To what extent do coupled changes in geometric scale and polynomial surface curvature, represented by changes in peak height (h) and curvature coefficient (a) in simplified vehicle profiles (y = h - ax²), influence frontal area, aerodynamic drag coefficient (Cd), aerodynamic drag force, and drag-induced energy loss (Eloss) under constant flow conditions?
Objective
The primary objective of this investigation is to determine how coupled changes in geometric scale and polynomial surface curvature, represented by the function y = h - ax², affect aerodynamic performance. Using CAD and custom computational processing, the study compares vehicle models with different profile heights (h) and curvature coefficients (a) to evaluate their combined influence on frontal area, drag coefficient (Cd), aerodynamic drag force, and drag-induced energy loss (Eloss) under constant-flow conditions. Because h and a vary simultaneously between models, the investigation examines their coupled effect rather than treating either variable as independently isolated.