Abstract

This project explores the mathematical foundations, derivations, and applications of some of the most important and foundational aerodynamics and fluid dynamics equations relevant to road vehicles. It also examines the historical development and growing relevance of road vehicle aerodynamics, highlighting the main phases of aerodynamic vehicle design as well as the major breakthroughs and advancements that have shaped modern aerodynamic design. It introduces, explains, and derives some of the most significant equations that govern the behavior of airflow over, around, and through road vehicles. Beyond the background and derivation of these equations, this research paper emphasizes the necessary assumptions and simplifications that apply to these equations and their role in the derivations to make the equations easier to solve without the use of computers. This project also explains how these equations model the behavior of air as it flows around road vehicles, and will discuss various methods that take advantage of these effects to increase fuel efficiency, performance, stability, and other attributes. This project also models a simplified full-size pickup truck inside of a cylindrical wind tunnel test section to model a simplified wind tunnel scenario using the viscous incompressible Navier-Stokes equations as the governing equations. This problem goes through all the setup steps, from defining regions and boundaries to prescribing an initial condition.

Advisor

Lester, Cynthia

Second Advisor

Bush, Michael

Department

Mathematics

Disciplines

Analysis | Applied Mathematics | Partial Differential Equations

Keywords

aerodynamics, car, streamline

Publication Date

2025

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis

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