Hybrid STOL Aircraft Designed for Short Urban Operations
Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
individual
Campus
Daytona Beach
Authors' Class Standing
Kassandra Durst, Senior
Lead Presenter's Name
Kassandra Durst
Lead Presenter's College
DB College of Engineering
Faculty Mentor Name
Ronald Adams
Abstract
This capstone project investigates the mathematical foundations of shock wave formation. Shock waves are abrupt, propagating disturbances in a compressible fluid like air or water, characterized by a near-instantaneous change in pressure, density, and velocity. The analysis centers on the mathematical framework governing these nonlinear waves, particularly hyperbolic conservation laws. The method of characteristics reveals how intersecting characteristics produce discontinuities, representing shock waves. The Rankine-Hugoniot jump conditions are examined, providing precise relationships between physical quantities across the shock front. Entropy conditions, essential for selecting physically admissible solutions, are also discussed. A deeper understanding of aerodynamic phenomena, specifically supersonic flows where shock waves are prominent, is achieved through these mathematical principles. This project demonstrates how a rigorous mathematical foundation improves the ability to model and predict shock wave behavior, contributing to advancements in aerodynamic design and analysis.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Hybrid STOL Aircraft Designed for Short Urban Operations
This capstone project investigates the mathematical foundations of shock wave formation. Shock waves are abrupt, propagating disturbances in a compressible fluid like air or water, characterized by a near-instantaneous change in pressure, density, and velocity. The analysis centers on the mathematical framework governing these nonlinear waves, particularly hyperbolic conservation laws. The method of characteristics reveals how intersecting characteristics produce discontinuities, representing shock waves. The Rankine-Hugoniot jump conditions are examined, providing precise relationships between physical quantities across the shock front. Entropy conditions, essential for selecting physically admissible solutions, are also discussed. A deeper understanding of aerodynamic phenomena, specifically supersonic flows where shock waves are prominent, is achieved through these mathematical principles. This project demonstrates how a rigorous mathematical foundation improves the ability to model and predict shock wave behavior, contributing to advancements in aerodynamic design and analysis.