Wolfram Library Archive

All Collections Articles Books Conference Proceedings
Courseware Demos MathSource Technical Notes
Title Downloads

Airfoil Aerodynamics

Richard L. Fearn
Organization: University of Florida
Department: Mechanical and Aerospace Engineering
Revision date


This collection of documents uses interactive graphics powered by Mathematica (version 11.01) to illustrate the use of complex analysis to solve the classical problem of potential flow over Joukowski airfoils. This collection of six documents.

Preface: Some of conventions of Mathematica, and assumptions about the reader’s background are discussed.

Table of Contents: A list hyperlinks to documents and major sections serve as a roadmap.

1 Review of Vector Fields: A brief and elementary review of vector fields includes illustrations using Mathematica functions.

2 Introduction to Complex Analysis: The basic tools of complex analysis used in airfoil aerodynamics are discussed. Five interactive figures illustrate: modular surfaces. Pólya vector fields for a selection of complex functions. Pólya vector field for a combined source and vortex. complex mapping for a selection of complex functions. mapping at critical points.

3 Review of 2-D Potential Flow: A brief review of potential flow emphasizing the use of complex analysis including an interactive graph for potential flow over a centered unit circle with circulation.

4 Potential Flow over Joukowski Airfoils: The tools of the previous three sections are applied to the problem of potential flow over Joukowski airfoils. Six interactive figures illustrate: geometry of a Joukowski airfoil. potential flow over a translated circle. annotated free-body diagram for Joukowski airfoils. surface pressure distribution for Joukowski airfoils. region plots guiding formulation of inverse Joukowski transformation. flow field for potential flow over Joukowski airfoils.

Joukowski Airfoil: Flowfield has been accepted by Wolfram Demonstrations http://demonstrations.wolfram.com/JoukowskiAirfoilFlowField/

Two other Demonstrations based on these documents have been submitted.

*Engineering > Aeronautical and Astronautical Engineering
*Mathematics > Calculus and Analysis > Complex Analysis
*Science > Physics > Fluid Mechanics

fluid mechanics, aerodynamics. potential flow, airfoil aerodynamics, Joukowski airfoil

Archive.zip (769.3 KB) - ZIP archive
IntroductionToComplexAnalysis.cdf (635.8 KB) - CDF Document
JoukowskiAirfoil.cdf (1.2 MB) - CDF Document
Preface.cdf (50.5 KB) - CDF Document
ReviewOf2DPotentialFlow.cdf (247.1 KB) - CDF Document
ReviewOfVectorFields.cdf (596.2 KB) - CDF Document
TableOfContents.cdf (34.2 KB) - CDF Document