Complex Mapping of Aerofoils--A Different Perspective

Autor/in	Matthews, Miccal T.
Titel	Complex Mapping of Aerofoils--A Different Perspective
Quelle	In: International Journal of Mathematical Education in Science and Technology, 43 (2012) 1, S.43-65 (23 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2011.582174
Schlagwörter	Test Use; Statistical Distributions; Geometric Concepts; Calculus; Geometry; Teaching Methods; Undergraduate Study; Theories; Computer Uses in Education; Concept Mapping; Equations (Mathematics); Computer Software; Spreadsheets + Suchen Sie Ihr Suchwort? Testanwendung; Wahrscheinlichkeitsverteilung; Elementare Geometrie; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Geometrie; Teaching method; Lehrmethode; Unterrichtsmethode; Grundstudium; Theory; Theorie; Computernutzung; Concept Map; Equations; Mathematics; Gleichungslehre; Spread sheet; Spredsheets; Spreadsheet; Tabellenkalkulation
Abstract	In this article an application of conformal mapping to aerofoil theory is studied from a geometric and calculus point of view. The problem is suitable for undergraduate teaching in terms of a project or extended piece of work, and brings together the concepts of geometric mapping, parametric equations, complex numbers and calculus. The Joukowski and Karman-Trefftz aerofoils are studied, and it is shown that the Karman-Trefftz aerofoil is an improvement over the Joukowski aerofoil from a practical point of view. For the most part only a spreadsheet program and pen and paper is required, only for the last portion of the study of the Karman-Trefftz aerofoils a symbolic computer package is employed. Ignoring the concept of a conformal mapping and instead viewing the problem from a parametric point of view, some interesting mappings are obtained. By considering the derivative of the mapped mapping via the chain rule, some new and interesting analytical results are obtained for the Joukowski aerofoil, and numerical results for the Karman-Trefftz aerofoil. (Contains 13 figures and 4 notes.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10