Use of Wagner Functions in Airfoil Design Optimization

The feasibility of using a series of Wagner functions to represent airfoil contours in design procedures was investigated. It was demonstrated that a large class of airfoils can be adequately described by a relatively small number of terms. A least squares type of procedure was used to determine the...

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Bibliographic Details
Main Authors: Sahai,Vireshwar, Tsao,Chen-Pierce
Format: Report
Language:English
Subjects:
Aircraft
AIRFOILS
CONTOURS
FOURIER SERIES
FUNCTIONS(MATHEMATICS)
LEAST SQUARES METHOD
PE61102F
SYMMETRY
Wagner functions
WUAFOSR2307D9
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Summary:The feasibility of using a series of Wagner functions to represent airfoil contours in design procedures was investigated. It was demonstrated that a large class of airfoils can be adequately described by a relatively small number of terms. A least squares type of procedure was used to determine the unknown coefficients in the series representation. The use of Wagner function representation in thin symmetrical airfoil design was investigated. Both the direct method of analysis in which the velocity distribution is calculated for a known shape and the inverse method of design in which the airfoil shape corresponding to a specified velocity distribution is determined were considered. Standard airfoil data was used to test the suitability of the Wagner function representation, and the results were found to be satisfactory. Rapid calculations were possible even in the inverse mode since the use of Wagner functions allowed the determination of all the improper integrals that appear in thin airfoil theory in closed form. (Author)