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Journal ArticleDOI

Minimum swept-wing induced drag with constraints on lift and pitching moment.

01 Jan 1967-Journal of Aircraft (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 4, Iss: 1, pp 73-74
TL;DR: In this article, the authors defined the coefficients for span loading series and the reference area for coefficients, including aspect ratio, chord lift coefficient, and pitch-moment coefficient, as well as the nonelliptical portion of the span loading.
Abstract: A = coefficient for span-loading series CD = drag coefficient CL = lift coefficient CM = pitching-moment coefficient ACM = CM contributed by the nonelliptical portion of the span loading N = number of terms in the span-loading series S = reference area for coefficients a = aspect ratio b = span c = chord ci = section lift coefficient Cm = section pitching-moment coefficient m = mean aerodynamic chord x, y = longitudinal and lateral coordinates A = quarter-chord sweep angle 0 = transformed lateral coordinate, cos0 — —2y/b \ = taper ratio
Citations
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Journal ArticleDOI
TL;DR: In this paper, minimum induced drag for fixed gross weight and wingspan is obtained from the elliptic lift distribution for steady level flight, but this is not obtained by imposing the constrain.
Abstract: Minimum induced drag for fixed gross weight and wingspan is obtained from the elliptic lift distribution. However, minimum induced drag for steady level flight is not obtained by imposing the const...

38 citations

Journal ArticleDOI
TL;DR: In this paper, an analysis of hyperelliptic cambered span wing configurations, optimized for minimum drag, is presented, which encompasses a multidimensional design optimization approach wherei...
Abstract: The current study considers an analysis of hyperelliptic cambered span wing configurations, optimized for minimum drag. This study encompasses a multidimensional design optimization approach wherei...

8 citations

Journal ArticleDOI
TL;DR: In this article, the authors presented analytic solutions for the optimum wingspan and wing-structure weight for rectangular wings with four different sets of design constraints, i.e., fixed lift distribution and net weight combined with fixed maximum stress and wing loading.
Abstract: Because the wing-structure weight required to support the critical wing section bending moments is a function of wingspan, net weight, weight distribution, and lift distribution, there exists an optimum wingspan and wing-structure weight for any fixed net weight, weight distribution, and lift distribution, which minimises the induced drag in steady level flight. Analytic solutions for the optimum wingspan and wing-structure weight are presented for rectangular wings with four different sets of design constraints. These design constraints are fixed lift distribution and net weight combined with 1) fixed maximum stress and wing loading, 2) fixed maximum deflection and wing loading, 3) fixed maximum stress and stall speed, and 4) fixed maximum deflection and stall speed. For each of these analytic solutions, the optimum wing-structure weight is found to depend only on the net weight, independent of the arbitrary fixed lift distribution. Analytic solutions for optimum weight and lift distributions are also presented for the same four sets of design constraints. Depending on the design constraints, the optimum lift distribution can differ significantly from the elliptic lift distribution. Solutions for two example wing designs are presented, which demonstrate how the induced drag varies with lift distribution, wingspan, and wing-structure weight in the design space near the optimum solution. Although the analytic solutions presented here are restricted to rectangular wings, these solutions provide excellent test cases for verifying numerical algorithms used for more general multidisciplinary analysis and optimisation.

6 citations


Cites background from "Minimum swept-wing induced drag wit..."

  • ...(9) Equations for computing values of C for some common beam cross-sections are presented in Ref....

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  • ...Equation (5) could be applied in the early stages of preliminary design, if no conflicting constraint is placed on the weight distribution....

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  • ...Phillips, Hunsaker, and Joo [9] have shown that Prandtl’s 1933 lift distribution also yields a minimum in induced drag for the stress-limited design of a rectangular wing with fixed weight and chord-length constraints combined with the weight distribution constraint given by )( ~)( ~ )()( ~ zW L zL WWzW srn (5) Equation (5) alone does not completely specify the weight distribution )( ~ zWn ....

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  • ...Equation (27) gives the minimum possible induced drag for the stress-limited design of a rectangular wing with fixed wing loading, the weight distribution specified by Eq....

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  • ...(6), (8), and (16) with the relation sn WWW yields W b nn nn ctEC SWB WW gm gm n 6 max 2 max 2 3 )1( )(32 )()1( (28) Equation (28) is easily solved for the gross weight, and using the relation ns WWW yields 6 max 2 max 2 3 2 )1( )(32 )()1( 42 b nn nn ctEC SWBWWW gm gmnn s (29) Using this wing-structure weight with the relation sn WWW in Eq....

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References
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Book
01 Jan 1926
TL;DR: The aerofoil in three dimensions has been studied in this article, where Bernoulli's equation and the potential function are used to transform a circle into an acerofoil.
Abstract: 1. Introduction 2. Bernoulli's equation 3. The stream function 4. Circulation and vorticity 5. The velocity potential and the potential function 6. The transformation of a circle into an aerofoil 7. The aerofoil in two dimensions 8. Viscosity and drag 9. The basis of aerofoil theory 10. The aerofoil in three dimensions 11. The monoplane aerofoil 12. The flow round an acerofoil 13. Biplane aerofoils 14. Wind tunnel interference on areofoils 15. The airscrew: momentum theory 16. The airscrew: blade element theory 17. The airscrew: wind tunnel interference Appendix Bibliography Index.

668 citations

Book
16 Jan 1991
TL;DR: Airplane performance Stability and control, Airplane performance stability and control , مرکز فناوری اطلاعات و اشاوρزی
Abstract: Airplane performance stability and control , Airplane performance stability and control , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

339 citations

Book ChapterDOI
TL;DR: The theory of ordinary maxima and minima as mentioned in this paper is concerned with the problem of finding the values of each of n independent variables x 1, x 2, …., x n at which some function of the n variables f (x 1, x 2, …., X n ) reaches either a maximum or a minimum (an extremum).
Abstract: Publisher Summary This chapter discusses the theory of maxima and minima. The theory of ordinary maxima and minima is concerned with the problem of finding the values of each of n independent variables x 1 , x 2 , …., x n at which some function of the n variables f (x 1 , x 2 , …., x n ) reaches either a maximum or a minimum (an extremum). This problem may be interpreted geometrically as the problem of finding a point in an n-dimensional space at which the desired function has an extremum. The basic problem of the theory of ordinary maxima and minima is to determine the location of local extrema and then, compare these so as to determine which is the absolute extremum. The existence of a solution to an ordinary minimum problem is guaranteed by the theorem of Weierstrass, as long as the function is continuous. The theorem of Weierstrass indicates that the extrema may occur on the boundary of the region. There are a number of practically important problems that can be solved by using the theory of ordinary maxima and minima to optimize integrals rather than functions. A typical problem of the theory of ordinary maxima and minima would be the determination of the values of thrust and propellant weight in each stage of a multistage space vehicle that will maximize the payload for some specific mission. Several practical applications of the theory of maxima and minima are also presented in the chapter.

28 citations