scholarly journals Some accurate solutions of the lifting surface integral equation

1993 ◽  
Vol 35 (2) ◽  
pp. 127-144 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Integral Equation ◽  
Aspect Ratio ◽  
Surface Integral ◽  
Surface Integral Equation ◽  
Lifting Surface ◽  
Line Theory ◽  
Limiting Behaviour ◽  
Ratio Limit ◽  
Wing Tips

AbstractThis note describes a simple numerical method for solution of the lifting surface integral equation of aerodynamics, and provides benchmark computations of up to 7 figure accuracy for flat rectangular wings of arbitrary aspect ratio. The nature of the large aspect ratio limit is also investigated numerically and asymptotically. This enables determination of the limiting behaviour near the wing tips, which is compared to the predictions of lifting line theory. Generalisations to non-rectangular wings are discussed.

scholarly journals Accuracy of surface integral equation matrix elements in plasmonic calculations

2015 ◽  
Vol 32 (3) ◽  
pp. 485 ◽  
Author(s):  
T. V. Raziman ◽  
W. R. C. Somerville ◽  
O. J. F. Martin ◽  
E. C. Le Ru
Keyword(s):  
Integral Equation ◽  
Matrix Elements ◽  
Surface Integral ◽  
Surface Integral Equation

The Unsteady Loading on a Marine Propeller in a Nonuniform Flow

1964 ◽  
Vol 8 (05) ◽  
pp. 29-38
Author(s):  
Michael D. Greenberg
Keyword(s):  
Free Stream ◽  
Marine Propeller ◽  
Nonuniform Flow ◽  
Surface Integral ◽  
Practical Applications ◽  
Vortex Model ◽  
Surface Integral Equation ◽  
Lifting Surface ◽  
Finite Wing ◽  
Unsteady Loading

The lifting-surface integral equation governing the unsteady loading on a marine propeller in a nonuniform free stream is derived using a classical vortex model. The induced downwash is split into a part corresponding to a locally tangent flat finite wing and wake, plus parts corresponding to the effects of the "helicoidal deviation" from this, of the true blade and wake, and the interference from the other blades and their wakes. Strip-type approximations are tolerated on these terms while a lifting-surface formulation is retained for the dominant finite flat-wing portion. A simple numerical example is carried out and these effects are indeed found to be quite small; so small, in fact, that it may suffice to retain only the flat finite-wing terms in practical applications.

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