Modern Adaptation of Prandtl's Classic Lifting-Line Theory

Phillips, Warren F.; Snyder, Deryl O.

doi:10.2514/2.2649

Cited by 227 publications

(156 citation statements)

References 4 publications

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“…This agrees closely with the Hoerner and Borst [1] It has been shown that the numerical lifting-line method of Phillips and Snyder [9] can be used to accurately predict the induced drag acting on a lifting wing. One convenient way to model an aircraft in ground effect using any potential flow algorithm is to replace the surface of the ground with an image of the aircraft, positioned and oriented as though it were reflected in the surface of the ground.…”

supporting

confidence: 87%

“…9. (10) and (11) with results obtained from the numerical lifting-line method of Phillips and Snyder [9] for wings of elliptic planform.…”

Section: Wings Of Elliptic Planformmentioning

confidence: 99%

“…In the present work, closed-form relations for estimating induced-drag and lift coefficients for untwisted wings in ground effect are developed by correlating results obtained from numerical solutions [9] to Prandtl's lifting-line theory [32,33], which produces results in good agreement with inviscid CFD solutions [34] at a small fraction of the computational cost.…”

Section: Ratio Of Wing Height To Wingspanmentioning

confidence: 99%

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Lifting-Line Predictions for Induced Drag and Lift in Ground Effect

Phillips

Hunsaker

2013

31st AIAA Applied Aerodynamics Conference

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Closed-form relations are presented for estimating ratios of the induced-drag and lift coefficients acting on a wing in ground effect to those acting on the same wing outside the influence of ground effect. The closed-form relations for these ground-effect influence ratios were developed by correlating results obtained from numerical solutions to Prandtl's liftingline theory. Results show that these influence ratios are not unique functions of the ratio of wing height to wingspan, as is sometimes suggested in the literature. These ground-effect influence ratios also depend on the wing planform, aspect ratio, and lift coefficient. = tapered-wing correction coefficients, Eqs. (13) and (15)

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supporting

confidence: 87%

“…9. (10) and (11) with results obtained from the numerical lifting-line method of Phillips and Snyder [9] for wings of elliptic planform.…”

Section: Wings Of Elliptic Planformmentioning

confidence: 99%

Section: Ratio Of Wing Height To Wingspanmentioning

confidence: 99%

See 1 more Smart Citation

Lifting-Line Predictions for Induced Drag and Lift in Ground Effect

Phillips

Hunsaker

2013

31st AIAA Applied Aerodynamics Conference

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“…This extension might be achieved by coupling cross-sectional domains through a circulation relation, much like is done in classical lifting-line theory [71,95]. While lifting-line theory relies on quasi-steady hydrodynamic relationships, the small-amplitude theory does not constrain the driving frequency σ to be small and therefore offers the ability to capture a range of different dynamic states.…”

Section: Discussionmentioning

confidence: 99%

A fast Chebyshev method for simulating flexible-wing propulsion

Moore¹

2017

Journal of Computational Physics

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We develop a highly efficient numerical method to simulate small-amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid. We allow the wing's elastic modulus and mass density to vary arbitrarily, with an eye towards optimizing these distributions for propulsive performance. The method to determine the wing kinematics is based on Chebyshev collocation of the 1D beam equation as coupled to the surrounding 2D fluid flow. Through small-amplitude analysis of the Euler equations (with trailing-edge vortex shedding), the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1D wing kinematics. A class of semi-analytical solutions permits fast evaluation of this operator with O (N log N ) operations, where N is the number of collocation points on the wing. This is in contrast to the minimum O N 2 cost of a direct 2D fluid solver. The coupled wing-fluid problem is thus recast as a PDE with nonlocal operator, which we solve using a preconditioned iterative method. These techniques yield a solver of nearoptimal complexity, O (N log N ), allowing one to rapidly search the infinite-dimensional parameter space of all possible material distributions and even perform optimization over this space.

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“…The aerodynamic model is based off of Prandtl's lifting-line algorithm with modifications suggested by Phillips 12 and further explored by the author. This approach has shown to be accurate for wings with sweep, taper, and washout and requires only a fraction of the computational time of panel methods.…”

Section: Wing Lift Distributionmentioning

confidence: 99%

A Numerical Blade Element Approach to Estimating Propeller Flowfields

Hunsaker

2007

45th AIAA Aerospace Sciences Meeting and Exhibit

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A numerical method is presented as a low computational cost approach to modeling an induced propeller flowfield. This method uses blade element theory coupled with momentum equations to predict the axial and tangential velocities within the slipstream of the propeller, without the small angle approximation assumption common to most propeller models. The approach is of significant importance in the design of tail-sitter vertical takeoff and landing (VTOL) aircraft, where the propeller slipstream is the primary source of air flow past the wings in some flight conditions. The algorithm is presented, the model is characterized, and the results (including the results of coupling the propeller model with a lifting-line aerodynamic model) are compared with published experimental data.

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Modern Adaptation of Prandtl's Classic Lifting-Line Theory

Cited by 227 publications

References 4 publications

Lifting-Line Predictions for Induced Drag and Lift in Ground Effect

Lifting-Line Predictions for Induced Drag and Lift in Ground Effect

A fast Chebyshev method for simulating flexible-wing propulsion

A Numerical Blade Element Approach to Estimating Propeller Flowfields

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