Minimum Induced Drag Theorems for Joined Wings, Closed Systems, and Generic Biwings: Theory

Demasi, Luciano; Monegato, Giovanni; Dipace, Antonio; Cavallaro, Rauno

doi:10.1007/s10957-015-0849-y

Cited by 24 publications

(20 citation statements)

References 25 publications

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“…Conversely, for the BWS having infinitely distant horizontal wings, Σ BWS → ∞ . As a result, the corresponding induced drag tends to zero, in agreement with the results presented in [12][13][14].…”

Section: Prandtl Methods For the Best Wing Systemsupporting

confidence: 90%

“…However, Eq. (28) does not equal 1 when k = 0 (see [12,13] for more details). Indeed, when two wings, generating a lift force L 1 = L 2 = L∕2 , tend to coincide, the resulting induced drag can be seen as the induced drag of a single wing generating a lift force equal to L. Considering the values of k up to 0.5 obtained through numerical integration of Eq.…”

Section: Two Elliptic Circulationsmentioning

confidence: 99%

“…The problem is hence solved. 1 In [12,13], the authors show how the optimal lift distribution for a symmetric box-wing is not elliptic-plus-constant. They further investigate the behaviour of the box-wing as the vertical gap increases.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Simple Model for Minimum Induced Drag of Multiplanes: Could Prandtl Do the Same?

Scardaoni

2020

Aerotec. Missili Spaz.

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In a famous report about the induced drag of multiplanes, L. Prandtl conceived the Best Wing System: the lifting system having the minimum induced drag among all the other ones, for assigned wingspan and lift. The resulting shape was a boxwing, asymptotically equivalent to a multiplane having infinite wings. At the end of the report, he gave the performance of this optimal lifting system (in terms of dimensionless induced drag and vertical gap) through a curve, without presenting the method he used. Nowadays, modern computational aerodynamics show an excellent agreement between the numerical results and Prandtl's prevision. The first part of the paper aims at clarifying which method Prandtl used for the Best Wing System only. In the second part of the paper, starting from Prandtl's different approach for the biplane and triplane problem, we propose a simple model for the evaluation of the induced drag of multiplanes, using notions an aerodynamicist of 1920s likely had. We show that the limit multiplane having infinitely many wings, under the ansatz of elliptic lift distribution on the outermost wings and constant lift distribution on the innermost ones, matches the Best Wing System curve. This leads to a simple but interesting interpretation of the actual results.

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Section: Prandtl Methods For the Best Wing Systemsupporting

confidence: 90%

Section: Two Elliptic Circulationsmentioning

confidence: 99%

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A Simple Model for Minimum Induced Drag of Multiplanes: Could Prandtl Do the Same?

Scardaoni

2020

Aerotec. Missili Spaz.

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“…On the aerodynamic side, there was no mention of the fundamental Prandtl's work (see reference [272]) on the Best Wing System and its superior characteristics on induced drag reduction; however there was a discussion on the work conducted by Letcher [205], almost 50 years later, on the induced drag of diamondshaped closed systems. The reader should note that the aerodynamic efficiency improvement is actually limited for Diamond Wings, as also reported in references [89,90,[96][97][98][99].…”

Section: Other Aeroelastic Investigationsmentioning

confidence: 76%

Challenges, Ideas, and Innovations of Joined-Wing Configurations: A Concept from the Past, an Opportunity for the Future

Cavallaro

Demasi

2016

Progress in Aerospace Sciences

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122

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“…This was already shown in reference [82], where a free-wake modelling was shown to predict a lower induced drag whereas the lift coefficient was not experiencing differences. It is then suggested that, application of classic formulae [83][84][85][86] for a first evaluation of the induced drag may be slightly penalizing.…”

Section: Effects Of Solver's Choice and Structural Damping On Fluttermentioning

confidence: 99%

Phenomenology of Nonlinear Aeroelastic Responses of Highly Deformable Joined-wings Configurations

Cavallaro

Iannelli

Demasi

et al. 2014

55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Dynamic aeroelastic behaviour of structurally nonlinear Joined Wings is presented.Three configurations, two characterized by a different location of the joint and one presenting a direct connection between the two wings (Sensorcraft-like layout) are investigated.As a first step, the snap-divergence is studied from a dynamic perspective in order to assess the real response of the configuration. Later on, the investigations focus on the flutter occurrence (critical state) and go further in analyzing postcritical phenomena: Limit Cycle Oscillations (LCOs) are observed followed by a lost of periodicity of the solution as speed is further increased. In some cases, it is also possible to ascertain the presence of period doubling (flip-) bifurcation.Differences between flutter (Hopf 's bifurcation) speed evaluated with linear and nonlinear analyses are discussed in depth, in order to understand if a less computationally intense approach may be used with confidence.Both frequency and time-domain approaches are compared. Moreover, aerodynamic solvers based on the potential flow are critically examined and discussed. In particular, it is assessed in what measure the use of more sophisticated (and computationally more intensive) aerodynamic and interface models impacts the aeroelastic predictions. These differences range from the methods adopted for load transferring to the models employed to describe the wake.When the use of the tools gives different results, a physical interpretation of the leading mechanism generating the mismatch is provided. In particular, for PrandtlPlane-like configurations the aeroelastic response is very sensitive to the wake's shape. As a consequence, it is suggested that a more sophisticated modelling of the wake positively impacts the reliability of aerodynamic and aeroelastic analysis.For Sensorcraft-like configurations some LCOs are characterized by a non-synchronous motion of the inner and outer portion of the lower wing: the wings' tip exhibits a small oscillation during the descending or ascending phase, whereas the mid-span station describes a sinusoidal-like trajectory in the time domain.

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Minimum Induced Drag Theorems for Joined Wings, Closed Systems, and Generic Biwings: Theory

Cited by 24 publications

References 25 publications

A Simple Model for Minimum Induced Drag of Multiplanes: Could Prandtl Do the Same?

A Simple Model for Minimum Induced Drag of Multiplanes: Could Prandtl Do the Same?

Challenges, Ideas, and Innovations of Joined-Wing Configurations: A Concept from the Past, an Opportunity for the Future

Phenomenology of Nonlinear Aeroelastic Responses of Highly Deformable Joined-wings Configurations

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