Lifting line theory for supersonic flow applications

Jadic, I.; Constantinescu, V. N.

doi:10.2514/3.11718

Cited by 8 publications

(7 citation statements)

References 3 publications

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“…The reason for the different behavior of the quasi-analytical method is that the design variables also affect the aerodynamic loads required by the EMWET method. From Figs 5 and 6 it can be deduced that the Torenbeek (1) and Howe method are insensitive to the tip thickness to chord ratio. For the turbojet aircraft, Fig.…”

Section: Methods Turboprop Aircraft Error [%] Turbojet Aircraft Error [%]mentioning

confidence: 95%

“…Each method depends on the wing span, sweep angle, taper ratio and the root thickness-to-chord ratio. Except the Torenbeek (1) method, the other methods are sensitive to maximum take-off weight.Investigating the method presented by Howe (Equation (7)) closely, it can be concluded that the root chord length is canceled out by the reference wing area and the aspect ratio (as they include c r ). Hence, the Howe method is the only method that does not depend on c r .…”

Section: Methods Comparisonmentioning

confidence: 98%

“…Torenbeek (2) and EMWET methods require the maximum zero-fuel weight as input. Torenbeek (1) and Howe are the only methods independent of the tip and kink thickness-to-chord ratio. Torenbeek (1) 3 3 3 3 3 3 Torenbeek (2) 3 3 3 3 3 3 3 3 3 Howe 3 3 3 3 3 EMWET 3 3 3 3 3 3 3 3 3 3 Shevell 3 3 3 3 3 3 3 3 LTH 3 3 3 3 3 3 3 3 Table 5 Sensitivity of the wing weight estimation methods to various wing variables…”

Section: Methods Comparisonmentioning

confidence: 99%

“…. (1) where b s is the structural wing span defined as b s = b/CosL 1/2 . The factor of proportionality, k w , and W G are as follows (for metric units):…”

Section: Torenbeek (1) Methodsmentioning

confidence: 99%

“…For instance a variety of methods are available for the aerodynamic analysis of a wing. From a simple lifting line theory or a vortex lattice method (1,2) up to the complex Euler and RANS methods (3)(4)(5) . Similarly for weight estimation, various methods with different levels of fidelity are available.…”

Section: Introductionmentioning

confidence: 99%

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Influence of weight modelling on the outcome of wing design using multidisciplinary design optimisation techniques

Mariens

Elham

Tooren

2013

Aeronaut. j. (1968)

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Weight estimation methods are categorised in different classes based on their level of fidelity. The lower class methods are based on statistical data, while higher class methods use physics based calculations. Statistical weight estimation methods are usually utilised in early design stages when the knowledge of designers about the new aircraft is limited. Higher class methods are applied in later design steps when the design is mature enough. Lower class methods are sometimes preferred in later design stages, even though the designers have enough knowledge about the design to use higher class methods. In high level multidisciplinary design optimisation (MDO) fidelity is often sacrificed to obtain models with shorter computation times. There is always a compromise required to select the proper weight estimation method for an MDO project.An investigation has been performed to study the effect of using different weight estimation methods, with low and medium levels of fidelity, on the results of a wing design using multidisciplinary design optimisation techniques. An MDO problem was formulated to design the wing planform of a typical turboprop and a turbofan passenger aircraft. The aircraft maximum take-off

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Section: Methods Turboprop Aircraft Error [%] Turbojet Aircraft Error [%]mentioning

confidence: 95%

Section: Methods Comparisonmentioning

confidence: 98%

Section: Methods Comparisonmentioning

confidence: 99%

“…. (1) where b s is the structural wing span defined as b s = b/CosL 1/2 . The factor of proportionality, k w , and W G are as follows (for metric units):…”

Section: Torenbeek (1) Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Influence of weight modelling on the outcome of wing design using multidisciplinary design optimisation techniques

Mariens

Elham

Tooren

2013

Aeronaut. j. (1968)

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A numerical method for the approximation of singular integrals of functions with a pole of order two

Jadic

1994

Applied Numerical Mathematics

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Minimising induced drag with weight distribution, lift distribution, wingspan, and wing-structure weight

2020

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ABSTRACTBecause 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.

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Lifting line theory for supersonic flow applications

Cited by 8 publications

References 3 publications

Influence of weight modelling on the outcome of wing design using multidisciplinary design optimisation techniques

Influence of weight modelling on the outcome of wing design using multidisciplinary design optimisation techniques

A numerical method for the approximation of singular integrals of functions with a pole of order two

Minimising induced drag with weight distribution, lift distribution, wingspan, and wing-structure weight

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