Investigation into the Effect of Shape Deviation on Variable Camber Compliant Wing Performance

Marks, Christopher R.; Zientarski, Lauren; Joo, James J.

doi:10.2514/6.2016-1313

Cited by 21 publications

(16 citation statements)

References 15 publications

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“…The optimum wingspans given in Eqs. (25), (31), (41), and (59) all minimize induced drag for a rectangular wing with fixed net weight and any fixed all-positive spanwise-symmetric lift distribution combined with other design constraints. Equation 25is for a stress-limited design with fixed wing loading; Eq.…”

Section: Resultsmentioning

confidence: 99%

“…The optimum wing-structure weights corresponding to the optimum wingspans given in Eqs. (25), (31), (41), and (59) are respectively given in Eqs. (26), (32), (42), and (60).…”

Section: Resultsmentioning

confidence: 99%

“…(1), for an arbitrary lift distribution, the optimum wingspans computed from Eqs. (25), (31), (41), and (59) depend only on the single Fourier coefficient B3.…”

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Minimizing Induced Drag with Weight Distribution, Lift Distribution, Wingspan, and Wing-Structure Weight

Phillips

Hunsaker

Taylor

2019

AIAA Aviation 2019 Forum

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Section: Resultsmentioning

confidence: 99%

“…The optimum wing-structure weights corresponding to the optimum wingspans given in Eqs. (25), (31), (41), and (59) are respectively given in Eqs. (26), (32), (42), and (60).…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Minimizing Induced Drag with Weight Distribution, Lift Distribution, Wingspan, and Wing-Structure Weight

Phillips

Hunsaker

Taylor

2019

AIAA Aviation 2019 Forum

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“…Therefore, in order for this constraint to be satisfied, we must assume that wing twist can be varied during flight to maintain a single lift distribution at all loading conditions. This can be done using variable geometric and/or aerodynamic twist (30)(31)(32)(33)(34)(35) . However, the designer is not always constrained to a single lift distribution.…”

Section: Introductionmentioning

confidence: 99%

“…However, the designer is not always constrained to a single lift distribution. Variable geometric and/or aerodynamic twist can also be used to implement different lift distributions during different flight phases (4,5,7,8,(30)(31)(32)(33)(34)(35) . For example, the lift distribution given by Equation (13) could be implemented during high-loadfactor manoeuvers; other lift distributions could be implemented during takeoff and landing; and the elliptic lift distribution could be implemented during steady level flight.…”

Section: Introductionmentioning

confidence: 99%

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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Minimum‐series twist distributions for yawing‐moment control during pure roll*

2021

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The main wings of most aircraft produce adverse yaw during roll. In order to control the lateral direction of the aircraft during the roll, the rudder is often mixed with the aileron. Lifting-line theory is used here to develop spanwise lift distributions that require the minimum number of terms in the Fourier-series solution for controlling the yawing moment during pure rolling motion using only the main wing. It is shown that the yawing moment can be controlled for arbitrary rolling moments and/or rolling rates by adding symmetric twist in the main wing. The induced-drag penalty for using this method to control the yawing moment is significant and discussed in detail. For example, it is shown that if zero yawing moment is prescribed, the induced drag can increase by 108% for a prescribed rolling moment or by 300% during a steady rolling rate relative to the induced drag in steady level flight. Because this is the minimum-series solution, it does not represent the solution for yaw control with minimum induced drag, since more terms could be used in the Fourier series describing the lift distribution to control yaw with less induced drag. However, the solutions presented here can be useful for aircraft with continuous trailing-edge technologies that are Nomenclature:, Fourier coefficients in the lifting-line solution for the section-lift distribution, Eq. (1); , coefficients in the decomposed Fourier-series solution to the lifting-line equation related to planform, Eqs. (8) and ( 9); b, wingspan; , coefficients in the decomposed Fourier-series solution to the lifting-line equation related to symmetric baseline twist, Eqs. ( 8) and (10);, induced-drag coefficient; , induced-drag coefficient produced by the elliptic lift distribution for a given aspect ratio and lift coefficient, Eq. (21); , total lift coefficient;̃, section-lift coefficient;̃, , section-lift slope; , rolling-moment coefficient; , yawing-moment coefficient; , , change in yawing moment with rolling moment; ,̄, change in yawing moment with rolling rate; c, section chord length;̄, wing mean chord length; , coefficients in the decomposed Fourier-series solution to the lifting-line equation due to antisymmetric twist related to roll control, Eqs. ( 8) and (11); c root , chord length at wing root; , coefficients in the decomposed Fourier-series solution to the lifting-line equation related to rolling rate, Eqs. (8) and ( 12); , coefficients in the decomposed Fourier-series solution to the lifting-line equation due to symmetric twist related to yaw control, Eqs. (8) and (13); j, term in the infinite series;̃, section lift; N, number of terms retained when truncating the infinite Fourier series; , angular rigid-body rolling rate;̄, dimensionless angular rigid-body rolling rate [pb/(2V ∞ )]; , wing aspect ratio ( 2 ∕ ); , wing taper ratio; , wing planform area; ∞ , freestream airspeed; z, spanwise coordinate relative to the midspan, positive out left wing; , spanwise variation in local geometric angle of attack relative to the freestream; 0 , spanwise varia...

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Investigation into the Effect of Shape Deviation on Variable Camber Compliant Wing Performance

Cited by 21 publications

References 15 publications

Minimizing Induced Drag with Weight Distribution, Lift Distribution, Wingspan, and Wing-Structure Weight

Minimizing Induced Drag with Weight Distribution, Lift Distribution, Wingspan, and Wing-Structure Weight

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

Minimum‐series twist distributions for yawing‐moment control during pure roll*

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