David J. Pate

Lift Distributions for Minimum Induced Drag with Generalized Bending Moment Constraints

The previous works of Prandtl, Jones, and Klein and Viswanathan addressed the problem of determining the lift distribution that minimizes induced drag for a given lift and specified bending moment. In these formulations, bending moment is considered to be a surrogate for wing weight. These classical methods require the bending constraints to be imposed at the same lift coefficient at which drag is minimized. In practice, however, it is commonly desired to minimize drag at a representative cruise lift coefficient while imposing the bending constraints at a limiting structural load condition, such as a maneuver lift coefficient. This paper presents an approach to extend the classical methods by allowing the bending constraints to be imposed at different lift coefficients than that at which induced drag is minimized. An example for a wing planform similar to that of a Boeing 737 shows that the penalty for optimizing induced drag at the maneuver lift coefficient as implied in the classical methods results in ...

Optimizing Families of Reconfigurable Aircraft for Multiple Missions

Aircraft with modular airframe components may offer significant flexibility in mission performance by enabling reconfiguration between sorties. This paper introduces an approach for optimizing a family of aircraft variants defined by a library of interchangeable components such as wings, tails, engines, and payloads. First, the combinatorial problemof composing interchangeable components into feasible aircraft variants and assigning the variants to missions is posed. Next, two methods are presented to determine optimal reconfigurable family designs. The methods are then applied to an example problem to define optimal families of modular unmanned aerial vehicles consisting of interchangeable wings and engines. The results indicate a rich trade space of family architectures and aircraft configurations that depends strongly on the type and diversity of the required missions.

Performance Flexibility of a Reconfigurable Family of UAVs

This paper demonstrates approaches to assess the performance exibility of recon gurable unmanned air vehicles consisting of modular airframe components that can be interchanged between sorties. A notional family of aircraft based on a xed forward fuselage and a library of interchangeable engines and wings of di erent sizes is de ned. The performance of the family is quanti ed for a spectrum of intelligence, surveillance, and reconnaissance and strike mission pro les using a multidisciplinary aircraft performance analysis toolset. Performance exibility is assessed through three approaches: (1) point performance capability, (2) mission performance boundaries for canonical mission pro les, and (3) a probabilistic technique to quantify the likelihood that emergent missions can be accomplished. The probabilistic method also incorporates logic for determining which aircraft variant should be con gured for each mission based on the assessment of its performance exibility. Results demonstrate a substantial increase in overall mission capability of the family as compared to individual variants within the family. This exibility is achieved with a manageable recon guration frequency that is promising for the pace of practical operations.

Off-Design Lift Distribution Characteristics for Subsonic Trapezoidal Wings

A common practice in wing design is to twist the airfoil sections of a speci ed planform to achieve a particular lift distribution at a design operating condition. Ideally, the twist distribution is selected to achieve a high span e ciency, acceptable stall behavior, and a particular tailoring of the root bending moment, not only at the design condition, but also at common or critical o -design operating points. One challenge in this design activity is that the shape of the lift distribution will generally change with ight condition. Since an aircraft must operate e ectively throughout a range of ight conditions, it is important to understand the variation in the o -design lift distribution and its in uence on wing performance. In this paper, the sensitivity of o -design span e ciency, root bending moment, and section lift coe cient to the design planform, ight conditions, and on-design lift distribution shape is examined. The study is based on a Weissinger lifting line formulation that models the lift behavior of planar trapezoidal wings, and induced drag is calculated by integration in the Tre tz plane. O -design lift characteristics for wings representative of a business jet and a commercial transport are explored, and sensitivities to planform parameters are illustrated. A general observation is that the more closely the lift distribution of the untwisted wing matches the speci ed design lift distribution, the less the change in shape of the lift distribution during o -design operation. This observation is consistent with the well-known result that straight wings of intermediate taper are similar to wings with elliptical planform in terms of achieving a nearly elliptical lift distribution at both on-design and o -design conditions.

Performance Flexibility of Reconfigurable Families of Unmanned Aerial Vehicles

Nomenclature A = area D = drag PS = specific excess power T = thrust TSFC = thrust-specific fuel consumption W = aircraft weight Wf = fuel weight w = weighting factor for mission mix selection V = velocity

Methods for Optimizing a Family of Recongurable Aircraft

Aircraft with modular aerostructure components may o er signi cant exibility in mission performance by enabling recon guration between sorties. This paper introduces an approach for optimizing a family of aircraft variants de ned by a library of large-scale interchangeable components such as wings, tails, engines, and payloads. First, the combinatorial problem of composing multiple interchangeable components into feasible aircraft variants is posed. Next, the paper develops two methods to determine optimal recon gurable family architectures. The optimization approaches are then applied to an example problem to de ne families of modular UAVs consisting of interchangeable wings and engines. The results indicate a rich nonlinear trade space of component library de nitions and aircraft con gurations that depends strongly on the diversity of the required missions.

Superposition of Spanwise Circulation Distributions: Accuracy Assessment and Application in Wing Design

Superposition of spanwise lift distributions is a familiar concept from lifting-line theory. However, even for linear potential flows, superposition is not rigorously applicable for aerodynamic models and wing geometries in which the shape of the wake vortex system changes with angle of attack. Nonetheless, the influence of these wake effects could generally be expected to be small, insofar as downstream vortices have a weaker influence than the vortex system in the near field of the wing. In this paper, the theoretical framework for lift distribution superposition is first examined. Next, empirical studies conducted with a panel code are presented that show that superposition remains a very good approximation for a wide range of wing geometries and operating conditions. A method for correcting the small errors in induced drag predictions that result from the application of superposition is also provided. Finally, an application for wing design in which an additional and a design distribution are superimp...

Improved Computation of Induced Drag for Wakes of Arbitrary Shape

In 1976, Blackwell provided a robust method for calculating the induced drag of an arbitrarily shaped wake at the Trefftz plane. However, to acheive an accuracy within one percent, the required discretization may exceed the number of panels that can be used in a typical vortex lattice method or panel method. Alternatively, a method given by Lundry fits a sine series to a set of loading points and obtains high accuracy by computing induced drag using the lifting-line theory formulation. Unfortunately, this is valid only for planar wakes. Therefore, the authors developed a hybrid method that uses Lundry’s method for sine series fitting to interpolate additional lifting elements to then use with Blackwell’s method for a general wake shape. The predictions from these three methods were compared for a prescribed loading and the hybrid method demonstrated significant improvement over Blackwell’s method. However, when the predictions were implemented following a loads calculation from an aerodynamics model, the improvement was reduced.

Planform Optimization of a Flying Wing with a Solid Homogeneous Structure

Trapezoidal flying wing gliders were optimized for maximum payload and lift to drag ratio, subject to trim and flight-worthiness constraints. Aeroelastic analysis was included for the solid homogeneous structure, in which the structural properties of the wing are directly determined by the airfoil shape. As payload weight increased, the optimum wings became larger, sleeker, and heavier in order to maximize lift to drag ratio while meeting the constraints. The smaller wings were constrained by the material ultimate stress limit, while the heavier wings were constrained by stall speed. The resulting Pareto frontier presents a large amount of knowledge of the design space that can help a designer select the best wing in the conceptual design phase.