Brian J. German

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.

Form Factor and Critical Mach Number Estimation for Finite Wings

Empirical methods used in conceptual aircraft design for the calculation of form factor drag and critical Mach number typically have been based on two-dimensional profile considerations alone or, at most, limited wing parameters. This paper compares many of these legacy methods. Motivated by the limited wing features modeled in current approaches, surrogate models for form factor and critical Mach number have been built as functions of airfoil thickness and trapezoidal wing parameters. These surrogate models are regressed from the results of a threedimensional potential flow solution coupled to a profile boundary-layer analysis. The surrogates are physics based, yet their simple functional forms make them applicable for inclusion in aircraft sizing algorithms for rapid conceptual and preliminary design trade studies. The models capture the increasing influence of tip effects and spanwise flow as the aspect ratio is decreased and sweep is increased. A primary finding is the strongly beneficial effects of reduced aspect ratio on the form drag and critical Mach number of thick wings.

Wing Aerodynamic Analysis Incorporating One-Way Interaction with Distributed Propellers

The use of electric motors on general aviation aircraft may enable new aircraft designs that are noticeably different from conventional configurations due to the reduced weight and volume of electric motors compared to conventional engines. One potential design involves distributing multiple propellers over the wing span to augment lift at low speeds. This paper describes initial conceptual design-level work in modeling the aerodynamics of wing configurations with multiple tractor propellers distributed upstream of the leading edge. The approach leverages a vortex lattice model of the wing aerodynamics and propeller slipstream velocities obtained from the XROTOR code augmented with corrections based on the Conway actuator disk model. The technique captures only the “one-way coupling” between the propellers and the wing in which only the propellers’ impact on the wing is considered. This method provides quick results that may aid in design space exploration of DEP concepts in the conceptual design stage. Results indicate that substantial lift improvements may be obtained through leading edge propellers. Furthermore, distributing an equivalent amount of total power over four propellers instead of two provides additional increases in wing lift augmentation even when the propeller design and diameter are held fixed. These results should be verified with more detailed analyses that can capture the full mutual coupling between the wing and all propellers, but these initial tests indicate promise for distributed propeller configurations to provide lift augmentation at low speeds.

Nondomination-Level Coordinate System for Parameterizing and Exploring Pareto Frontiers

This paper presents a method for defining a barycentric coordinate system on a k-objective Pareto frontier that is constructed from nondomination levels calculated over subsets of the objectives taken k−1 at a time. Unlike past approaches, these “nondomination-level coordinates” are not limited by the dimensionality, convexity, or curvature of the frontier, and they have an inherent meaning as relative preferences for the competing objectives. This intuitive behavior makes the coordinates particularly useful as the basis for parametric models of the frontier and for conducting sensitivity studies and interactive trade-space exploration. The method is demonstrated on three mathematical example problems exhibiting different geometric properties and on a conceptual wing-sizing problem.

Simplified Aerodynamics Models to Predict the Effects of Upstream Propellers on Wing Lift

In this paper we describe simple, two-dimensional aerodynamic models that incorporate the effects of the propeller installation angle to quickly estimate the lift augmentation from configurations in which multiple propellers are distributed upstream of a wing. The approach predicts variations in the apparent lift curve slope and zero-lift angle of attack of airfoils in the presence of propeller slipstreams of varying height. The angle of the slipstream relative to the airfoil and the height of the slipstream are both shown to have significant impacts on the lift augmentation. The methods presented in this paper are intentionally simple and can be used to help build a designer’s intuition about the effects of distributed leading edge propellers employed as high-lift devices.

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...

Designing air traffic concepts of operation for thin-haul aviation at small airports

Thin-haul aviation offers the potential for transforming mobility. The thin-haul commuter concept envisions four to nine passenger aircraft operating very short flights for scheduled and/or on-demand air services from smaller airports. However, achieving safe, cost-effective, and high-volume operations will require novel air traffic management concepts integrating these thin-haul aircraft into existing operations, particularly at small airports. This paper describes a process to design such air traffic concepts of operations. The process is demonstrated by designing concept of operations applying helical descents at Wittman Regional Airport in Oshkosh, Wisconsin, the site of the EAA AirVenture air show. The process includes both the design of the geometric airspace structures and the actions that represent the work that needs to be done in the concept of operations.