Timothy T. Takahashi

Optimum Aspect Ratio for Subsonic Air Vehicles

This fundamental study considers airframes engineered to meet range and/or efficiency goals that span several orders of magnitude in size (from approximately 1000 lb to one million lb maximum flight weights). A simplified, analytical model is used to demonstrate the influence of key constraints (maximum ceiling and desired cruise speed) and design parameters (wing loading, wing aspect ratio, wing sweep, wing technology, and allowable excrescence drag) upon aerodynamic performance and fuel volume. This model illustrates factors that drive the optimum wing loading, technology, and aspect ratio for an airframe engineered to meet improved range and efficiency goals. The performance of airframes over a 200,000 lb flight weight is well represented by classical theory. For many airframes under 100,000 lb,flight at the typicalmission cruise point is dominated by zero-lift drag.A statistical design approach to refine these configurations reveals counterintuitive design insight. To simultaneously improve range and efficiency of a conventionally configured zero-lift–drag-dominated airframe, analysis of a full factorial design exploration suggests changes, such as increasing its service ceiling (though larger engines), increasing its certification ceiling, and revisions to the wing planform, that, in some cases, call for a reduction in aspect ratio and wingspan.

Optimum Transverse Span Loading for Subsonic Transport Category Aircraft

This study considers the overall system impact of the design transverse aerodynamic load distribution on future subsonic, transport category aircraft. The fundamental question revisited here concerns wing design ground rules. Should the wing be designed to favor an aerodynamically optimal, “elliptical” transverse span load that minimizes induced drag? Or, should the wing be tailored to have a reduced root bending moment in order to save structural weight at some expense of increased drag? The problem is examined at three levels of technical scrutiny: from a qualitative, rational basis perspective; from a quantitative, intermediate-fidelity parametric performance perspective; and from the results of a quantitative, coupled multidisciplinary optimization trade. The quantitative tradesindicatethattailoringofthedesigntransverseloaddistributiontofavorareducedwingrootbendingmoment resultsinsomestructuralweightsavings,butattheexpenseofhigherdrag,increasedfuelconsumption,andreduced mission performance. These trades substantiate a different rational basis argument: a balancing test that will typically recommend the aerodynamically optimal design for all but the shortest-range aircraft.

Non Planar Span Loads for Minimum Induced Drag

Future transport category aircraft for both military and commercial customers will need to offer significant reductions in fuel burn in comparison to current technology aircraft. Non-planar lifting system configurations, such as wings with large winglets, upswept wing tips, bi-planes and strut braced configurations have been proposed as promising from an induced drag reduction perspective. This paper surveys recent and historical literature as to the theoretical limits of drag reduction enabled by such configurations. This paper also suggests specific transverse span loads and their associated efficiencies that may be realized for use in the conceptual and preliminary design process. The authors find some configurations where practicable non-planar wings can attain the theoretical limits of efficiency. For other geometries, the performance approaching the theoretical limit of efficiency does not appear to be easily realized with a practical wing.

Measurement of Air Flow Characteristics Using Seven-Hole Cone Probes

The motivation for this work has been the development of a wake survey system. A seven-hole probe can measure the distribution of static pressure, total pressure, and flow angularity in a wind tunnel environment. The author describes the development of a simple, very efficient algorithm to compute flow properties from probe tip pressures. Its accuracy and applicability to unsteady, turbulent flow are discussed.

A Method to Allocate Camber, Thickness and Incidence on a Swept Wing

Numerous methods exist to choose the design of camber, incidence, and thickness ratio of an unswept infinite wing. Applying these methods to a swept, finite planform is more troublesome. While control-theory non-linear CFD based wing design algorithms can develop successful transonic lofts, the underlying non-linearity stems from effects beyond that of shock wave formation. A linear potential-flow analysis reveals inadequacies in the accepted methods developed and verified for infinite aspect ratio swept wings. Because seemingly universal principles, such as the Prandtl-Glauert Mach scaling effect, thin-airfoil pressure superposition theory and Simple Sweep Theory, behave unpredictably when applied to finite aspect ratio swept wings, we revisited the fundamental aerodynamic basis of sweep theory. From this, we suggest better design principles to translate 2D airfoil data for use lofting finite, swept wings.

Enhanced Conceptual Wing Weight Estimation Through Structural Optimization and Simulation

This paper reviews the ability to create a design tool utilizing a combination of Microsoft Excel, Visual Basic for Applications, CATIA, and ABAQUS that is capable of providing an optimized wing structural weight and available fuel volume for a given wing planform with certain mission parameters. This calculated weight and volume is based on real structure and geometry as opposed to empirical and parametric equations that are based on historical data that may or may not be optimized or relevant. This design tool is also capable of providing internal wing structure geometry including 3D CAD models and finite element models that can be used to take the conceptual design into a preliminary design. Because of the fidelity of the structure that the design tool is able to generate, the conceptual design phase can be reduced from weeks and months to hours or days.

The Search for the Optimal Wing Configuration for Small Subsonic Air Vehicles

This paper describes a comprehensive study of wing sizing and configuration for subsonic cruise air-vehicles spanning several orders of magnitude in size (from approximately 1000-lb to 1,000,000-lb maximum flight weight). The concept of effective aircraft density (MTOW normalized by nominal fuselage volume) is introduced as a design parameter. Its effect upon the optimal airframe is of particular interest to the designer of cruise missiles and other unmanned aerial systems (UAS) where human factors no longer dictate minimum fuselage dimensions. Correlations of historical data will be shown that demonstrate the influence of key constraints (maximum ceiling, desired cruise speed, structure, Mach buffet limits) upon wing loading (W/S), wing aspect ratio (AR), wing sweep (Λ), wing technology (k) and allowable excrescence drag (%CRUD). A simplified, coupled MDO-type sizing model will be developed and interrogated to demonstrate key observations concerning the relative impact of the mission constraints upon the wing geometry and crud -drag allocation as a function of air vehicle size.

Curious Circumstances Surrounding Optimal Non-Planar Wings

Highly non-planar lifting system configurations (wings with large winglets, gull wings, wings with highly upswept tips, and “lumpy” dihedral distributions) have been proposed as a means to reduce overall aircraft drag. This paper presents a comprehensive design space search, using a potential flow code, exploring the practical limits of non-planar wing drag reduction. The study yields an unanticipated discovery regarding the optimal transverse span load associated with “lumpy” dihedral non-planarity: the optimum system solution, taking into consideration structural weight, zero-lift-drag as well as induced drag comprises a nearly “elliptical” normal force distribution and minimal non-planarity.

Wing Section Thickness and Camber Allocation for Conceptual and Preliminary Aircraft Design

Allocating a wing section thickness and camber for a given aircraft wing configuration is an essential task that has significant impacts across several engineering disciplines. This provided the motivation to develop a method to allocate wing section thickness and camber for a desired critical Mach number and required section lift coefficient. Various airfoil families were analyzed using a potential flow code to observe trends in section lift coefficient and critical Mach number. A method to allocate wing section thickness and camber for a given critical Mach number and desired section lift coefficient was developed for each of these families of airfoils. The method was designed to be rapidly repeatable so that it can easily be applied to other airfoil families, particularly non-conventional or custom airfoils.

Zero Lift Drag and Drag Divergence Prediction for Finite Wings in Aircraft Conceptual Design

This paper reviews the basis of current methods used for the calculation of zero-lift drag and drag divergence Mach number and proposes an improved set of methods. The majority of past methods are based on profile considerations alone and, at most, limited wing parameters. These methods are reviewed and compared for their applicability to the low aspect ratio and highly swept wing configurations that are being considered for many future aircraft. Based on the limitations of current methods, a new technique comprising a vortex lattice solution coupled to a profile boundary layer analysis is developed. Using results from this new method, metamodels are created that are applicable for inclusion in aircraft sizing and synthesis codes for conceptual and preliminary aircraft design.