Douglas F. Hunsaker

Lifting-Line Predictions for Induced Drag and Lift in Ground Effect

Closed-form relations are presented for estimating ratios of the induced-drag and lift coefficients acting on a wing in ground effect to those acting on the same wing outside the influence of ground effect. The closed-form relations for these ground-effect influence ratios were developed by correlating results obtained from numerical solutions to Prandtl’s lifting-line theory. Results show that these influence ratios are not unique functions of the ratio of wing height to wingspan, as is sometimes suggested in the literature. These ground-effect influence ratios also depend on the wing planform, aspect ratio, and lift coefficient.

A Numerical Blade Element Approach to Estimating Propeller Flowfields

A numerical method is presented as a low computational cost approach to modeling an induced propeller flowfield. This method uses blade element theory coupled with momentum equations to predict the axial and tangential velocities within the slipstream of the propeller, without the small angle approximation assumption common to most propeller models. The approach is of significant importance in the design of tail-sitter vertical takeoff and landing (VTOL) aircraft, where the propeller slipstream is the primary source of air flow past the wings in some flight conditions. The algorithm is presented, the model is characterized, and the results (including the results of coupling the propeller model with a lifting-line aerodynamic model) are compared with published experimental data.

Smooth-Wall Boundary Conditions for Dissipation-Based Turbulence Models

It is shown that the smooth-wall boundary conditions specified for commonly used dissipation-based turbulence models are mathematically incorrect. It is demonstrated that when these traditional wall boundary conditions are used, the resulting formulations allow an infinite number of solutions. Furthermore, these solutions do not enforce energy conservation and they do not properly enforce the no-slip condition at a smooth surface. This is true for all dissipation-based turbulence models, including the k-e, k-ω, and k-ζ models. Physically correct wall boundary conditions must force both k and its gradient to zero at a smooth wall. Enforcing these two boundary conditions on k is sufficient to determine a unique solution to the coupled system of differential transport equations. There is no need to impose any wall boundary condition on e, ω, or ζ at a smooth surface and it is incorrect to do so. The behavior of e, ω, or ζ approaching a smooth surface is that required to force both k and its gradient to zero at the wall. Nomenclature 1 C – 5 C = arbitrary constants of integration, Eq. (43) 1 e C , 2 e C = turbulence model closure coefficients, Eqs. (6) and (7) 1 ω C , 2 ω C = turbulence model closure coefficients, Eqs. (73) and (74) µ C = turbulence model closure coefficient, Eqs. (2) and (7) 1

Momentum Theory with Slipstream Rotation Applied to Wind Turbines

A momentum theory which includes the effects of slipstream rotation for wind turbines is presented. The theory accounts for the axial and radial pressure gradients within the slipstream as well as the wake expansion caused by wake rotation. Because of the limiting approximations of previous methods, the effects of slipstream rotation have not been accurately realized. The method included here, which does not suffer from the unrealistic approximations of previous methods, predicts that the effects of slipstream rotation are manifest entirely through an increase in the turbine thrust coefficient. The method predicts, as previous methods do, that the Lanchester–Betz–Joukowski limit of 16/27 is an upper limit for the maximum efficiency, or power coefficient, of a wind turbine. Unlike the results from classical methods that are traditionally reported in terms of the axial induction factor, results of this work are presented in terms of two independent variables, the tip-speed ratio and the torque coefficient. The results included here allow the dependent variables including the thrust coefficient, power coefficient, axial induction factor, and circumferential induction factor to be evaluated in terms of the tip-speed ratio and torque coefficient. Additionally, relationships for the ideal operating conditions of a wind turbine are presented.

Decomposed Lifting-Line Predictions and Optimization for Propulsive Efficiency of Flapping Wings

A decomposed Fourier series solution to Prandtl’s classical lifting-line theory is used to predict the lift, induced-thrust, and power coefficients developed by a flapping wing. A significant advantage of this quasi-steady analytical solution over commonly used numerical methods is the utility provided for optimizing wing flapping cycles. The analytical solution involves five time-dependent functions that could all be optimized to maximize thrust, propulsive efficiency, and/or other performance measures. Results show that by optimizing only two of these five functions, propulsive efficiencies exceeding 97% can be obtained. Results are presented for untwisted rectangular wings in pure plunging, rectangular wings with linear washout and the minimum-power washout magnitude, and rectangular wings with the minimum-power washout distribution and magnitude.

Pitch Dynamics of Unmanned Aerial Vehicles

Dynamic stability requirements for manned aircraft have been in place for many years. However, we cannot expect stability constraints for UAVs to match those for manned aircraft; and dynamic stability requirements specific to UAVs have not been developed. The boundaries of controllability for both remotely-piloted and auto-piloted aircraft must be established before UAV technology can reach its full potential. The development of dynamic stability requirements specific to UAVs could improve flying qualities and facilitate more efficient UAV designs to meet specific mission requirements. As a first step to developing UAV stability requirements in general, test techniques must be established that will allow the stability characteristics of current UAVs to be quantified. This paper consolidates analytical details associated with procedures that could be used to experimentally determine the pitch stability boundaries for good UAV flying qualities. The procedures require determining only the maneuver margin and pitch radius of gyration and are simple enough to be used in an educational setting where resources are limited. The premise is that these procedures could be applied to UAVs now in use, in order to characterize the longitudinal flying qualities of current aircraft. This is but a stepping stone to the evaluation of candidate metrics for establishing flying-quality constraints for unmanned aircraft.

Minimizing Induced Drag with Lift Distribution and Wingspan

Minimum induced drag for fixed gross weight and wingspan is obtained from the elliptic lift distribution. However, minimum induced drag for steady level flight is not obtained by imposing the const...

A Propeller Model Based on a Modern Numerical Lifting-Line Algorithm with an Iterative Semi-Free Wake Solver

A Propeller Model Based on a Modern Numerical Lifting-Line Algorithm with an Iterative Semi-Free Wake Solver

Optimization of Iris, a Small Autonomous Surveillance UAV

A flying wing design, previously developed as a senior project, was optimized for endurance using a gradient-based algorithm. Chord, sweep, taper ratio, and wingspan were varied within the model while all other design parameters were held constant from the original design. The model was produced from a combination of basic equations for flying wing aircraft and was validated using the previous designs experimental results. These equations are presented and the design space is explored. The optimal design produced an aircraft with a smaller wingspan, but higher aspect ratio. This design increased predicted flight endurance by 15.5% and experimental flight endurance by 13%. The optimized design was constrained by material yield strength of the airframe structure and the aircraft static margin.