An Alternate Dimensionless Form of the Linearized Rigid-Body Aircraft Equations of Motion with Emphasis on Dynamic Parameters

The equations of motion for an aircraft can be linearized about a reference condition within the assumptions of small disturbances and linear aerodynamics. The resulting system of equations is typically solved to obtain the eigenvalues and eigenvectors that describe the small disturbance motion of the aircraft. Results from such an analysis are often used to predict the rigid-body dynamic modes of the aircraft and associated handling qualities. This process is typically carried out in dimensional form in most text books, or in nondimensional form using dimensionless parameters rooted in aerodynamic theory. Here we apply Buckingham’s Pi theorem to obtain nondimensional parameters based on the aircraft rigid-body dynamics rather than aerodynamics. This approach may be more useful for understanding how aircraft dynamics scale with appropriate design parameters

Implementation of OpenFOAM for Inviscid Incompressible Aerodynamic Flows

This paper is the description of the Utah State University AeroLab’s Aerodynamic Center Analysis Tool (AeroCAT), which is an implementation of the OpenFOAM CFD toolbox. AeroCAT takes in a user input file, generates a mesh, and solves a steady, inviscid, incompressible flow, automatically repeating the process for a range of angles of attack. It then processes the results to predict the wing’s span-wise locus of aerodynamic centers. The mesh generator used in this tool is GridX, developed by a former PhD student at USU, and the CFD solver is OpenFOAM

Simplified Mass and Inertial Estimates for Aircraft with Components of Constant Density

Aircraft mass and inertial properties are required for predicting the dynamics and handling qualities of aircraft. However, such properties can be difficult to estimate since these depend on the external shape and internal structure, systems, and mass distributions within the airframe. Mass and inertial properties of aircraft are often predicted using computer-aided design software, or measured using various experimental techniques. The present paper presents a method for quickly predicting the mass and inertial properties of complete aircraft consisting of components of constant density. Although the assumption of constant density may appear limiting, the method presented in this paper can be used to approximate mass properties of complex internal structures. Inertial estimates for rectangular cuboids, cylinders, spheres, wing segments, and rotors are presented here. The influence of geometric properties of wing segments such as sweep, taper, airfoil geometry, and dihedral are included. The utility of the method is presented and the accuracy is evaluated with various test cases

A Sine-Summation Algorithm for the Prediction of Ship Deck Motion

Landing a fixed-wing aircraft on a moving aircraft carrier is a risky and inefficient process. Having an accurate prediction of ship deck motion decreases the risk posed to both the pilot and the aircraft and increases the efficiency of landing maneuvers. The present work proposes the use of a sine-summation algorithm to predict future ship motion. The algorithm decomposes recorded ship acceleration data into its characteristic harmonic parameters using a fast Fourier transform. The harmonic parameters are then used in a summation of sine waves to create a fit for the acceleration data, which is projected into future time intervals to predict ship motion. An aircraft carrier can supply the prediction made by the algorithm to an autopilot, which then decides to land or make another attempt. Included in this work is a brief overview of ship motion with six degrees of freedom and a description of the method. The results generated by the algorithm are presented for a specific ship motion dataset to provide a point of comparison between the proposed method and other common methods used. The proposed method appears to be accurate in comparison to similar prediction methods, while reducing the computational cost required to make a prediction

3D-Printed Wings with Morphing Trailing-Edge Technology

In recent years, various groups have attempted to improve aircraft efficiency using wings with morphing trailing-edge technology. Most of these solutions are difficult to manufacture or have limited morphing capability. The present paper outlines a research effort to develop an easy to manufacture, fully 3D-printed morphing wing. This approach is advantageous due to the low cost, minimal man-hours required for manufacturing, and speed at which design iterations can be explored. Several prototypes were designed and tested and lessons learned from these iterations have been documented. Additionally, printer settings have been tested and catalogued to assist others attempting to reproduce these results. Performance was considered in terms of total deflection. Two concepts are presented as potential 3D-printed morphing-wing mechanisms. The Airfoil Recambering Compliant System (ARCS) is presented as a solution for a wing using continuous trailing-edge technology. The Kinetic Internal Nexus Compliant System (KINCS) is presented as a solution for a wing using discontinuous trailing-edge technology. The final KINCS design used for a prototype flying-wing aircraft is presented

Comparison of Theoretical and Multi-Fidelity Optimum Aerostructural Solutions for Wing Design

As contemporary aerostructural research for aircraft design trends toward high-fidelity computational methods, aerostructural solutions based on theory are often neglected or forgotten. In fact, in many modern aerostructural wing optimization studies, the elliptic lift distribution is used as a benchmark in place of theoretical aerostructural solutions with more appropriate constraints. In this paper, we review several theoretical aerostructural solutions that could be used as benchmark cases for wing design studies, and we compare them to high-fidelity solutions with similar constraints. Solutions are presented for studies with 1) constraints related to the wing integrated bending moment, 2) constraints related to the wing root bending moment, and 3) structural constraints combined with operational constraints related to either wing stall or wing loading. It is shown that for each set of design constraints, the theoretical optimum lift distribution is consistently in excellent agreement with high-fidelity results. It follows that theoretical optimum lift distributions can often serve as a good benchmark for higher fidelity aerostructural wing optimization methods. Moreover, a review of solutions for the optimum wingspan and corresponding drag reveals important insights into the effects of viscosity, aeroelasticity, and compressibility on the aerodynamic and structural coupling involved in wing design and optimization

Nitrogen Fertilizer and Irrigation Effects on Seed Yield and Oil in Camelina

Interest is growing in camelina (Camelina sativa L. Crantz) as a biofuel feedstock. However, there has been little camelina research in irrigated arid systems. A 2-yr field study in Maricopa, AZ, under an overhead sprinkler irrigation system determined the effects of 10 water levels (irrigation fraction 0.5–1.1) and five N fertilizer rates (38–150 kg N ha–1) on seed yield, seed oil content, and N use efficiency. Cultivar Robinson was planted in December 2012 and 2013. Nitrogen fertilizer (urea ammonium nitrate) was applied in three split applications. Irrigation amounts were from 125 to 380 mm, and in-season rain was 70 and 50 mm, in 2013 and 2014, respectively. Camelina seed yields were maximum at water level 7 (irrigation fraction 0.93) in 2013 at 1800 kg ha–1. Maximum seed yields were 1600 kg ha–1 at water level 6 (irrigation fraction 0.83) in 2014. These highest seed yields were achieved with 150 kg N ha–1 in both years. Oil content (maximum 41%) decreased with N rate but increased with water level. Seed N increased with N rate but decreased with irrigation level. Recovery efficiency of N fertilizer by camelina ranged from 12 to 72%. The results indicate that good high-oil camelina yields can be produced in the southwestern United States with 320 to 380 mm irrigation plus rain and N fertilizer rates of 150 kg N ha–1

Numerical Algorithm for Wing-Structure Design

Low-fidelity aerostructural optimization routines have often focused on determining the optimal spanloads for a given wing configuration. Several analytical approaches have been developed that can predict optimal lift distributions on rectangular wings with a specific payload distribution. However, when applied to wings of arbitrary geometry and payload distribution, these approaches fail. Increasing the utility and accuracy of these analytical methods can result in important benefits during later design phases. In this paper, an iterative algorithm is developed that uses numerical integration to predict the distribution of structural weight required to support the bending moments on a wing with arbitrary geometry and payload distribution. It is shown that the algorithm’s predictions for the structural weight of a rectangular test wing match those found using an analytical approach. The structural weight distribution for a spanwise-constant non-structural weight distribution is also found. Coupling the algorithm with an optimization routine, the optimal lift distributions for the rectangular test wing are found and are shown to match analytical results. Finally, the optimal lift distributions for a test wing configuration with a spanwise-constant non-structural weight distribution are found using the algorithm

Aerodynamic Centers of Arbitrary Airfoils Below Stall

The aerodynamic center of an airfoil is commonly estimated to lie at the quarter-chord. This traditional estimate is based on thin airfoil theory, which neglects aerodynamic and geometric nonlinearities. Even below stall, these nonlinearities can have a significant effect on the location of the aerodynamic center. Here, a method is presented for accurately predicting the aerodynamic center of any airfoil from known lift, drag, and pitching-moment data as a function of angle of attack. The method accounts for aerodynamic and geometric nonlinearities, and it does not include small-angle, small-camber, and thin-airfoil approximations. It is shown that the aerodynamic center of an airfoil with arbitrary amounts of thickness and camber in an inviscid flow is a single, deterministic point, independent of angle of attack, and lies at the quarter-chord only in the limit as the airfoil thickness and camber approach zero. Furthermore, it is shown that, once viscous effects are included, the aerodynamic center is not a single point but is a function of angle of attack. Differences between this general solution and that predicted by the thin airfoil theory can be on the order of 3%, which is significant when predicting flutter speeds. Additionally, the results have implications for predicting the neutral point of a complete aircraft

Attainable Moment Set and Actuation Time of a Bio-Inspired Rotating Empennage

Future tactical aircraft will likely demonstrate improvements in efficiency, weight, and control by implementing bio-inspired control systems. This work analyzes a novel control system for a fighter aircraft inspired by the function of – and the degrees of freedom available in – a bird’s tail. The control system is introduced to an existing fighter aircraft design by removing the vertical tail and allowing the horizontal tail surfaces to rotate about the roll axis. Using a low-fidelity aerodynamic model, an analysis on the available controlling moments and actuation speeds of the baseline aircraft is compared to that of the bio-inspired rotating empennage design. The results of this analysis at a takeoff and approach flight condition indicate that the bio-inspired tail design is able to improve upon the baseline in terms of control power available for yaw by up to 170%, while also improving the actuation speed by about 450 milliseconds for moments about the pitch axis. The bio-inspired design is shown to have actuation times that are up to 600 milliseconds slower for generating yawing moments and a reduced roll control contribution from the tail in certain moment combinations. The impacts of these issues on control will need to be determined with analysis at additional flight conditions and a flight dynamics analysis