Validation of a Mid-Fidelity Approach for Aircraft Stability and Control Characterization

I. Introduction Many complex distributed hybrid and electric propulsion aircraft have emerged to enable future Advanced Air Mobility (AAM) transportation missions [ 1 – 5 ]. There are many design concepts with a variety of mission profiles including vertical takeoff and landing (VTOL), short takeoff and landing (STOL), and conventional takeoff and landing (CTOL) configurations. Although the operational utility of distributed propulsion aircraft has great potential, there are many research areas that need to be addressed prior to introduction of these unique vehicles for AAM missions in the national airspace system. Vehicle technical challenges include: airworthiness certification, air traffic management, pilot-operator interface, handling qualities, simplified vehicle operations, contingency management, vehicle autonomy, and flight controls strategies. One important enabling tool for many research efforts is a vehicle flight dynamics simulation driven by an aero-propulsive model. Efficient and accurate aero-propulsive model development, however, is challenged by several vehicle attributes including: many control surfaces and propulsors, substantial propulsion-airframe interactions, and large flight envelopes that need to be characterized by a global aero-propulsive model.

Previous research has investigated methods for efficient full-envelope electric VTOL (eVTOL) aircraft aero-propulsive model development using computational fluid dynamics (CFD) simulations [ 6 , 7 ] and wind-tunnel testing [ 8 – 13 ]. These techniques were successful in developing accurate aero-propulsive models well-suited for flight dynamics simulations of complex aircraft; however, they required time consuming CFD simulations with substantial subject matter expertise to effectively execute or the availability of a physical aircraft model and wind-tunnel test facility. Other related work has investigated using low-to-mid fidelity analytical and/or computational methods for developing dynamic models applicable for flight controls applications [14–19].

The present effort builds on this previous eVTOL aircraft modeling research to make progress towards developing an approach for rapid aero-propulsive model development using mid-fidelity computational experiments, allowing a flight dynamics model to be developed early in the aircraft design process. This paper specifically focuses on prediction of performance, stability, and control characteristics for a NASA subscale eVTOL aircraft in its isolated-airframe configuration (i.e., without propellers installed). Future work is expected to be expanded to powered-airframe studies focused on reduced order aero-propulsive model development suitable for flight dynamics simulations. Contributions of this paper include development of an approach enabling efficient computational prediction of vehicle aerodynamics ® and comparison of the results to static wind-tunnel data. FlightStream , a commercial surface-vorticity flow solver developed by Research in Flight [ 20 ], is employed to compute aerodynamic forces and moments as a function of airflow angles, body-axis angular velocity, and control surface deflection angles which yields an isolated-airframe aerodynamic ® model suitable to perform flight simulations. FlightStream has been used previously to develop aerodynamic predictions for aircraft with significant propeller-airframe interactions at a fraction of the expense of running CFD ® simulations [ 21 – 29 ]. FlightStream has also been successfully applied to make aerodynamic predictions for numerous other aircraft configurations and components [30–41].

The paper is organized as follows: Section II introduces the research aircraft. Section III presents background ® ® information on the FlightStream flow solver software. The process used to automatically execute FlightStream ® simulations starting from OpenVSP geometry is outlined in Sec. IV. Comparisons of FlightStream predictions to wind-tunnel data are shown in Sec. V. Overall conclusions are summarized in Sec. VI.

II. Aircraft The modeling approach developed in this paper is applied to the Research Aircraft for eVTOL Enabling techNologies (RAVEN) Subscale Wind Tunnel and Flight Test (SWFT) model built at NASA Langley Research Center (LaRC).

The RAVEN SWFT is a 28.625% scale version of the RAVEN 1000-lb eVTOL aircraft concept [ 42 ], which has been conceptualized as a collaborative effort between NASA LaRC and the Georgia Institute of Technology. The RAVEN aircraft is a tilt-rotor eVTOL aircraft configuration with six variable-pitch propellers. The front four propellers tilt forward and are operational throughout the entire flight envelope. The rear two propellers do not tilt and serve as lifting propellers in hover and transition. The rear propellers are inactive in forward flight. The aircraft control surfaces included six flaperons, an all moving stabilator, and a rudder. In total, the vehicle has 24 independent control effectors: • Six propeller rotational speeds ( 𝑛 , 𝑛 , ..., 𝑛 ) 1 2 6 • Six propeller collective pitch angles ( 𝛿 , 𝛿 ,..., 𝛿 ) 𝑐 𝑐 𝑐 1 2 6 • Four nacelle tilt angles ( 𝛿 , 𝛿 , 𝛿 , 𝛿 ) 𝑡 𝑡 𝑡 𝑡 1 2 3 4 • Six flaperon deflection angles ( 𝛿 , 𝛿 ,..., 𝛿 ) 𝑓 𝑓 𝑓 1 2 6 • One stabilator deflection angle ( 𝛿 ) 𝑠 • One rudder deflection angle ( 𝛿 ) 𝑟 A schematic of the RAVEN aircraft with annotations showing the vehicle propulsor and control surface definitions is shown in Fig. 1. Flaperon and stabilator deflections are defined as positive trailing edge downward. Rudder deflection is defined as positive trailing edge left. As currently configured, propeller 1, 3, and 5 rotate counterclockwise and propeller 2, 4, and 6 rotate clockwise, as viewed from the perspective of each respective electric motor.

𝜹 𝒇 𝜹 𝟓 𝒕 𝟒 𝒏 , 𝜹 𝟔 𝒄 𝟔 𝜹 𝒓 𝜹 𝒇 𝟔 𝜹 𝜹 𝒇 𝒔 𝟑 𝜹 𝒇 𝟒 𝒏 , 𝜹 𝟒 𝒄 𝟒 𝜹 𝒕 𝟑 𝒏 , 𝜹 𝜹 𝟓 𝒄 𝟓 𝒇 𝟐 𝜹 𝒇 𝟏 𝒏 , 𝜹 𝟑 𝒄 𝜹 𝟑 𝒕 𝟐 𝜹 𝒕 𝟏 𝒏 , 𝜹 𝟐 𝒄 𝟐 𝒏 , 𝜹 𝟏 𝒄 𝟏 Fig. 1 RAVEN control effector definitions.

The RAVEN SWFT, pictured in the NASA Langley 12-Foot Low-Speed Tunnel (LST) [43] in Fig. 2, is a subscale aircraft configuration designed as a flight dynamics and controls testbed to advance eVTOL aircraft technology. As its name suggests, the vehicle is designed for use in both wind-tunnel and flight-test experiments. The RAVEN SWFT was (a) Front view (cruise configuration) (b) Overhead view (hover configuration) (c) Side view (mid-transition configuration) (d) Rear view (mid-transition configuration) Fig. 2 RAVEN SWFT mounted in the NASA Langley 12-Foot Low-Speed Tunnel.

(Credit: Lee Pollard, NASA Langley Research Center)

developed at NASA LaRC as one of several subscale eVTOL research aircraft intended to explore their unique flight characteristics and resolve implementation challenges to help bring similar full-scale vehicles into mainstream operation.

Previous aircraft have included the LA-8 [ 44 , 45 ] and GL-10 [ 46 ], which have enabled research in computational aerodynamic predictions [ 27 , 37 ], wind-tunnel testing [ 8 , 11 , 47 ], high incidence angle propeller aerodynamics [ 48 – 50 ], aero-propulsive modeling [9, 12, 13, 46, 51], flight controls [52, 53], and flight-test strategies [54–57].

Initial RAVEN SWFT wind-tunnel tests have been performed in the 12-Foot LST for the isolated 19.5-inch variable-pitch propeller [ 58 ], the isolated airframe (without propellers operating), and powered airframe (with propellers operating). RAVEN SWFT wind-tunnel data collected during the isolated airframe experiments is used as validation ® data for FlightStream predictions shown later in the paper.

® III. FlightStream Background ® The mid-fidelity flow solutions for this effort were performed using the FlightStream viscous surface-vorticity ® flow solver. FlightStream has been developed by Research in Flight [ 20 ] as a highly efficient compressible subsonic, ® three-dimensional viscous-coupled, surface-vorticity panel-method flow solver. FlightStream allows for rapid analysis ® of unconventional aircraft in both powered and unpowered configurations. The FlightStream flow solver has been developed under several NASA and USAF Small Business Innovation Research (SBIR) developmental contract awards [59–63].

® FlightStream makes use of the resolved surface-vorticity to compute aerodynamic load distributions using advanced ® Fast Multipole Method and wake proximity avoidance algorithms. These innovations allow FlightStream to generate ® aerodynamic results in minutes for multirotor simulations using an unstructured surface mesh. FlightStream works directly with commercial computer-aided design (CAD) software for its geometry input by merging the surface boundary ® conditions with the analytical CAD provided by the designer. FlightStream also works with OpenVSP [ 64 , 65 ] and ® The Engineering Sketch Pad [ 66 ]. As part of NASA SBIR work [ 59 , 60 ], FlightStream was expanded to allow for nonlinear aerodynamics, including unsteady flow, prediction of the onset of stall, 𝐶 , and post-stall aerodynamics.

𝐿 max ® Key features of FlightStream are summarized in Table 1.

® Table 1 Summary of key FlightStream features 1. The use of unstructured surface meshes (volume meshing is not required).

2. A subsonic, transonic, and supersonic panel-method solver capable of solutions in seconds.

3. A Fast Multipole Method solver allowing very large mesh sizes solved in seconds-to-minutes with 𝑂 ( 𝑛 log 𝑛 ) efficiency in the potential flow solver.

4. Nonlinear solver capabilities which include models for the boundary layer and flow separation.

5. A fully steady or unsteady time-domain solver.

6. Advanced control surface modeling and flight control system integration capabilities.

7. Fluid-structure interactions modeling with embedded static and dynamic aeroelastic, flutter, and aeroservoelastic modeling tools integrated with the core flow solvers.

8. The ability to execute of six-degree-of-freedom (6DOF) motion simulations.

9. A modern user interface/experience with a fully-scriptable application programming interface (API).

10. Integration with commercial and open-source CAD software.

IV. Aerodynamic Modeling Approach A new approach was formulated and applied to convert OpenVSP [ 64 ] geometry into a form compatible with the ® ® FlightStream software [ 20 ]. This was followed by automatic execution of flow simulations using the FlightStream scripting capabilities. The steps are as follows: 1) Create an OpenVSP model for the aircraft geometry. A RAVEN SWFT OpenVSP model in its cruise (forward flight) configuration was developed for this study. The vehicle components modeled in OpenVSP included the fuselage, main wing, horizontal tail, vertical tail, propellers, landing gear, inboard sponsons, outboard nacelles, and simplified representations of the electric motors. The model is a 28.625%-scale version of the 1000-lb RAVEN OpenVSP model with slight modifications made to emulate the as-built RAVEN SWFT aircraft geometry. The RAVEN SWFT OpenVSP model is shown in Fig. 3.

(a) Isolated airframe (b) Powered airframe Fig. 3 RAVEN SWFT OpenVSP model.

® 2) Adjust the tessellation and clustering for each component in the OpenVSP model. The FlightStream User Guide [ 67 ] contains guidance on how to set mesh controls for lifting and non-lifting components to facilitate ® successful grid generation in FlightStream . Furthermore, it is important to ensure that the OpenVSP mesh ® resolution is finer than the mesh resolution used in FlightStream .

3) Export the aircraft geometry from OpenVSP by creating a degenerate geometry (DegenGeom) file. For ® this work, the DegenGeom m-file export option was used to create a script that could be run in MATLAB . The propeller components were not included in the DegenGeom file, but their locations were stored to be incorporated into the model later in the process.

4) Convert the DegenGeom file into a Component Cross Section (CCS) file. The CCS file, discussed in the ® ® FlightStream User Guide [ 67 ], is a text file that allows the user to import aircraft geometry into FlightStream in a manner suitable for automatic mesh generation. The CCS file also allows the user to define control surfaces ® and set several meshing options. For this work, a MATLAB script was written to automatically convert the DegenGeom m-file into the CCS file format along with control surface positions and certain user-specified ® meshing parameters. The RAVEN SWFT isolated-airframe FlightStream representation created from the CCS file is shown in Fig. 4.

® Fig. 4 RAVEN SWFT isolated-airframe FlightStream mesh and boundary conditions.

5) Perform a mesh refinement study. Executing a mesh refinement study for each geometric component is an ® essential task to ensure that FlightStream predictions are reliable and accurate. For each isolated component, the first step is to perform a mesh refinement study in the direction of the highest curvature, while holding the number of grid points in the lower curvature direction fixed to a reasonably dense value. The results have sufficiently converged when the percent difference of the dominant force and moment components between neighboring grid refinement levels is less than 1-2%, which specifies the number of grid points that should be used for subsequent analyses. The second step is to perform a mesh refinement study in the lower curvature direction while holding the number of grid points in the higher curvature direction fixed to the value determined in the first step. For the most reliable results, the mesh refinement study should be performed at a non-zero angle of incidence relative to the oncoming flow (i.e., running the analysis at a non-zero angle of attack and angle of sideslip) and using the inviscid solver (i.e., viscous coupling and flow separation options should be disabled). For this work, the grid refinement was adjusted in a CCS file using the user-defined meshing parameters “Mesh_U” and “Mesh_V” [ 67 ]. The mesh refinement process is demonstrated for the RAVEN SWFT main wing in Fig. 5.

A mesh refinement study is first performed in the chordwise direction by varying the number of chordwise grid points while holding the spanwise grid fixed at 40 points. Figure 5a shows that the percent difference of the 𝐶 and 𝐶 values is less than 1% using 200 chordwise points, which was selected as the number of chordwise 𝐿 𝑚 grid points for the wing. A mesh refinement study was then performed in the spanwise direction holding the chordwise grid fixed at 200 points. As shown in Fig. 5b, the 𝐶 and 𝐶 values appear to sufficiently converge 𝐿 𝑚 using 50 spanwise grid points.

(a) Step 1: chordwise grid refinement (40 spanwise points) (b) Step 2: spanwise grid refinement (200 chordwise points) Fig. 5 Mesh refinement study for the RAVEN SWFT wing (inviscid solver, 𝜶 = 2 deg, 𝜷 = 0 deg, 𝑽 = 54 . 3 ft/s).

® ® 6) Create FlightStream script files to automatically execute simulations. A MATLAB script was written ® ® to automatically generate a FlightStream script file for each simulation run. The FlightStream script files were configured to perform tasks such as importing a CCS file, creating coordinate systems, creating propellers (modeled as Conway actuator discs [ 68 ]), specifying boundary conditions, setting flow solver options, setting ® control effector settings, running FlightStream simulations, and saving results.

® ® 7) Execute FlightStream script files to generate aerodynamic predictions. A MATLAB script was written to ® automatically run a set of FlightStream script files for automatic data generation for an arbitrary number of ® flow conditions and control effector settings. An example RAVEN SWFT powered-airframe FlightStream flow solution visualization is shown in Fig. 6.

® Fig. 6 Example powered-airframe FlightStream surface pressure predictions for the RAVEN SWFT aircraft.

® The set of procedures outlined in this section is summarized in Fig. 7. This process allows FlightStream solutions to be run automatically at a variety of user-specified flight conditions for efficient prediction of applied forces and moments which can be used for aerodynamic database development.

OpenVSP DegenGeom Batch Script CCS File FlightStream Model File Execution Script Mesh Aerodynamic Experiment Aircraft Generation Refinement Predictions Information Geometry ® Fig. 7 Process to execute FlightStream simulations.

V. Results ® To demonstrate and validate the approach outlined in the previous section, FlightStream was used to compute predictions of the isolated-airframe performance, stability, and control characteristics for the RAVEN SWFT aircraft.

This includes computing the nondimensional aerodynamic force coefficients L D 𝑌 𝐶 = , 𝐶 = , 𝐶 = 𝐿 𝐷 𝑌 ¯ 𝑞𝑆 ¯ 𝑞𝑆 ¯ 𝑞𝑆 and moment coefficients 𝐿 𝑀 𝑁 𝐶 = , 𝐶 = , 𝐶 = 𝑙 𝑚 𝑛 ¯ 𝑞𝑆𝑏 ¯ 𝑞𝑆 ¯ 𝑐 ¯ 𝑞𝑆𝑏 variation with angle of attack, angle of sideslip, angular rates, and control surface deflection angles. The current estimated RAVEN SWFT forward flight center of gravity position was used as the moment reference location. Several ® comparisons of FlightStream predictions to wind-tunnel data collected for the RAVEN SWFT aircraft were made ® ® to validate FlightStream solutions and determine suitable FlightStream settings for modeling the RAVEN SWFT ® aircraft. FlightStream solutions were run with a fully turbulent boundary layer and the pressure-based calculations were taken as the final results. Inviscid solutions were run for all cases; furthermore, angle of attack and angle of sideslip ® sweeps were performed with Stratford flow separation models enabled [ 59 ]. For this paper, the FlightStream solutions ® were executed with the viscous coupling option disabled. FlightStream Build #3092023 was used to compute the results shown in this paper.

® The static wind-tunnel data used for validation of the FlightStream solutions were collected using randomized test factor sweeps and statistically designed experiments (e.g., see Refs. [ 69 , 70 ]) varying the airflow angles and control surface deflection angles. The data were collected in this manner to quantify the uncertainty of the wind-tunnel measurements and enable development of a response surface equation (RSE) for each aerodynamic force and moment component. Note that the randomized data collection strategy is intended to expose and characterize the uncertainty in the measured data and, consequently, makes the raw data quality look noisier than a traditional one-factor-at-a-time sweep where a single test factor is varied by sequentially increasing or decreasing its value. The wind-tunnel data are plotted as individual data points with repeat points shown where available to convey the magnitude of the measurement uncertainty. The wind-tunnel data are also displayed in the form of RSE predictions of the mean response along with a 95% confidence interval (CI) on the mean response and a 95% prediction interval (PI) characterizing the uncertainty in the response predictions for individual data points [ 70 ]. All wind-tunnel data were collected at a dynamic pressure of ® ¯ 𝑞 = 3 . 5 psf (freestream velocity of 𝑉 = 54 . 3 ft/s at standard sea level conditions) and, accordingly, the FlightStream solutions were run at these freestream settings.

A. Angle of Attack and Sideslip Sweep Predictions ® Figure 8 shows FlightStream predictions and wind-tunnel measurements of the lift, drag, and pitching moment ® coefficients for an angle of attack sweep at 𝛽 = 0 deg. The results for two types of FlightStream flow simulations are ® shown: an inviscid flow simulation and a flow simulation including the effects of flow separation (using the FlightStream ® axial flow separation setting for the wing and horizontal tail, and the FlightStream longitudinal crossflow setting for ® the fuselage and sponsons). The lift coefficient variation with angle of attack is well captured by both FlightStream solutions below stall. The solution with flow separation modeled accurately predicts the stall location and maximum lift coefficient, as a result of employing the axial flow separation model on the wing and horizontal tail. The overall drag coefficient is underpredicted by the inviscid model, but the curvature matches the wind-tunnel data reasonably well.

Below stall, the solution including flow separation effects better approximates the drag variation with angle of attack.

This improvement was primarily gained by employing the longitudinal crossflow model for the fuselage and sponsons.

® The post-stall drag increase exhibited in the wind-tunnel data is not captured by either FlightStream solution. The Fig. 8 Angle of attack sweep at ¯ 𝒒 = 3 . 5 psf ( 𝑽 = 54 . 3 ft/s), 𝜷 = 0 deg, and zero control surface deflection.

® pitching moment variation with angle of attack is reasonably well predicted by the inviscid FlightStream solution for an angle of attack greater than approximately 2 deg. The solution with flow separation includes non-physical nonlinear behavior in the angle of attack range of 5 to 11 deg as a result of non-smooth introduction of the flow separation models, ® ® which is expected to be addressed and improved in a future version of FlightStream . Furthermore, both FlightStream solutions do not capture the decreasing stability, and eventual instability, of the pitching moment slope exhibited in the wind-tunnel data at a negative angle of attack. Resolving this discrepancy will be the subject of future work.

® Figure 9 shows FlightStream predictions and wind-tunnel measurements of side force, rolling moment, and yawing ® moment coefficients for an angle of sideslip sweep at 𝛼 = 2 deg. To aid in comparison of the FlightStream results and wind-tunnel measurements, small asymmetries in the lateral-directional force and moment measurements have ® been removed by subtracting the force and moment values at 𝛽 = 0 deg from all of the data. Two FlightStream flow solutions are shown: an inviscid solution and a solution computed using the crossflow flow separation model enabled on ® the fuselage. For 𝐶 , the FlightStream solution with flow separation well-represents the measured wind-tunnel data; 𝑌 ® the inviscid FlightStream solution predicts a slope that is lower in magnitude compared to the wind-tunnel data. For ® 𝐶 , both FlightStream model predictions agree well with the wind-tunnel data, with the inviscid solution slightly more 𝑙 ® closely following the mean response predicted by the RSE. For 𝐶 , the inviscid FlightStream model exhibits a better 𝑛 match to the wind-tunnel data compared to the model with flow separation enabled, which overpredicts the yaw stiffness.

Fig. 9 Angle of sideslip sweep at ¯ 𝒒 = 3 . 5 psf ( 𝑽 = 54 . 3 ft/s), 𝜶 = 2 deg, and zero control surface deflection.

The 𝛼 and 𝛽 stability derivatives at 𝛼 = 2 deg and 𝛽 = 0 deg computed from the wind-tunnel-derived RSEs ® and FlightStream predictions using a smoothed polynomial representation of the data are shown in Table 2. The ® inviscid FlightStream stability derivative predictions are closer to the wind-tunnel derived values compared to the flow separation model predictions, except for 𝐶 where the flow separation model prediction is closer to the 𝑌 𝛽 wind-tunnel-derived value.

Table 2 Comparison of static stability derivatives at ¯ 𝒒 = 3 . 5 psf ( 𝑽 = 54 . 3 ft/s), 𝜶 = 2 deg, and 𝜷 = 0 deg FlightStream FlightStream Parameter Wind Tunnel (inviscid) (flow separation) 𝐶 +4.39 +4.64 +5.10 𝐿 𝛼 𝐶 +0.214 +0.342 +0.353 𝐷 𝛼 𝐶 -0.271 -0.312 -0.413 𝑚 𝛼 𝐶 -1.24 -0.737 -1.21 𝑌 𝛽 𝐶 -0.0650 -0.0685 -0.0593 𝑙 𝛽 𝐶 +0.0169 +0.0137 +0.0289 𝑛 𝛽 B. Control Surface Effectiveness Predictions ® Each of the control surfaces were modeled in FlightStream by specifying their geometry in the CCS file and ® executing geometry rotation commands in the FlightStream script files where applicable. Because the aircraft has an all-moving stabilator, the stabilator deflections were modeled by rotating the whole horizontal tail component about its hinge point. The flaperon and rudder control surfaces were modeled using two different approaches possible in ® FlightStream : morphing control surfaces and physically separating/deflecting control surfaces, which are depicted in Fig. 10a and Fig. 10b, respectively. The morphing surface approach rotates the surface about its hinge location which stretches the mesh and maintains a continuous trailing edge on the lifting surface. The separated surface approach results in a gap between the deflected control surface and lifting surface with a separate trailing edge on each component.

® To expedite the FlightStream computations, the stabilator predictions were run without the landing gear, sponsons, ® motor representations, and nacelles. Similarly, the rudder and flaperon FlightStream solutions were computed by only ® including the vertical tail and main wing components, respectively. Only inviscid FlightStream solutions at 𝛼 = 2 deg and 𝛽 = 0 deg were executed for the control surface predictions shown in this paper.

(a) Morphing control surface deflection (b) Physical control surface deflection ® Fig. 10 Comparison of FlightStream control surface deflection options.

® Figure 11 shows a stabilator sweep comparison between the inviscid FlightStream solution and wind-tunnel measurements. The plot shows the change in lift, drag, and pitching moment coefficients relative to zero stabilator ® ® deflection. The FlightStream predictions show overall good agreement with the wind-tunnel data. The FlightStream solution is seen to slightly overpredict the change in lift and pitching moment due to stabilator deflection.

Fig. 11 Stabilator sweep at ¯ 𝒒 = 3 . 5 psf ( 𝑽 = 54 . 3 ft/s), 𝜶 = 2 deg, and 𝜷 = 0 deg.

® A rudder sweep comparison between wind-tunnel data and FlightStream predictions for 𝐶 , 𝐶 , and 𝐶 is shown 𝑌 𝑙 𝑛 in Fig. 12. The results for morphing and physical control rudder deflection models are similar and agree well with the ® wind-tunnel data. The FlightStream solution slightly overpredicts the yawing moment resulting from rudder deflection exhibited in the wind-tunnel data.

® Figures 13-15 show FlightStream left inboard, midboard, and outboard flaperon sweep predictions compared to Fig. 12 Rudder sweep at ¯ 𝒒 = 3 . 5 psf ( 𝑽 = 54 . 3 ft/s), 𝜶 = 2 deg, and 𝜷 = 0 deg.

® wind-tunnel data for 𝐶 , 𝐶 , and 𝐶 . The right wing flaperon FlightStream predictions were nearly identical and 𝐿 𝐷 𝑙 are, thus, not shown. For this study, the morphing control surface approach yielded more reliable solutions for the flaperons and is the only deflection method shown on the plots. The outboard flaperon predictions ( 𝛿 ) agree very 𝑓 well with the wind-tunnel data with only a slight over-prediction of control effectiveness. The midboard and inboard flaperon deflections ( 𝛿 and 𝛿 ) agree reasonably well with the wind-tunnel data, but overpredict the flaperon control 𝑓 𝑓 2 3 effectiveness for lift and rolling moment production.

Fig. 13 Left outboard flaperon sweep at ¯ 𝒒 = 3 . 5 psf ( 𝑽 = 54 . 3 ft/s), 𝜶 = 2 deg, and 𝜷 = 0 deg.

Fig. 14 Left midboard flaperon sweep at ¯ 𝒒 = 3 . 5 psf ( 𝑽 = 54 . 3 ft/s), 𝜶 = 2 deg, and 𝜷 = 0 deg.

Fig. 15 Left inboard flaperon sweep at ¯ 𝒒 = 3 . 5 psf ( 𝑽 = 54 . 3 ft/s), 𝜶 = 2 deg, and 𝜷 = 0 deg.

® The control derivatives at 𝛼 = 2 deg and 𝛽 = 0 deg computed from the wind-tunnel-derived RSEs and FlightStream ® predictions using a smoothed polynomial representation of the data are shown in Table 3. The FlightStream control ® derivative computations are for the morphing rudder and morphing flaperon predictions. The FlightStream control derivative predictions are seen to overpredict the control effectiveness compared to the wind-tunnel-derived values, as would be expected from an inviscid flow solution. However, given the low computational expense of the mid-fidelity ® aerodynamic prediction tool, the FlightStream control derivative predictions are acceptably close to the wind-tunnel results.

Table 3 Comparison of control derivatives at ¯ 𝒒 = 3 . 5 psf ( 𝑽 = 54 . 3 ft/s), 𝜶 = 2 deg, and 𝜷 = 0 deg Parameter Wind Tunnel FlightStream 𝐶 +0.412 +0.548 𝐿 𝛿𝑠 𝐶 +0.0220 +0.0274 𝐷 𝛿𝑠 𝐶 -1.21 -1.65 𝑚 𝛿𝑠 𝐶 +0.135 +0.152 𝑌 𝛿𝑟 𝐶 +0.00661 +0.00680 𝑙 𝛿𝑟 𝐶 -0.0533 -0.0647 𝑛 𝛿𝑟 𝐶 +0.411 +0.450 𝐿 𝛿 𝑓 𝐶 +0.0314 +0.0349 𝐷 𝛿 𝑓 𝐶 +0.131 +0.135 𝑙 𝛿 𝑓 𝐶 +0.203 +0.332 𝐿 𝛿 𝑓 𝐶 +0.00834 +0.0238 𝐷 𝛿 𝑓 𝐶 +0.0460 +0.0745 𝑙 𝛿 𝑓 𝐶 +0.270 +0.452 𝐿 𝛿 𝑓 𝐶 +0.0140 +0.0293 𝐷 𝛿 𝑓 𝐶 +0.0281 +0.0432 𝑙 𝛿 𝑓 C. Dynamic Derivative Predictions ® FlightStream can be used to predict dynamic derivatives using both its Stability and Control Toolbox and by setting a rotational flowfield. The later approach was used for this work so that a sweep of rotation rates about the aircraft center of gravity location could be collected. The results generally agreed with physical intuition, but are not shown because wind-tunnel data was not used to validate the predictions. Future dynamic wind-tunnel testing is expected to

® yield dynamic derivative values that can be compared to FlightStream predictions.

VI. Conclusions

® FlightStream , a mid-fidelity surface-vorticity flow solver, was employed to predict the variation of aerodynamic force and moment coefficients with airflow angles, angular rates, and control surface deflection angles to analyze aircraft performance, stability, and control characteristics. The analysis approach was applied to the RAVEN SWFT aircraft in ® its isolated-airframe configuration. The FlightStream results were compared to static wind-tunnel data collected for the ® RAVEN SWFT aircraft. The general character of the FlightStream predictions agree well with the wind-tunnel data.

The computational predictions were deemed a sufficiently accurate representation of the actual aircraft aerodynamics, ® prefaced with the understanding that FlightStream is a mid-fidelity tool that yields quick flow solutions accessible early in the aircraft design process. Given the suitable results obtained for the isolated airframe, future work seeks to apply and refine the approach for the RAVEN SWFT powered airframe, as well as other eVTOL aircraft configurations, to enable development of aero-propulsive models intended for use in flight dynamics simulations. Future work is also ® expected to include using the FlightStream viscous coupling settings, validation of dynamic derivative predictions, and enhancement of the range of applicability and accuracy for control surface deflection predictions.

Acknowledgments

This research was funded by the NASA Aeronautics Research Mission Directorate (ARMD) Transformational Tools and Technologies (TTT) project and Convergent Aeronautics Solutions (CAS) project. Wind-tunnel test support was provided by Ronald Busan, Wes O’Neal, Gregory Howland, Matthew Gray, Neil Coffey, Clinton Duncan, Earl Harris, and Richard Thorpe.

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