Stability Derivatives Research Articles

Aerodynamic and flight dynamic interaction in spin

PurposeThe purpose of this paper is to describe an integrated approach to spin analysis based on 6-DOF (degrees of freedom) fully nonlinear equations of motion and a three-dimensional multigrid Euler method used to specify a flow model. Another purpose of this study is to investigate military trainer performance during a developed phase of a deliberately executed spin, and to predict an aircraft tendency while entering a spin and its response to control surface deflections needed for recovery.Design/methodology/approachTo assess spin properties, the calculations of aerodynamic characteristics were performed through an angle-of-attack range of −30 degrees to +50 degrees and a sideslip-angle range of −30 degrees to +30 degrees. Then, dynamic equations of motion of a rigid aircraft together with aerodynamic loads being premised on stability derivatives concept were numerically integrated. Finally, the examination of light turboprop dynamic behaviour in post-stalling conditions was carried out.FindingsThe computational method used to evaluate spin was positively verified by comparing it with the experimental outcome. Moreover, the Euler code-based approach to lay down aerodynamics could be considered as reliable to provide high angles-of-attack characteristics. Conclusions incorporate the results of a comparative analysis focusing especially on comprehensive assessment of output data quality in relation to flight tests.Originality/valueThe conducted calculations take into account aerodynamic and flight dynamic interaction of an aerobatic-category turboprop in spin conditions. A number of manoeuvres considering different aircraft configurations were simulated. The computational outcomes were subsequently compared to the results of in-flight tests and the collected data were thoroughly analysed to draw final conclusions.

Aircraft neural modeling and parameter estimation using neural partial differentiation

PurposeThe purpose of this paper is to build a neural model of an aircraft from flight data and online estimation of the aerodynamic derivatives from established neural model.Design/methodology/approachA neural model capable of predicting generalized force and moment coefficients of an aircraft using measured motion and control variable is used to extract aerodynamic derivatives. The use of neural partial differentiation (NPD) method to the multi-input-multi-output (MIMO) aircraft system for the online estimation of aerodynamic parameters from flight data is extended.FindingsThe estimation of aerodynamic derivatives of rigid and flexible aircrafts is treated separately. In the case of rigid aircraft, longitudinal and lateral-directional derivatives are estimated from flight data. Whereas simulated data are used for a flexible aircraft in the absence of its flight data. The unknown frequencies of structural modes of flexible aircraft are also identified as part of estimation problem in addition to the stability and control derivatives. The estimated results are compared with the parameter estimates obtained from output error method. The validity of estimates has been checked by the model validation method, wherein the estimated model response is matched with the flight data that are not used for estimating the derivatives.Research limitations/implicationsCompared to the Delta and Zero methods of neural networks for parameter estimation, the NPD method has an additional advantage of providing the direct theoretical insight into the statistical information (standard deviation and relative standard deviation) of estimates from noisy data. The NPD method does not require the initial value of estimates, but it requires a priori information about the model structure of aircraft dynamics to extract the flight stability and control parameters. In the case of aircraft with a high degree of flexibility, aircraft dynamics may contain many parameters that are required to be estimated. Thus, NPD seems to be a more appropriate method for the flexible aircraft parameter estimation, as it has potential to estimate most of the parameters without having the issue of convergence.Originality/valueThis paper highlights the application of NPD for MIMO aircraft system; previously it was used only for multi-input and single-output system for extraction of parameters. The neural modeling and application of NPD approach to the MIMO aircraft system facilitate to the design of neural network-based adaptive flight control system. Some interesting results of parameter estimation of flexible aircraft are also presented from established neural model using simulated data as a novelty. This gives more value addition to analyzing the flight data of flexible aircraft as it is a challenging problem in parameter estimation of flexible aircraft.

Flight dynamics and parametric modeling of a 2-DOF lab aircraft

This paper presents two degrees-of-freedom (2-DOF) modeling of a lab aircraft extending corresponding author’s previous work on 1-DOF. The yaw motion is an additional DOF introduced along with the earlier work on pitch plane alone. The test-rig is designed, developed, instrumented, and interfaced with PC employing data acquisition card and real-time visualization software. Detailed mathematical models from first principles are developed incorporating important stability and control derivatives. The theoretical models are iteratively improved and validated through experimentation. The comparison reveals close agreement between math models and experimental ones. The developed high-fidelity models are to be employed for closed-loop control design and evaluation of system performance.

The impact of changing the type of understeer on vehicle handling

The transient response of a truck with a step control action on the steering studies in the paper. The car is represented by a one-mass flat design model. The equations of the machine motion are written in the form of stability derivatives. Calculation of direct estimates of the quality of the transition process on the angular velocity of the car at a stepwise (step) control action is made. The influence of the of the rotation type change on the car handling is presented.

Computation of Stability Derivatives of an oscillating cone for specific heat ratio = 1.66

In this paper the expressions for stiffness and Damping derivatives are obtained in a closed form for perfect gas where the flow is quasi-steady and axi-axisymmetric, and the nose semi angle of the cone is such that the Mach number M2 behind the shock M2 ≥ 2.5. Results are presented for an oscillating cone for gas with = 1.666, at different Mach numbers and semi cone angles. The Stiffness derivative decreases with pivot position and also with semi vertex angle, there is substantial change in the stiffness derivative when semi-vertex has been increased from 5 degrees to ten degrees, further increase in the semi-vertex angle results in marginal change in the stiffness derivative. Due the marginal change in the Mach number level there is marginal increase in the magnitude of the stability and with further increase in the inertia level the stability derivative conform to the Mach number independence principle. The present theory for Oscillating cone is restricted to quasi-steady case. Viscous effects have been neglected. The expressions so obtained for stability derivative in pitch are valid for a slender ogive which often approximates to the whole fuselage of an aircraft.

Estimation of Stability Derivatives in Newtonian Limit for Oscillating Cone

Stability derivatives in Newtonian limit for an oscillating cone are obtained. Stiffness derivative decreases with pivot position for the entire range of cone angles. For cone angles in the range 20 to 30 degrees there is substantial increase in the stiffness derivative. Damping derivative decreases with pivot position for various cone angles and attains a minima at h = 0.75 and then again with increase in pivot position there is non-linear increment in damping derivatives. There is considerable change in the magnitude, for higher cone angles in the range of 20 degrees and above as the centre of pressure has further moved towards the trailing edge of the cone at pivot position around h = 0.88. Stiffness derivative increases with cone angle for various pivot positions. Damping derivative with cone angle for various fixed pivot positions is seen to increase linearly with cone angle, it is also observed that this trend of linear increment tend to become non-linear for cone angles in the range 20 degrees and beyond. Damping derivative decreases with pivot position h = 0.8 for the entire range of cone angles, however, for pivot position h = 1.0, shows almost constant values up to cone angle of 20 degrees. For cone angle 30 degrees value of damping derivative coincides irrespective of pivot position being at h = 0.8 or 1.0 and this trend is attributed to the 3-D effect of the flow field.

Stability analysis of nonlinear dynamic system with linear observer for a multilink flexible manipulator

In this paper, the stability of nonlinear dynamic system for a multilink flexible manipulator (MLFM) is investigated by designing of linear observer to construct a closed-loop system such that for all admissible parameter uncertainties, unknown nonlinearities, and exogenous disturbances input. In a Lagrangian approach, one closed-loop augmented system is unfolded and proven to be asymptotically stable in the mean square (ASMS) by utilizing a Lyapunov theory. Further, if the stability of dynamic closed-loop system of the manipulator is maintained, a desired linear observer will be obtained by solving several algebraic Riccati inequalities. Simulation studies are used to verify the effectiveness of the proposed approach.One of the main contributions of this work is in the derivation of dynamic system stability with a suitable linear observer for the MLFM, based on Lyapunov theory, which: (1) explains physical mechanism for flexible-link movements and dynamics in a Lagrangian approach and (2) sufficient and necessary conditions of the dynamic system stability are derived through seeking the optimal feasible solutions of several algebraic Riccati matrix inequalities.

Stability derivatives of a oscillating wedges in viscous hypersonic flow

In this paper an oscillating wedge has been considered, and the fluid slabs are kept at 900 to the wedge surface. The solutions of the continuity, momentum,and energy equations are obtained. By using the Rankine-Hugoniot relations for shockwaves, we can find the conditions behind the shock.This theory is unsteady one because of the consideration of effect of secondary wave reflections.Solutions are obtained for hypersonic flow over the wedge by varying different wedge semi vertex angles.These results shows extremely good consistency with Hui’s predictions. When the effects of unsteadiness are considered then there is considerable change in the magnitude of the damping derivatives near the leading edge or initial 40 percent of the pivot positions and this difference is only marginal when we further down towards the trailing edge. However, this effect of unsteadiness is not visible in case of the stiffness derivatives. It is observed that the stiffness derivative increases with the increase in the wedge angle due to the increase in the plan form area of the wedge, resulting in the variation in the surface pressure distribution of the wedge. Further, due to the increment in the wedge angle the centre of pressure shifts towards the trailing edge.

ESTIMATION OF THE LATERAL AERODYNAMIC COEFFICIENTS FOR SKYWALKER X8 FLYING WING FROM REAL FLIGHT-TEST DATA

Stability and control derivatives of Skywalker X8 flying wing from flight-test data are estimated by using the combination of the output error and least square methods in the presence of the wind. Data is collected from closed loop flight tests with a proportional-integral-derivative (PID) controller that caused data co-linearity problems for the identification of the unmanned aerial vehicle (UAV) dynamic system. The data co-linearity problem is solved with a biased estimation via priori information, parameter fixing and constrained optimization, which uses analytical values of aerodynamic parameters, the level of the identifiability and sensitivity of the measurement vector to the parameters. Estimated aerodynamic parameters are compared with the theoretically calculated coefficients of the UAV, moreover, the dynamic model is validated with additional flight-test data and small covariances of the estimated parameters.

Unsteady aerodynamic effects in landing operation of transport aircraft and controllability with fuzzy-logic dynamic inversion

Aircraft landing in strong wind has been a safety problem for all types of aircraft. The specific issues involve hard landing, roll oscillation and runway veer-off. These issues are related to atmospheric disturbances, and/or dynamic ground effect. As a result, the aerodynamics will be different from those in steady flow concept. In this paper, some of the pertinent stability and control derivatives based on a small-disturbance concept will be presented. How these local stability and control characteristics affect global controllability will be examined with Fuzzy-Logic Dynamic Inversion. Controllability is judged from whether necessary control deflections exceed the imposed limits. Specific examples involving a twin-jet transport with hard landing, rolling oscillation before touchdown and runway veer-off event due to varying crosswind after touchdown are illustrated.

Aerodynamic Parameters Estimation Using Radial Basis Function Neural Partial Differentiation Method

Aerodynamic parameter estimation involves modelling of force and moment coefficients and computation of stability and control derivatives from recorded flight data. This problem is extensively studied in the past using classical approaches such as output error, filter error and equation error methods. An alternative approach to these model based methods is the machine learning such as artificial neural network. In this paper, radial basis function neural network (RBF NN) is used to model the lateral-directional force and moment coefficients. The RBF NN is trained using k-means clustering algorithm for finding the centers of radial basis function and extended Kalman filter for obtaining the weights in the output layer. Then, a new method is proposed to obtain the stability and control derivatives. The first order partial differentiation is performed analytically on the radial basis function neural network approximated output. The stability and control derivatives are computed at each training data point, thus reducing the post training time and computational efforts compared to hitherto delta method and its variants. The efficacy of the identified model and proposed neural derivative method is demonstrated using real time flight data of ATTAS aircraft. The results from the proposed approach compare well with those from the other.

Forced motions design for aerodynamic identification and modeling of a generic missile configuration

This article is focused on the design of forced motions and developing models that can accurately and rapidly predict the aerodynamic stability derivatives of air vehicles over a wide range of air speeds using time-accurate computational fluid dynamic (CFD) simulations. The test case is a generic missile configuration known as the Army–Navy (basic) Finner (ANF) missile. Longitudinal stability coefficients are available from a combination of free-flight and wind tunnel tests for Mach numbers in range of 0.5–4.5. Estimating stability derivatives of this vehicle requires a large number of static and dynamic CFD simulations using a brute-force approach. The present study instead uses a single forced motion to estimate vehicle's stability derivatives over a wide range of speed regimes. The results of this study show that identification of aerodynamic coefficients from time-accurate simulation of the forced motions requires significantly less computational time. A new aerodynamic model is also proposed that captures the aerodynamic coefficients' dependence on the angle of attack, pitch rate, time rate of change of angle of attack, and Mach number including the transonic region. The results presented show that the model predictions agree well with experimental data and those calculated from a brute-force approach. The methods of this work could reduce the computational cost of estimating stability derivatives up to 90%.

AEROM: NASA's Unsteady Aerodynamic and Aeroelastic Reduced-Order Modeling Software.

The origins, development, implementation, and application of AEROM, NASA's patented reduced-order modeling (ROM) software, are presented. Full computational fluid dynamic (CFD) aeroelastic solutions and ROM aeroelastic solutions, computed at several Mach numbers using the NASA FUN3D CFD code, are presented in the form of root locus plots in order to better reveal the aeroelastic root migrations with increasing dynamic pressure. The method and software have been applied successfully to several configurations including the Lockheed-Martin N+2 supersonic configuration and the Royal Institute of Technology (KTH, Sweden) generic wind-tunnel model, among others. The software has been released to various organizations with applications that include CFD-based aeroelastic analyses and the rapid modeling of high-fidelity dynamic stability derivatives. Recent results obtained from the application of the method to the AGARD 445.6 wing will be presented that reveal several interesting insights.

Flight Dynamic Simulation of Fighter In the Asymmetric External Store Release Process

In the fighter design, it is important to evaluate and analyze the flight dynamic of the aircraft earlier in the development process. One of the case is the dynamics of external store release process. A simulation tool can be used to analyze the fighter/external store system’s dynamics in the preliminary design stage. This paper reports the flight dynamics of Jet Fighter Experiment (JF-1 E) in asymmetric Advance Medium Range Air to Air Missile (AMRAAM) release process through simulations. The JF-1 E and AIM 120 AMRAAAM models are built by using Advanced Aircraft Analysis (AAA) and Missile Datcom software. By using these softwares, the aerodynamic stability and control derivatives can be obtained and used to model the dynamic characteristic of the fighter and the external store. The dynamic system is modeled by using MATLAB/Simulink software. By using this software, both the fighter/external store integration and the external store release process is simulated, and the dynamic of the system can be analyzed.

Effects of Structural Failure on the Safe Flight Envelope of Aircraft

The research presented in this paper focuses on the effects of structural failures on the safe flight envelope of an aircraft, which is the set of all the states in which safe maneuver of the aircraft can be assured. Nonlinear reachability analysis based on an optimal control formulation is performed to estimate the safe flight envelope using actual aircraft control surface inputs. This approach uses the physical model of an aircraft, where the aerodynamic stability and control derivatives are calculated using Digital Datcom. Symmetrical damages to a Cessna Citation II are considered with 25, 50, 75, and 100% spanwise vertical tail tip losses, leading to gradual shrinkage in the safe flight envelope. Based on the estimated safe flight envelopes, a discussion on the effects of structural damages and different flight conditions on the safe flight envelope is presented. In particular, the interpolatibility of the resulting safe flight envelopes is demonstrated. This property is essential for a novel database-driven flight envelope prediction method, where a database of safe flight envelopes is created offline to be accessed later in real time.

RANS study of Strouhal number effects on the stability derivatives of an autonomous underwater vehicle

This paper presents a numerical procedure to calculate the stability derivatives of an Autonomous Underwater Vehicle (AUV). In addition, the effects of Strouhal number on the stability derivatives are investigated. The stability derivatives are obtained by finding the body hydrodynamic responses to some specified time variant motions. Here, three distinct oscillating maneuvers: surge, pure-heave, and pure-pitch are proposed based on the linearized equations of motion. A Computational Fluid Dynamics (CFD) method based on Reynolds Averaged Navier–Stokes (RANS) equations with dynamic mesh technique is used to simulate the specified maneuvers. To verify the numerical scheme, computational results for simulation of the flow field are then validated by comparison with experimental data. In addition, a comparison between quasi-steady (Theodorsen’s theory) and RANS approaches is taken into account, which shows that the quasi-steady methods do not guarantee the solution accuracy for the purpose of stability derivative calculation. Finally, the effects of Strouhal number variations on these coefficients are investigated which shows that the dimensionless damping coefficients (except longitudinal damping coefficient) are evidently dependent on the Strouhal number, specially at high frequencies. However, the Strouhal number variation effects on the added-mass coefficients are small.

Calculation Method of Stability Derivatives and Verification for Power-lift Aircraft

It is difficult to realize the STOL and high-speed cruise at one time when designing an aircraft, whereas the application of power-lift technology has successfully solved this technical problem. The research about the dynamic characteristics of power-lift aircraft in hover and low speed flight regime is key important for the selection of control strategy in transition process. However, if adopting the traditional aerodynamic calculation method based on thrust coefficient concept, the hover and low speed forward flight of power-lift aircraft cannot be studied as a unified process and the stability derivatives cannot be accurately calculated in low speed. In this paper, a method for calculating the stability derivatives and model the aircraft by using full dimensional aerodynamic data is proposed, which can not only solve the problems mentioned above, and it is very convenient for the design of the control law in the transient process.

The Computation of Stiffness Derivative for an Ogive in the Hypersonic Flow

Expression for Stiffness derivative for an Ogive is derived with the suppositions of the arc on the nose of the cone from the air is being considered as perfect gas and the viscosity being neglected, the motion is quasi-steady, and the nose deflection angle of the Ogive θ is in such a way that the M2 after the shock is > 2.5. It is seen that due to the increment in angle θ, the stiffness derivative increases linearly due the progressive increase in the plan form area of the nose shape. The results indicate that there is a 38 percent increase in the stability derivative when the flow deflection θ was enhanced in the range of 5 to 10 degrees. With the further enhancement in the flow deflection angle θ from ten degrees and above, does not yield substantial increase in the stability derivative. Due to this change in the surface pressure distribution will lead to shift the location of centre of pressure, from the hinged position h = 0.5 to 0.8. The centre of pressure also has shifted towards the downstream, which lies in the range from h = 0.72 to 0.85.

Low Reynolds Number Numerical Simulation of the Aerodynamic Coefficients of a 3D Wing

A low Reynolds number, three-dimensional CFD analysis is carried out for a finite flat plate wing using the commercial CFD code STAR CCM+. The six-aerodynamic force and moment components CL, CD, CM, CN, Cl, CY and their derivatives are computed at a Reynolds numbers of 3x105 by varying the pitch, roll and yaw angles about the quarter chord point. The computed results have been validated with experimental aerodynamic balance data when possible. The results indicate that roll and yaw angle affect the aerodynamic coefficients of the flat plate wing along with the pitch angle. The influence of roll and yaw angles on the six aerodynamics coefficients were found to be significant for high pitch angles specially 10 and 15. Stability derivatives have also been reported. This data is important for the design of MAVs and small UAVs and is currently perhaps not available in the open literature.

Non-Static error tracking control for near space airship loading platform

A control scheme based on internal model with non-static error is presented against the uncertainty of the near space airship loading platform system. The uncertainty in the tracking table is represented as interval variations in stability and control derivatives. By formulating the tracking problem of the uncertainty system as a robust state feedback stabilization problem of an augmented system, sufficient condition for the existence of robust tracking controller is derived in the form of linear matrix inequality (LMI). Finally, simulation results show that the new method not only has better anti-jamming performance, but also improves the dynamic performance of the high-order systems.