An analysis of methods for predicting the stability characteristics of an elastic airplane. Appendix B - Methods for determining stability derivatives
Stability derivatives for predicting stability characteristics of elastic aircraft
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Steady-State Computation of Constant Rotational Rate Dynamic Stability Derivatives
Dynamic stability derivatives are essential to predicting the open and closed loop performance, stability, and controllability of aircraft. Computational determination of constant-rate dynamic stability derivatives (derivatives of aircraft forces and moments with respect to constant rotational rates) is currently performed indirectly with finite differencing of multiple time-accurate computational fluid dynamics solutions. Typical time-accurate solutions require excessive amounts of computational time to complete. Formulating Navier-Stokes (N-S) equations in a rotating noninertial reference frame and applying an automatic differentiation tool to the modified code has the potential for directly computing these derivatives with a single, much faster steady-state calculation. The ability to rapidly determine static and dynamic stability derivatives by computational methods can benefit multidisciplinary design methodologies and reduce dependency on wind tunnel measurements. The CFL3D thin-layer N-S computational fluid dynamics code was modified for this study to allow calculations on complex three-dimensional configurations with constant rotation rate components in all three axes. These CFL3D modifications also have direct application to rotorcraft and turbomachinery analyses. The modified CFL3D steady-state calculation is a new capability that showed excellent agreement with results calculated by a similar formulation. The application of automatic differentiation to CFL3D allows the static stability and body-axis rate derivatives to be calculated quickly and exactly.
Park, Michael A.↗
AERONAUTICAL LAB. EXAMINATION OF RECENT LATERAL-STABILITY-DERIVATIVE DATA
Stability derivatives affecting lateral behavior of aircraft and missiles
LATERAL STABILITY↗
A parametric study of planform and aeroelastic effects on aerodynamic center, alpha- and q- stability derivatives. Appendix A: A computer program for calculating alpha- and q- stability derivatives and induced drag for thin elastic aeroplanes at subsonic and supersonic speeds
The computer program used to determine the rigid and elastic stability derivatives presented in the summary report is listed in this appendix along with instructions for its use, sample input data and answers. This program represents the airplane at subsonic and supersonic speeds as (a) thin surface(s) (without dihedral) composed of discrete panels of constant pressure according to the method of Woodward for the aerodynamic effects and slender beam(s) for the structural effects. Given a set of input data, the computer program calculates an aerodynamic influence coefficient matrix and a structural influence coefficient matrix.
Roskam, J.↗
Curved-flow, rolling-flow, and oscillatory pure-yawing wind-tunnel test methods for determination of dynamic stability derivatives
Dynamic stability derivatives are evaluated on the basis of rolling-flow, curved-flow and snaking tests. Attention is given to the hardware associated with curved-flow, rolling-flow and oscillatory pure-yawing wind-tunnel tests. It is found that the snaking technique, when combined with linear- and forced-oscillation methods, yields an important method for evaluating beta derivatives for current configurations at high angles of attack. Since the rolling flow model is fixed during testing, forced oscillations may be imparted to the model, permitting the measurement of damping and cross-derivatives. These results, when coupled with basic rolling-flow or rotary-balance data, yield a highly accurate mathematical model for studies of incipient spin and spin entry.
Chambers, J. R.↗
Correlation of Predicted and Flight Derived Stability and Control Derivatives with Particular Application to Tailless Delta Wing Configurations
Flight derived longitudinal and lateral-directional stability and control derivatives were compared to wind-tunnel derived values. As a result of these comparisons, boundaries representing the uncertainties that could be expected from wind-tunnel predictions were established. These boundaries provide a useful guide for control system sensitivity studies prior to flight. The primary application for this data was the space shuttle, and as a result the configurations included in the study were those most applicable to the space shuttle. The configurations included conventional delta wing aircraft as well as the X-15 and lifting body vehicles.
Weil, J.↗
Experimental Determination of Nonlinear Rotary Stability Derivatives
Nonlinear rotary stability derivatives - dynamic stability investigation - aerodynamics
DYNAMIC STABILITY↗
CFD-Based Frequency Domain Method for Dynamic Stability Derivative Estimation with Application to Transonic Truss-Braced Wing
This paper presents a dynamic stability estimation technique obtained from high-fidelity CFD simulations of the Mach 0.8 Transonic Truss-Braced Wing (TTBW). A series of unsteady RANS CFD simulations in FUN3D is performed on the TTBW in pitch and plunge oscillations at various reduced frequencies. The time-domain data are transformed into the frequency-domain data by Fourier series. Transfer functions of the dynamic stability derivatives are then estimated by a frequency-domain regression. The dynamic stability derivatives with respect to the angle of attack are determined by the regression of the unsteady aerodynamic coefficients for the plunge motion. The dynamic stability derivatives with respect to the pitch rate are deter-mined by the regression of the differential unsteady aerodynamic coefficients for the pitch motion upon the removal of the angle of attack contribution by the plunge motion. The steady-state stability derivatives are then compared to the results obtained from a stability analysis code VSPAERO as well as steady-state FUN3D simulations. The comparison of the steady-state stability derivatives shows excellent agreement.
Dynamic Stability Derivatives↗
Estimation of Aerodynamic Stability Derivatives for Space Launch System and Impact on Stability Margins
This paper describes the techniques involved in determining the aerodynamic stability derivatives for the frequency domain analysis of the Space Launch System (SLS) vehicle. Generally for launch vehicles, determination of the derivatives is fairly straightforward since the aerodynamic data is usually linear through a moderate range of angle of attack. However, if the wind tunnel data lacks proper corrections then nonlinearities and asymmetric behavior may appear in the aerodynamic database coefficients. In this case, computing the derivatives becomes a non-trivial task. Errors in computing the nominal derivatives could lead to improper interpretation regarding the natural stability of the system and tuning of the controller parameters, which would impact both stability and performance. The aerodynamic derivatives are also provided at off nominal operating conditions used for dispersed frequency domain Monte Carlo analysis. Finally, results are shown to illustrate that the effects of aerodynamic cross axis coupling can be neglected for the SLS configuration studied
Pei, Jing↗
A modified Newton-Raphson method for determining stability derivatives from flight data
Stability derivatives from flight data of fixed-wing aircraft determined by modified Newton-Raphson method
Iliff, K. W.↗
Effect of Horizontal-Tail Chord on the Calculated Subsonic Span Loads and Stability Derivatives of Isolated Unswept Tail Assemblies in Sideslip and Steady Roll
Subsonic span loads and the resulting stability derivatives have been calculated using the discrete-horseshoe-vortex method for a systematic series of horizontal tails in combination with a vertical tail of aspect ratio 1.0 in order to provide information on the effect of varying the chord of the horizontal tail for isolated tail assemblies performing sideslip and steady-roll motions. In addition, the effects of horizontal-tail dihedral angle for the sideslip case were obtained. Each tail surface considered had a taper ratio of 0.5 and an unswept quarter-chord line. The investigation covered variations in horizontal-tail chord, horizontal-tail span, and vertical location of the horizontal tail. The span loads and the resulting total stability derivatives as well as the vertical- and horizontal-tail contributions to these tail-assembly derivatives are presented in the figures for the purpose of showing the influence of the geometric variables. The results of this investigation showed trends that were in agreement with the results of previous investigations for variations in horizontal-tail span and vertical location of the horizontal tail. Variations in horizontal-tail chord expressed herein in terms of the root-chord ratio, that is, the ratio of horizontal-tail root chord to vertical-tail root chord, were found to have a pronounced influence on most of the span loads and the resulting stability derivatives. For most of the cases considered, the rate of change of the span load coefficients and the stability derivatives with the root-chord ratio was found to be a maximum for small values of root-chord ratio and to decrease as root-chord ratio increased.
Booth, Katherine W.↗
Stability derivatives of cones at supersonic speeds
The aerodynamic stability derivatives due to pitching velocity and vertical acceleration are derived for circular cones traveling at supersonic speeds. Both first-order and a combination of first and second order potential solutions are obtained, and in calculations for the forces, no approximations are made to the tangency condition or the isentropic pressure relation. In addition, expressions for the forces, moments, and stability derivatives of arbitrary bodies of revolution are derived from Newtonian impact theory.
Tobak, Murry↗
Dynamic Longitudinal and Directional Stability Derivatives for a 45 deg. Sweptback-Wing Airplane Model at Transonic Speeds
An investigation was made at transonic speeds to determine some of the dynamic stability derivatives of a 45 deg. sweptback-wing airplane model. The model was sting mounted and was rigidly forced to perform a single-degree-of-freedom angular oscillation in pitch or yaw of +/- 2 deg. The investigation was made for angles of attack alpha, from -4 deg. to 14 deg. throughout most of the transonic speed range for values of reduced-frequency parameter from 0.015 to 0.040 based on wing mean aerodynamic chord and from 0.04 to 0.14 based on wing span. The results show that reduced frequency had only a small effect on the damping-in-pitch derivative and the oscillatory longitudinal stability derivative for all Mach numbers M and angles of attack with the exception of the values of damping coefficient near M = 1.03 and alpha = 8 deg. to 14 deg. In this region, the damping coefficient changed rapidly with reduced frequency and negative values of damping coefficient were measured at low values of reduced frequency. This abrupt variation of pitch damping with reduced frequency was a characteristic of the complete model or wing-body-vertical-tail combination. The damping-in-pitch derivative varied considerably with alpha and M for the horizontal-tail-on and horizontal-tail-off configurations, and the damping was relatively high at angles of attack corresponding to the onset of pitch-up for both configurations. The damping-in-yaw derivative was generally independent of reduced frequency and M at alpha = -4 deg. to 4 deg. At alpha = 8 deg. to 14 deg., the damping derivative increased with an increase in reduced frequency and alpha for the configurations having the wing, whereas the damping derivative was either independent of or decreased with increase in reduced frequency for the configuration without the wing. The oscillatory directional stability derivative for all configurations generally decreased with an increase in the reduced-frequency parameter, and, in some instances, unstable values were measured for the model configuration with the horizontal tail removed.
Bielat, Ralph P.↗
Summary of Methods for Calculating Dynamic Lateral Stability and Response and for Estimating Lateral Stability Derivatives
A summary of methods for making dynamic lateral stability and response calculations and for estimating the aerodynamic stability derivatives required for use in these calculations is presented. The processes of performing calculations of the time histories of lateral motions, of the period and damping of these motions, and of the lateral stability boundaries are presented as a series of simple straightforward steps. Existing methods for estimating the stability derivatives are summarized and, in some cases, simple new empirical formulas are presented. Reference is also made to reports presenting experimental data that should be useful in making estimates of the derivatives. Detailed estimating methods are presented for low-subsonic-speed conditions but only a brief discussion and a list of references are given for transonic- and supersonic-speed conditions.
Campbell, John P↗
Summary of methods for calculating dynamic lateral stability and response and for estimating aerodynamic stability derivatives
A summary of methods for making dynamic lateral stability and response calculations and for estimating the aerodynamic stability derivatives required for use in these calculations is presented. The processes of performing calculations of the time histories of lateral motions, of the period and damping of these motions, and of the lateral stability boundaries are presented as a series of simple straightforward steps. Existing methods for estimating the stability derivatives are summarized and, in some cases, simple new empirical formulas are presented. Detailed estimation methods are presented for low-subsonic-speed conditions but only a brief discussion and a list of references are given for transonic and supersonic speed conditions.
Campbell, John P↗
A comparison of two methods of extracting stability derivatives from flight test data
Two methods for extracting stability derivatives from flight data are compared. A modified Newton-Raphson quasilinearization minimization technique and a digital-analog (hybrid) matching technique were used to analyze the same data maneuvers obtained from two aircraft. About 70 maneuvers from an F-111E aircraft were analyzed over a Mach number range of 0.3 to 2.0 and an angle of attack range of 3 to 19 degrees. About 20 maneuvers were analyzed for the X-24A lifting body at Mach numbers of 0.5, 0.8, and 0.9, and an angle of attack range of 4 to 13 degrees. Stability derivatives were extracted from these maneuvers and the results from the two techniques, along with wind tunnel results, were compared.
Kirsten, P. W.↗
Definition and application of longitudinal stability derivatives for elastic airplanes
A set of longitudinal stability derivatives for elastic airplanes is defined from fundamental principles allowing perturbations in forward speed. Application of these derivatives to longitudinal stability analysis by use of approximate expressions for static stability and control parameters as well as the dynamic equations of motion is illustrated. One commonly used alternative formulation for elastic airplanes is shown to yield significant inaccuracies because of inappropriate interpretation of inertial effects.
Kemp, W. B., Jr.↗
Theoretical stability derivatives of thin sweptback wings tapered to a point with sweptback or sweptforward trailing edges for a limited range of supersonic speeds
The stability derivatives valid for a limited range of supersonic speeds are presented for a series of sweptback wings tapered to a point with sweptback or sweptforward trailing edges. These wings were derived by modifying the trailing edge of a basic triangular wing so that it coincided with lines drawn from the wing tips to the wing axis of symmetry. The stability derivatives were formulated by using the pressure distributions previously obtained for the basic triangular wing for angle of attack, constant vertical acceleration, sideslip, pitching, rolling, and yawing. Explicit expressions are given for the stability derivatives with respect to principal body axes, and conversion formulas are provided for the transformation to stability axes. The results are limited to Mach numbers for which the wing is contained within the Mach cones springing from the vertex and from the trailing edge of the center section of the wing.
Malvestuto, Frank S , Jr↗