Applications of model structure determination to flight test data

Several statistical and information criteria need to be considered when selecting an adequate model. Incorrect stability and control derivates result from inadequate aerodynamic model structure. Stepwise regression is used to determine the structure for an adequate model. Flight data which covers a nonlinear aerodynamic model range may be analyzed as a single data set or partitioned into several distinct sets. Stepwise regression for model structure detemination and parameter estimation was successfully applied to three aircraft types (single engine general aviation, unaugmented modern jet fighter, jet transport)

Determination of airplane model structure from flight data using splines and stepwise regression

A procedure for the determination of airplane model structure from flight data is presented. The model is based on a polynomial spline representation of the aerodynamic coefficients, and the procedure is implemented by use of a stepwise regression. First, a form of the aerodynamic force and moment coefficients amenable to the utilization of splines is developed. Next, expressions for the splines in one and two variables are introduced. Then the steps in the determination of an aerodynamic model structure and the estimation of parameters are discussed briefly. The focus is on the application to flight data of the techniques developed

Lateral and longitudinal aerodynamic stability and control parameters of the basic vortex flap research aircraft as determined from flight test data

The aerodynamics of the basic F-106B were determined at selected points in the flight envelope. The test aircraft and flight procedures were presented. Aircraft instrumentation and the data system were discussed. The parameter extraction procedure was presented along with a discussion of the test flight results. The results were used to predict the aircraft motions for maneuvers that were not used to determine the vehicle aerodynamics. The control inputs used to maneuver the aircraft to get data for the determination of the aerodynamic parameters were discussed in the flight test procedures. The results from the current flight tests were compared with the results from wind tunnel test of the basic F-106B

Analysis of oscillatory motion of a light airplane at high values of lift coefficient

A modified stepwise regression is applied to flight data from a light research air-plane operating at high angles at attack. The well-known phenomenon referred to as buckling or porpoising is analyzed and modeled using both power series and spline expansions of the aerodynamic force and moment coefficients associated with the longitudinal equations of motion

Determination of airplane model structure from flight data by using modified stepwise regression

The linear and stepwise regressions are briefly introduced, then the problem of determining airplane model structure is addressed. The MSR was constructed to force a linear model for the aerodynamic coefficient first, then add significant nonlinear terms and delete nonsignificant terms from the model. In addition to the statistical criteria in the stepwise regression, the prediction sum of squares (PRESS) criterion and the analysis of residuals were examined for the selection of an adequate model. The procedure is used in examples with simulated and real flight data. It is shown that the MSR performs better than the ordinary stepwise regression and that the technique can also be applied to the large amplitude maneuvers

STEP and STEPSPL: Computer programs for aerodynamic model structure determination and parameter estimation

The successful parametric modeling of the aerodynamics for an airplane operating at high angles of attack or sideslip is performed in two phases. First the aerodynamic model structure must be determined and second the associated aerodynamic parameters (stability and control derivatives) must be estimated for that model. The purpose of this paper is to document two versions of a stepwise regression computer program which were developed for the determination of airplane aerodynamic model structure and to provide two examples of their use on computer generated data. References are provided for the application of the programs to real flight data. The two computer programs that are the subject of this report, STEP and STEPSPL, are written in FORTRAN IV (ANSI l966) compatible with a CDC FTN4 compiler. Both programs are adaptations of a standard forward stepwise regression algorithm. The purpose of the adaptation is to facilitate the selection of a adequate mathematical model of the aerodynamic force and moment coefficients of an airplane from flight test data. The major difference between STEP and STEPSPL is in the basis for the model. The basis for the model in STEP is the standard polynomial Taylor's series expansion of the aerodynamic function about some steady-state trim condition. Program STEPSPL utilizes a set of spline basis functions

Determination of longitudinal aerodynamic derivatives using flight data from an icing research aircraft

A flight test was performed with the NASA Lewis Research Center's DH-6 icing research aircraft. The purpose was to employ a flight test procedure and data analysis method, to determine the accuracy with which the effects of ice on aircraft stability and control could be measured. For simplicity, flight testing was restricted to the short period longitudinal mode. Two flights were flown in a clean (baseline) configuration, and two flights were flown with simulated horizontal tail ice. Forty-five repeat doublet maneuvers were performed in each of four test configurations, at a given trim speed, to determine the ensemble variation of the estimated stability and control derivatives. Additional maneuvers were also performed in each configuration, to determine the variation in the longitudinal derivative estimates over a wide range of trim speeds. Stability and control derivatives were estimated by a Modified Stepwise Regression (MSR) technique. A measure of the confidence in the derivative estimates was obtained by comparing the standard error for the ensemble of repeat maneuvers, to the average of the estimated standard errors predicted by the MSR program. A multiplicative relationship was determined between the ensemble standard error, and the averaged program standard errors. In addition, a 95 percent confidence interval analysis was performed for the elevator effectiveness estimates, C sub m sub delta e. This analysis identified the speed range where changes in C sub m sub delta e could be attributed to icing effects. The magnitude of icing effects on the derivative estimates were strongly dependent on flight speed and aircraft wing flap configuration. With wing flaps up, the estimated derivatives were degraded most at lower speeds corresponding to that configuration. With wing flaps extended to 10 degrees, the estimated derivatives were degraded most at the higher corresponding speeds. The effects of icing on the changes in longitudinal stability and control derivatives were adequately determined by the flight test procedure and the MSR analysis method discussed herein

Principal scientific results of the Surveyor 3 Mission

The fine lunar surface material at the Surveyor 3 landing site has about 3 × 10^3-dyne/cm^2 cohesion, 35° angle of internal friction, 3 × 10^5-dyne/cm^2 static bearing capacity. A small rock withstood a local pressure of 2 × 10^7 dynes/cm^2. Soil strength and density increase significantly at depths of a few centimeters. Exposed surface has a considerably higher albedo than the material just below it. The photometric function changed when the surface was slightly compressed. Fine surface material appears to be gradually moving downslope

Principal science results from Surveyor 5

The area of Mare Tranquillitatis in which Surveyor 5 landed appears to be similar to sites in Oceanus Procellarum. The gross elemental composition of the surface material and its response to a magnet are similar to those of a basalt. The debris layer appears to consist of aggregates of the order of 1 cm in diameter consisting of fine grains and set in a matrix of less-coherent fine grains (most of them 2 to 60 μ in diameter) mixed with some rocky fragments 1 mm and larger. The static bearing strength is less than 10^4 dynes/cm^2 for the upper few millimeters and averages approximately 3 × 10^5 dynes/cm^2 for the upper few centimeters. The evidence suggests that chemical differentiation has occurred in the moon, probably owing to internal heat sources; this is consistent with the hypothesis that the maria are basaltic volcanic flows

Two-sided Grassmann-Rayleigh quotient iteration

The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right $p$-dimensional invariant subspaces of $C$. Moreover, Grassmannian versions of the Rayleigh quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.Comment: The text is identical to a manuscript that was submitted for publication on 19 April 200