Browsing by Author "Christopher, P. A. T."
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Item Open Access The application of perturbation methods to nonlinear problems in flight mechanics(Cranfield University, 1976-09) Padfield, Gareth D.; Christopher, P. A. T.Analytical-techniques are developed for deriving approximate solutions to a class of problems that arise in nonlinear flight mechanics typically when an aeroplane is flying close to a stability boundary. The techniques are based on pertoz-bation methods and the method of multiple scales is used to correct for_nonuriformities otherwise present in the asymptotic expai!,. 3ions. Applications are mainly concerned with the lateral dynamics of slender aircraft flying at high incidence. Approximations are derived for both linear and nonlinear lateral motions that serve to illustrate the importance of particular parameters in the problem. For the linear theory the approximations are achieved by reducing the fourth order system to two. weakly coupled second order systems. The nonlinear theory is mainly concerned with the effect of aerodynamic nonlinearity on the lateral oscillation when the latter has marginal stability or instability, as predicted by the linear theory. The analytic approximations are extended for use in the problem of estimating damping moments on aircraft in oscillatory motion. For this purpose approximations are constructed for the logarithmic decrement of a nonlinear oscillation that can be used to fit experimental measurements. Some thoughtis given to-the issue of memory effects in the representation of aerodynamic forces and moments.Item Open Access An approximate method for estimating the lifting characteristics of thin bodies of non-circular cross-section(Cranfield Institute of Technology; College of Aeronautics, 1990) Christopher, P. A. T.Item Open Access The identification of aircraft stability and control parameters in turbulence(Cranfield University, 1982-07) Foster, G. W.; Christopher, P. A. T.A technique for the identification of aircraft stability and control parameters from flight test recordings made in either calm or turbulent air is presented. The maximum likelihood output error method is used with a steady-state Kalman filter incorporated to account for atmospheric turbulence. A modified Newton-Raphson search technique, enhanced by a line search, is employed for parameter identification. Separate algorithms are developed for estimating the biases and noise levels in the observations. Some areas of practical problems in the application of such methods are stressed. A computer program for the identification of longitudinal stability derivatives is described and the aircraft instrumentation required is exemplified by that in Gnat XPSOS. The wind tunnel calibration of the flow-direction sensing nose probe assembly of Conrad yawmeters on this aircraft is detailed. The problems of handling the flight observations recorded are covered and some of the troubles experienced with the instruments are noted. The performance of the identification technique is investigated. The data required, the choices open to the analyst and the statistical information produced being highlighted. The identification of the process noise level, in this instance the turbulence intensity, is addressed and it is found that the value specified for this level can influence the other parameters. The longitudinal stability and control derivatives obtained for Gnat XPSOS are presented.Item Open Access Incompressible flow about ellipsoids of revolution(Cranfield Institute of Technology; College of Aeronautics, 1988) Christopher, P. A. T.Item Open Access The interaction of an oscillating airfoil and/or flap with a separating flow(1975-01) Lang, James D.; Christopher, P. A. T.At present little is known of the dynamics of a separating and reattaching flowfield. This unsteady flow topic relates to a wide range of aerodynamic problems such as dynamic stall and contfol-sürface-buzz. An experiment was performed with the purpose of investigating the dynamics of a separated region and the effect of the region on the motion of a flap-type control surface. A NACA 0012 airfoil section was fitted with a movable spoiler and flap. Measurements were made of the unsteady, non-linear hinge-moment due to spoiler oscillation. Aerodynamic hinge-moment was also investigated with the spoiler fixed and the flap oscillated harmonically. Flap response to spoiler-induced forcing was also observed in addition to observations of coupled spoiler and flap system behavior. The coupled system exhibited limit-eyele oscillations. Flap response to spoiler-induced loading can be predicted well by use of a linear equation for flap motion which is forced by the effect of spoiler motion. The equation of motion includes attached flow values of aerodynamic damping and stiffness. A theory is developed which models separation bubble dynamics. It includes a quasi-steady model for the external shear-layer, and flow of mass within the bubble at a mean reversed-flow velocity. Pressure perturbations along the bubble are modeled also. The theory is used with the method of Beecham and Titchener in order to predict limit-cycle behavior of the coupled system. Good agreement with experimental results is achieved. The instant of instability and of growth of a laminar separation bubble at the leading-edge of an oscillating airfoil is also investigated theoretically. The beginning of dynamic stall is seen to be related to the dynamics of a separation bubble and the inviscid flowfield. The theory is applied also to a study of the phenomena of control-surface-buzz, where separation is induced by shock waves.Item Open Access A new method for predicting the vortex induced aerodynamic characteristics of a body of revolution(Cranfield University, 1995-08) Smith, Howard; Christopher, P. A. T.The problem of mathematically modelling the symmetric vortex pair formed on the lee side of a body of revolution at moderate incidence to the freestream direction is addressed with a view to predicting its aerodynamic characteristics. The objective being to develop a model simple enough to enable rapid calculation whilst maintaining acceptable levels of accuracy. Existing techniques are reviewed and their strengths and weaknesses evaluated. The physics of the flow are explored with an emphasis on its three dimensional aspects. Experimental results, including surface pressure tapping data and flow visualisation, are used to investigate the nature of the flow. To gain a deeper insight into the flow processes less measurable experimentally, Navier-Stokes solutions are examined in considerable detail. The mechanisms of vorticity generation and propagation are explored. A simple mathematical model is presented, based upon an extension to slender body theory, which predicts aerodynamic characteristics that compare well with experiment.Item Open Access Numerical techniques for predicting aerodynamic characteristics of bodies(1986-01) Deo, H. S.; Christopher, P. A. T.Two methods are presented characteristics of bodies SUMMARY for predicting the aerodynamic in inviscid and irrotational flow. The first method is limited to incompressible flow and makes use of panels of ring sources to approximate the body surface. The technique is dedicated to single, axisymmetric body configurations in either uniform longitudinal or rectilinear motion. The versatility of the method is due to the use of sources as singularities placed on the body surface, allowing discontinuous body profiles to be analysed. The method has been compared for accuracy and efficiency with experimental and theoretical results. Further investigation showed that at present there existed no numerical technique which could predict the aerodynamic behaviour of multiple bodies in compressible flow. Hence, a fully three-dimensional method was developed which made use of the Full Potential Equation (F.P.E.) in conservative form. A computational mesh is placed around the body configuration and at each mesh node the F.P.E. is satisfied ~n finite difference form. The method is able to give a complete description of the flow around the bodies at transonic mach numbers. Comparisons to test the accuracy and efficiency of the method are limited to either, purely subsonic flow for two body configurations or zero incidence for transonic flow around a single body.Item Open Access Some experimental and theoretical studies in aircraft stability at high angles of attack(Cranfield University, 1983-09) Thorne, R.; Christopher, P. A. T.A review of techniques for stability and response investigations is presented and the averaging technique of Beecham- Titchener-Simpson is applied to the lateral equations of. motion for two combat aircraft. The analytic technique predicts oscillation amplitudes and frequencies accurately, for non-linear aerodynamic characteristics with respect to sideslip or roll rate. However, limitations of the method are apparent when non-linearities in roll rate and sideslip are treated simultaneously. Rates of growth to limit cycle oscillations are predicted by the averaging method and two formulations for a local damping factor are compared with simulation results. Results from extensive wind tunnel tests on a High Incidence Research Model (HIRM) are presented along with estimates of dynamic stability derivatives and polynomial fits to the wind tunnel data. The lateral stability and response of the HIRM at high angles of attack, is investigated using the analytic techniques described earlier, as well as simulations. Six degree of freedom eigenvalue results for the HIRM are shown. An investigation into the effects of cross-coupling derivatives and different forms of roll rate data, using non-linear and linearised simulations, concludes the thesis.Item Open Access 'Studies in stability and control analysis of airframes having nonlinear aerodynamic characteristics'(College of Aeronautics, 1966-06) Christopher, P. A. T.The problem of longitudinal stability and control of an airframe, having nonlinearity in its principal aerodynamic characteristics, is considered. It is shown that the equation describing the response in w, and thus the incidence, is a nonlinear differential equation of the fourth order. This equation, and its degenerate forms, is used as an example to demonstrate various nonlinear techniques and their shortcomings.