This paper describes the research into the flight dynamics modelling and flight control of a flapping wing micro aerial vehicle (MAV). The equations of motion based on a multi-body representation of the vehicle and the flapping wings were derived and form the basis for the simulation program, which was developed using MATLAB and SIMULINK. The aerodynamic forces were obtained through experimental methods and form the basis for the aerodynamic model.

The hovering and low speed flight of the MAV was investigated using a SIMULINK simulation model. Various flight control concepts, inspired by observation of insect and bird flight, were investigated in some detail. The concepts include the control of flap frequency, flap and pitch phasing (wing beat kinematics) and shift in centre of gravity position. The paper concludes with a comparison of the control concepts and their feasibility for a practical vehicle application.

This paper examines the dynamic stalling of three wing planforms and characterises the main features of the stalling process in each case. The particular data were obtained during a three year research programme in the Department of Aerospace Engineering, University of Glasgow to collect high-resolution unsteady pressure data on the dynamic stalling characteristics of finite wing planforms. In this study, which was motivated by the pressing need for a greater understanding of the strongly three-dimensional effects in the tip region of helicopter rotors, the three wing planforms considered were a straight rectangular wing, a rectangular wing with swept tips and a delta wing. The initial test programme was followed by a further three years of detailed analysis and interpretation of the test data. Results from this analysis are presented in the present paper for cases in which the wings were subject to ramp motions.

Experiments have been made to find the effect of the ratio of sting to base diameter on the base pressure of an axially symmetric body at zero incidence in a supersonic stream. The Mach number of the flow was 1·994 and the model boundary layer was turbulent. The model used was a one inch diameter circular cylinder without boat-tailing. It passed through and was supported upstream of the nozzle throat. This method of support allowed measurements to be made in the important (and hitherto unexplored) case of zero sting diameter.

As the sting to base diameter ratio was increased from 0 to 0·85, the base pressure decreased. The minimum value reached was approximately 0·8 of the value it would have at the base of a two-dimensional body with a similar ratio of boundary layer thickness to base height. The base pressure coefficient rose rapidly to zero as the ratio was further increased to unity.

Under the conditions of the experiments, with a sting to base diameter ratio of 0·4 the base pressure coefficient differed from that without a sting by approximately ten per cent. With the more modest ratio of 0·2, the difference was approximately three per cent.

The Paper describes a metal and composite recurrent cost model of a large civil aircraft wing structure for a multidisciplinary design, analysis and optimisation (MDO) environment. The work was part of a recent European MDO project (BE95-2056) which investigated methods for the integration of structures, aerodynamics, dynamics and manufacturing cost at the preliminary design stage.

The paper discusses the cost modelling approach, which is based on parametric and process cost model methods, and the integration of the cost models into an MDO process. Results for the cost models are shown.

A framework has been successfully developed which allows the incorporation of manufacturing cost models into an MDO environment. It allows a designer to evaluate cost changes with respect to specific design changes such as rib pitch, stringer pitch, wing area and wing sweep.

We continue our fundamental discourse on the natural modes in an element and extend our considerations to large displacements. First, we present a general procedure for establishing the so-called geometrical stiffness kG, when the natural modes of the complete element are given. The theory is a substantial generalisation and clarification of the method initially given in refs. 2 and 3 and shows that in establishing the modification to the transformation matrix aN it is necessary to ignore the contribution of the natural modes, which cause rotation at the nodal points but no displacement there. The point is subtle and was not made in ref. 2, although the applications given there are correct. As an example, the geometrical stiffness of a straight beam in space with all degrees of freedom is established. There follows the extension of the geometrical stiffness concept to a sub-element. This is of great practical significance for two reasons. First, it allows to derive the geometrical stiffness of elements of complex shape and behaviour, e.g. curved beams in space subjected to normal forces, bending moments and torque.

The properties of equilibrium turbulent boundary layers have been examined using Thompson’s family of velocity profiles along with alternative π – G relationships. The relationship which is in best agreement with measurements of equilibrium layers confirms an earlier suggestion that (νT/Uδ*)max is not a universal constant for such layers but decreases for small and negative values of π. A close relationship is established between eddy viscosity and entrainment, and it is shown that veδ/νT is effectively constant for π > 2.

The 776th Lecture was read before the Society on the 31st March 1949 at the Institution of Civil Engineers, Great George Street, London, S.W.I. Dr. H. Roxbee Cox, B.Sc, D.I.C., F.R.Ae.S., F.I.Ae.S., President of the Society, introduced the lecturer, Dr. P. B. Walker, M.A., F.R.Ae.S., Head of the Structures Department at the Royal Aircraft Establishment.

A rational method of lumping inertia forces by considering the equilibrium of the vibrating element has been developed. This method requires the selection of a suitable displacement distribution function over each element. The closer it is to the true mode shape, the better the result.

Considering a linear displacement distribution function over each element, the natural frequencies and mode shapes are obtained for transverse vibrations of a stretched string, torsional vibrations of a cantilever shaft (fixed at one end and free at the other) and transverse vibrations of a uniform cantilever beam. It is found that, even with a few elements, a reasonable accuracy can be obtained in the natural frequency, while the mode shapes are exact in the first two cases and almost exact in the third at the points considered.

In Appendix A, it is shown that, for the torsional vibration of a uniform cantilever shaft and with a linear displacement function over each element, this method gives exact mode shapes at the points considered, while the natural frequency is always an upper bound and the error follows an inverse square law when the number of elements considered is large.

In Appendix B, it is shown that a combination of this method with the conventional lumped mass method reduces the error in the natural frequency. The error follows an inverse fourth-power law when the number of elements considered is large and the mode shapes are exact at the points considered.

This method can incorporate better displacement distribution functions, to obtain better results and convergence, and can easily be adapted to the buckling of columns, the vibration of beam columns and forced vibrations, as well as more complicated problems such as the vibration or buckling of plates and shells.

The rotary derivatives of a Delta wing pitching or rolling at supersonic speed are obtained in addition to the lift curve slope first given in an earlier investigation.

The properties of weak shock waves in a vibrationally relaxing gas are discussed with particular application to waves in carbon dioxide. An account of various methods of generating weak shock waves in a shock tube is given. The best method requires the insertion of a perforated plate in the low pressure section of the shock tube. A suitable choice for the open-to-total area ratio of the plate leads to transmitted waves in the appropriate strength regime. These waves were observed using a Mach-Zehnder interferometer and were either fully or partly dispersed by vibrational relaxation. Values for the relaxation frequency of carbon dioxide at room temperature were obtained.

This paper presents a theoretical analysis of the behaviour of thin-walled lipped channel beams subjected to end moments. In the analysis the beam section is assumed to be composed of a number of flat plates, joined at the edges. The mechanics of local instability of the walls of the beam are examined from a consideration of the strain energy stored in the component plates, and critical moments to cause local buckling are evaluated. The behaviour of the beam after local buckling is studied using a semi-energy method, whereby the stress and deflection systems throughout the section are linked by solving von Kármán’s compatibility equation for the component plates and the stress and deflection magnitudes are found from energy considerations. As collapse of the beam is approached, a simple plasticity analysis is incorporated in the theory in order to evaluate the collapse moment for the beam.

The results of the analysis are compared with the findings of an extensive experimental investigation and it is shown that the theory is very accurate in its prescription of the experimental stresses and deflections. Comparison of the theoretical and experimental collapse moments also verifies the validity of the theoretical analysis.

The main objectives of Missile Evaluation Trials are a complete evaluation of the operational performance of the missile tested, a comprehensive assessment of the practical implications of regular operation of the weapon system from the user's point of view, and the feedback of scientific information to assist in future designs. This means that the trials must be planned to provide data on the following aspects: —

• (a) Scientific evaluation, i.e. determination of performance in the various conditions which will arise in operational use.

• (b) Technical evaluation, i.e. assessment of the detail design, workmanship, engineering and reliability and its influence on operational performance.

• (c) User evaluation, i.e. a practical critical examination of (and evolution of) handling and servicing procedures, personnel training requirements, installation requirements, logistics, and the numerous organisational steps necessary for the introduction of a new weapon into service.

A mathematical model is presented of the aircraft program flight along a predetermined trajectory, with or without a specified speed history. Moreover, the aircraft is constrained to coordinated turns, which implies zero value of sideslip angle. The final equations of program motion are derived as a set of differential/algebraic equations. The aircraft control input ensuring the exact realisation of program constraints results from the transient dynamic solution of the equations of program motion. A simple numerical illustration is included.

The paper contains an analysis of the flow of a perfect gas with constant specific heats through a rotating channel of constant cross-sectional area, as used in certain helicopter propulsion systems and wind-driven gas turbines. The analysis is restricted to the adiabatic one-dimensional treatment, the Coriolis accelerations acting across a section being disregarded.

The equations of motion and energy are deduced and, together with the equation of continuity, reduced to an ordinary non-linear differential equation of the first order, involving a dimensionless form of velocity and distance.

The patterns of the integral curves of the differential equation are discussed and sketched by examining their asymptotic behaviour as well as that in the neighbourhood of singular points. It is shown that there exists a critical value of the angular velocity below which the flow remains subsonic in the pipe, if the entrance velocity is subsonic; it may, however, become sonic at the exit of the pipe. For supercritical angular velocities the flow may become sonic or supersonic in the pipe if the entrance velocity attains a given “ correct” but subsonic value. A method of examining for the possibility of shock formation is indicated.

The initial conditions for the differential equation are deduced for the design and for the performance problem, two new flow functions being introduced and tabulated to facilitate practical calculations. Formulae are also deduced for the calculation of the pressure and Mach number variation from the previously calculated velocity variation along the pipe.

Finally an approximate solution in closed terms is given for the case of small entrance velocities.

Using a modified model of the axially-loaded Timoshenko beam, nine field transfer matrices for the homogeneous case and three field matrices for the non-homogeneous case have been derived, covering thus all the “cases of state” of continuous beams loaded axially and laid on an elastic foundation. The loads and restraints (translatory and rotatory) may be both concentrated and distributed. The matrices make possible a simultaneous treatment of free vibrations, forced vibrations, statics and buckling.

In the note “Aerodynamically induced vibration in coolers”, by D. G. Mabey (pp 876-7, December 1965 Journal), the results of Grotz and Arnold concerning the frequency of the Karman vortex streets in tube banks, such as in heat exchangers, are mentioned, as is also the law of the linear relation between f(T—d)/V and (2T-L)/d, as found by Putnam, where

f frequency of vortex shedding

T transverse distance

L longitudinal distance between tubes

d outer diameter of tube

V mean stream velocity based on minimum flow area between the tubes

This linear relation has no theoretical justification and cannot be accurate, as is admitted by the author cited. A further investigation on a theoretical basis seems to be necessary.

There are several situations of practical importance where it is essential to maintain a satellite in a fixed orientation relative to the earth. Of the numerous methods proposed for such station keeping, gravity gradient stabilisation has gained considerable attention primarily due to the passive nature of the system. The pioneering work for pure gravity orientated satellites was carried out by Klemperer who obtained the exact solution for planar librations of a dumbbell satellite in circular orbit, and by Baker who found periodic solutions of the problem for small orbit eccentricity. Schechter attempted, with limited success, to extend Klemperer's solution to non-circular orbital motion by perturbation methods. Zlatousov et al and, more recently, Brereton and Modi successfully employed numerical methods, involving the use of the stroboscopic phase plane, to analyse motion in the large for orbits of arbitrary eccentricity.

This paper reports the findings of a flutter investigation on a low-pressure turbine blade using a 3D, non-linear, integrated aeroelasticity method. The approach has two important features: (i) the calculations are performed in a time-accurate and integrated fashion, whereby the structural and fluid domains are linked via an exchange of boundary conditions at each time step, and (ii) the analysis is performed on the entire bladed-disk assembly, thus removing the need to assume a critical vibration mode shape. Although such calculations are both CPU and in-core memory intensive, they do not require prior knowledge of the flutter mode and hence allow a better understanding of the aeroelasticity phenomena involved.

The flow is modelled inviscidly but the steady-state viscous effects are accounted for using a distributed loss model. The structural model was obtained from a standard finite element (FE) representation and a large number of assembly modes were included in the calculations. The study focused on three part-speed conditions at which a number of unstable modes were known to exist from the available experimental data. The whole assembly was modelled using about 664,000 mesh points and predictions were made of aeroelastic modal time histories. From these time histories it was possible to identify the forward and backward travelling waves and to deduce the unstable modes of vibration. The theoretical predictions were found to be in very good agreement with the experimental findings.

The modelling and vibration of composite thin-walled pre-twisted rotating blades of non-uniform cross-sections along their span, and featuring the extension-twist elastic coupling are addressed. To this end, Hamilton’s principle is used to derive the equations of motion and the associated boundary conditions. In addition to the pretwist and warping restraint, the exotic properties of advanced composite material are used, and the efficiency of implementing the tailoring technique toward the enhancement, without weight penalties, of the vibratory behaviour of rotating blades is illustrated. Comparisons between the predictions by both Wagner’s and Washizu’s approaches are presented, and pertinent conclusions regarding the implications of the various geometrical and physical characteristics of the blade are outlined.

This paper looks at active control of the swept shock wave/turbulent boundary-layer interaction using smart flap actuators. The actuators are manufactured by bonding piezoelectric material to an inert substrate to control the bleed/suction rate through a plenum chamber. The cavity provides communication of signals across the shock, allowing rapid thickening of the boundary-layer approaching the shock, which splits into a series of weaker shocks forming a lambda shock foot, reducing wave drag. Active control allows optimum control of the interaction, as it would be capable of positioning the control region around the original shock position and control the rate of mass transfer.