This paper concentrates on the trajectory tracking problem for a stratospheric airship subject to underactuated dynamics, unmeasured velocities, modeling inaccuracies and environmental disturbances. First, a coordinate transformation is performed to solve the underactuated issue, which simultaneously permits a priori assignment of the tracking accuracy. Second, a finite-time observer is integrated into the control structure to offer the exact information of unmeasured velocities and uncertainties in an integral manner. Then, by combining the backstepping technique with the method of adding a power integrator, a new output-feedback control strategy is derived with several salient contributions: (1) the airship’s position errors fall into a predetermined residual region near zero within a finite settling time and stay there, while all the closed-loop signals maintain bounded during operation; and (2) no artificial neural networks and filters are adopted, resulting in a low-complexity control property. Furthermore, the presented method can be extended readily to a broad range of second-order mechanical systems as its design builds upon a transformed system model. Rigorous mathematical analysis and simulations demonstrate the above theoretical findings.

This paper presents a theoretical investigation of the interactions which occur when a laminar boundary layer on a flat surface encounters an expansive corner followed by a shock or other compressive agency. The method consists basically of two equations; the first relates deflections in the external streamlines to pressure changes and the second relates pressure changes to thickening or thinning of the boundary layer. For simplicity it is assumed that the pressure changes and streamline deflections are small.

A comparison is made with the only available experimental results, under conditions which are far outside the range of applicability of the theory. In these circumstances the agreement between the predicted and experimental pressure distributions is reasonable.

Small, steady perturbations of general two-dimensional steady, shock-free, supersonic flows are studied and the perturbation fields of symmetrical nozzle flows are described in detail. The relation between errors in the shape of the supersonic part of the nozzle liners and the deviations from uniformity of the flow in the test section is given to an approximation sufficient for the treatment of a number of problems arising from experiment and in the design of nozzles.

This paper contains results for the response of a helicopter rotor blade under stationary random excitation when the helicopter is in forward flight. The blade model takes into account the bending and torsional modes as well as the root-rigidity conditions. The resulting linear dynamical system equations with periodic coefficients are treated within the framework of the filtering theory to yield matrix ordinary differential equations for the required response-statistics themselves.

Incompressible flow perpendicular to a flexible, impervious membrane has been studied for two-dimensional conditions. The membrane was mounted on relatively thin supports spaced c apart. Measurements of drag, base pressure and the frequency of membrane oscillation are presented for various lengths ℓ, and for two densities, of membrane. These parameters are related to one another theoretically and in particular Bearman′s universal correlation for Strouhal number agrees with the experimental results. It is found that for values of < 0.50 the drag is independent of membrane density. The drag decreases at larger values of and this is related to a periodic reattachment of the separated flow to the back of the membrane. For a given ℓ the drag is greatest when is very small and the membrane is almost flat.

The following theoretical investigation is concerned with the stability of the flow through a system composed of a multi-stage axial flow compressor followed by a throttle.

Such an investigation was carried out by Pearson and Bowmer in 1949. In 1962 Pearson’s work on the analysis of axial flow compressor characteristics, and the accumulation of empirical data regarding factors affecting the surge line, re-awakened interest in the possibility of predicting the surge line of a multi-stage axial flow compressor-throttle system.

In this paper the equations governing the stability of flow at any operating point in such a system are obtained by applying Kirchhoff’s laws to the associated electric circuit at that operating point, and the analysis is applied to a wide range of flows of the calculated characteristics of a seven-stage axial flow compressor.

A study of the simplest compressor-throttle system is given, in which the equations of motion of the system are derived mechanically and electrically, and the range of validity of the equations and their stability are discussed in order to bring out the relation between the mathematics and physics of the simple system before applying these methods to multi-stage axial flow compressors.

For the relatively simple electrical representation used in this paper for an axial compressor of n stages, there are shown to be 2n possible values of p, the transient rotational frequency, and these are determined over a sufficiently wide range of flows on the seven-stage compressor studied.

As a result, a region of the compressor characteristic map can be marked out in which all the values of the transient rotational frequency have their real parts less than zero, corresponding to stability of operation, a region where at least one of the values of p is real and positive corresponding to non-oscillatory instability of operation, and an intermediate region where some of the values of the rotational frequency p are complex with positive real part, corresponding to oscillatory instability of operation.

It is suggested that the non-oscillatory instability found here is associated with the surge and the line of inception of non-oscillatory instability with the surge line.

The subject of three-dimensional flow in axial compressors and turbomachines has been extensively studied since 1945. This paper gives a means of calculating the approximate three-dimensional flow in an axial compressor by giving expressions for the slope of the velocity profile as a function of the axial co-ordinate. These expressions bring out the rôle of the ratio of stage inlet annulus height to stage length in the three-dimensional flow in these machines. The effect of the three-dimensional flow on the stage temperature rise at mean radius is discussed by introducing a work done factor.

Surface pressure distributions have been measured on a cylinder with a double-wedge cross section in a two-dimensional channel flow. The flow is sheared in the direction of the cylinder axis, using a grid of parallel wires with variable spacing, in order to simulate the type of geometry and velocity variation which occur for annulus support struts in turbomachines. The strut had a 38° included angle at the leading and trailing edges and an aspect ratio of 1.33 based on the maximum thickness. This was fixed between the parallel walls of a rectangular wind tunnel with end leakage eliminated. Surface pressure distributions were measured over a Reynolds number range of 0.5 × 105 to 1.5 × 105 for three different shear flow conditions. Despite the presence of sharp edges at the mid-chord position, delayed boundary-layer separation beyond the plane of maximum thickness has been found for sufficiently high spanwise shear in the upstream flow. Surprisingly, therefore, some similarity with previous results for struts of circular cross section appears to exist. The influence of the shear flow conditions on the pressure drag force has been determined by numerical integration of the data. Only a slight dependence on the upstream flow conditions is found, although the effect of secondary velocity components may still be observed if the spanwise variations in the local drag force are examined.

The results of wind tunnel tests carried out on a semi-span ‘lambda’ planform model with leading and trailing edges swept at 40° are presented. The planform investigated has been specified as having features likely to be encountered on future ‘ow observable’ aircraft. Balance data has been acquired to angles of attack beyond stall for both forward and reverse flow orientations. Dynamic calibration of surface pressure tappings has allowed both time-averaged and unsteady pressures to be measured over the entire upper surface of the wing. Unsteady pressure time histories have been analysed in the frequency domain to identify their spatial resolution, dominant frequencies and associated magnitudes.

In forward flow conditions, maximum buffet is observed between the primary attachment of the leading edge vortex system and the vortex core. The dominant buffet frequency is shown to be dependant on the chordwise location, incidence and free stream velocity as expected. A second coherent buffet frequency has been identified in the region of high buffet over a wide range of operating conditions. Inboard of this region a third dominant frequency has been observed. This is of an intermediate frequency and varies in a similar manner. A simple mechanism has been proposed to explain both the spanwise RMS distribution and the presence of a number of coherent buffet frequencies.

The design of control systems for helicopters in hover and at low speed is a basic requirement for the extension of mission profiles and new mission demands. A special task for various applications is the position hold under wind and gust conditions above a ground fixed or moving target, like a shipboard reference, or a small vessel or lifeboat in rescue missions. For the solution of this problem a controller concept was developed and the feasibility was proven and successfully demonstrated in flight tests.

The in-flight helicopter simulator ATTHeS of the DLR has been equipped by the Institute of Flight Mechanics with an innovative measurement system for the hover position above a target. A video camera in combination with a highly parallel computer system for processing the optical information was used as an integra ted sensor system for the measurement of the relative position of the aircraft to a target. Based on the existing well-proven flight control laws of ATTHeS for the forward flight condition, which are implemented for handling qualities investigations, these control laws were modified and adapted to fulfil the special requirements of the position hold task, including altitude hold and heading hold capabilities. The integrated system of optical position sensor and control computer enables the helicopter to hover automatically above a defined target in constant altitude and with constant heading. Flight tests above a moving car under wind and gust conditions underline the future potential of the overall system to be used under operational conditions.

Flow separation followed by aerodynamic stall limits the operation of aircraft. Expanding the flight envelope of aircraft has been a goal of aerodynamicists for decades. This work presents findings from tests in the Oregon State University wind tunnel investigating the effectiveness of a passively actuated suction-surface flap on membrane wings. Experiments were conducted on a rigid plate and membrane wings with and without a pop-up flap. All wings had an aspect ratio of 2, while membrane pre-strain and Reynolds number were varied. An increase in lift at stall was observed for all testing conditions with flap deployment. The observed average increase in maximum lift varied from 5% to 15% for different test conditions. The variation in flap effectiveness is compared to membrane pre-strain, Reynolds number, and wing camber. A quadratic relationship between modelled camber and flap effectiveness is observed, and an optimal level of membrane camber is found to maximise flap effectiveness.

Steady and unsteady pressure measurements are conducted for a tailless aircraft model. The main aim with the presented experimental work is to investigate the difficulties and possibilities involved in using an available pressure sensing system for accurate unsteady pressure measurement. The experimental procedure which is utilised for unsteady pressure measurements is described in detail. In particular, the importance of synchronised timing is recognised. For a harmonically varying pressure a small time delay in the measurement chain can result in a significant phase shift. Also, difficulties and uncertainties that are still present are pointed out. The results from these experiments are compared to numerical results based on unsteady potential flow theory. In general, the experimental and computational results show similar trends. Especially good agreement is found for the steady pressure measurements. For the unsteady pressure measurements a possible Reynolds number dependency is found for the considered test conditions.

One key task in computational aeroelasticity is to calculate frequency response functions of aerodynamic coefficients due to structural excitation or external disturbance. Computational fluid dynamics methods are applied for this task at edge-of-envelope flow conditions. Assuming a dynamically linear response around a non-linear steady state, two computationally efficient approaches in time and frequency domain are discussed. A non-periodic, time-domain function can be used, on the one hand, to excite a broad frequency range simultaneously giving the frequency response function in a single non-linear, time-marching simulation. The frequency-domain approach, on the other hand, solves a large but sparse linear system of equations, resulting from the linearisation about the non-linear steady state for each frequency of interest successively. Results are presented for a NACA 0010 aerofoil and a generic civil aircraft configuration in very challenging transonic flow conditions with strong shock-wave/boundary-layer interaction in the pre-buffet regime. Computational cost savings of up to 1 order of magnitude are observed in the time domain for the all-frequencies-at-once approach compared with single-frequency simulations, while an additional order of magnitude is obtained for the frequency-domain method. The paper demonstrates the readiness of computational aeroelasticity tools at edge-of-envelope flow conditions.

The RAF has been undertaking peacetime repairs on composite rotor blades, fibreglass radomes and panels on a variety of combat aircraft types for many years. However, the Service's main experience in the repair of aircraft structures manufactured from carbon fibre composite (CFC) material has been related to the Harrier II. In any future conflict involving air power, battle damaged aircraft, including the Harrier II, will have to be repaired rapidly to meet operational requirements. The repair techniques used may have to differ from those undertaken in peacetime but they must still aim to restore the full static strength of the aircraft within the time constraints imposed by the operational situation. Therefore, aircraft battle damage repair (ABDR) is a carefully planned alternative to conventional repair techniques. This paper describes the main CFC structures of the Harrier II and outlines the variety of RAF peace and wartime structural repair procedures applied to the aircraft. Examples are provided of various simple and complex repairs. Greater emphasis on adhesively bonded repairs is called for if Harrier II experience is to aid in the logistic support of Eurofighter 2000 (EF2000) in peace and war.

The subject of tail buffeting first came into prominence in this country early in 1931 when the Accidents Investigation Sub-Committee of the Aeronautical Research Committee issued their report on the accident to a Junkers monoplane at Meopham, Kent. The Sub-Committee gave it as their opinion that tail buffeting was the probable primary cause of this accident, and recommended that the phenomenon should be investigated. At this time tail buffeting (Leitwerkschutteln) was quite well known in Germany, where the low-wing monoplane, which is peculiarly susceptible to this trouble, was a popular type of aircraft; and some full-scale experiments on the subject had already been made by the Deutsche Versuchsanstalt fiir Luftfahrt. The findings of the Accidents Investigation Sub-Committee caused an intensive study of buffeting to be undertaken both in Germany and in this country, and the enquiry was also taken up in the United States at a later date. As a result of these studies tail buffeting is now quite well understood, and methods for its avoidance have been established.

This paper considers four alternative sets of actions that a pilot may use to recover an aeroplane from the stall. These actions: those published by the UK CAA and the US FAA, as well as a power delayed sequence and a pitch delayed sequence, were evaluated on 14 single engine piston aeroplane types. In a limited number of types (five in cruise configuration, two in landing configuration) the pitch delayed recovery gave a safe response and least height loss, but in a greater number of types (six and eight in cruise and landing configurations respectively) it resulted in further post-stall uncommanded motion. The other sets of actions all gave a consistent recovery from the stall, but the least height loss in recovery was also consistently the CAA sequence of simultaneous full power and nose-down pitching input, which normally resulted in approximately two thirds the height loss of the FAA’s pitch first then power method, which in turn resulted in about 90% of the height loss of the trialled power delayed recovery. Additionally the CAA recovery gave the least variation in height loss during stall recovery. It was also found that all of the aeroplane types evaluated except for one microlight aeroplane of unusual design, displayed a pitch-up with increased power in the normal (pre-stall) flight regime. Reducing this to separate components it was therefore shown that pitch control is of primary importance and should be used to provide immediate stall recovery. The thrust control can additionally be used as early as possible to minimise height loss, but if the thrust control is used before the pitch control in the stall or post-stall flight regime, there is some risk of subsequent loss of control. Finally, from the discussion on stall recovery methods, questions for Regulatory Authorities are put forward that should address the current practices.

The linearised time dependent momentum integral equation is used in conjunction with assumed velocity profiles and a quasi-static skin friction approximation to predict the turbulent boundary layer response to sinusoidal streamwise velocity fluctuations in the freestream. The mean zero pressure gradient case, corresponding to flat plate flow, is presented in detail and verified by comparison with experimental data and alternative calculations. The asymptotic turbulent boundary layer response to very high frequency perturbations is also derived. It is shown that a travelling wave component in the freestream, with its associated time dependent streamwise pressure gradient, has a dominant effect on the turbulent boundary layer response.

The supersonic flow past an elliptic cone of small eccentricity is treated as a pertubation of the axially-symmetric conical flow. The perturbation is singular; a uniformly valid solution is constructed by formulating the problem in sphero-conal coordinates (in which the cone surface is always a level surface of one of the coordinates) and by using the method of matched asymptotic expansions. This formulation enables first-order results to be obtained economically. In a numerical example for the flow past a cone of quite large eccentricity at incidence, it is shown that the present first-order solution (of three terms) agrees as well with experiment as a ten-term approximation obtained by Martellucci using the method of linearised characteristics.

It is shown that considerable improvement is achieved in the most popular classical approach to the vibration of structural members by giving new meaning to the generalised coordinate term in the infinite series expansion of the product of the generalised coordinate and eigenfunction. A transform employing the eigenfunction as a kernel efficiently generates a universal solution that embraces arbitrary loading, time-dependent boundary conditions, and such in-span conditions as supports and changes in cross section, axial load, and elastic foundation modulus. The method is applied to the Timoshenko beam as a representative structural member.

Aerial top-dressing, or the spreading of inorganic fertilisers from aircraft, introduces stringent flying conditions at extremely low altitudes. During release of the fertiliser there are large load and centre-of-gravity changes, and aerodynamic effects the cause of which has hitherto been conjectural. The experiments described in this paper were aimed at obtaining a knowledge of the aerodynamic effects of the cloud of falling material beneath the plane, and the effects of air flow through the empty hopper. The implications upon aircraft design are discussed. The high accident rate experienced in this industry emphasises the necessity for the production of a suitable aircraft designed solely for top-dressing.