In a recent technical note, Squire discussed the approximate solution of certain second-order linear differential equations by the method attributed variously to Riccati, Madelung, Wentzel, Kramers and Brillouin (the W.K.B. method), and others. The problem of eigenvalues, frequently met with in this type of equation, does not, however, appear to have received much attention by this method, and in this note a simple formula is developed which appears to give excellent numerical results in many cases.

The aeroelastic properties of modern aircraft are such that necessary calculations, of critical flutter speeds for instance, can be remarkably complicated. A flutter analyst requires an inordinate degree of skill and experience if he is to acquire a “sense of feel” in calculations. The difficulty of deciding how to adjust a critical flutter speed predictably by some structural modification is a typical outcome of this complication.

Minimum drag shapes of given length and base area are investigated for hypersonic flow using both Newtonian impact theory and free molecular flow theory. The drag of Newton’s minimum drag body, which has previously been evaluated by numerical means, is derived as an analytic expression. The analytical results are applicable to a range of local pressure laws allowing minimum drag shapes obtained using impact theory to be directly compared with low density flow equivalents using free molecular flow. The low density shapes are found to have larger blunt regions at the nose and significantly larger drag coefficients. For free molecular flow the drag varies with the surface reflection characteristics. As the fraction of diffuse reflection at the surface increases, the drag increases and the sensitivity of the drag to changes in the minimum drag shape is reduced.

For many years there have been used in aircraft construction aluminium alloys to a steadily increasing extent, and particularly alloys of Al.-Cu.-, Mg. and Al.-Cu. capable of being improved by heat treatment. Among the different methods known for permanent connection of structural parts, the rivet is still to-day the most reliable and safest connecting element. According to the special quality of this light metal group, due to their natural material characteristics and owing to the fact that in most cases the connections of aircraft structural parts are very complicated and highly stressed, the rivets are always driven cold. Due to these conditions, the tools, machines and working methods for strengthening of riveting diverge essentially from the commonly known riveting methods of general machine construction. In the course of my lecture I shall give further details regarding these questions.

Sadly, recent events continue to keep this subject to the fore — and memories of Dawsons Field, Entebbe, Mogadishu, Stansted, Beirut and Malta, to mention but a few of the most dramatic hijack incidents, are recalled, as are other events such as those of the early morning of 23rd June 1985 when one Boeing 747 of Air India was blown up in mid-air off the West Coast of Ireland, killing all 329 on board, with chance preventing the simultaneous destruction of another at Tokyo.

The seriousness of such incidents has, in recent months, grown from the mere appalling and tragic but occasional incident to one of major world importance having substantial effect on world peace and economic survival. The fact that this is no exaggeration is shown by the bombing raid carried out by the USA on Libya in April 1986, in retaliation for that country’s alleged involvement in or support of international terrorism. The subsequent reported mass cancellation of travel to Europe by Americans with consequential serious commercial implications not only for the airlines operating on the North Atlantic, where, for instance, British Airways reported a 25% drop in passenger traffic, is but one example of the effect of terrorism on the stability of world trade.

A simple and convenient “ endurance chart” for the presentation of basic fatigue data is described, where static failure is regarded as simply fatigue failure in one cycle of loading.

This chart shows the effects of mean stress, residual stress and pre-tension, and displays several interesting features of fatigue data. It is easily constructed directly from fatigue test results, and is very well suited to the calculation of stress concentration effects, including “ plastic relief ” effects.

With the aid of such charts the relative fatigue strengths and structural efficiencies of different materials may be readily compared, and it is clearly shown that in certain circumstances a “ high-strength” alloy may in fact have considerably less fatigue strength than a “ medium-strength ” alloy at a given life, or conversely a lower life at a given stress level.

It is demonstrated that the fatigue life of a component subjected to combined mean stress and alternating stress may be found only with a knowledge of the complete fatigue characteristics of the material (such as are presented in the endurance chart); and that attempts to estimate fatigue life from spot-value comparisons, such as the fatigue strength at an arbitrary given endurance, can be dangerously inaccurate. A chart of the form described thus forms a valuable step towards the accurate calculation of fatigue life.

The method is illustrated by the provision of endurance charts for 14S-T (L.65), 75S-T, and D.T.D.683; and with experimental results for notched components of L.65 and D.T.D.683.

An example illustrates the application of the chart to the calculation of the fatigue life for the case of two independent systems of loading acting on a pressure cabin with circular window cut-outs.

Plume interference effects on the axisymmetric flowfields around powered missiles are investigated using computational techniques. The study is mainly to understand the physics of the plume-induced shock and separation particularly at high plume to exit pressure ratios with and without shock-turbulent boundary layer control methods. Mass-averaged Navier-Stokes equations with the RNG k-ε turbulence model are solved using a fully implicit finite volume scheme and time-marching algorithm. The shock position and extent of separation was found to be dependent on the freestream Mach number and plume pressure ratio. Rounding the tail or a groove on the surface near the tail moved the shockwave downstream of the tail fin which should enhance the control of the missile.

The available methods of braking a modern aeroplane with its high landing speed are not entirely satisfactory. This difficulty in braking is particularly noticeable with pure jet aircraft. Owing to the absence of propellers, reversible pitch propellers are no longer a solution to this problem and the under-carriage can be simplified so that it occupies a smaller fraction of the all-up weight of the aeroplane.

A trajectory optimisation procedure is addressed to generate a reference trajectory for Satellite Launch Vehicles (SLVs). Using a grid-based discrete scheme, a Modified Minimum Cost Network Flow (MCNF)-based algorithm over a large-scale network is proposed. By using the network grid around the Earth and the discrete dynamic equations of motion, the optimum trajectory from a launch point to the desired orbit is obtained exactly by minimisation of a cost functional subject to the nonlinear dynamics and mission constraints of the SLV. Several objectives such as the flight time and terminal conditions may be assigned to each arc in the network. Simulation results demonstrate the capability of the proposed algorithm to generate an admissible trajectory in the minimum possible time compared with previous works.

The Purpose of this note is to present a table of the receptances of simple epicyclic gears and to show how they may be used. This table of results has two main uses. In the first place the receptances simplify the calculation of the natural frequencies of torsional systems containing these gears by the methods explained previously. Secondly, responses of systems (which incorporate these gears) to given harmonic excitations may be estimated, either in the absence of damping, or when there is damping present of known amount in the component sub-systems. This second use of receptances is illustrated by a simple example in this note; it is based upon the fact that the receptances of a compound system may be built up from those of its sub-systems irrespective of whether there is damping present or not.

Flight-deck Interval Management (FIM) is a modern airborne self-spacing technology that improves arrival route throughput and runway utilisation and increases hourly arrival capacity by up to four aircraft per hour and per runway, compared to conventional air traffic controller guided arrivals. The National Aeronautics and Space Administration (NASA) has been the leader in FIM research and formulated a logic that was put to an actual flight test in 2017. Despite the overall success of the project, operational deficiencies concerning the number of speed commands, which led to several recommendations for future research before operational implementation, were discovered. In this study, a new logic that implements a two-stage rule-based selection algorithm was developed to overcome those deficiencies. The proposed logic was compared to NASA’s logic on an arrival in Tokyo International Airport with multiple induced error patterns. The results indicate that the new logic significantly decreases the number of speed commands with only minor aggravations in spacing performance. The results that highlight the strengths and weaknesses of both concepts are discussed, and an outlook on and ideas for future research on FIM and the proposed logic are presented.

It was proposed in Ref. 1 that cryogenic temperatures can be achieved by the adiabatic isentropic expansion of a gas. The scheme is shown in Fig. 1. High pressure gas contained in A expands by means of valve 1 and cools. Valve 2 is then opened along with nozzle valve to push cold test gas through the working section.

In the ideal case the process is isentropic. To achieve reservoir conditions of T=120K and P = 4·4 bars, the initial pressure needed would be 110 bars. However, because of heat transfer from the walls of the tube, the process is not ideal and the actual initial pressure needed is higher. The main parameters which affect the heat transfer are the internal surface area of the tube, the rate of expansion governed by the size of valve 1 and the initial pressure of the gas.

A transient sound wave is generated by discharging a spark in an air stream, the velocity and temperature of which are required. After a time interval of about 25 microseconds a shadowgraph photograph of the sound wave is taken; a second photograph is obtained after a further known time interval of the same order. The two exposures, both on the same negative, show the propagation of the sound wave in the air stream and from this the Mach number, the true velocity, the local velocity of sound, and hence the temperature, can be calculated.

Using this method, measurements of Mach numbers of the order of 0·5 gave values between 98 per cent, and 100 per cent, of those calculated from pressure measurements. Typical examples of the sound wave photographs are shown. With further development along the lines indicated in the paper greater accuracy should be possible. The local speed of sound was measured to an estimated accuracy of ±1·5 per cent.

Since only a very short time interval is needed to obtain the photographs, the method appears promising for investigating explosions of brief duration, or dealing with flows of pulsating character.

In References (1), (2), Dr. Lachmann develops a method for calculating the growth of the laminar boundary layer over an aerofoil surface with spanwise suction slots placed at intervals along the chord. For this form of control, the laminar flow develops normally from the downstream edge of a slot until it attains the critical Reynolds number (expressed in terms of either the displacement or momentum thickness) at which transition is imminent. The layer then encounters another slot which so thins and stabilises the part not removed by suction, that it is able to continue downstream in the laminar state.

A new feature of the above investigation is the establishment of a second critical Reynolds number which provides an initial condition on the downstream side of a slot. Essentially it defines the minimum value of the displacement or momentum thickness for which, in relation to the local surface roughness, there is no danger of transition due to this form of disturbance.

Due to the safety threats caused by icing, the de-icing system is essential in the aviation industry. As an effective method, the electromechanical de-icing system (EDS) is a new ice-protection system based on mechanical vibration principles. For the majority of the current research on system de-icing capability estimation, the effect of impedance-matching is not considered. Impedance matching plays a very important role in improving the performance of the electromechanical system, so we must also consider the impact of impedance matching when designing the EDS. In the present study, a de-icing capability prediction method considering the impact of an impedance-matching device is established based on experimental and numerical methods. The results indicate that the impedance-matching effect has no impact on the mechanical vibration of the structure for the same load power. Meanwhile, impedance-matching devices can significantly improve the power factor and increase the interface shear stress/strain for de-icing. Eight different vibrational modes were tested, and the experimental results showed that the actual interface shear strain after impedance matching is inversely proportional to the de-icing time. The verification experiments were conducted and the accuracy of the proposed prediction method was verified.

In this work, a three degrees-of-freedom (3-DoF) static quadcopter unmanned aerial vehicle (UAV) test-rig of a pendulum-type configuration is custom-designed, developed, instrumented, and interfaced with a PC. The rig serves as a test bed to develop high-fidelity mathematical models as well as to investigate autopilot designs and real-time closed-loop controllers’ performances. The Simulink Desktop Real-Time software is employed for the quadcopter’s attitude signals acquisition and real-time implementation of closed-loop controllers on a target microcontroller hardware. The mathematical models for pitch, roll, and yaw axes are derived via the first principle and validated with the experimental linear system identification (SI) techniques. Subsequently, employing the multi-parameter root contour technique, the classical proportional integral derivative (PID) controllers are designed and implemented in real-time on the quadcopter UAV test rig. This served as a benchmark controller for comparing it with an integral-based linear quadratic regulator (LQR) controller. Further, to improve the transient response of the LQR controller, a novel robust integral-based LQR controller with a feedforward term (LQR-FF) is implemented, which shows much superior performance than the benchmark and basic LQR controller. This work thus will act as a precursor for a more complex 3-DoF autopilot design of an untethered quadcopter.