· · · Aerospace Engineering reports

In this report a method is presented to determine optimum shapes of bodies of revolution taking into account the shape dependent part of the base drag. The latter is achieved by using the Chapman assumption that the base pressure coefficient, when correlated with conditions at a suitable point near the base, depends only on the free-stream Mach number if the boundary layer is turbulent. The present method enables the determination of quantitative results, which show the known trend that the optimum bodies have their maximum cross section ahead the base area. The drag reductions obtained are the most significant for relatively slender bodies in the lower supersonic Mach number range.

A survey is given of the results obtained at the NLR with respect to the determination of optimum body-ring wing configurations at zero lift. It is shown that if reliable data are required for practical shapes the use of exact flow theories is essential. The pressure distribution on the optimum configuration considered here is such that the conclusion seems justified that no separation of the boundary layer will take place in an actual application.

The Coanda effect, being an expedient for the application of blowing boundary layer control^, has been investigated by the NLH to gain an insight into the basic principle and the laws by which it is governed, Within the framework of this investigation a potential theory is developed which, at any rate leads to a qualitative prediction of the increase in volume flow from the slot and the force on the deflecting surface and which will be used as a basis for farther theoretical analysis,

In this report the drag-coefficient of an optimum body with a conical nose has been determined. The body was designed for a Mach number of the undisturbed stream equal to 3. It is found that the curve for the drag coefficient shows a definite kink at the design Mach number. The conclusion is reached that a more general approach for designing optimum bodies will lead to lower values of the wave drag than those obtained by applying current theories.

This report presents a method for the determination of axially-symmetric shapes with a given base area that are optimum with respect to wave drag in supersonic flow and which have finite nose angles. Use has been made of the exact non-linear differential equations for supersonic flow together with the shock equations. The computed results indicate that the optimum bodies with a finite nose angle have a lower drag than those with cusped noses. This would make their practical application of a certain significance. A number of such shapes have been presented in this report.

Results are presented which are obtained by a new elaborate method developed at NLR for the determination of the characteristics of thin wings in subsonic flow. Attention is paid to the rate of convergence of the numerical solutions, especially with respect to the number of collocation points. Two rectangular wings have been treated in order to examine the influence of the aspect ratio. The influence of the rounding of a kink is demonstrated by means of a series of constant choird wings with hyperbolic edges.

A method is given for the calculation of the noise field of a propeller. This method is slightly different from that of Garrick and Watkins. It is believed that the differences in the results indicate the order of the inaccuracy due to the approximations inherent in the two methods. The noise field of two propellers is calculated to show these differences. To estimate the influence of the diffraction around a fuselage some numerical results are given for the diffraction of a plane wave around a circular cylindrical fuselage.

In this paper, a discussion is given of some of the aerodynamic difficulties involved in the design of wings for high-subsonic speeds, and of the theoretical methods available to calculate sub-critical pressure distributions. It appears that until now only one of these methods, being in fact a semi-emperical one, is developed far enough to be of some help in the design stage. The main features of the method are discussed by giving attention to the two-dimensional flow problem and by describing the so-called centre solution of an infinite swept wing. The applicability of the method is shown both for two and three-dimensional flows by giving comparisons between measured and calculated pressure distributions. Nevertheless the method can not be regarded as a final statement. The development of digital computers in principle has made available for practical application a variety of more general promising approaches to the theoretical solution of subsonic flows around wings. It seems desirable in the authors views to pay full attention to the exploration cf the new possibilities.

This report gives a programme for the determination of the flow around a circular cone. Both the cases of zero-inclination and of a small inclination have been considered. The programme is written in the international machine language ALGOL and can therefore be operated on any computer having an ALGOL compiler. The purpose of this investigation was mainly to provide an accurate solution for these conical flows in view of their application as initial data along a "first characteristic". These data will enable the determination of the flow field around an axially symmetric configuration having a nose contour which may be considered as conical along a certain distance from the vertex. The programme is discussed in detail and some results obtained by it are included as an example.

This report presents a new method to find shapes that attain minimum wave drag under certain constraints. The constraints considered here are given values for the base area and the lift. The configuration is assumed to be embedded in a volume enclosed by two opposing circular Mach cones, one going through the most forward point of the configuration, the other through the rim of the base. The flow field inside this volume is entirely governed by the perturbation velocities on the Mach cone through the base. In fact, the method deals with the procedure to determine the value of these velocities. Once the velocity distribution along the Mach cone is known the flow field and thus the shape of possible configurations can be found by applying characteristic methods. Two cases are considered; in the first only the value of the base area is prescribed, while in the second also the lift is given. As an example the shape and the axis inclinations of a possible ring-wing configuration are calculated. The analysis is based on linearized supersonic flow theory. However, the method can also be adapted to non-linear flows around shapes with circular cross-sections.

The present report deals with the numerical treatment of the linearised lifting surface theory through a method which is based upon the representation of the pressure distribution on chordwise direction by a series of Chebyshew polynomials according to Laschka, and upon the determination of the spanwise integral involved by means of trigonometric polynomials such as also appUed by Multhopp. When calculations are performed using Multhopp's method the results show strong variations with increasing number of the spanwise stations and chordwise points, to which the boundary condition is applied. This makes it impossible to obtain a plausible solution. Hence a new method has been developed, where the representation of the pressure distribution in spanwise direction is separated from the representation of the regularised kernel function in spanwise direction. This makes it possible to obtain accurate integrals for a given distribution of pivotal points and leads to results which show a rapid decrease of variation as either the number of spanwise stations or the number df chordwise points or both are increased. This is demonstrated by including a number of results for some well-known wings. As the method allows of the possibility to take arbitrary positions for the pivotal points, some computations have been performed for different distributions of spanwise stations. The results indicate that further investigations may be useful.