First derivatives of flow quantities behind two-dimensional, nonuniform supersonic flow over a convex corner

A method of determining spatial derivatives of flow quantities behind an expansion fan as a function of the curvature of the streamline behind the fan is developed. Taylor series expansions of flow quantities within the fan are used and boundary conditions satisfied to the first and second order so that the curvature of the characteristics in the fan may be determined. A system of linear equations for the spatial derivatives is then developed. An application of the method to shock coalescence including asymmetric effects is described

Spatial derivatives of flow quantities behind curved shocks of all strengths

Explicit formulas in terms of shock curvature are developed for spatial derivatives of flow quantities behind a curved shock for two-dimensional inviscid steady flow. Factors which yield the equations indeterminate as the shock strength approaches 0 have been cancelled analytically so that formulas are valid for shocks of any strength. An application for the method is shown in the solution of shock coalescence when nonaxisymmetric effects are felt through derivatives in the circumferential direction. The solution of this problem requires flow derivatives behind the shock in both the axial and radial direction

Wind-tunnel investigation of the validity of a sonic-boom-minimization concept

The Langley unitary plan unitary plan wind tunnel was used to determine the validity of a sonic-boom-minimization theory. Five models - two reference and three low-boom constrained - were tested at design Mach numbers of 1.5 and 2.7. Results show that the pressure signatures generated by the low-boom models had significantly lower overpressure levels than those produced by the reference models and that small changes in the Mach number and/or the lift caused relatively small changes in the signature shape and overpressure level. Boundary-layer effects were found in the signature shape and overpressure level. Boundary-layer effects were found to be sizable on the low-boom models, and when viscous corrections were included in the analysis, improved agreement between the predicted and the measured signatures was noted. Since this agreement was better at Mach 1.5 than at Mach 2.7, it was concluded that the minimization method was definitely valid at Mach 1.5 and was probably valid at Mach 2.7, with further work needed to resolve the uncertainty

Current research in sonic-boom minimization

A review is given of several questions as yet unanswered in the area of sonic-boom research. Efforts, both here at Langley and elsewhere, in the area of minimization, human response, design techniques and in developing higher order propagation methods are discussed. In addition, a wind-tunnel test program being conducted to assess the validity of minimization methods based on a forward spike in the F-function is described

Minimization of sonic-boom parameters in real and isothermal atmospheres

The procedure for sonic-boom minimization introduced by Seebass and George for an isothermal atmosphere was converted for use in the real atmosphere by means of the appropriate equations for sonic-boom pressure signature advance, ray-tube area, and acoustic impedance. Results of calculations using both atmospheres indicate that except for low Mach numbers or high altitudes, the isothermal atmosphere with a scale height of 7620 m (25 000 ft) gives a reasonable estimate of the values of overpressure, impulse, and characteristic overpressure obtained by using the real atmosphere. The results also show that for aircraft design studies, propagation of a known F-function, or minimization studies at low supersonic Mach numbers, the isothermal approximation is not adequate

Charts for determining potential minimum sonic-boom overpressures for supersonic cruise aircraft

Charts which give an estimation of minimum achievable sonic-boom levels for supersonic cruise aircraft are presented. A minimization method based on modified linear theory was analyzed. Results show several combinations of Mach number, altitude, and aircraft length and weight. Overpressure and impulse values are given for two types of sonic boom signatures for each of these conditions: (1) a flat top or minimum overpressure signature which has a pressure plateau behind the initial shock, and (2) a minimum shock signature which allows a pressure rise after the initial shock. Results are given for the effects of nose shape

An analysis of shock coalescence including three-dimensional effects with application to sonic boom extrapolation

A method for analyzing shock coalescence which includes three dimensional effects was developed. The method is based on an extension of the axisymmetric solution, with asymmetric effects introduced through an additional set of governing equations, derived by taking the second circumferential derivative of the standard shock equations in the plane of symmetry. The coalescence method is consistent with and has been combined with a nonlinear sonic boom extrapolation program which is based on the method of characteristics. The extrapolation program, is able to extrapolate pressure signatures which include embedded shocks from an initial data line in the plane of symmetry at approximately one body length from the axis of the aircraft to the ground. The axisymmetric shock coalescence solution, the asymmetric shock coalescence solution, the method of incorporating these solutions into the extrapolation program, and the methods used to determine spatial derivatives needed in the coalescence solution are described. Results of the method are shown for a body of revolution at a small, positive angle of attack

Effect of leading-edge load constraints on the design and performance of supersonic wings

A theoretical and experimental investigation was conducted to assess the effect of leading-edge load constraints on supersonic wing design and performance. In the effort to delay flow separation and the formation of leading-edge vortices, two constrained, linear-theory optimization approaches were used to limit the loadings on the leading edge of a variable-sweep planform design. Experimental force and moment tests were made on two constrained camber wings, a flat uncambered wing, and an optimum design with no constraints. Results indicate that vortex strength and separation regions were mildest on the severely and moderately constrained wings

Flight transition data for angles of attack at Mach 22 with correlations of the data

Boundary-layer transition data for angles of attack from 2.5 to 47 deg from a flight experiment with a cone that reentered at angles of attack up to 75 deg were analyzed and their local flow conditions are presented. The transition data were obtained from both acoustic and electrostatic sensors. The data from the acoustic and electrostatic sensors were correlated by use of three different sets of correlating parameters. For each set of correlating parameters, the transitional and turbulent data from the acoustic and electrostatic sensors were plotted separately. Each of the correlations was compared with a linear curve fit of previous cone-flight data at near zero angle of attack. Results indicate that the data from acoustic sensors falls below the linear curve fits to the flight data and indicates the sensitivity of the sensors. It is shown that the transition data from the electrostatic sensors tends to scatter much more than the data from the acoustic sensors. However, the data from the electrostatic sensors tends to scatter about the linear curve fits based on previous flight data

Evolution of non-kin cooperation: social assortment by cooperative phenotype in guppies

This is the final version. Available from The Royal Society via the DOI in this record.Data accessibility: The data used in this study are available at the Dryad Digital Repository: doi:10.5061/dryad.js446q8Cooperation among non-kin constitutes a conundrum for evolutionary biology. Theory suggests that non-kin cooperation can evolve if individuals differ consistently in their cooperative phenotypes and assort socially by these, such that cooperative individuals interact predominantly with one another. However, our knowledge of the role of cooperative phenotypes in the social structuring of real-world animal populations is minimal. In this study, we investigated cooperative phenotypes and their link to social structure in wild Trinidadian guppies (Poecilia reticulata). We first investigated whether wild guppies are repeatable in their individual levels of cooperativeness (i.e. have cooperative phenotypes) and found evidence for this in seven out of eight populations, a result which was mostly driven by females. We then examined the social network structure of one of these populations where the expected fitness impact of cooperative contexts is relatively high, and found assortment by cooperativeness, but not genetic relatedness. In contrast, in accordance with our expectations we did not find assortment by cooperativeness in a population where the expected fitness impact of cooperative contexts is lower. Our results provide empirical support for current theory and suggest that assortment by cooperativeness is important for the evolution and persistence of non-kin cooperation in real-world populations.Leverhulme TrustDanish Council for Independent Researc