A Note on the Impact Pressure Loading of a Rigid Plastic Spherical Shell

Abstract

approximation hand computation utilizing normal-shock equations and graphical thermodynamic-state data. The accuracy of the method is dependent on the assumed curvature between data points in plotting the tabular data of Gilmore and the error in logarithmic interpolation between curves. I t was estimated that these errors are between 1 and 10 per cent, with the error of the major portion of the data less than 5 per cent. The charts, in general, are not as accurate as could be obtained with an electronic computer, but the method is justified on the basis of the relatively low cost in time and effort. The charts should, nonetheless, prove useful to those working in hypervelocity gasdynamics until more refined calculations are available. The series of gasdynamic charts of reference 1 include the following properties: flow velocity, density, pressure, temperature, internal energy and enthalpy associated with a traveling normal shock, stationary normal shock (bow wave), stagnation point, and reflected normal shock. Curves are plotted versus incident-shock velocity for initial air densities of 10 1 to 10 ~ times atmospheric density and an initial temperature of 273.2°K. The range of incident-shock speeds is from Mach 10 to Mach 50 or to the limit of the thermodynamic data, 24,000°K. Included is a plot of Gilmore's data in the form of a Mollier diagram. The thermodynamic-state data were plotted as enthalpy versus density with lines of constant entropy and temperature because the curves become more orthogonal and, therefore, greater accuracy in reading is obtainable. This general plot is presented in Fig. 1. I t is felt that the gasdynamic charts are of general usefulness to many scientists and engineers and may satisfy a current need. However, the volume of the charts precludes publishing in a technical journal. The report is available to those interested and copies may be obtained by request to the author.