Hypersonic Flight Mechanics

The effects of aerodynamic forces on trajectories at orbital speeds are discussed in terms of atmospheric models. The assumptions for the model are spherical symmetry, nonrotating, and an exponential atmosphere. The equations of flight, and the performance in extra-atmospheric flight are discussed along with the return to the atmosphere, and the entry. Solutions of the exact equations using directly matched asymptotic expansions are presented

Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions

The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations

Optimum three-dimensional atmospheric entry from the analytical solution of Chapman's exact equations

The general solution for the optimum three-dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere is developed. A set of dimensionless variables, modified Chapman variables, is introduced. The resulting exact equations of motion, referred to as Chapman's exact equations, have the advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a completely general lift-drag relationship is used in the derivation. The results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary drag polar, and entering any planetary atmosphere. The aerodynamic controls chosen are the lift coefficient and the bank angle. General optimum control laws for these controls are developed. Several earlier particular solutions are shown to be special cases of this general result. Results are valid for both free and constrained terminal position

An approach to the problem of optimizing orbital maneuvers

Problem of time open maneuvering of orbital vehicle in Newtonian gravitational field while conserving characteristic velocity of maneuve

Analytic theory of orbit contraction

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory

Temperature measurements behind reflected shock waves in air

A radiometric method for the measurement of gas temperature in self-absorbing gases has been applied in the study of shock tube generated flows. This method involves making two absolute intensity measurements at identical wavelengths, but for two different pathlengths in the same gas sample. Experimental results are presented for reflected shock waves in air at conditions corresponding to incident shock velocities from 7 to 10 km/s and an initial driven tube pressure of 1 torr. These results indicate that, with this technique, temperature measurements with an accuracy of + or - 5 percent can be carried out. The results also suggest certain facility related problems

The Plasma Interaction Experiment (PIX) description and test program

The plasma interaction experiment (PIX) is a battery powered preprogrammed auxiliary payload on the LANDSAT-C launch. This experiment is part of a larger program to investigate space plasma interactions with spacecraft surfaces and components. The varying plasma densities encountered during available telemetry coverage periods are deemed sufficient to determine first order interactions between the space plasma environment and the biased experimental surfaces. The specific objectives of the PIX flight experiment are to measure the plasma coupling current and the negative voltage breakdown characteristics of a solar array segment and a gold plated steel disk. Measurements will be made over a range of surface voltages up to plus or minus kilovolt. The orbital environment will provide a range of plasma densities. The experimental surfaces will be voltage biased in a preprogrammed step sequence to optimize the data returned for each plasma region and for the available telemetry coverage

Racial and Socioeconomic Disparities in Melanoma Incidence Rates in Georgia: 2000-2011

Background: The objective of this research was to investigate melanoma incidence rates and health outcomes in Georgia over time and by race, socio-economic status (SES), and gender. Methods: Age-adjusted melanoma incidence rates were obtained from the Georgia Comprehensive Cancer Registry SEER*Stat Database (2000-2011). To compare incidence rates across counties, and public health districts and by race, SES and gender, maps were generated using Geographic Information Systems (GIS). A cluster analysis was performed by use of SaTScan, and maps were created to visualize clusters of melanoma cases. Results: In Georgia, from 2000-2011, age-adjusted incidence rates for melanoma were higher among Whites than Blacks (28.0 vs. 1.1 per 100,000 population). For both races, high rates were found to be associated with high SES. For Whites, high rates were concentrated in urban areas relative to Blacks in rural areas. Clusters of melanoma incident cases were found mainly in the north central region of Georgia. Conclusions: For Georgia, results for map comparisons are consistent with previous research findings that higher melanoma incidence rates are associated with high SES for Whites and, to a lesser extent, for Blacks. Melanoma interventions in Georgia should focus on urban White and rural Black at-risk populations, especially those with high SES