Engineering topics

Busemann, A.

Publications and source records attributed to Busemann, A..

At least 19 records

NASA NTRS1980

Hypersonic and planetary entry flight mechanics

The book treats hypersonic flight trajectories and atmospheric entry flight mechanics in light of their importance for space shuttle entry. Following a review of the structures of planetary atmospheres and aerodynamic forces, equations are derived for flight over a spherical planet, and the performance of long-range hypervelocity vehicles in extra-atmospheric flight is analyzed. Consideration is then given to vehicle trajectories in the powered and atmospheric reentry phases of flight, and several first-order solutions are derived for various planetary entry situations. The second-order theory of Loh for entry trajectories is presented along with the classical theories of Yaroshevskii and Chapman for entry into planetary atmospheres, and the thermal problems encountered in hypersonic flight are analyzed. A unified theory for entry into planetary atmospheres is then introduced which allows the performance of a general type of lifting vehicle to be studied, and applied to the analysis of orbit contraction due to atmospheric drag, flight with lift modulation and lateral maneuvers.

Vinh, N. X.↗

NASA NTRS1979

Analytic theory of orbit contraction due to atmospheric drag

Theory of space vehicle flight in near vacuum and in a planetary atmosphere is unified for the case of a spherically symmetric atmosphere with exponential variation of density with height. Dimensionless equations of motion are established that bridge the gap between satellite theory and entry theory. Integration is done by Poincare's method of perturbations. Solutions for the dimensionless semimajor axis are numerically obtained.

Vinh, N. X.↗

NASA NTRS1977

Flight with lift modulation inside a planetary atmosphere

A set of dimensionless variables is introduced to derive the equations for flight with lift and bank modulation inside a planetary atmosphere in a Newtonian gravitational field. Flight subject to constraints on state variables is discussed and a general approach is presented. Two examples are analyzed in detail: flight at constant speed, and flight at constant sinking speed.

Vinh, N. X.↗

NASA NTRS1977

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.

Vinh, N. X.↗

NASA NTRS1976

Flight with lift modulation inside a planetary atmosphere

A set of dimensionless variables (modified Chapman's variables) is introduced in a derivation of general equations for lifting flight and bank modulation within a planetary atmosphere. The atmosphere is assumed spherical and at rest, and a generalized lift-drag polar is also introduced. Corresponding equations for flight over a flat planet model are attained via a straightforward transformation. Two planar flight cases: flight at constant absolute speed over a spherical planet, and flight at constant descent rate over a flat planet, are analyzed, and the required lift control law (with negative or positive lift) is exhibited in each case. Glide at very high descent rate and plane flows of trajectories are analyzed.

Vinh, N. X.↗

NASA NTRS1976

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.

Busemann, A.↗

NASA NTRS1976

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.

Busemann, A.↗

NASA NTRS1974

Analytical solution of the optimal three dimensional reentry problem using Chapman's exact equations

This paper presents the general solution for the optimal three dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere. A set of dimensionless variables is introduced, and the resulting exact equations of motion have the distinctive advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a general lift-drag polar is used to define the aerodynamic control. Hence, the results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary polar and entering any planetary atmosphere.

Vinh, N. X.↗

NASA NTRS1974

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.

Busemann, A.↗

NASA NTRS1969