Engineering topics

Boltz, Frederick W.

Publications and source records attributed to Boltz, Frederick W..

5 records

NASA NTRS1992

Orbital motion under continuous tangential thrust

The effect of continuous tangential thrust on the orbital motion and mass loss of a vehicle initially in a circular orbit is investigated analytically. It is shown that, for a thrust-to-weight ratio of greater than 0.16175, escape speed will eventually be reached along an unwinding spiral trajectory. For lower thrust-to-weight ratios, escape speed is never attained, and the flight path oscillates around a logarithmic spiral trajectory. Formulas are obtained for the approximate orbital motion and time of flight along each type of trajectory and for mass loss due to expenditure of rocket propellant.

Boltz, Frederick W.↗

NASA NTRS1989

Analytic solution for vertical launch into orbit

An approximate analytic solution is presented for the motion and heating of nonlifting spacecraft launched vertically for ascending flight through the atmosphere into earth orbit. The solution is based on Chapman's Z-function transformation of the equations of motion with the assumption of an exponential atmosphere. The transformed equations have been modified to include the effects of thrusting with mass loss. It is assumed that the vehicle negotiates a gravity turn during ascent so that the thrust vector is aligned in the flight-path direction. Numerical results are presented to document the analytic solution and provide evidence of the useful information generated by it.

Boltz, Frederick W.↗

NASA NTRS1987

Inverse solution of Kepler's equation for hyperbolic orbits

An algorithm is presented for efficient inverse solution of Kepler's equation for hyperbolic orbits. It is shown that an expansion of Barker's equation into a bicubic polynomial provides a good approximation to obtain accurate starting values for rapid numerical solution of Kepler's equation. In the approximate equation a cubic in normalized elapsed flight time from pericenter is set equal to a cubic in a function S of eccentricity and true anomaly. The initial estimate of S to use in an iteration formula is obtained by evaluating the cubic in normalized flight time and finding in most cases the single real root of the other cubic. This initial estimate has an accuracy corresponding to values of true anomaly in error by less than 0.5 degrees generally.

Boltz, Frederick W.↗

NASA NTRS1986

Efficient inverse solution of Kepler's equation

A bicubic polynomial approximation to Kepler's equation for elliptic orbits is shown to provide accurate starting values for efficient numerical solution of this equation for eccentric anomaly. In the approximate equation, a cubic in mean anomaly is set equal to a cubic in eccentric anomaly. The coefficients in the two cubics are obtained as functions of eccentricity by specifying values of function and slope at the midpoint and the endpoint of the complete interval (0 to pi). The initial estimate of eccentric anomaly to use in an iteration formula is obtained by evaluating the cubic in mean anomaly and finding the single real root of the cubic in eccentric anomaly. Numerical results are presented which indicate that the estimate accuracy of this method is roughly an order of magnitude better than that of other recently-reported formulas.

Boltz, Frederick W.↗

NASA NTRS1960

Effects of Sweep Angle on the Boundary-Layer Stability Characteristics of an Untapered Wing at Low Speeds

An investigation was conducted in the Ames 12-Foot Low-Turbulence Pressure Tunnel to determine the effects of sweep on the boundary-layer stability characteristics of an untapered variable-sweep wing having an NACA 64(2)A015 section normal to the leading edge. Pressure distribution and transition were measured on the wing at low speeds at sweep angles of 0, 10, 20, 30, 40, and 50 deg. and at angles of attack from -3 to 3 deg. The investigation also included flow-visualization studies on the surface at sweep angles from 0 to 50 deg. and total pressure surveys in the boundary layer at a sweep angle of 30 deg. for angles of attack from -12 to 0 deg. It was found that sweep caused premature transition on the wing under certain conditions. This effect resulted from the formation of vortices in the boundary layer when a critical combination of sweep angle, pressure gradient, and stream Reynolds number was attained. A useful parameter in indicating the combined effect of these flow variables on vortex formation and on beginning transition is the crossflow Reynolds number. The critical values of crossflow Reynolds number for vortex formation found in this investigation range from about 135 to 190 and are in good agreement with those reported in previous investigations. The values of crossflow Reynolds number for beginning transitions were found to be between 190 and 260. For each condition (i.e., development of vortices and initiation of transition at a given location) the lower values in the specified ranges were obtained with a light coating of flow-visualization material on the surface. A method is presented for the rapid computation of crossflow Reynolds number on any swept surface for which the pressure distribution is known. From calculations based on this method, it was found that the maximum values of crossflow Reynolds number are attained under conditions of a strong pressure gradient and at a sweep angle of about 50 deg. Due to the primary dependence on pressure gradient, effects of sweep in causing premature transition are generally first encountered on the lower surfaces of wings operating at positive angles of attack.

Boltz, Frederick W.↗