Ballistic Parameters Research Articles

A Unified Model for the Acceleration-Produced Burning Rate Augmentation of Metalized Solid Propellants

Abstract Experiments have shown that acceleration of metalized composite propellants can affect an increased burning rate. The pressure-time trace of an accelerated propellant, which under static conditions would be neutral, exhibits a rapid increase to a maximum pressure and then decays asymptotically toward a quasi-equilibrium value. The model presented here attributes the augmented burning rate to the inertial retention of metal-metal oxide globules in pits on the propellant surface and the attendant heat transfer from the hot globules to the surface. A burning rate augmentation analysis for the initial period when the globules have near-spherical shapes predicts the burning-rate dependence on internal ballistic parameters and explains the observed transient behavior. As burning continues the globules grow and deform into irregularly shaped platelets and sheets which characterize the quasi-equilibrium period. Extending the model to include platelet shapes yields a functional relationship between burnin...

Probability distribution of latitudes of re- entry and impact following decay of polar orbits.

Satellites in near-circular decaying polar orbits experience drag forces at equatorial latitudes substantially greater than those at polar latitudes (due to the oblateness of the atmosphere). The effect of this drag variation upon probability distributions of re-entry and impact latitude is investigated by determining a probability distribution of orbit altitude a revolution or so prior to re-entry; deriving functional relationships between orbit altitude, re-entry latitude, and impact latitude; and transforming variables to form the latitude distributions. Results for the particular case of satellites with ballistic parameters of 16 psf indicate that the probability density of re-entry latitude is about three times greater at the equator than at the poles. The probability density of impact latitude is comparatively uniform.

Errors in orbital predictions for meteorological and geodetic satellites

The results of a theory which accounts for observed errors in orbital predictions are presented. The errors in predictions are assumed to arise from three causes: a sinusoidal variation in atmospheric density with a 27-day period, a random fluctuation in atmospheric density, and errors of observation. The theoretical errors are evaluated for Vanguard 1 and for the Tiros weather satellites as a function of the length of the predictions. Errors in predictions for the Anna 1-B geodetic satellite are expected to be approximately the same as for the Tiros satellites because the altitudes and ballistic parameters are similar. The theoretical errors are compared with errors in actual predictions issued by the Vanguard and National Aeronautics and Space Administration computing centers. The errors for Vanguard 1 are also given as a function of the year in which the prediction was made, illustrating the influence of perigee insolation. The problem of determining the location of clouds which appear on the Tiros weather photographs is discussed.

The Analysis of Solid Rocket Motor Performance Errors by Monte Carlo Techniques

In the captive testing of conventional solid rocket motors, a large number of fundamental physical measurements are normally implemented. These include the determination of instantaneous motor force, pressure, temperature, deflection, acceleration and electrical power data associated with the particular motor configuration. In the majority of applications, however, the motor performance indicators of most general interest are not measured directly, but are calculated from these basic data. Thus, for example, motor specific impulse is computed from given instantaneous values of measured thrust, pressure and weight parameters. All physical measurements are subject to inaccuracies, i.e., even the most sophisticated data acquisition system will necessarily inject discrepancies into the measured data. Hence, the mechanisms through which errors inherent in the measured quantities affect the accuracy of the calculated ballistic parameters are of extreme practical importance and must be quantitatively defined. At the Aerojet-General Corporation, an intensive and continuing analysis of overall measurement system errors (through rigorous analytical and experimental techniques) has permitted the statistical characterization of the error parameters within the framewcrk of each current large scale motor development program. Based upon these data and for a specific ballistic parameter computational routine, an extensive error analysis is required to deduce the errors associated with the computed performance parameters. Because of the nonlinearities and interactions inherent within the ballistic computations, a Monte Carlo technique is invoked.

A Practical Mathematical Approach to Grain Design

Equations were developed relating solid propellant grain geometry to the important ballistic parameters of crosssectional loading density, sliver or tail-off fraction, progressivity ratio, initial surface and web. The equations were then solved by means of high speed computers and the results graphed in a readily usable form. If the loading fraction, sliver, progressivity ratio and web are given, grain designs which meet or most nearly meet given requirements can be found from the graphs. The graphs are useful in determining the effect of slight variations in design parameters. Illustrations of the use of the graphs are given for the internal-burning star and the internal-burning wagon wheel configurations. Calculations have also been made on a modified form of the wagon wheel which permits one, two or three levels of thrust during burning.

Design, Fabrication and Testing of the Vanguard Satellite

1 Price, E. W., Geometry and Ballistic Parameters for Solid Propellant Motor s / ' J E T PROPULSION, vol. 24, Jan.-Feb. 1954, p. 16. 2 Vogel, J. M., A Quasi-Morphological Approach to the Geometry of Charges for Solid Propellant Rockets: Family Tree of Charge Designs, J E T PROPULSION, vol. 26, Feb. 1956, p. 102. 3 Epstein, L. I., The Design of Cylindrical Propellant Grains, JET PROPULSION, vol. 26, Sept. 1956, p. 757. 4, 5 These graphs, though unclassified, appear in classified reports. Copies may be obtained from the author. 6 Wimpress, R. N., Internal Ballistics of Solid-Fuel Rockets , McGraw-Hill, New York, 1950. 7 Rocket Fundamentals , OSRD 3992.