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This work describes the application of original computer graphics methods to examine the effect of inclusionswithin the solid rocket motor thrust chamber. The adoptance of a dynamic three-dimensional triangular mesh with aself-intersection removal algorithm, as the core of the burning surface regression module, allows the aforementionedtargetto bereached.Manyphenomena notmeasurablein an analyticalclosed form, likedifferent-shapedvoidswithinthe grain, can be investigated. Indeed, both local heterogeneities and surface imperfections could generate unexpectedvariations in the combustion chamber pressure pattern and early thermal protections exposure. The aforementionedtechniques are developed and tested on a ballistic simulator developed using computer graphics methods to improvemesh handling. Simulation results are carried out and discussed.

Microdebris particles generated by hypervelocity impacts between complex projectiles and ballistic missile targets can affect sensitive components of such aerospace systems. Current models assume an isotropic dispersion of this microdebris about the postimpact debris cloud center of mass. Data collected from recent tests indicate that a nonisotropic microdebris dispersion model is needed. The results are presented of a study aimed at improving the capabilities of an existing model that characterizes the microdebris environment created in a high-speed impact. Following a review of test data collection techniques, a nonisotropic microdebris dispersion model is developed as a series of modifications to the existing microdebris size distribution model. Relevant test data are then used to evaluate the proposed nonisotropic model. It is found that the modified model is more correct in accounting for the microdebris fragment population created in a high-speed impact than the current isotropic dispersion model.

The effect of lift and drag forces and aerodynamic moment on the flight of a spinning projectile in the atmosphere is investigated. The influence of the spin rate of the projectile on the range and height of flight is also studied, taking into consideration the progressive decay in the spin rate during the flight. The governing equations of motion of the projectile have been solved numerically, and the results are presented graphically. The effect of various parameters such as angle of projection, initial velocity, and spin on the flight of projectiles are plotted. From the results it can be concluded that the lift and drag forces and the aerodynamic moment, which are dependent on the spin rate of the projectile, influence the range and height of the trajectory significantly. Only planar motion of the projectile is considered

Analyses of internal ballistics and criteria for reaction propagation in nonelectrical tube explosive lines were performed based on explosive loading density, average particle size, and typical geometry using an approach based on heat transfer and decomposition kinetics in the explosive particles in quasi steady state. The results indicate the existence of a critical or maximum average explosive particle size for a given explosive loading density beyond which sustained propagation may cease. Large variations usually exist in the explosive loading density, so that fine particle sizes below 20 μm are preferable. Fine particle size also may increase the adhesion to the inner tube wall for mitigation of powder migration problems. Computer simulations of detonating end tip to nondetonating end tip transfer were performed using the CTH hydrodynamic code developed by the Sandia National Laboratories. Preliminary results indicate that the hot gas from the detonating end tip is more effective for initiating pyrotechnics in the nondetonating end tip and that a larger gap between the end tips is essential for the success of hot gas initiation

Theoretical and experimental studies are conducted on the quantitative evaluation of a friction force at the interface between a projectile and the launch tube wall in a ballistic range. From a mechanical balance relation applied to the projectile, the friction force is expressed theoretically as a function of the net acceleration of the projectile. With this formulation, experimentally measured in-bore projectile velocity proe les obtained using a velocity interferometer system for any ree ector are well interpreted. If the initial projectile motion is signie cantly suppressed by the friction force while the burning rate of the propellant remains signie cant, the base pressure becomes much higher than that with a negligibly small friction force, thereby enhancing the net acceleration. However, if the projectile-tube e t is excessively high, the main function of the friction force is to decrease the muzzle velocity.

A concept for propelling a projectile to hypervelociti es is described, and the feasibility is demonstrated by numerical simulations. In theory, the concept employs imploding blast waves to accelerate a projectile as it travels down a launch tube. The launch tube can be open to the atmosphere or sealed and maintained at some low pressure to minimize internal drag. The launch tube has a liner that contains a suitable explosive or energetic material. The explosive is configured with inert annular rings to prevent upstream detonation. A suitable trigger detonates each explosive ring sequentially as the projectile passes. The resulting blast wave causes an elevated pressure on the afterbody of the projectile. The acceleration continues until the projectile exits the launch tube.

We consider supersonic flight of a blunt slender body of revolution through a large-scale cloud of heated gas (thermal) floating in the stratified atmosphere. An efficient numerical method to determine the body motion is proposed.

A transient ballistics and combustion model is derived to represent the closed vessel experiment that is widely used to characterize the high pressure burning rates of solid propellants. The model is applied to explain why burning rates deduced from the closed vessel are in basic agreement with those measured from an equilibrium strand burner in the case of homogeneous propellants, but differ significantly in the case of nitramine composite propellants. Thermal profile time lag effects become small at high pressure because the burning rates become high. However, the development of the burning surface structure of those nitramine propellants which exhibit shifts in pressure exponent causes the mass burning rate to lag and then exceed the equilibrium value. It is necessary to consider this mechanism in applications dealing with high pressures and pressurization rates.

HE inclusion of small quantities of various lead compounds in the double-base propellant system results in increased burning rate at low pressure, followed by a plateau burning region, where the burning rate remains almost independent of variation in pressure, and the postplateau region, in which the burning rate/pressure relationship is similar to that of an unleaded propellant (Fig. 1). This phenomenon of independence of burning rate to pressure, generally known as "platonizatio n," implies a low value of pressure index n in the plateau region. A low value of n permits the design of lighter rocket motors because of lower safety factors. The magnitude of n is one of the important factors in determining the suitability of a propellant for rocket propulsion applications. The importance of low-pressure ballistics was realized as early as in 1939 with the widespread use of rockets. Earlier studies centered around low-energy nitrocellulose propellants with a view toward minimizing nozzle erosion, burning rate, and pressure index. However, the real impetus to the platonization of double-base propellants came from the observation that the use of lead stearate as a lubricant in the extrusion of large rocket charges actually had modified their burning characteristics. This paper reviews the literature on platonization of double-base propellant with different inorganic and organic compounds of lead and other metals, and presents various theories to explain the mechanism of the plateau effect.

An analytical model is developed for the linearized velocity-coupled combustion response function. The model treats elements of response to perturbations in pressure, in composition due to the heterogeneity of composite propellants, and in crossflow velocity. The effects of AP particle size are accounted for in terms of effects on controlling ballistics properties and in terms of fluctuations in propellant composition. There are two facets of the crossflow problem: the effect of crossflow velocity on the various response elements, and the response to velocity perturbations. Both are dealt with in this paper. Important trends derived from series of parametric computations are described.

The effect of the oxidizer size and size distribution on the pressure and temperature sensitivity for a nonaluminized composite solid propellant was investigated using a new mathematical model called the Petite Ensemble Model. Calculations were made using the new model, taking into account the oxidizer size and size distribution in determining the burning rates, rate exponents, and temperature sensitivities. Results were obtained for both unimodal and bimodal propellants with oxidizer particle sizes ranging from ultrafine (0.7 /*) to coarse (400 /*). For unimodal propellants, it was determined that the burning rate was higher for the smaller oxidizer sizes, as would be expected. Moreover, the rate exponent was larger for the small and large oxidizer particles with a minimum exponent obtained for some intermediate oxidizer diameter. Temperature sensitivity was found to be higher for propellants with larger oxidizer particles. However, it was found that the temperature sensitivity was constant for small particles. It was shown that for large particles, the temperature sensitivity and rate exponent decreased as the oxidizer distribution was widened.

An experimental and theoretical investigation of the performance of a ballistic compressor is described. Comparison of the computed ideal behavior of the ballistic compressor with experimental test pressures show that the ideal theory overestimates the generated pressure by as much as 30%. An assessment of the factors responsible for the nonideal behavior of the ballistic compressor is given. These factors include: valve losses, external and internal (blow-by) leakage, friction of the inertia! piston, nonideal behavior of the driver and test gases, shock wave formations, and heat losses. The valve losses and both the internal and external leakages have been measured experimentally. A parametric study shows that the choice of equation of state of the test gas is not very critical. The heat loss experienced by the test gas was estimated to be l°7o of the total energy imparted to the test gas. Shock-wave formations have negligible effect on the performance of the ballistic compressor for the mass of the inertial piston (1.34 kg) used.

T-burner experiments have provided the most fruitful technique for obtaining the acoustic admittance of burning solid propellants The objections to the findings of these experiments are: 1) the admittance values are questioned on the grounds that acoustic losses in the appaiatus are not well enough understood for adequate corrections to be made, and 2) relative acoustic losses are great enough that some operational propellants, known to produce oscillations in motors, burn stably in the T-burner The first objection is largely removed by demonstrating that three different methods for operating the burner and analyzing the data give results in close agreement Besides confirming the results of the other two, one method described here also provides a means to study more stable propellants, thus removing the second objection to the T-burner technique

Surface ignition of solid propellants has been represented by several analytical models, each involving obvious compromises with regard to scope of applicability. These models are distinguishable primarily in terms of site of the exothermic reaction governing ignition. Early research with nitrocellulose led to development of a theory involving chemical heat generation in the condensed phase. Two subsequent theoretical models were developed to explain ignition of the solid fuel ingredient of a composite propellant in an oxidizing atmosphere, and these two models were then extended on a heuristic basis to encompass a composite propellant in an inert atmosphere in which the oxidizing gas was produced by decomposition of the solid oxidizer. These two models are distinguished by whether the oxidation occurs at the surface or in the gas film above the surface. This report reviews the solid, heterogeneous, and gas-phase ignition theories and reviews the nature and implications of the assumptions involved. It is concluded that, while possessing certain drastic simplifications in common, the various quantitative models differ so conspicuously in their assumptions regarding external initiating stimulus as to make quantitative comparisons or tests of validity impossible.

The angular motion of a spin stabilized solid rocket is computed, considering the effect of jet damping about axes normal to the spin axis. The approximate formula used is chosen for computational accuracy and to fit the rocket geometry. Results are compared with measurements of body angular acceleration made during the rocket's flight in space. The comparison indicates that the jet damping is a very strong effect in this case, and that the approximate formula gives adequate accuracy for computing the reduction in conical precession motion due to jet damping. It is probable that the same formula can be used to estimate jet damping for other solid rockets. I. Introduction T HE term jet damping refers to the change in the angular rates of a thrusting rocket due to the torques exerted by the gases flowing out the nozzle. The jet damping effect is especially important in spin stabilized rockets where it acts to reduce the amplitude of the conical free precession motion and, therefore, to reduce the motion to a steady spin. It is important to know what the cone angle is at staging, as this strongly influences the attitude error of the next stage. In rockets operating in air, jet damping is usually second in importance to aerodynamic moments. In vacuum, however, the jet damping can be the most important torque acting on the rocket. Several simplified theories have been proposed to give estimates of the rate of damping for a particular rocket.1"5 In general, these theories use one-dimensional gas flow in the rocket and characterize the thrust chamber and nozzle by certain approximate dimensions. Proper verification of these approximate theories has been difficult to obtain because of the lack of experimental data on the attitude of a spinning rocket in vacuum flight. In the present paper, a formula for pitch jet damping is derived from the general rocket equations in a body-fixed coordinate system assuming one-dimensional flow. The formula is selected to use quantities that are known accurately and to be compatible with the geometry of the rocket considered. The formula, a modification of the one presented in Ref. 4, is evaluated to give the predicted rate of cone angle damping for a particular frequently used spin-stabilized rocket, the Allegany Ballistics Laboratory! X-248 with a satellite payload. The resulting prediction of jet damping is then compared with measurements of the angular motion made in actual flight.

Effort has recently been devoted to finding a means to alleviate the effects of the reflection at the walls of the range tank of the bow and wake shock system originating with a hypersonic projectile. (Author)

the spatial distribution of particle mass. Assumption of uniform number distribution gives an over-estimation of particle damping. For noncircular cylindrical rocket chambers, steady state internal ballistics must be considered to determine the particle distribution. Particle size growth should in general have a stabilizing effect. Quantitative prediction must await better knowledge of how particles grow within the combustion chamber.