SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Multivariable least squares approximation polynomials and transcendental function problem solving for missile trajectories
Site manual for radar intelligence system capable of precise missile trajectory measurements
Formulations useful for engineering formulations are sought, with a view to a clearer physical understanding, of the phenomena that govern convective aerodynamic heating at the elevated speeds encountered in atmospheric missile trajectories. After discussing cold-wall laminar boundary layer heating, the complex boundary layer transition phenomenon and cold-wall turbulent boundary layer heating are treated. The current understanding of separated flow-region and shock-interaction heating is presented, together with an evaluation of heat-protection methods and a characterization of the influence of mass addition on laminar and turbulent boundary layers. Finite-difference method-based CFD code results are evaluated.
Explore the source record for details and available documents.
The mission performance characteristics of ramjet-propelled missiles are highly dependent upon the trajectory flown. Integration of the trajectory profile with the ramjet propulsion system performance characteristics to achieve optimal missile performance is very complex. Past trajectory optimization methods have been extremely problem dependent and require a high degree of familiarity to achieve success. A general computer code (CTOP) has been applied to ramjet-powered missiles to compute open-loop optimal trajectories. CTOP employs Chebyshev polynomial representations of the states and controls. This allows a transformation of the continuous optimal control problem to one of parameter optimization. With this method, the trajectory boundary conditions are always satisfied. State dynamics and path constraints are enforced via penalty functions. The presented results include solutions to minimum fuel-to-climb, minimum time-to-climb, and minimum time-to-target intercept problems.
Parameters that enter into equation of trajectory of a missile are discussed. Investigation is made of normal pursuit, of constant, proportional, and line--of-sight methods of navigation employing target seeker, and of deriving corresponding pursuit paths. Pursuit paths obtained under similar conditions for different methods are compared. Proportional navigation is concluded to be best method for using target seeker installed in missile.
Perturbation solutions of differential equations of motion for low-thrust rocket trajectories
Craters in natural materials at White Sands Missile Range, N. Mex., were produced by the impact of high-velocity to hypervelocity missiles traveling along oblique trajectories with kinetic energies between 2.1 and 81 × 1014 ergs. The oblique impacts produce craters 2 to 10 m across with morphologies and ejecta that are bilaterally symmetrical with respect to the plane of the missile trajectory. Rims are high and the amount of ejecta large in down-trajectory and lateral directions, whereas rims are low to nonexistent and ejecta thin to absent up-trajectory. Symmetry development and modifications of the symmetry are a function of target material, local topography, and angle of impact. Seven mappable units can be recognized in and around the craters. Three of these are ejecta: thick ejecta near the crater, thin to discontinuous ejecta at greater distances, and scattered ejecta at the greatest distances to the limit of throwout. These ejecta units may be absent on the up-trajectory side; if present, they are rarely as thick or continuous as on other sides of the crater. Three units are target materials: undeformed target material exposed in local patches through thin to discontinuous ejecta and everywhere between the fragments of scattered ejecta, tilted and broken target material exposed in upper crater walls, and shattered and fractured target material exposed on the up-trajectory crater wall. The seventh unit is slope material composed of talus and fallback within the crater. Development, character, and exposure of these units varies chiefly with the target material. Ejecta from the craters is chiefly broken but relatively undeformed target material that may range in size from very fine grained debris to large blocks. Where the target is porous, significant amounts of the ejecta are composed of sheared and compressed fragments, some coated with dark layers of mixed projectile pieces, powder, and fused metal mixed with crushed target material. For layered targets, the original stratigraphic sequence is crudely preserved and in inverted order in thick ejecta. Secondary impact craters are produced by the impact of ejected fragments when the surrounding surface materials are sufficiently weak. A wide variety of secondary impact crater relations may result. Secondary craters nearest the primary crater have blocks in them that are larger than or the same size as the crater they produced. Farther from the primary crater, the fragments are generally smaller than the secondary crater and are ejected from it. Excavation of four craters revealed a mixed breccia beneath the crater floor composed of missile pieces, sheared and compressed target material, and crushed debris. Banded, disaggregated target material and nonmixed breccia surrounded the mixed breccia, and these breccias were surrounded by a zone of conjugate fractures. Beneath the ejecta on the lateral and down-trajectory crater flanks, the target materials were tilted upward and broken. Up-trajectory, open fractures and downward displacement occurred in two of the craters. No displacement was observed for the other two. Beneath the down-trajectory rims of craters with distinct layering, overturned synclines were observed. Missile breakup and behavior during cratering are a function of target and missile properties. Missile breakup depends on missile velocity and is most extensive at high velocities, where the missile is fragmented, powdered, and partly fused. Burial of missile or its fragmented, powdered, and fused remains is greatest for porous targets and least for dense cohesive targets. For very porous targets, camouflet structures containing the fragmented missile may form. Least squares fit to the data on craters in dry to moist targets indicate V(a) = 10^(-11.433)E(p)^(1.205) where V(a) is the volume of the apparent crater and E(p) is the kinetic energy of the missile. This equation is consistent with expectations of the equations relating apparent depth and radius to kinetic energy. Extrapolation of displaced masses and kinetic energies for laboratory impacts with sand and rock converge near 10^(15) to 10^(16) ergs, where the extrapolations are near the data on missile impact craters, corrected for impact angle. Displaced masses of craters produced by missile impacts and by chemical explosives with small scaled depths of burial are about the same when the kinetic energies of the missiles (corrected for angle of impact) are equal to the TNT equivalent energy of the explosive. The problem of equivalent scaled depth of burst for an impact crater is complicated and not entirely resolved, however. Both missile impact craters and chemical explosive craters in water-saturated targets are larger than their counterparts in dry to moist materials. Data collected during the study of missile impact craters have helped resolve a number of problems in lunar research: (1) the soillike nature of lunar surface materials was predicted, (2) sizes of craters produced by artificial impacts were correctly predicted, (3) certain features imaged by Surveyor were found to be analogous to features associated with missile impact craters, {4) missile impacts were used in support of the Apollo passive seismic experiment, (5) craters seen in Apollo orbital photographs were found to be similar to some missile impact craters, (6) missile impact craters supplied data on sample collection and crater phenomenology used in training astronauts, and (7) some returned lunar samples are similar to coated, sheared, and compressed fragments ejected from missile impact craters.
Calculating small rocket trajectories using rocket to launcher radial velocity data
Between the years of 1995 and 2014 the number of small satellites (1-500 kg) went up from 20 to 180. [1] Out of the 180 launched in 2014 66% were Nano satellites (1-10 kg). [1] With this trend of smaller satellites, one would expect a rise in number of small launch vehicles (SLVs are defined by capability to carry 1-100 kg to orbit), but this has not happened: [3] only 8% of all small satellites are launched on SLVs and the others become secondary payloads on regular launch vehicles. [1] This results in small satellites being placed into either suboptimal orbits or waiting for launch schedules to align with bigger launches, resulting in long waiting times. Dedicated SLVs could improve the responsiveness of small satellite launches, but SLV design is complicated by the large architecture space needed to be explored in order to find efficient and affordable designs. The SLV architecture trade space contains many discrete options, e.g. solid vs. liquid fuels, air launch vs. ground launch, number of stages, etc. [2][3] Performing detailed analysis for all the options at once would be prohibitive. Thus, a sizing environment/framework that is capable of providing necessary information for conceptual-level trade studies and can rapidly explore the vast SLV architecture space is necessary. The framework, illustrated in Figure 1, consists of four disciplines central to the sizing and synthesis of launch vehicles: propulsion, aerodynamics, structures, and trajectory. For the aerodynamics and trajectory disciplines, Missile DATCOM and POST2 are used, respectively. The propulsion and structures disciplines are represented in the framework with tools developed at ASDL Georgia Tech. For propulsion, the Solid Motor Analysis Code (SMAC) is a physics-based conceptual design tool for solid rocket motors. SMAC is capable of geometric burn simulation, ballistic analysis, and prediction of thrust performance. [4] For structures, Launch Vehicle Structural Analysis (LVSA) tool is a physics-based tool that focuses on structural dynamic analysis with sizing capability. These tools are integrated into the framework illustrated in Figure 1 with the corresponding connections described in Table 1. The process flow is as follows: first, SMAC sizes insulation and calculates maximum operating pressures for each vehicle stage. The MEOP and insulation thickness values from SMAC are fed to LVSA which then utilizes this information to size the motor casing. This creates a feedback loop between LVSA and SMAC that converges on the radius available for fuel, casing, and insulation thickness. Once the stage sizing is converged on SMAC creates an engine deck that is passed to POST2. Next, the data from SMAC and LVSA goes into Missile DATCOM which generates an aerodynamics database for POST2. Finally, POST2 performs a targeting optimization while maximizing the payload mass to orbit. Within the framework, POST2 is automated in order to be robust to a wide variety of possible designs by performing a Monte Carlo simulation over the initialization vector of the POST2 optimization variables. To demonstrate the capability of this framework, a sample problem of exploring the design space of an SLV capable of placing satellites into a low Earth orbit (inclination=47 deg, 196.5 by 211.3 nm) is used. This sample problem is a ground-launched SLV consisting of four in-line SRM stages. The multidisciplinary design analysis (MDA) environment is utilized to explore a design space consisting of 22 continuous and 12 discrete variables, shown by Table 1 by blocks 1,2,3. Running a full factorial design of experiments (DOE) would have been prohibitively expensive even with this reduced design space, thus a space filling design with 3,502 and then additional expansion of 2,602 cases was used. The first DOE consisted of 3,502 cases, and all of the variables were varied. These input variables are listed in blocks 1, 2, and 3 in Table 1. Most of the variables are propulsion related with stage lengths determining the delta-V split of the SLV. The expansion consisted of 2,602 cases, and the continuous variables were set to be equal to the most promising designs from the sizing of first DOE. For each set of continuous variables, the discrete variables (grain type, star points, and propellant) were to varied. The results of the DOE can be seen in Figure 2; each of the points in this plot represents a closed launch vehicle that reaches the targeted orbit. For each of the cases, there is information on flown trajectory, structural, and propulsion properties of the SLV. For example, Figure 3 shows changes in altitude and velocity with time for a particular case. The right side of Figure 3 clearly shows the coasting (slow decrease) and burning phases (sharp increase) of the SLV mission. LV mass is positively correlated with the optimized payload mass to orbit because heavier LVs carry more fuel and thus have more stored chemical energy. Furthermore, for any given payload mass to orbit, the most efficient design would result in the smallest LV. The results as visualized in Figure 2 shows this tradeoff, and the Pareto frontier of the efficient designs can be seen along the dotted line. Figure 2 can be divided into regions with the lowest mass vehicles corresponding to the minimum bound on radius, and the highest mass vehicles corresponding to the maximum bound on radius. Within a mass region, the discrete variables, such as propellant type and propellant grain arrangement, have the most effect on payload mass. This paper presents an MDA framework that can perform an automated physics-based sizing of SLV designs and a corresponding methodology to utilize the MDA to explore the design space of SLVs. The proposed methodology was applied to a perform a design space exploration for a four stage SLV. The outputs show the expected pareto frontier forming and provide detailed information about the SLV performance and staging. Using the produced data, it will be possible to select a set of pareto optimal designs that can then be further explored in subsequent design cycles. This demonstration shows that automated design space exploration should be used in the early phase design of future SLV concepts.
Explore the source record for details and available documents.
Liquid-Propellant Rocket Engines (LREs) are capable of on-command variable thrust or thrust modulation, an operability advantage that has been studied intermittently since the late 1930s. Throttleable LREs can be used for planetary entry and descent, space rendezvous, orbital maneuvering including orientation and stabilization in space, and hovering and hazard avoidance during planetary landing. Other applications have included control of aircraft rocket engines, limiting of vehicle acceleration or velocity using retrograde rockets, and ballistic missile defense trajectory control. Throttleable LREs can also continuously follow the most economical thrust curve in a given situation, compared to discrete throttling changes over a few select operating points. The effects of variable thrust on the mechanics and dynamics of an LRE as well as difficulties and issues surrounding the throttling process are important aspects of throttling behavior. This review provides a detailed survey of LRE throttling centered around engines from the United States. Several LRE throttling methods are discussed, including high-pressure-drop systems, dual-injector manifolds, gas injection, multiple chambers, pulse modulation, throat throttling, movable injector components, and hydrodynamically dissipative injectors. Concerns and issues surrounding each method are examined, and the advantages and shortcomings compared.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
Exact linearized solutions are provided for the longitudinal oscillations of missiles when the trajectory is nearly horizontal and the thrust is either zero, a specified constant value, or increasing with the square of the increasing flight speed. The results indicate that in all cases any increase in the thrust, or any acceleration along the nearly horizontal trajectory, will directly increase the damping of the angle-of-attack oscillations, whose increase in frequency is at first negligible, and then grows very slightly with time.
This project addresses the problem of adaptive trajectory generation for a robot arm. Conventional trajectory generation involves computing a path in real time to minimize a performance measure such as expended energy. This method can be computationally intensive, and it may yield poor results if the trajectory is weakly constrained. Typically some implicit constraints are known, but cannot be encoded analytically. The alternative approach used here is to formulate domain-specific knowledge, including implicit and ill-defined constraints, in terms of fuzzy rules. These rules utilize linguistic terms to relate input variables to output variables. Since the fuzzy rulebase is determined off-line, only high-level, computationally light processing is required in real time. Potential applications for adaptive trajectory generation include missile guidance and various sophisticated robot control tasks, such as automotive assembly, high speed electrical parts insertion, stepper alignment, and motion control for high speed parcel transfer systems.
Trajectory parameter determination in relation to various AROD airborne range and orbital determination ground stations