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NASA NTRS1953

Maximum Evaporation Rates of Water Droplets Approaching Obstacles in the Atmosphere Under Icing Conditions

When a closed body or a duct envelope moves through the atmosphere, air pressure and temperature rises occur ahead of the body or, under ram conditions, within the duct. If cloud water droplets are encountered, droplet evaporation will result because of the air-temperature rise and the relative velocity between the droplet and stagnating air. It is shown that the solution of the steady-state psychrometric equation provides evaporation rates which are the maximum possible when droplets are entrained in air moving along stagnation lines under such conditions. Calculations are made for a wide variety of water droplet diameters, ambient conditions, and flight Mach numbers. Droplet diameter, body size, and Mach number effects are found to predominate, whereas wide variation in ambient conditions are of relatively small significance in the determination of evaporation rates. The results are essentially exact for the case of movement of droplets having diameters smaller than about 30 microns along relatively long ducts (length at least several feet) or toward large obstacles (wings), since disequilibrium effects are then of little significance. Mass losses in the case of movement within ducts will often be significant fractions (one-fifth to one-half) of original droplet masses, while very small droplets within ducts will often disappear even though the entraining air is not fully stagnated. Wing-approach evaporation losses will usually be of the order of several percent of original droplet masses. Two numerical examples are given of the determination of local evaporation rates and total mass losses in cases involving cloud droplets approaching circular cylinders along stagnation lines. The cylinders chosen were of 3.95-inch (10.0+ cm) diameter and 39.5-inch 100+ cm) diameter. The smaller is representative of icing-rate measurement cylinders, while with the larger will be associated an air-flow field similar to that ahead of an airfoil having a leading-edge radius comparable with that of the cylinder. It is found that the losses are less than 5 percent. It is concluded that such losses are, in general, very small (less than 1 percent) in the case of smaller obstacles (of icing-rate measurement- cylinder size); the motional dynamics are such, however, that exceptions will occur by reason of failure of very small droplets (moving along stagnation lines) to impinge upon obstacle surfaces. In such cases, the droplets will evaporate completely.

Lowell, H. H.↗

NASA NTRS1978

Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles

The analysis concerns the alterations produced when small amplitude disturbances, including entropy and vorticity disturbances, are imposed on steady potential flows. For the most general nonacoustic incident distortion field that can be imposed on the uniform upstream flow, it is shown that the perturbation velocity at any point of the resulting unsteady compressible and vortical flow consists of a part that is a known function of the imposed upstream distortion field and the mean flow variables and a potential part that can be found by solving a linear inhomogeneous wave equation with a dipole-type source term whose strength is a known function of the imposed upstream distortion field. The theory is applied to the unsteady flow past a corner, and a closed-form analytical solution is found.

Goldstein, M. E.↗

NASA NTRS1983

Ship waves and lee waves

Dynamics analogous to those of surface ship waves on water of finite depth are noted for the three-dimensional trapped lee wave modes produced by an isolated obstacle in a stratified fluid. This vertical trapping of wave energy is modeled by uniform upstream flow and stratification, bounded above by a rigid lid, and by a semiinfinite fluid of uniform stability whose wind velocity increases exponentially with height, representing the atmosphere. While formal asymptotic solutions are produced, limited quantitative usefulness is obtained through them because of the limitations of the approximations and the infinity of modes in the solution. Time-dependent numerical models are accordingly developed for both surface ship waves and internal and atmospheric ship waves, yielding a variety of results.

Sharman, R. D.↗

NASA NTRSDate not supplied

Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

This paper presents an integration of Differential Dynamic Programming (DDP) with the Optimal Reciprocal Collision Avoidance (ORCA) algorithm as the basis for a new algorithm, titled Combined Bernstein Polynomial Optimal Reciprocal Collision Avoidance DDP (COBRA-DDP), for trajectory replanning and collision avoidance for Urban Air Mobility (UAM) vehicles. State-constrained variants of DDP provide the ability to plan trajectories while avoiding obstacles, but these methods require a large increase in computational time per iteration which hinders the overall speed of the algorithm. ORCA utilizes simplified dynamics to recognize potential collisions along a trajectory and provides an optimal velocity for the avoidance of multiple vehicles. These velocity commands, however, may not result in a dynamically feasible trajectory for DDP to plan around. As such, a Bernstein polynomial curve that considers the general dynamic constraints of the vehicle is generated to approximate a trajectory based on the velocity commands. COBRA-DDP optimizes this suggested trajectory via unconstrained DDP to provide a dynamically feasible trajectory that provides collision avoidance. This new trajectory can be applied to the vehicle or used to warm start the state constrained DDP algorithms to decrease computation time. Its benefits and effectiveness of the algorithm are demonstrated on a UAM Vertical Takeoff and Landing (VTOL) vehicle simulation with highly nonlinear dynamics.

Optimal Reciprocal Collision Avoidance↗

NASA NTRS1985

Mechanical obstacles to the movement of continent-bearing plates

Selected geophysical problems associated with the concept of continental drift as an incidental corollary of plate movement are discussed. The problems include the absence of a suitable plate-driving mechanism for plates with continental leading edges, the absence of the low-velocity zone under shields, and continental roots of 400 to 700 km depths. It is shown that if continental drift occurs, it must use mechanisms not now understood, or that it may not occur at all, plate movement being confined to ocean basins.

Lowman, P. D., Jr.↗

NASA NTRS2004

Autonomous Navigation Results from the Mars Exploration Rover (MER) Mission

In January, 2004, the Mars Exploration Rover (MER) mission landed two rovers, Spirit and Opportunity, on the surface of Mars. Several autonomous navigation capabilities were employed in space for the first time in this mission. ]n the Entry, Descent, and Landing (EDL) phase, both landers used a vision system called the, Descent Image Motion Estimation System (DIMES) to estimate horizontal velocity during the last 2000 meters (m) of descent, by tracking features on the ground with a downlooking camera, in order to control retro-rocket firing to reduce horizontal velocity before impact. During surface operations, the rovers navigate autonomously using stereo vision for local terrain mapping and a local, reactive planning algorithm called Grid-based Estimation of Surface Traversability Applied to Local Terrain (GESTALT) for obstacle avoidance. ]n areas of high slip, stereo vision-based visual odometry has been used to estimate rover motion, As of mid-June, Spirit had traversed 3405 m, of which 1253 m were done autonomously; Opportunity had traversed 1264 m, of which 224 m were autonomous. These results have contributed substantially to the success of the mission and paved the way for increased levels of autonomy in future missions.

autonomous↗

NASA NTRS1991

An optimal control strategy for collision avoidance of mobile robots in non-stationary environments

An optimal control formulation of the problem of collision avoidance of mobile robots in environments containing moving obstacles is presented. Collision avoidance is guaranteed if the minimum distance between the robot and the objects is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. Furthermore, time consistency with the nominal plan is desirable. A numerical solution of the optimization problem is obtained. Simulation results verify the value of the proposed strategy.

Kyriakopoulos, K. J.↗

NASA NTRS1986

Preliminary floor, seat, and dummy data

According to preliminary examination of the data, out of 179 data channels that were onboard the aircraft in support of the seat experiments, there is data from 168. There was somewhat more severe environment imposed in the structure of the obstacles than by the ground impact. Therefore, both ground impact and obstacle impact are of interest for crashworthiness experiments. Most of the data channels that were studied are fairly consistent with the physical evidence: they show acceleration levels that are reasonable, and in many cases these integrate out to a reasonable velocity change. Finally, from observation thus far, the ground impact did not fail or significantly damage any seat. Nor did any of the energy absorbers in the modified seats extend. The accelerations do not appear high enough and/or energetic enough to cause this to happen. At this time, the onboard films have not been studied; only some videotape have been viewed. Some of the seats were so badly damaged by the fire that any failures which might have occurred were obscured. A close examination of the onboard films using a stop-action projector will allow a more thorough evaluation.

Cannon, M. R.↗

NASA NTRS2017

Simulation Based Studies of Low Latency Teleoperations for NASA Exploration Missions

Human exploration of Mars will involve both crewed and robotic systems. Many mission concepts involve the deployment and assembly of mission support assets prior to crew arrival on the surface. Some of these deployment and assembly activities will be performed autonomously while others will be performed using teleoperations. However, significant communications latencies between the Earth and Mars make teleoperations challenging. Alternatively, low latency teleoperations are possible from locations in Mars orbit like Mars' moons Phobos and Deimos. To explore these latency opportunities, NASA is conducting a series of studies to investigate the effects of latency on telerobotic deployment and assembly activities. These studies are being conducted in laboratory environments at NASA's Johnson Space Center (JSC), the Human Exploration Research Analog (HERA) at JSC and the NASA Extreme Environment Mission Operations (NEEMO) underwater habitat off the coast of Florida. The studies involve two human-in-the-loop interactive simulations developed by the NASA Exploration Systems Simulations (NExSyS) team at JSC. The first simulation investigates manipulation related activities while the second simulation investigates mobility related activities. The first simulation provides a simple real-time operator interface with displays and controls for a simulated 6 degree of freedom end effector. The initial version of the simulation uses a simple control mode to decouple the robotic kinematic constraints and a communications delay to model latency effects. This provides the basis for early testing with more detailed manipulation simulations planned for the future. Subjects are tested using five operating latencies that represent teleoperation conditions from local surface operations to orbital operations at Phobos, Deimos and ultimately high Martian orbit. Subject performance is measured and correlated with three distance-to-target zones of interest. Each zone represents a target distance ranging from beyond 10m in Zone 1, through 1 cm to contact in Zone 5 with a step size factor of 10. Collected data consists of both objective simulation data (time, distance, hand controller inputs, velocity) and subjective questionnaire data. The second simulation provides a simple real-time operator interface with displays and control of a simulated surface rover. The rover traverses a synthetic Mars-like terrain and must be maneuvered to avoid obstacles while progressing to its destination. Like the manipulator simulation, subjects are tested using five operating latencies that represent teleoperation conditions from local surface operations to orbital operations at Phobos, Deimos and ultimately high Martian orbit. The rover is also operated at three different traverse speeds to assess the correlation between latency and speed. Collected data consisted of both objective simulation data (time, distance, hand controller inputs, braking) and subjective questionnaire data. These studies are exploring relationships between task complexity, operating speeds, operator efficiencies, and communications latencies for low latency teleoperations in support of human planetary exploration. This paper presents early results from these studies along with the current observations and conclusions. These and planned future studies will help to inform NASA on the potential for low latency teleoperations to support human exploration of Mars and inform the design of robotic systems and exploration missions.

Gernhardt, Michael L.↗

NASA NTRS1945

Graphical and analytical methods for the determination of a flow of a compressible fluid around an obstacle

Chaplygin introduced the hodograph method in the theory of compressible fluid flows and developed a method for constructing stream functions of such flows. This method, which has been extensively used in investigation of compressible fluid flows, is limited in certain respects. The expression for the stream function obtained in this manner can represent only certain types of flow patterns. In general, flow patterns obtained in this way cannot represent the whole flow around an obstacle, but only a part of such a flow, and therefore several expressions are needed in order to obtain the whole flow. On the other hand, in many instances it is important to have a single expression representing the whole flow. Recently Von Karman and Tsien constructed more general types of stream functions, but only by replacing the true pressure density relation by the linear pressure-specific volume relation so that their method is essential limited to flows the maximum Mach number of which is not too large. In a companion report the author derived a new formula for stream functions based on the true pressure density relation. It is not subject to the limitations of the Chaplygin method. In the present report this formula is employed to construct two-dimensional subsonic compressible fluid flows around a body similar in shape to a given symmetric obstacle. The methods described in the report are illustrated by numerical examples.

FLOW, COMPRESSIBLE-MEASUREMENT↗

NASA NTRS1982

Wakes from arrays of buildings

Experiments were carried out in a small wind tunnel in which atmospheric flow around buildings was simulated. Arrays of one, two, three, and four model buildings were tested, and wake profiles of velocity and turbulence were measured. The data indicate the effect of the buildings on the wind environment encountered by aircraft during landing or takeoff operations. It was possible to use the results to locate the boundaries of the air regions affected by the obstacles and to recommend preferred arrangements of buildings to maximize light safety.

Logan, E., Jr.↗

NASA NTRS1983

Wakes from arrays of buildings

Logan, E., Jr.↗

NASA NTRS1993

The North Atlantic circulation in the early 1980s - An estimate from inversion of a finite-difference model

A finite-difference model of the North Atlantic is constructed for the purpose of making an estimate of the circulation through an inverse calculation. The data base is eclectic, and includes hydrography, oxygen, nutrients, current meter and float records, atmospheric momentum, heat and water vapor transfers, as well as estimates of certain integral fluxes. Owing to the available hydrographic database, the model resolution is restricted to 1 deg at best, and is much coarser in many aspects. This limited resolution is a major obstacle to accurate estimates of climatological fluxes. In its final form, there are about 9000 constraints in 29,000 formal unknowns plus 9000 noise unknowns. The system is solved as a tapered least-squares system by a sparse conjugate gradient algorithm. With the exception of a few float velocities, all constraints are found to be consistent within error estimates. The model produces estimates of large-scale fluxes and flux divergences for all conventional properties including heat and nutrients as well as carbon dioxide and alkalinity. Meridional fluxes of carbon are found to be indistinguishable from zero, whereas the North Atlantic tends to export nutrients to the south, but carry heat to the north. Traditional oceanographic depictions of the circulation through combination of nonsynoptic data into steady models may have reached their useful limit in the present calculation, as the conflicts between the data and physical requirements become quantitatively apparent.

Martel, Francoise↗

NASA NTRS1942

On the use of residue theory for treating the subsonic flow of a compressible fluid

A new mathematical technique, due to Milne-Thomson, is used to obtain an improved form of the method of Poggi for calculating the effect of compressibility on the subsonic flow past an obstacle. By means of this new method, the difficult surface integrals of the original Poggi method can be replaced by line integrals. These line integrals are then solved by the use of residue theory. In this way an equation is obtained giving the second-order effect of compressibility on the velocity of the fluid. The method is practicable for obtaining the higher-order effects of compressibility on the velocity field. As an illustration of the general result, the flow past an elliptic cylinder is discussed.

Kaplan, Carl↗

NASA NTRS1992

Optimal motion planning for collision avoidance of mobile robots in non-stationary environments

An optimal control formulation of the problem of collision avoidance of mobile robots moving in general terrains containing moving obstacles is presented. A dynamic model of the mobile robot and the dynamic constraints are derived. Collision avoidance is guaranteed if the minimum distance between the robot and the object is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. Time consistency with the nominal plan is desirable. A numerical solution of the optimization problem is obtained. A perturbation control type of approach is used to update the optimal plan. Simulation results verify the value of the proposed strategy.

Kyriakopoulos, K. J.↗

NASA NTRS2012

Hybrid Simulation of the Shock Wave Trailing the Moon

A standing shock wave behind the Moon was predicted by Michel (1967) but never observed nor simulated. We use 1D hybrid code in order to simulate the collapse of the plasma-free cavity behind the Moon and for the first time to model the formation of this shock. Starting immediately downstream of the obstacle we consider the evolution of plasma expansion into the cavity in the frame of reference moving along with the solar wind. Well-known effects as electric charging of the cavity affecting the plasma flow and counterstreaming ion beams in the wake are reproduced. Near the apex of the inner Mach cone where the plasma flows from the opposite sides of the obstacle meet, a shock wave arises. We expect the shock to be produced at periods of high electron temperature solar wind streams (T(sub i) much less than T(sub e) approximately 100 eV). The shock is produced by the interaction of oppositely directed proton beams in the plane containing solar wind velocity and interplanetary magnetic field vectors. In the direction across the magnetic field and the solar wind velocity, the shock results from the interaction of the plasma flow with the region of the enhanced magnetic field inside the cavity that plays the role of the magnetic barrier. The appearance of the standing shock wave is expected at the distance of approximately 7R(sub M) downstream of the Moon.

Moon↗

NASA NTRS1987

Collision-free trajectory planning algorthm for manipulators

Collision-free trajectory planning for robotic manipulators is investigated. The task of the manipulator is to move its end-effector from one point to another point in an environment with polyhedral obstacles. An on-line algorithm is developed based on finding the required joint angles of the manipulator, according to goals with different priorities. The highest priority is to avoid collisions, the second priority is to plan the shortest path for the end effector, and the lowest priority is to minimize the joint velocity for smooth motion. The pseudo-inverse of the Jacobian matrix is applied for inverse kinematics. When a possible collision is detected, a constrained inverse kinematic problem is solved such that the collision is avoided. This algorithm can also be applied to a time-variant environment.

Pourboghrat, F.↗

NASA NTRS1987

Phase space simulation of collisionless stellar systems on the massively parallel processor

A numerical technique for solving the collisionless Boltzmann equation describing the time evolution of a self gravitating fluid in phase space was implemented on the Massively Parallel Processor (MPP). The code performs calculations for a two dimensional phase space grid (with one space and one velocity dimension). Some results from calculations are presented. The execution speed of the code is comparable to the speed of a single processor of a Cray-XMP. Advantages and disadvantages of the MPP architecture for this type of problem are discussed. The nearest neighbor connectivity of the MPP array does not pose a significant obstacle. Future MPP-like machines should have much more local memory and easier access to staging memory and disks in order to be effective for this type of problem.

White, Richard L.↗