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NASA NTRS1998

Mars Atmospheric Dynamics

The Martian atmosphere is dynamically similar to the Earth's. Its spin-axis rotation rate is only minutes longer than Earth's so the Coriolois force is nearly identical to Earth's. The inclination of its spin axis is also similar to Earth's giving it similarity in seasonal change. And the Martian atmosphere is nearly transparent to solar radiation (except during dust periods) such that it is heated primarily by upwelling infrared radiation from the surface. These characteristics make Mars an ideal laboratory for studying the dynamics of rapidly rotating differentially heated atmospheres. This talk reviews what we have learned about Mars atmospheric dynamics and how if compares with Earth. The source of information to make such a comparison comes from observations and models. The former are sparse and that the latter have played a major role in shaping our thinking about the general circulation on Mars. However, the models need validation. Fortunately, the first two orbiters in NASA's Mars Surveyor Program have instrumentation to address many of the issues related to the general circulation and climate of Mars. The first, Mars Global Surveyor, is already at Mars gathering data. The second, the Mars 98 Orbiter to be launched later this year, carries a dedicated atmospheric sounder. Thus, much will be learned about Mars' atmosphere in the next few years.

Haberle, Robert↗

NASA NTRS1983

Steady-state and dynamic evaluation of the electric propulsion system test bed vehicle on a road load simulator

The propulsion system of the Lewis Research Center's electric propulsion system test bed vehicle was tested on the road load simulator under the DOE Electric and Hybrid Vehicle Program. This propulsion system, consisting of a series-wound dc motor controlled by an infinitely variable SCR chopper and an 84-V battery pack, is typical of those used in electric vehicles made in 1976. Steady-state tests were conducted over a wide range of differential output torques and vehicle speeds. Efficiencies of all of the components were determined. Effects of temperature and voltage variations on the motor and the effect of voltage changes on the controller were examined. Energy consumption and energy efficiency for the system were determined over the B and C driving schedules of the SAE J227a test procedure.

Dustin, M. O.↗

NASA NTRS1987

General purpose algorithms for characterization of slow and fast phase nystagmus

In the overall aim for a better understanding of the vestibular and optokinetic systems and their roles in space motion sickness, the eye movement responses to various dynamic stimuli are measured. The vestibulo-ocular reflex (VOR) and the optokinetic response, as the eye movement responses are known, consist of slow phase and fast phase nystagmus. The specific objective is to develop software programs necessary to characterize the vestibulo-ocular and optokinetic responses by distinguishing between the two phases of nystagmus. The overall program is to handle large volumes of highly variable data with minimum operator interaction. The programs include digital filters, differentiation, identification of fast phases, and reconstruction of the slow phase with a least squares fit such that sinusoidal or psuedorandom data may be processed with accurate results. The resultant waveform, slow phase velocity eye movements, serves as input data to the spectral analysis programs previously developed for NASA to analyze nystagmus responses to pseudorandom angular velocity inputs.

Lessard, Charles S.↗

NASA NTRS1970

Dynamic characteristics of a variable-mass flexible missile

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions.

Meirovitch, L.↗

NASA NTRS1974

Finite element solution algorithm for incompressible fluid dynamics

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the transient motion of a viscous incompressible fluid, i.e., hydrodynamics. Dependent variable transformation renders the differential equation description uniformly elliptic. The finite element algorithm is established using the Galerkin criterion on a local basis within the Method of Weighted Residuals. It is unconstrained with respect to system linearity, computational mesh uniformity or solution domain closure regularity. The finite element matrices are established using a linear 'natural coordinate function' description. Computational solutions using the COMOC computer program illustrate the various features of the algorithm including recirculating flows.

Baker, A. J.↗

NASA NTRS1993

CSI flight experiment projects of the Naval Research Laboratory

The Naval Research Laboratory (NRL) is involved in an active program of CSI flight experiments. The first CSI flight experiment of the Naval Research Laboratory, the Low Power Atmospheric Compensation Experiment (LACE) dynamics experiment, has successfully measured vibrations of an orbiting satellite with a ground-based laser radar. The observations, made on January 7, 8 and 10, 1991, represent the first ever measurements of this type. In the tests, a narrowband heterodyne CO2 laser radar, operating at a wavelength of 10.6 microns, detected vibration induced differential-Doppler signatures of the LACE satellite. Power spectral densities of forced oscillations and modal frequencies and damping rates of free-damped vibrations were obtained and compared with finite element structural models of the LACE system. Another manifested flight experiment is the Advanced Controls Technology Experiment (ACTEX) designed to demonstrate active and passive damping with piezo-electric (PZT) sensors and actuators. This experiment was developed under the management of the Air Force Phillips Laboratory with integration of the experiment at NRL. It is to ride as a secondary, or 'piggyback,' experiment on a future Navy satellite.

Fisher, Shalom↗

NASA NTRS1989

Real-time approximate optimal guidance laws for the advanced launch system

An approach to optimal ascent guidance for a launch vehicle is developed using an expansion technique. The problem is to maximize the payload put into orbit subject to the equations of motion of a rocket over a rotating spherical earth. It is assumed that the thrust and gravitational forces dominate over the aerodynamic forces. It is shown that these forces can be separated by a small parameter epsilon, where epsilon is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in a series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The zeroth-order problem is that of putting maximum payload into orbit subject to the equations of motion of a rocket in a vacuum over a flat earth. The neglected inertial and aerodynamic terms are included in higher order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only quadrature integrations. These quadrature integrations can be performed rapidly, so that real-time approximate optimization can be used to construct the launch guidance law.

Speyer, Jason L.↗

NASA NTRS2007

Measurement and Characterization of Helicopter Noise in Steady-State and Maneuvering Flight

A special acoustic flight test program was performed on the Bell 206B helicopter outfitted with an in-flight microphone boom/array attached to the helicopter while simultaneous acoustic measurements were made using a linear ground array of microphones arranged to be perpendicular to the flight path. Air and ground noise measurements were made in steady-state longitudinal and steady turning flight, and during selected dynamic maneuvers. Special instrumentation, including direct measurement of the helicopter s longitudinal tip-path-plane (TPP) angle, Differential Global Positioning System (DGPS) and Inertial Navigation Unit (INU) measurements, and a pursuit guidance display were used to measure important noise controlling parameters and to make the task of flying precise operating conditions and flight track easier for the pilot. Special care was also made to test only in very low winds. The resulting acoustic data is of relatively high quality and shows the value of carefully monitoring and controlling the helicopter s performance state. This paper has shown experimentally, that microphones close to the helicopter can be used to estimate the specific noise sources that radiate to the far field, if the microphones are positioned correctly relative to the noise source. Directivity patterns for steady, turning flight were also developed, for the first time, and connected to the turning performance of the helicopter. Some of the acoustic benefits of combining normally separated flight segments (i.e. an accelerated segment and a descending segment) were also demonstrated.

Schmitz, Fredric H.↗

NASA NTRS1978

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

Morozov, S. K.↗

NASA NTRS1990

Reduced-order filtering for flexible space structures

There is a need for feedback control of the large flexible space structures which are going to be increasingly important in the future of the space program. These structures are very lightly damped, and vibrations may persist for a long time when the system is disturbed unless an active feedback control strategy is used to damp out the vibrations. The system is best described by a partial differential equation description, but the more common approach is to use a large set of second order differential equations, where a large number of modes must be retained if the mathematics is to provide an adequate description of the dynamical process. Sensors, such as accelerometers and rate gyros, may provide data to the feedback controller so that it may respond appropriately to control the system. The data from the sensors is not perfect, but is subject to noise, called measurement noise, and the dynamical process itself is subject to disturbances referred to as process noise. Filtering the sensor signals to remove the measurement noise, and using the resulting state estimates to control the system are investigated.

Sims, Craig S.↗

NASA NTRSDate not supplied

A Verification Framework for Runtime Assurance of Autonomous UAS

Runtime Assurance (RTA) is a design-time architecture for safety-critical systems where an internal monitor acts upon detecting a violation of a property. The simplex architecture is an instance of RTA, where the action taken is to hand control of the overall system to a trusted controller when an untrusted one violates a safety property. Simplex RTA is emerging as a method for allowing AI/ML and other unverified software to be integrated into safety-critical applications like aircraft. To this end, the American Society for Testing and Materials (ASTM) and NASA have each published guidelines on the use of RTA in such systems. In the simplex RTA framework, a system has an advanced controller (AC) and a reversionary controller (RC). The system is allowed to operate with the AC until a runtime monitor detects that some property has been violated and then the RC takes over. Assuming that the sample rate of the monitor will detect improper functioning with enough time for the RC to correct the impending problem, and that the RC is trusted, the system will operate as intended. This use of the simplex RTA framework can allow for the integration of untrusted, but possibly more performant, controllers in a safe way. This paper presents a formalization of a simplex RTA framework in the Prototype Verification System (PVS) theorem prover using an embedding of differential dynamic logic (DDL) called Plaidypvs. A novel feature of this framework is that it can be instantiated at different levels of abstraction. This feature allows for the formal verification of a system with an untrusted black box component, such as an AI/ML controller. This paper does not address the many difficulties in deploying RTA in an industrial-level system. Instead, the focus is on the formal verification of the simplex RTA framework in the language of hybrid programs. Hybrid programs are programs that include both discrete and continuous dynamics and can be used to model complex cyber-physical systems. Plaidypvs is a tool that enables formalization of hybrid programs in the PVS theorem prover. Plaidypvs enables the verification of the general simplex RTA framework and then, by specializing some components of the hybrid program, verifying instances of the framework while treating the untrusted component as a black box. A selection of Unmanned Aircraft Systems (UAS) operations are shown as instances of the general RTA framework in PVS. This offers the benefit of design time verification of relevant safety properties to the system, and it also gives requirements on the sample rate of sensors that determine the time interval in which the ‘switch’ property of the RTA framework is checked.

PVS↗

NASA NTRS1989

Prototype secondary mirror assembly design for the space infrared telescope facility

The authors describe the design of a liquid helium temperature prototype secondary mirror assembly (PSMA) under developement for the NASA Space Infrared Telescope Facility (SIRTF) program. The SIRTF secondary mirror assembly must operate below 4 K and provide highly precise two-axis dynamic tilting (chopping) in addition to the conventional functions needed by the SIRTF observatory. The PSMA design uses a fused quartz mirror kinematically attached at its center to an aluminum cruciform. The mirror/cruciform assembly is driven in tilt about its combined center of mass using a unique flexure pivot and a four-actuator control system with feedback provided by pairs of differential position sensors. The voice coil actuators are mounted on a second flexture-pivoted mass, enhancing servo system stability and isolating the telescope from vibration-induced disturbances. The mirror/cruciform and the reaction mass are attached to opposite sides of an aluminum mounting plate whose dimensional characteristics are nominally identical to those of the aluminum flexure pivot material. The mounting plate is connected to the outer housing by a six-degree-of-freedom focus and centering mechanism using pivoted actuation levers driven by lead screw/harmonic drive/stepper motor assemblies.

Stier, M.↗

NASA NTRS1989

A vectorized algorithm for 3D dynamics of a tethered satellite

Equations of motion characterizing the three dimensional motion of a tethered satellite during the retrieval phase are studied. The mathematical model involves an arbitrary number of point masses connected by weightless cords. Motion occurs in a gravity gradient field. The formulation presented accounts for general functions describing support point motion, rate of tether retrieval, and arbitrary forces applied to the point masses. The matrix oriented program language MATLAB is used to produce an efficient vectorized formulation for computing natural frequencies and mode shapes for small oscillations about the static equilibrium configuration; and for integrating the nonlinear differential equations governing large amplitude motions. An example of time response pertaining to the skip rope effect is investigated.

Wilson, Howard B.↗

NASA NTRS1990

A computational algorithm for spacecraft control and momentum management

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Dzielski, John↗

NASA NTRS2004

Further Improvement in 3DGRAPE

3DGRAPE/AL:V2 denotes version 2 of the Three-Dimensional Grids About Anything by Poisson's Equation with Upgrades from Ames and Langley computer program. The preceding version, 3DGRAPE/AL, was described in Improved 3DGRAPE (ARC-14069) NASA Tech Briefs, Vol. 21, No. 5 (May 1997), page 66. These programs are so named because they generate volume grids by iteratively solving Poisson's Equation in three dimensions. The grids generated by the various versions of 3DGRAPE have been used in computational fluid dynamics (CFD). The main novel feature of 3DGRAPE/AL:V2 is the incorporation of an optional scheme in which anisotropic Lagrange-based trans-finite interpolation (ALBTFI) is coupled with exponential decay functions to compute and blend interior source terms. In the input to 3DGRAPE/AL:V2 the user can specify whether or not to invoke ALBTFI in combination with exponential-decay controls, angles, and cell size for controlling the character of grid lines. Of the known programs that solve elliptic partial differential equations for generating grids, 3DGRAPE/AL:V2 is the only code that offers a combination of speed and versatility with most options for controlling the densities and other characteristics of grids for CFD.

Alter, Stephen↗

NASA NTRS1969

Dynamic characteristics of a variable-mass flexible missile: Dynamics of a two-stage variable-mass flexible rocket

The dynamic characteristics of two-stage slender elastic body were investigated. The first stage, containing a solid-fuel rocket, possesses variable mass while the second stage, envisioned as a flexible case, contains packaged instruments of constant mass. The mathematical formulation was in terms of vector equations of motion transformed by a variational principle into sets of scalar differential equations in terms of generalized coordinates. Solutions to the complete equations were obtained numerically by means of finite difference techniques. The problem has been programmed in the FORTRAN 4 language and solved on an IBM 360/50 computer. Results for limited cases are presented showing the nature of the solutions.

Meirovitch, L.↗

NASA NTRSDate not supplied

Progress of 2.05 μm Fiber Laser Development for CO2 DIAL Measurements of Martian CO2 and Pressure

The Decadal Survey by the US National Academy of Sciences in the United States and NASA’s Science Mission Directorate (SMD) Science Plan both require global CO2 observations for the Martian atmospheric pressure, dynamics and CO2 variations. However, there are significant observational gaps in polar regions and during nighttime for global air pressure and CO2 on Mars. Therefore, recently we proposed a new concept of Martian differential absorption lidar (DIAL) operating in the 2.05 μm CO2 absorption band for global, including poles, atmospheric CO2 and pressure observations day and night. Based on the concept, we are awarded to develop 2.05 μm fiber lasers by the NASA Planetary Instrument Concepts for the Advancement of Solar System Observations (PICASSO) Program. The laser is designed to be an all-fiber master oscillator and power amplifier (MOPA) system with laser out put of ~3 mJ at a repetition frequency of 2 kHz. The primary master oscillator (PMO) is locked to the center (2.0504280 μm) of the selected CO2 absorption line. The frequency of a second MO (SMO) is locked to that of PMO. This SMO frequency is adjustable and switched between the online (2.05044156 μm) and offline (2.05050812 μm) wavelengths. The online wavelength is optimally selected so that the CO2 absorption optical depth (AOD) is ~1.1 at 3 km and the measurement in the low Martian atmosphere has largest signal-to-noise ratio. The online wavelength can also be adjusted to a line slope location where AOD is larger to observe atmospheric pressure at higher altitudes. We will present more details about this project and instrument development.

CO2↗

NASA NTRS1995

Ground-to-Flight Handling Qualities Comparisons for a High Performance Airplane

A flight test program was conducted in conjunction with a ground-based piloted simulation study to enable a comparison of handling qualities ratings for a variety of maneuvers between flight and simulation of a modern high performance airplane. Specific objectives included an evaluation of pilot-induced oscillation (PIO) tendencies and a determination of maneuver types which result in either good or poor ground-to-flight pilot handling qualities ratings. A General Dynamics F-16XL aircraft was used for the flight evaluations, and the NASA Langley Differential Maneuvering Simulator was employed for the ground based evaluations. Two NASA research pilots evaluated both the airplane and simulator characteristics using tasks developed in the simulator. Simulator and flight tests were all conducted within approximately a one month time frame. Maneuvers included numerous fine tracking evaluations at various angles of attack, load factors and speed ranges, gross acquisitions involving longitudinal and lateral maneuvering, roll angle captures, and an ILS task with a sidestep to landing. Overall results showed generally good correlation between ground and flight for PIO tendencies and general handling qualities comments. Differences in pilot technique used in simulator evaluations and effects of airplane accelerations and motions are illustrated.

Brandon, Jay M.↗