Preliminary mathematical specifications for area targets and space volumes
The preliminary level B/C mathematical specifications for the Mission Control Center (MCC) area targets and space volumes processor are presented.
Bishop, M.↗
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A mathematical representation of an advanced helicopter for piloted simulator investigations of control system and display variations
A mathematical model of an advanced helicopter is described. The model is suitable for use in control/display research involving piloted simulation. The general design approach for the six degree of freedom equations of motion is to use the full set of nonlinear gravitational and inertial terms of the equations and to express the aerodynamic forces and moments as the reference values and first order terms of a Taylor series expansion about a reference trajectory defined as a function of longitudinal airspeed. Provisions for several different specific and generic flight control systems are included in the model. The logic required to drive various flight control and weapon delivery symbols on a pilot's electronic display is also provided. Finally, the model includes a simplified representation of low altitude wind and turbulence effects. This model was used in a piloted simulator investigation of the effects of control system and display variations for an attack helicopter mission.
Aiken, E. W.↗
Mathematical concepts for modeling human behavior in complex man-machine systems
Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.
Johannsen, G.↗
A mathematical and experimental simulation of the hematological response to weightlessness
A mathematical model of erythropoiesis control was used to simulate the effects of bedrest and zero-g on the circulating red cell mass. The model incorporates the best current understanding of the dynamics of red cell production and destruction and the associated feedback regulation. Specifically studied were the hemodynamic responses of a 28-day bedrest study devised to simulate Skylab experience. The results support the hypothesis that red cell loss during supine bedrest is a normal physiological feedback process in response to hemoconcentration enhanced tissue oxygenation and suppression of red cell production. Model simulation suggested the possibilities that this period was marked by some combination of increased oxygen-hemoglobin affinity, small reduction in mean red cell life span, ineffective erythropoiesis, or abnormal reticulocytosis.
Kimzey, S. L.↗
A mathematical model of the CH-53 helicopter
A mathematical model suitable for real time simulation of the CH-53 helicopter is presented. This model, which is based on modified nonlinear classical rotor theory and nonlinear fuselage aerodynamics, will be used to support terminal-area guidance and navigation studies on a fixed-base simulator. Validation is achieved by comparing the model response with that of a similar aircraft and by a qualitative comparison of the handling characteristics made by experienced pilots.
Sturgeon, W. R.↗
Propulsion system mathematical model for a lift/cruise fan V/STOL aircraft
A propulsion system mathematical model is documented that allows calculation of internal engine parameters during transient operation. A non-realtime digital computer simulation of the model is presented. It is used to investigate thrust response and modulation requirements as well as the impact of duty cycle on engine life and design criteria. Comparison of simulation results with steady-state cycle deck calculations showed good agreement. The model was developed for a specific 3-fan subsonic V/STOL aircraft application, but it can be adapted for use with any similar lift/cruise V/STOL configuration.
Cole, G. L.↗
Evaluation of orbits with incomplete knowledge of the mathematical expectancy and the matrix of covariation of errors
The problem of selecting the optimal algorithm of filtration and the optimal composition of the measurements is examined assuming that the precise values of the mathematical expectancy and the matrix of covariation of errors are unknown. It is demonstrated that the optimal algorithm of filtration may be utilized for making some parameters more precise (for example, the parameters of the gravitational fields) after preliminary determination of the elements of the orbit by a simpler method of processing (for example, the method of least squares).
Bakhshiyan, B. T.↗
A Mathematical Model for Vertical Attitude Takeoff and Landing (VATOL) Aircraft Simulation: Model Description Application - Volume 1
A mathematical model of a high performance airplane capable of vertical attitude takeoff and landing (VATOL) was developed. An off line digital simulation program incorporating this model was developed to provide trim conditions and dynamic check runs for the piloted simulation studies and support dynamic analyses of proposed VATOL configuration and flight control concepts. Development details for the various simulation component models and the application of the off line simulation program, Vertical Attitude Take-Off and Landing Simulation (VATLAS), to develop a baseline control system for the Vought SF-121 VATOL airplane concept are described.
Fortenbaugh, R. L.↗
Aerodynamic mathematical modeling - basic concepts
This lecture is a review of the basic concepts involved In the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers. The review leads from Bryan's original formulation through the concepts of linear aerodynamic indicial functions and superposition to the extension of these concepts into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well-defined characteristic motions, reproducible in principle either in wind-tunnel experiments or flow-field computations. A further generalization leads to a torn, accommodating the discontinuous and double-valued behavior characteristic of hysteresis in the steady-state aerodynamic response
Murray Tobak↗
Proceedings, Conference on the Computing Environment for Mathematical Software
Recent advances in software and hardware technology which make it economical to create computing environments appropriate for specialized applications are addressed. Topics included software tools, FORTRAN standards activity, and features of languages, operating systems, and hardware that are important for the development, testing, and maintenance of mathematical software.
Source record↗
Full-scale flammability test data for validation of aircraft fire mathematical models
Twenty-five large scale aircraft flammability tests were conducted in a Boeing 737 fuselage at the NASA Johnson Space Center (JSC). The objective of this test program was to provide a data base on the propagation of large scale aircraft fires to support the validation of aircraft fire mathematical models. Variables in the test program included cabin volume, amount of fuel, fuel pan area, fire location, airflow rate, and cabin materials. A number of tests were conducted with jet A-1 fuel only, while others were conducted with various Boeing 747 type cabin materials. These included urethane foam seats, passenger service units, stowage bins, and wall and ceiling panels. Two tests were also included using special urethane foam and polyimide foam seats. Tests were conducted with each cabin material individually, with various combinations of these materials, and finally, with all materials in the cabin. The data include information obtained from approximately 160 locations inside the fuselage.
Kuminecz, J. F.↗
Mathematical and physical modelling of materials processing
Mathematical and physical modeling of turbulence phenomena in metals processing, electromagnetically driven flows in materials processing, gas-solid reactions, rapid solidification processes, the electroslag casting process, the role of cathodic depolarizers in the corrosion of aluminum in sea water, and predicting viscoelastic flows are described.
Source record↗
Aeroelastic analysis for helicopter rotors with blade appended pendulum vibration absorbers. Mathematical derivations and program user's manual
Mathematical development is presented for the expanded capabilities of the United Technologies Research Center (UTRC) G400 Rotor Aeroelastic Analysis. This expanded analysis, G400PA, simulates the dynamics of teetered rotors, blade pendulum vibration absorbers and the higher harmonic excitations resulting from prescribed vibratory hub motions and higher harmonic blade pitch control. Formulations are also presented for calculating the rotor impedance matrix appropriate to these higher harmonic blade excitations. This impedance matrix and the associated vibratory hub loads are intended as the rotor blade characteristics elements for use in the Simplified Coupled Rotor/Fuselage Vibration Analysis (SIMVIB). Sections are included presenting updates to the development of the original G400 theory, and material appropriate to the user of the G400PA computer program. This material includes: (1) a general descriptionof the tructuring of the G400PA FORTRAN coding, (2) a detaild description of the required input data and other useful information for successfully running the program, and (3) a detailed description of the output results.
Bielawa, R. L.↗
A mathematical model of post-instability in fluid mechanics
Postinstability of fluids is eliminated in numerical models by introducing multivalued velocity fields after discarding the principle of impenetrability. Smooth functions are shown to be incapable of keeping the derivatives from going towards infinity when iterating solutions for the governing equations such as those defined by Navier-Stokes. Enlarging the class of functions is shown to be necessary to eliminate the appearance of imaginary characteristic roots in the systems of arbitrary partial differential equations, a condition which leads to physically impossible motions. The enlarging is demonstrated to be achievable by allowing several individual particles with different velocities to appear at the same point of space, and the subsequent multivaluedness of the solutions is purely a mathematical concern, rather than one of actual physical existence. Applications are provided for an inviscid fluid and for turbulence.
Zak, M. A.↗
Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes
A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.
Palusinski, O. A.↗
Mathematical Instability Criteria for Elastic Structures
Theoretical paper discusses physical significance of vanishing of hyperbolic coefficients in equations of elastodynamics. Paper presents generalized approach to structural elastodynamics as part of continuing effort to develop mathematical stability criteria for structures and simulate postinstabilty behavior of elastics in general.
Zak, M.↗
Mathematical Simulation of Flight Maneuvers
Mathematical model simulates response of spin-stabilized spacecraft to commanded thruster pulses, using set of equations based on known inertial properties of vehicle and previously-determined thrustor performance. Model used to generate sequence of thrustor commands to accomplish specified maneuver.
Frauenholz, R. B.↗
A mathematical model of a single main rotor helicopter for piloted simulation
A mathematical model, suitable for piloted simulation of the flying qualities of helicopters, is a nonlinear, total force and moment model of a single main rotor helicopter. The model has ten degrees of freedom: six rigid body, three rotor flapping, and the rotor rotational degrees of freedom. The rotor model assumes rigid blades with rotor forces and moments radially integrated and summed about the azimuth. The fuselage aerodynamic model uses a detailed representation over a nominal angle of attack and sideslip range of + or - 15 deg., as well as a simplified curve fit at large angles of attack or sideslip. Stabilizing surface aerodynamics are modeled with a lift curve slope between stall limits and a general curve fit for large angles of attack. A generalized stability and control augmentation system is described. Additional computer subroutines provide options for a simplified engine/governor model, atmospheric turbulence, and a linearized six degree of freedom dynamic model for stability and control analysis.
Talbot, P. D.↗