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At least 235 records · Page 13

Development of mathematical models of environmental physiology

Selected articles concerned with mathematical or simulation models of human thermoregulation are presented. The articles presented include: (1) development and use of simulation models in medicine, (2) model of cardio-vascular adjustments during exercise, (3) effective temperature scale based on simple model of human physiological regulatory response, (4) behavioral approach to thermoregulatory set point during exercise, and (5) importance of skin temperature in sweat regulation.

Stolwijk, J. A. J.↗

Fully Automatic Guidance and Control for Rotorcraft Nap-of-the-earth Flight Following Planned Profiles. Volume 2: Mathematical Model

Developing a single-pilot, all-weather nap-of-the-earth (NOE) capability requires fully automatic NOE (ANOE) navigation and flight control. Innovative guidance and control concepts are investigated in a four-fold research effort that: (1) organizes the on-board computer-based storage and real-time updating of NOE terrain profiles and obstacles in course-oriented coordinates indexed to the mission flight plan; (2) defines a class of automatic anticipative pursuit guidance algorithms and necessary data preview requirements to follow the vertical, lateral, and longitudinal guidance commands dictated by the updated flight profiles; (3) automates a decision-making process for unexpected obstacle avoidance; and (4) provides several rapid response maneuvers. Acquired knowledge from the sensed environment is correlated with the forehand knowledge of the recorded environment (terrain, cultural features, threats, and targets), which is then used to determine an appropriate evasive maneuver if a nonconformity of the sensed and recorded environments is observed. This four-fold research effort was evaluated in both fixed-base and moving-base real-time piloted simulations; thereby, providing a practical demonstration for evaluating pilot acceptance of the automated concepts, supervisory override, manual operation, and re-engagement of the automatic system. Volume one describes the major components of the guidance and control laws as well as the results of the piloted simulations. Volume two describes the complete mathematical model of the fully automatic guidance system for rotorcraft NOE flight following planned flight profiles.

Clement, Warren F.↗

Building Mathematical Models Of Solid Objects

Solid Modeling Program (SMP) version 2.0 provides capability to model complex solid objects mathematically through aggregation of geometric primitives (parts). System provides designer with basic set of primitive parts and capability to define new primitives. Six primitives included in present version: boxes, cones, spheres, paraboloids, tori, and trusses. Written in VAX/VMS FORTRAN 77.

Randall, Donald P.↗

Time and frequency-domain identification and verification of BO-105 dynamic models

Mathematical models for the dynamics of the DLR BO 105 helicopter are extracted from flight test data using two different approaches: frequency-domain and time-domain identification. Both approaches are reviewed. Results from an extensive data consistency analysis are given. Identifications for 6 degrees of freedom (DOF) rigid body models are presented and compared in detail. The extracted models compare favorably and their prediction capability is demonstrated in verification results. Approaches to extend the 6 DOF models are addressed and first results are presented. System identification is broadly defined as the deduction of system characteristics from measured data. It provides the only possibility to extract both non-parametric (e.g., frequency responses) and parametric (e.g., state space matrices) aircraft models from flight test data and therefore gives a reliable characterization of the dynamics of the actually existing aircraft. Main applications of system identification are seen in areas where higher accuracies of the mathematical models are required: Simulation validation, control system design (in particular model-following control system design for in-flight simulation), and handling qualities.

Kaletka, Juergen↗

Time and frequency-domain identification and verification of BO-105 dynamic models

Mathematical models for the dynamics of the DLR BO 105 helicopter are extracted from flight test data using two different approaches: frequency-domain and time-domain identification. Both approaches are reviewed. Results from an extensive data consistency analysis are given. Identifications for 6 degrees of freedom (DOF) rigid body models are presented and compared in detail. The extracted models compare favorably and their prediction capability is demonstrated in verification results. Approaches to extend the 6 DOF models are addressed and first results are presented. System identification is broadly defined as the deduction of system characteristics from measured data. It provides the only possibility to extract both non-parametric (e.g., frequency responses) and parametric (e.g., state space matrices) aircraft models from flight test data and therefore gives a reliable characterization of the dynamics of the actually existing aircraft. Main applications of system identification are seen in areas where higher accuracies of the mathematical models are required: Simulation validation, control system design (in particular model-following control system design for in-flight simulation), and handling qualities.

Kaletka, Juergen↗

A mathematical model for the doubly fed wound rotor generator

A mathematical analysis of a doubly-fed wound rotor machine used as a constant frequency generator is presented. The purpose of this analysis is to derive a consistent set of circuit equations which produce constant stator frequency and constant stator voltage. Starting with instantaneous circuit equations, the necessary rotor voltages and currents are derived. The model, thus obtained, is assumed to be valid, since the resulting relationships between mechanical power and active volt-amperes agrees with the results of others. In addition, the model allows for a new interpretation of the power flow in the doubly-fed generator.

Brady, F. J.↗

Mathematical Model Development and Experimental Verification of Electromagnetic Force Actuators for use in Space Applications

This technical memorandum shows the development of the mathematics needed to model several types of electromagnetic force actuators that may be of interest for use in space applications. The actuators described are capable of providing attractive, repulsive, and longitudinal forces between the actuator and a variety of metal surfaces. Potential applications for these propellant free actuators include spacecraft docking, in-space fabrication, robotic spacecraft inspection and servicing, deflection of metallic debris, and interaction with iron core asteroids (e.g., landing, repelling, and relocating).

Robert C. Youngquist↗

Thermal mathematical modeling and system simulation of Space Shuttle less subsystem

Applications, validation tests, and upgrades of the two- and three-dimensional system level thermal mathematical system simulation models (TMSSM) used for thermal protection system (TPS) analyses are described. The TMSSM were developed as an aid to predicting the performance requirements and configurations of the Shuttle wing leading edge (WLE) and nose cone (NC) TPS tiles. The WLE and its structure were subjected to acoustic, thermal/vacuum, and air loads tests to simulate launch, on-orbit, and re-entry behavior. STS-1, -2 and -5 flight data led to recalibration of on-board instruments and raised estimates of the thermal shock at the NC and WLE. Baseline heating data are now available for the design of future TPS.

Chao, D. C.↗

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗

A Mathematical Model of Oxygen Transport in Skeletal Muscle During Hindlimb Unloading

During hindlimb unloading (HU) dramatic fluid shifts occur within minutes of the suspension, leading to a less precise matching of blood flow to O2 demands of skeletal muscle. Vascular resistance directs blood away from certain muscles, such as the soleus (SOL). The muscle volume gradually reduces in these muscles so that eventually the relative blood flow returns to normal. It is generally believed that muscle volume change is not due to O2 depletion, but a consequence of disuse. However, the volume of the unloaded rat muscle declines over the course of weeks, whereas the redistribution of blood flow occurs immediately. Using a Krogh Cylinder Model, the distribution of O2 was predicted in two skeletal muscles: SOL and gastrocnemius (GAS). Effects of the muscle blood flow, volume, capillary density, and O2 uptake, are included to calculate the pO2 at rest and after 10 min and 15 days of unloading. The model predicts that 32 percent of the SOL muscle tissue has a pO2 1.25 mm Hg within 10 min, whereas the GAS maintains normal O2 levels, and that equilibrium is reached only as the SOL muscle cells degenerate. The results provide evidence that there is an inadequate O2 supply to the mitochondria in the SOL muscle after 10 min HU.

Mathematical models↗

A comparison of the various helicopter mathematical models used in the methodology assessment

Various features of the computer codes used in the helicopter industry and by government agencies for rotorcraft aeroelastic stability analysis are compared. Mathematical rigor in modeling rotorcraft is given primarily to the rotor-system dynamic behavior; the aerodynamic modeling is still limited to strip theory and to uneven application of corrections for stall, reversed flow, yawed flow, radial flow, and unsteady aerodynamic effects. The forward-flight regime analysis is included in five of the 11 codes surveyed. However, only two of these codes are capable of a Floquet analysis for aeroelastic stability. For the hover regime, nine of the 11 codes use eigen-analysis approach. The remaining codes perform a harmonic analysis of the transient response of system.

Stephens, Wendell B.↗

A mathematical model for the doubly-fed wound rotor generator. II

A mathematical analysis of a doubly-fed wound rotor generator is presented. The constraints of constant stator voltage and frequency to the circuit equations were applied and expressions for the currents and voltages in the machine obtained. The derived variables are redefined as direct and quadrature components. In addition, the apparent (complex) power for both the rotor and the stator are derived in terms of these redefined components.

Brady, F. J.↗

Mathematical modeling and simulation of the space shuttle imaging radar antennas

Simulations of space shuttle synthetic aperture radar antennas under the influence of space environmental conditions were carried out at L, C, and X-band. Mathematical difficulties in modeling large, non-planar array antennas are discussed, and an approximate modeling technique is presented. Results for several antenna error conditions are illustrated in far-field profile patterns, earth surface footprint contours, and summary graphs.

Campbell, R. W.↗

A mathematical model for the doubly-fed wound rotor generator, part 2

A mathematical analysis of a doubly-fed wound rotor generator is presented. The constraints of constant stator voltage and frequency to the circuit equations were applied and expressions for the currents and voltages in the machine obtained. The derived variables are redefined as direct and quadrature components. In addition, the apparent (complex) power for both the rotor and the stator are derived in terms of these redefined components.

Brady, F. J.↗

On the mathematical modeling of the Reynolds stress's equations

By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressure-velocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convection-like elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple one-dimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.

Lin, Avi↗

Mathematical modelling of flow distribution in the human cardiovascular system

The paper presents a detailed model of the entire human cardiovascular system which aims to study the changes in flow distribution caused by external stimuli, changes in internal parameters, or other factors. The arterial-venous network is represented by 325 interconnected elastic segments. The mathematical description of each segment is based on equations of hydrodynamics and those of stress/strain relationships in elastic materials. Appropriate input functions provide for the pumping of blood by the heart through the system. The analysis employs the finite-element technique which can accommodate any prescribed boundary conditions. Values of model parameters are from available data on physical and rheological properties of blood and blood vessels. As a representative example, simulation results on changes in flow distribution with changes in the elastic properties of blood vessels are discussed. They indicate that the errors in the calculated overall flow rates are not significant even in the extreme case of arteries and veins behaving as rigid tubes.

NASA Center JSC↗