Rapid near-optimal aerospace plane trajectory generation and guidance

Effort was directed toward the problems of the real time trajectory optimization and guidance law development for the National Aerospace Plane (NASP) applications. In particular, singular perturbation methods were used to develop guidance algorithms suitable for onboard, real time implementation. The progress made in this research effort is reported

Climb-dash real-time calculations

On-board rear-optimal climb-dash energy management, optimal symmetric flight with an intermediate vehicle model, and energy states are presented

An on-board near-optimal climb-dash energy management

On-board real time flight control is studied in order to develop algorithms which are simple enough to be used in practice, for a variety of missions involving three dimensional flight. The intercept mission in symmetric flight is emphasized. Extensive computation is required on the ground prior to the mission but the ensuing on-board exploitation is extremely simple. The scheme takes advantage of the boundary layer structure common in singular perturbations, arising with the multiple time scales appropriate to aircraft dynamics. Energy modelling of aircraft is used as the starting point for the analysis. In the symmetric case, a nominal path is generated which fairs into the dash or cruise state. Feedback coefficients are found as functions of the remaining energy to go (dash energy less current energy) along the nominal path

Optimal symmetric flight with an intermediate vehicle model

Optimal flight in the vertical plane with a vehicle model intermediate in complexity between the point-mass and energy models is studied. Flight-path angle takes on the role of a control variable. Range-open problems feature subarcs of vertical flight and singular subarcs. The class of altitude-speed-range-time optimization problems with fuel expenditure unspecified is investigated and some interesting phenomena uncovered. The maximum-lift-to-drag glide appears as part of the family, final-time-open, with appropriate initial and terminal transient exceeding level-flight drag, some members exhibiting oscillations. Oscillatory paths generally fail the Jacobi test for durations exceeding a period and furnish a minimum only for short-duration problems

Optimal symmetric flight studies

Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory

Solar Neutrinos and the Eclipse Effect

The solar neutrino counting rate in a real time detector like Super--Kamiokanda, SNO, or Borexino is enhanced due to neutrino oscillations in the Moon during a partial or total solar eclipse. The enhancement is calculated as a function of the neutrino parameters in the case of three flavor mixing. This enhancement, if seen, can further help to determine the neutrino parameters.Comment: 24 Pages Revtex, 8 figures as one ps file. To appear in Phys. Rev. D; Some typos corrected and a reference adde

An approach to three-dimensional aircraft pursuit-evasion

AbstractAn algorithm for obtaining a state-feedback control law for near-optimal aircraft pursuit-evasion in three dimensions is outlined. Key features of the approach are the use of singular-perturbation ideas to decouple the dynamics of each of the two players and the use of a reference frame that decouples the slow subsystem extremals of one player from those of the other. The resulting subproblems are then tractable for closed-loop solution, and the solutions may be combined to give a control law feasible for real-time implementation. Compared with past analyses of pursuit-evasion games, our dynamic model is higher order and more realistic; therefore, our results should be of practical value for aircraft control. And because we use fewer time-scales than were used in past analyses of flight dynamic problems by singular-perturbation methods, our algorithm should be more accurate

Exceptional Performance in Competitive Ski Mountaineering: An Inertial Sensor Case Study.

Organized biannually in the Swiss Alps since 1984, the "Patrouille des Glaciers" (PDG) is one of the most challenging long-distance ski mountaineering (skimo) team competitions in the world. The race begins in Zermatt (1,616 m) and ends in Verbier (1,520 m), covering a total distance of 53 km with a cumulated 4,386 m of ascent and 4,482 m of descent. About 4,800 athletes take part in this competition, in teams of three. We hereby present the performance analysis of the uphill parts of this race of a member (#1) of the winning team in 2018, setting a new race record at 5 h and 35 min, in comparison with two amateur athletes. The athletes were equipped with the Global Navigation Satellite System (GNSS) antenna, a heart rate monitor, and a dedicated multisensor inertial measurement unit (IMU) attached to a ski, which recorded spatial-temporal gait parameters and transition events. The athletes' GNSS and heart rate data were synchronized with the IMU data. Athlete #1 had a baseline VO <sub>2</sub> max of 80 ml/min/kg, a maximum heart rate of 205 bpm, weighed 69 kg, and had a body mass index (BMI) of 21.3 kg/m <sup>2</sup> . During the race, he carried 6 kg of gear and kept his heart rate constant around 85% of max. Spatiotemporal parameters analysis highlighted his ability to sustain higher power, higher pace, and, thus, higher vertical velocity than the other athletes. He made longer steps by gliding longer at each step and performed less kick turns in a shorter time. He spent only a cumulative 5 min and 30 s during skins on and off transitions. Skimo performance, thus, requires a high aerobic power of which a high fraction can be maintained for a prolonged time. Our results further confirm earlier observations that speed of ascent during endurance skimo competitions is a function of body weight and race gear and vertical energy cost of locomotion, with the latter function of climbing gradient. It is also the first study to provide some reference benchmarks for spatiotemporal parameters of elite and amateur skimo athletes during climbing using real-world data

Singular perturbation techniques for real time aircraft trajectory optimization and control

The usefulness of singular perturbation methods for developing real time computer algorithms to control and optimize aircraft flight trajectories is examined. A minimum time intercept problem using F-8 aerodynamic and propulsion data is used as a baseline. This provides a framework within which issues relating to problem formulation, solution methodology and real time implementation are examined. Theoretical questions relating to separability of dynamics are addressed. With respect to implementation, situations leading to numerical singularities are identified, and procedures for dealing with them are outlined. Also, particular attention is given to identifying quantities that can be precomputed and stored, thus greatly reducing the on-board computational load. Numerical results are given to illustrate the minimum time algorithm, and the resulting flight paths. An estimate is given for execution time and storage requirements