Minimum fuel horizontal flightpaths in the terminal area

The problem of minimum fuel airplane trajectories from arbitrary initial states to be fixed final state is considered. There are four state variables (two position coordinates, heading, and constrained velocity) and two constrained controls (thrust and bank angle). The fuel optimality of circular and straight line flightpaths is examined. Representative extremals (trajectories satisfying the necessary conditions of the minimum principle) of various types are computed and used to evaluate trajectories generated by an on line algorithm. Attention is paid to the existence of Darboux points (beyond which an extremal ceases to be globally optimal). One fuel flow rate model includes a term quadratic in thrust; hence, the optimal thrust is continuous and nonsingular. The other fuel flow rate model is linear in thrust, and consequently the optimal thrust is discontinuous and singular

Global optimality of extremals: An example

The question of the existence and location of Darboux points is crucial for minimally sufficient conditions for global optimality and for computation of optimal trajectories. A numerical investigation is presented of the Darboux points and their relationship with conjugate points for a problem of minimum fuel, constant velocity, and horizontal aircraft turns to capture a line. This simple second order optimal control problem shows that ignoring the possible existence of Darboux points may play havoc with the computation of optimal trajectories

Minimum-fuel turning climbout and descent guidance of transport jets

The complete flightpath optimization problem for minimum fuel consumption from takeoff to landing including the initial and final turns from and to the runway heading is solved. However, only the initial and final segments which contain the turns are treated, since the straight-line climbout, cruise, and descent problems have already been solved. The paths are derived by generating fields of extremals, using the necessary conditions of optimal control together with singular arcs and state constraints. Results show that the speed profiles for straight flight and turning flight are essentially identical except for the final horizontal accelerating or decelerating turns. The optimal turns require no abrupt maneuvers, and an approximation of the optimal turns could be easily integrated with present straight-line climb-cruise-descent fuel-optimization algorithms. Climbout at the optimal IAS rather than the 250-knot terminal-area speed limit would save 36 lb of fuel for the 727-100 aircraft

Minimum-fuel, 3-dimensional flightpath guidance of transfer jets

Minimum fuel, three dimensional flightpaths for commercial jet aircraft are discussed. The theoretical development is divided into two sections. In both sections, the necessary conditions of optimal control, including singular arcs and state constraints, are used. One section treats the initial and final portions (below 10,000 ft) of long optimal flightpaths. Here all possible paths can be derived by generating fields of extremals. Another section treats the complete intermediate length, three dimensional terminal area flightpaths. Here only representative sample flightpaths can be computed. Sufficient detail is provided to give the student of optimal control a complex example of a useful application of optimal control theory

Learning and growth processes facilitated in 9 to 12 year olds challenged with ADHD enrolled on a therapeutic horseback riding programme

This study investigated the outcomes and practice of Therapeutic Horseback Riding (THR) for children aged 9 to 12 diagnosed with Attention Deficit with Hyperactivity Disorder (ADHD). The study was carried out in order to gain new insights in the learning and growth processes facilitated by Therapeutic Horseback Riding (THR) and to improve practice. Two learning and growth processes were identified and investigated: establishing a therapeutic vision and infusing it into the therapeutic plan and facilitating the transfer of newly learned or improved skills and learning strategies from the riding learning environment to parallel learning environments such as the client’s school and home. The research also explored ways to amplify levels of skill acquired during THR sessions and to support the transformation process experienced by THR clients. A pilot exploratory survey was conducted among THR practitioners and participating parents. In depth interviews and observations were conducted. A multiple case study paradigm was selected for the purpose of the study. In depth interviews were conducted with children diagnosed with ADHD, parents, and teachers. In addition, relevant documents were examined. A THR manual for practitioners was developed to support and inform learning partnerships between school (teachers), THR practitioners (THRPs) and children and their family, in order to standardise THR practice. The findings of this research showed that the THR practitioners (THRPs) should facilitate the acquisition and transfer of skills and strategies learned during THR sessions to other environments, such as family and school, in order to improve the quality of life of children diagnosed having ADHD. The Knowing Therapeutic Horseback Riding (KTR) model of THR practice emerged and was shown to be effective in promoting a learning and growth partnership between school, THR practitioner, client and his family. The KTR model calls for the nurturing of this partnership in order to support the learned skills and amplify them

Recent Developments in Aerial Hijacking: The Issue of Liability

My part of the program insofar as hijacking is concerned is, as you might expect, the liability part of the program. I have been asked to discuss who is liable, if anybody, in hijacking incidents

The Guatemala Protocol

The vice in the new Guatemala Protocol is that no matter how responsible, no matter how faulty the airline is, and no matter how limited the fault of the manufacturer is, the manufacturer is going to end up paying practically everything. The author is an attorney representing passengers injured in airplane crashes