Search NASA⌕ Search

Engineering topics

Kreindler, E.

Publications and source records attributed to Kreindler, E..

9 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Minimum-fuel, three-dimensional flight paths for jet transports

A number of studies dealing with fuel minimization are concerned with three-dimensional flight. However, only Neuman and Kreindler (1982) consider cases involving commercial jet transports. In the latter study, only the climb-out and descent portions of complete long-range flight paths below 10,000 ft altitude have been investigated. The present investigation is concerned with the computation of minimum-fuel nonturning and turning flight paths for climb-outs from 2000 to 10,000 ft for long-range flights (greater than 50 n mi), and for complete flight paths of lengths between 5 and 50 n mi.

Neuman, F.↗
NASA NTRS1984

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.

Neuman, F.↗
NASA NTRS1983

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.

Neuman, F.↗
NASA NTRS1982

Optimal turning climb-out and descent of commercial jet aircraft

Optimal turning climb-out and descent flight-paths from and to runway headings are derived to provide the missing elements of a complete flight-path optimization for minimum fuel consumption. The paths are derived by generating a field of extremals, using the necessary conditions of optimal control. Results show that the speed profiles for straight and turning flight are essentially identical, except for the final horizontal accelerating or decelerating turn. The optimal turns, which require no abrupt maneuvers, could easily be integrated with present climb-cruise-descent fuel-optimization algorithms.

Neuman, F.↗
NASA NTRS1981

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.

Kreindler, E.↗
NASA NTRS1981

Darboux points in minimum-fuel aircraft landing problems

An algorithm for suboptimal flight paths is used to show the existence of Darboux points on extremals of a fourth-order minimum-fuel horizontal aircraft landing problem; the states are two position coordinates, velocity and heading. It is shown that there is no simple relationship between Darboux points and conjugate points for a special second-order case of capturing a line at constant velocity.

Kreindler, E.↗
NASA NTRS1980

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.

Kreindler, E.↗