Improved Aircraft Cruise By Periodic Control.
Lyons, Daniel Thomas
1980
Abstract
The possibility of improving aircraft cruise by periodic motion is investigated for subsonic aircraft with jet engines. Three cruise problems are studied: (1) maximum range, (2) maximum endurance, and (3) peak altitude. Normal steady state cruise is compared with periodic cruise in which the controls and state variables are time-dependent periodic functions. It is shown that periodic cruise results in improved performance under certain circumstances. The equations of motion are given by a point-mass model in which the controls are lift and thrust, and the states are range, altitude, velocity, and flight path angle. The following assumptions are used: constant mass, small angle of attack, conventional lift-drag model with constant coefficients, exponential atmospheric density, exponential maximum thrust, and constant and variable thrust-specific-fuel-consumption. Very simple models, such as the energy-state approximation, are analyzed because they are easy to solve and give insight into the nature of periodic cruise. The full-model is highly non-linear so a numerical minimization is required to obtain the optimal periodic trajectories. The costs for these trajectories correlate well with the values from the simplified models. The results for the problem of maximum range cruise depend on three non-dimensional parameters, (beta), (delta), and normalized maximum thrust. A constraint on the maximum altitude is shown to be especially important. (beta) increases as either the constraint altitude or the wing loading increase. (delta) is one half of the minimum drag-to-lift ratio. Periodic cruise is favored over steady state cruise when (beta) and (delta) are small and when the maximum thrust is large. Under the best conditions, the fuel consumption can be reduced by more than 25%. Optimal periodic cruise requires a maximum range glide arc followed by a transition to an efficient, full-thrust climb back to the initial altitude. The fuel efficiency of periodic cruise is better than that of steady state cruise because thrusting takes place at higher speeds so greater energy is obtained per pound of fuel. This improved efficiency outweighs the energy losses associated with the transitions between glide and climb and those due to higher speed during climb. The maximum endurance cruise problem requires a minimum, rather than a maximum, altitude constraint. Periodic cruise is favored when (beta) and (delta) are small and the maximum thrust is large. Since the minimum altitude is usually the ground, it is likely that (beta) is small and the thrust is large. Thus improved performance is likely for most aircraft. Under the most favorable conditions, periodic cruise can reduce the fuel consumption by more than 30%. Optimal periodic cruise requires a minimum rate-of-descent glide followed by a transition to a maximum rate-of-climb ascent at full thrust. Improved performance is possible for reasons similar to those for maximum range cruise. Periodic cruise is shown to give greater peak altitudes than are possible with steady state cruise. A state inequality constraint which limits the peak altitude is required to retain sufficient dynamic pressure for aerodynamic control at the peak altitude. A large energy-height is desirable for maximum peak altitude. However, the period increases rapidly as the energy height approaches the maximum energy height for steady cruise. The numerical algorithm for trajectory optimization uses an unusual approach which not only guarantees a periodic trajectory, but also does not require expensive integrations of the equations of motion. The altitude and velocity are specified by cubic periodic splines which are determined by a finite number of parameters that are optimized by a minimization algorithm. The equations of motion are solved for the other variables.Types
Thesis
Metadata
Show full item recordCollections
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.