Abstract

Canada’s greenhouse gas emissions increased by 20% between the years 1990 and 2014, and
the aviation industry is a large contributor to this increase. The optimization of fuel consumption
is therefore of paramount importance. This thesis focuses on minimizing the direct operating cost
(DOC) for a cruising turbojet and turboprop aircraft. The DOC is a trade-off of fuel costs and time
costs that are related by the cost index CI . By determining DOC-optimal trajectories, aircraft may
balance the need to arrive at their target destination in a timely fashion with the need to keep fuel
emissions low. The main contribution of this thesis is a two-part approach to determining the DOCoptimal
trajectories of a cruising turbojet and turboprop aircraft. For a turbojet, the first part of the
proposed methodology is the derivation of an analytic expression for the optimal speed in terms of
position and optimal initial speed, while the second part derives an analytic implicit definition of
the optimal initial speed. For a turboprop, the first part of the proposed methodology is concerned
with developing a suboptimal approximation for the DOC-optimal speed presented in terms of the
weight of the aircraft and the optimal final speed. The second part presents a recursive algorithm
by which the optimal final speed may be obtained. This thesis assumes that the aircraft cruises
below its drag divergence Mach number at constant altitude. Numerical examples will illustrate the
proposed methodologies.