CEAS 2015 paper 87 Page | 1
This work is licensed under the Creative Commons Attribution International License (CC BY). Copyright © 2015 by author(s).
ON THE MINIMIZATION OF CRUISE DRAG DUE TO PITCH TRIM
Luís Campos
IDMEC, CCTAE, Instituto Superior Técnico, Universidade de Lisboa
Avenida Rovisco Pais, 1049-001, Lisboa, Portugal
luis.campos@tecnico.ulisboa.pt
Joaquim Marques
IDMEC, CCTAE, Universidade Lusófona
Avenida Campo Grande, 376, 1749-024, Lisboa, Portugal
jmgmarques@ulusofona.pt
ABSTRACT
A blended-wing-body is an example of an aircraft configuration with multiple control surfaces. The most
effective use of these control surfaces, e.g. to minimize cruise drag due to pitch trim, or to maximize
pitching moment at low speed in an engine-out condition, leads to optimization problems. The method
investigated is this paper is applied to multiple control surfaces, taking into account their mutual
interactions and also the influence of shifts of center of gravity. It is shown in a particular case that it is
possible to achieve pitch trim in cruise with drag reduction relative to the untrimmed case.
1 INTRODUCTION
Minimizing drag in cruise is most important for aircraft emissions and economics since this is the longest
phase of most flights, and where a large proportion of the total fuel is burnt. It is therefore desirable to
achieve pitch trim at cruise with the smallest possible drag penalty relative to the untrimmed aircraft;
even better would be to achieve pitch trim in cruise with a drag reduction relative to the untrimmed
aircraft. There is a limited choice of control surfaces in the traditional aircraft configuration, with a
fuselage to carry payload, a wing to carry fuel and provide lift and roll control, and an empenage to
provide yaw and pitch control. In a blended wing body (BWB) configuration, with control surfaces both
on the centerbody and wing, there are multiple control surfaces; thus arises the question of which is the
best combination of all available control surfaces to achieve pitch trim with least drag.
The method to be presented applies to the trimming of an aircraft, for any axis and any flight phase,
when there is a choice of control surfaces to be used. It allows distinct control surfaces to have different
deflections, in order to minimize drag, for a given constant control moment e.g. in cruise. Conversely,
e.g. in a low-speed engine-out condition, with a given drag, it specifies the maximum control moment
available.
Among the multitude of optimization methods available [1,2], the method of Lagrange multipliers was
chosen; one of its major applications is in the calculus of variations [3], and hence in the analytical
dynamics [4] of mechanical systems with multiple degrees-of-freedom subject to various types of
constraints. The type of constraint in the present problem corresponds to anholonomic scleronomic in
classical mechanics [5]. The method of Lagrange multipliers has several attractive features in the present
application: (i) the magnitude of the final multiplier indicates how severely the constraint of pitch trim or
constant lift affects cruise drag; (ii) the differences between the Lagrange multipliers of distinct control
surfaces at each iteration indicates how far that particular state (or choice of control surface deflections)
is from the final optimal state. There are other methods of optimization applicable to the selection of
multiple control surfaces [6,7].