Mecanica De Vuelo

Fundamentals of Airplane Flight Mechanics

David G. Hull

Fundamentals of Airplane
Flight Mechanics
With 125 Figures and 25 Tables

123

Dedicated to
Angelo Miele
who instilled in me his love for flight mechanics.

Preface
Flight mechanics is the application of Newton’s laws (F=ma and M=Iα) to
the study of vehicle trajectories (performance), stability, and aerodynamic
control.There are two basic problems in airplane flight mechanics: (1) given
an airplane what are its performance, stability, and control characteristics?
and (2) given performance, stability, and control characteristics, what is the
airplane? The latter is called airplane sizing and is based on the definition
of a standard mission profile. For commercial airplanes including business
jets, the missionlegs are take-off, climb, cruise, descent, and landing. For a
military airplane additional legs are the supersonic dash, fuel for air combat,
and specific excess power. This text is concerned with the first problem, but
its organization is motivated by the structure of the second problem. Trajectory analysis is used to derive formulas and/or algorithms for computing
the distance, time, and fuelalong each mission leg. In the sizing process, all
airplanes are required to be statically stable. While dynamic stability is not
required in the sizing process, the linearized equations of motion are used in
the design of automatic flight control systems.
This text is primarily concerned with analytical solutions of airplane flight
mechanics problems. Its design is based on the precepts thatthere is only one
semester available for the teaching of airplane flight mechanics and that it is
important to cover both trajectory analysis and stability and control in this
course. To include the fundamentals of both topics, the text is limited mainly
to flight in a vertical plane. This is not very restrictive because, with the
exception of turns, the basic trajectory segments of both missionprofiles and
the stability calculations are in the vertical plane. At the University of Texas
at Austin, this course is preceded by courses on low-speed aerodynamics and
linear system theory. It is followed by a course on automatic control.
The trajectory analysis portion of this text is patterned after Miele’s
flight mechanics text in terms of the nomenclature and the equations of motionapproach. The aerodynamics prediction algorithms have been taken
from an early version of the NASA-developed business jet sizing code called
the General Aviation Synthesis Program or GASP. An important part of
trajectory analysis is trajectory optimization. Ordinarily, trajectory optimization is a complicated affair involving optimal control theory (calculus of
variations) and/or the use ofnumerical optimization techniques. However,
for the standard mission legs, the optimization problems are quite simple
in nature. Their solution can be obtained through the use of basic calculus.

Preface

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The nomenclature of the stability and control part of the text is based on the
writings of Roskam. Aerodynamic prediction follows that of the USAF Stability and Control Datcom. It isimportant to be able to list relatively simple
formulas for predicting aerodynamic quantities and to be able to carry out
these calculations throughout performance, stability, and control. Hence, it
is assumed that the airplanes have straight, tapered, swept wing planforms.
Flight mechanics is a discipline. As such, it has equations of motion, acceptable approximations, and solution techniques forthe approximate equations of motion. Once an analytical solution has been obtained, it is important to calculate some numbers to compare the answer with the assumptions
used to derive it and to acquaint students with the sizes of the numbers. The
Subsonic Business Jet (SBJ) defined in App. A is used for these calculations.
The text is divided into two parts: trajectory analysis and stability...