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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=I ) to

the study of vehicle trajectories (performance), stability, and aerodynamic

control. There are two basic problems in airplane ight 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 denition

of a standard mission prole. For commercial airplanes including business

jets, the mission legs are take-o, climb, cruise, descent, and landing. For a

military airplane additional legs are the supersonic dash, fuel for air combat,

and specic excess power. This text is concerned with the rst problem, but

its organization is motivated by the structure of the second problem. Tra-

jectory analysis is used to derive formulas and/or algorithms for computing

the distance, time, and fuel along 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 ight control systems.

This text is primarily concerned with analytical solutions of airplane ight

mechanics problems. Its design is based on the precepts that there is only one

semester available for the teaching of airplane ight 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 ight in a vertical plane. This is not very restrictive because, with the

exception of turns, the basic trajectory segments of both mission proles 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

ight mechanics text in terms of the nomenclature and the equations of mo-

tion approach. 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 opti-

mization is a complicated aair involving optimal control theory (calculus of

variations) and/or the use of numerical 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

vii

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 Sta-

bility and Control Datcom. It is important 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, ac-

ceptable approximations, and solution techniques for the approximate equa-

tions of motion. Once an analytical solution has been obtained, it is impor-

tant 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) dened in App. A is used for these calculations.

The text is divided into two parts: trajectory analysis and stability and

control. To study trajectories, the force equations (F=ma) are uncoupled

from the moment equations (M=I ) by assuming that the airplane is not

rotating and that control surface deections do not change lift and drag. The

resulting equations are referred to as the 3DOF model, and their investigation

is called trajectory analysis. To study stability and control, both F=ma and

M=I are needed, and the resulting equations are referred to as the 6DOF

model. An overview of airplane ight mechanics is presented in Chap. 1.

Part I: Trajectory Analysis. This part begins in Chap. 2 with the

derivation of the 3DOF equations of motion for ight in a vertical plane over

a at earth and their discussion for nonsteady ight and quasi-steady ight.

Next in Chap. 3, the atmosphere (standard and exponential) is discussed,

and an algorithm is presented for computing lift and drag of a subsonic

airplane. The engines are assumed to be given, and the thrust and specic

fuel consumption are discussed for a subsonic turbojet and turbofan. Next,

the quasi-steady ight problems of cruise and climb are analyzed in Chap. 4

for an arbitrary airplane and in Chap. 5 for an ideal subsonic airplane. In

Chap. 6, an algorithm is presented for calculating the aerodynamics of high-

lift devices, and the nonsteady ight problems of take-o and landing are

discussed. Finally, the nonsteady ight problems of energy climbs, specic

excess power, energy-maneuverability, and horizontal turns are studied in

Chap. 7.

Part II: Stability and Control. This part of the text contains static

stability and control and dynamic stability and control. It is begun in Chap.

8 with the 6DOF model in wind axes. Following the discussion of the equa-

tions of motion, formulas are presented for calculating the aerodynamics of

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