Nomenclatura Wph

Nomenclature [A]

airfoil coefficient matrix, pg 31

Am,µ dimensionless coefficient, pg 813

[A]

coefficient matrix in the generalized eigenproblem, pg 703

Anp

[ A ]ee coefficient matrix, pg 810 [ A ]eω coefficient matrix, pg 810

[ A] fv coefficient matrix, pg 809 [ A] fω coefficient matrix, pg 809 [ A ]mv coefficient matrix, pg 809 [ A ]mω coefficient matrix, pg 809

[ A] pe coefficient matrix, pg 810 [ A] pv coefficient matrix, pg 810 [ A ]w coefficient matrix, pg 809 {A} arbitrary quaternion

A

arbitrary quaternion with zero scalar component (vector)

A

complex amplitude, pg 708

Ae

engine exit area

Af

amplification factor, pg 701

Ag

dimensionless coefficient, pg 813

Ai

engine inlet area

Alp

matrix component, pg 809

Al, p( dimensionless coefficient, pg 814 Alq

matrix component, pg 809

Alr

matrix component, pg 809

Al,r(

dimensionless coefficient, pg 814

Al,α

dimensionless coefficient, pg 814

Al,β

dimensionless coefficient, pg 814

Amp

matrix component, pg 809

Amq

matrix component, pg 809

Amr

matrix component, pg 809

Am,q( dimensionless coefficient, pg 814

Am,α dimensionless coefficient, pg 814 Am,β dimensionless coefficient, pg 814

matrix component, pg 810

An, p(

dimensionless coefficient, pg 814

Anq Anr

matrix component, pg 810

An,r(

dimensionless coefficient, pg 814

matrix component, pg 810

An,α dimensionless coefficient, pg 814 An,β dimensionless coefficient, pg 814 Ap

area of prop circle

Ax

x-component of arbitrary quaternion

Ax,q(

dimensionless coefficient, pg 814

Ax,α dimensionless coefficient, pg 814 Ax,µ dimensionless coefficient, pg 813 Ay

y-component of arbitrary quaternion

Ay , p(

dimensionless coefficient, pg 814

Ay ,r( dimensionless coefficient, pg 814 Ay ,β dimensionless coefficient, pg 814 Az

z-component of arbitrary quaternion

Az ,q(

dimensionless coefficient, pg 814

Az ,α

dimensionless coefficient, pg 814

Az ,µ dimensionless coefficient, pg 813 A0

scalar-component of arbitrary quaternion

A ~ A An

aftward axial force, pg 2

An

coefficients in the infinite series solution to the lifting-line equation

a

speed of sound

aN

acceleration normal to the flight path

an

planform contribution to coefficients in the infinite series solution to Prandtl’s lifting-line equation

section axial force, pgs 2, 4 coefficients in the infinite series solution for thin airfoil theory

967

968 a0 a∞ [B ]

Nomenclature speed of sound at stagnation freestream speed of sound coefficient matrix in the generalized eigenproblem, pg 703

[B]iv coefficient matrix, pg 809 [B]m coefficient matrix, pg 809 {B}

arbitrary quaternion

B

apparent body-force vector, due to the vector sum of the acceleration of gravity and the aircraft acceleration, pg 556

[C]T transpose of direction-cosine matrix [C] f coefficient matrix, pg 810 [C]m coefficient matrix, pg 810 C

arbitrary constant

C

shorthand notation for cos(Θ/ 2)

CA ~ CA

axial force coefficient, pg 3 section axial force coefficient, pg 3

CAP control anticipation parameter, pg 840 CD ~ CD

drag coefficient, pg 3

C Dc

drag coefficient on a forward canard

section drag coefficient, pg 3

B

arbitrary quaternion with zero scalar component (vector)

B

leftward side force, pg 2

C Dh

B

drag coefficient on either an aft horizontal tail or a forward canard

arbitrary constant for stagnation flow, pg 17

C Di

induced drag coefficient

Bx

x-component of arbitrary quaternion

Bm,α ′ dimensionless coefficient, pg 813 Bm,µ ′ dimensionless coefficient, pg 813 Bx,α ′ dimensionless coefficient, pg 813 Bx,µ ′ dimensionless coefficient, pg 813 By

y-component of arbitrary quaternion

Bz

z-component of arbitrary quaternion

Bz ,α ′ dimensionless coefficient, pg 813 Bz ,µ ′ dimensionless coefficient, pg 813 B0 scalar-component of arbitrary quaternion

C DLO drag coefficient at liftoff C D ,M change in CD with respect to M ~ C DM 0 section drag coefficient at zero Mach number, pg 100

C Do

drag coefficient at the equilibrium reference state

C DOC drag coefficient at the obstacle clearance altitude

C Dp C Dt

parasitic drag coefficient

C Dw ~ C Dw

drag coefficient on the main wing

C D0

drag coefficient at zero lift

drag coefficient on an aft horizontal tail local section drag coefficient on the main wing

b b′

wingspan

bc

span of a forward canard

C D0 h drag coefficient at zero lift for either an

bh

span of either an aft horizontal tail or a forward canard

C D0 , L the linear coefficient in the parabolic

bn

washout contribution to coefficients in the infinite series solution to Prandtl’s lifting-line equation

CD0, Lh the linear coefficient in the parabolic

wingtip vortex spacing

bt

span of an aft horizontal tail

bw [C]

span of the main wing

[C]

coefficient matrix in the generalized linear control problem, pg 848 direction-cosine matrix, pg 870

aft horizontal tail or forward canard relation for drag coefficient as a function of lift coefficient

relation for drag coefficient as a function of lift coefficient for either an aft horizontal tail or forward canard

CD0, Lw the linear coefficient in the parabolic

relation for drag coefficient as a function of lift coefficient for the main wing

Nomenclature

C D0 w drag coefficient at zero lift for the main wing

C Lh 0 lift coefficient on either an aft

horizontal tail or a forward canard at zero fuselage angle of attack and zero elevator deflection

C D ,α change in drag coefficient with angle of attack

CHe

elevator hinge moment coefficient

C H e 0 elevator hinge moment coefficient with

969

C Lh ,α lift slope for either an aft horizontal tail or a forward canard

CHe ,αh change in elevator hinge moment coef-

C LLO lift coefficient at liftoff C L ,M change in CL with respect to M ~ C LM 0 section lift coefficient at zero Mach

CHe ,δe change in elevator hinge moment coef-

CLmax maximum lift coefficient

the local angle of attack, elevator deflection, and trim tab deflection at zero ficient with local angle of attack

ficient with elevator deflection

CHe ,δ t change in elevator hinge moment coefficient with trim tab deflection

CH s

stabilator hinge moment coefficient

C H s 0 stabilator hinge moment coefficient

with the local angle of attack, stabilator deflection, and elevator trim deflection at zero

CHs ,αh change in stabilator hinge moment coefficient with local angle of attack

CHs ,δ s change in stabilator hinge moment coefficient with stabilator deflection

CHs ,δ e change in stabilator hinge moment coefficient with elevator trim deflection

Cij

C& ij

components of the direction-cosine matrix time rate of change of components of the direction-cosine matrix

CL ~ CL

section lift coefficient, pg 3

C Lc

lift coefficient on a forward canard

lift coefficient, pg 3

CLcmax maximum lift coefficient for a forward canard

C Lc 0 lift coefficient on a forward canard at

zero fuselage angle of attack and zero elevator deflection

C Lc ,α lift slope for a forward canard C Ld

design lift coefficient

C Lh

lift coefficient on either an aft horizontal tail or a forward canard

CLh max maximum lift coefficient for either an aft horizontal tail or a forward canard

number, pg 97

C LOC lift coefficient at the obstacle clearance altitude

C Lt

lift coefficient on an aft horizontal tail

CLtmax maximum lift coefficient for an aft horizontal tail

C Lt 0 lift coefficient on an aft horizontal tail

at zero fuselage angle of attack and zero elevator deflection

C Lt ,α lift slope for an aft horizontal tail C Lv lift coefficient on a vertical tail C Lv ,α lift slope for a vertical tail C Lw lift coefficient on the main wing CLw max maximum lift coefficient for the main wing

C Lw 0 lift coefficient on the main wing at zero fuselage angle of attack and zero elevator deflection

C Lw ,α lift slope for the main wing ~ C Lw ,α in situ section lift slope for the main wing, including the effects of local induced downwash, pg 476

CL0

aircraft lift coefficient at zero fuselage angle of attack and zero elevator deflection

C L,α lift slope, change in lift coefficient with angle of attack

C L′ ,α stick-free change in lift coefficient with angle of attack

~ C L ,α section lift slope, change in section lift coefficient with angle of attack

C L ,δ e change in aircraft lift coefficient with elevator deflection

970

Nomenclature

Cl

aircraft rolling moment coefficient about the aircraft center of gravity, pgs 72, 441, 654

Cl

propeller torque coefficient, pg 144

Cl,M change in Cl with respect to M Cl, p change in Cl with respect to p

Cl , r

change in Cl with respect to r

Cl,β change in Cl with respect to β Cl,δ a change in Cl with respect to δa

~ Cmle

Cm,M change in Cm with respect to M ~ CmM 0 section moment coefficient at zero Mach number, pg 97

Cmnp aircraft pitching moment coefficient about the stick-fixed neutral point

Cm,q change in Cm with respect to q

Cmt

Cl,δ r change in Cl with respect to δ r Cm

aircraft pitching moment coefficient about the aircraft center of gravity, pgs 3, 654

~ Cm section moment coefficient, pg 3 ~ Cmac section moment coefficient about the pitching moment coefficient for a canard about its aerodynamic center

Cmc 0 pitching moment coefficient for a

forward canard about its aerodynamic center at zero fuselage angle of attack and zero elevator deflection

Cmc ,δ e change in forward canard pitching moment coefficient about its aerodynamic center with elevator deflection angle

~ Cmc / 4 quarter-chord section moment coefficient

Cm f Cmh

pitching moment coefficient for the fuselage about the aircraft center of gravity pitching moment coefficient for either an aft horizontal tail or a forward canard about its aerodynamic center

Cmh 0 pitching moment coefficient for either

an aft horizontal tail or a forward canard about its aerodynamic center at zero fuselage angle of attack and zero elevator deflection

Cmh ,δ e change in the pitching moment

coefficient for either an aft horizontal tail or a forward canard about its aerodynamic center with elevator deflection angle

aft horizontal tail pitching moment coefficient about its aerodynamic center

Cmt 0 aft horizontal tail pitching moment

coefficient about its aerodynamic center at zero fuselage angle of attack and zero elevator deflection

Cmt ,δ e change in aft horizontal tail pitching moment coefficient about its aerodynamic center with elevator deflection angle

aerodynamic center

Cmc

leading-edge section moment coefficient

Cmv ,δ r change in vertical tail moment

coefficient about its aerodynamic center with rudder deflection angle

Cmw

~ C mx Cm 0

wing pitching moment coefficient about its aerodynamic center section moment coefficient about point with axial coordinate x aircraft pitching moment coefficient at zero fuselage angle of attack and zero elevator deflection

Cm,α change in pitching moment coefficient with respect to angle of attack

Cm′ ,α stick-free change in pitching moment coefficient with respect to angle of attack

Cm,αˆ change in Cm with respect to αˆ ~ Cm,α change in section pitching moment coefficient with angle of attack

~ Cm,δ change in section quarter-chord moment coefficient with flap deflection, pg 38

Cm,δ e change in Cm with respect to δe Cm,µ change in Cm with respect to µ Cm,µˆ change in Cm with respect to µˆ CN

normal force coefficient, pg 3

Nomenclature

~ CN

section normal force coefficient, pg 3

CN p

propeller normal force coefficient

C N p ,α change in propeller normal force Cn

Cn f

CY ,M change in CY with respect to M CYp

aircraft yawing moment coefficient about the aircraft center of gravity, pgs 74, 441, 654

CY ,r change in CY with respect to r

yawing moment coefficient for the fuselage about the aircraft center of gravity propeller yawing moment coefficient

Cn p ,α change in propeller yawing moment coefficient with angle of attack

Cn, p change in Cn with respect to p

C n ,r

force coefficient for the yb-component of aerodynamic force, excluding thrust

coefficient with propeller angle of attack

Cn,M change in Cn with respect to M Cn p

CY

change in Cn with respect to r

Cn,α change in Cn with respect to α Cn,β change in Cn with respect to β Cn,δ a change in Cn with respect to δa Cn,δ r change in Cn with respect to δ r CP

propeller power coefficient

Cp

constant pressure specific heat

Cp

pressure coefficient, pg 31

C pl

lower surface pressure coefficient

C pM 0 pressure coefficient at zero Mach

propeller side force coefficient

CY , p change in CY with respect to p CYp ,β change in propeller side force

coefficient with sideslip angle

CY ,β change in CY with respect to β CY ,δ a change in CY with respect to δa CY ,δ r change in CY with respect to δ r CZ

force coefficient for the zb-component of aerodynamic force, excluding thrust

CZ ,M change in CZ with respect to M CZ ,q change in CZ with respect to q

CZ ,α change in CZ with respect to α CZ ,αˆ change in CZ with respect to αˆ CZ ,δ e change in CZ with respect to δe C Z ,µ change in CZ with respect to µ

CZ ,µˆ change in CZ with respect to µˆ CΘ

shorthand notation for cos(Θ )

Cθ

shorthand notation for cos(θ )

Cθo

shorthand notation for cos(θ ο )

Cθ

2

shorthand notation for cos(θ / 2) shorthand notation for cos(φ )

number, pg 97

Cφ

C pu

upper surface pressure coefficient

Cφo

shorthand notation for cos(φ ο )

CT

propeller thrust coefficient

Cφ

shorthand notation for cos(φ / 2)

CW

weight coefficient, pg 508

Cψ

shorthand notation for cos(ψ )

CX

force coefficient for the xb-component of aerodynamic force, excluding thrust

Cψ o

shorthand notation for cos(ψ ο )

C X ,M change in CX with respect to M C X ,q change in CX with respect to q C X ,α change in CX with respect to α C X ,αˆ change in CX with respect to αˆ

C X ,δ e change in CX with respect to δe C X ,µ change in CX with respect to µ C X ,µˆ change in CX with respect to µˆ

971

2

Cψ

2

shorthand notation for cos(ψ / 2)

CΩ t

shorthand notation for cos (Ω t )

c

section chord length, pg 23

c

damping coefficient, Sec. 8.1

c

mean chord length

cb

propeller blade section chord length

cˆb

dimensionless propeller blade section chord length ratio, pg 145

972

Nomenclature mean chord of a forward canard

D y ,δ a dimensionless coefficient, pg 814

ce

mean elevator chord

cf

flap chord length, pg 36

D y ,δ r dimensionless coefficient, pg 814 Dz ,δ e dimensionless coefficient, pg 814

cf

fuselage chord length, pg 417

E

modulus of elasticity

ch

mean chord of either an aft horizontal tail or a forward canard

dF

differential aerodynamic force vector

cn

df

characteristic fuselage diameter, pg 417

control surface contribution to the coefficients in the infinite series solution to Prandtl’s lifting-line equation

dl

differential vortex length vector

dn

roll contribution to the coefficients in the infinite series solution to the liftingline equation

d gc

great-circle distance or arc length measured over the Earth’s surface, pg 926

cc

cr

root chord length

ct

tip chord length

ct

mean chord of an aft horizontal tail

cv

mean chord of a vertical tail

dp

propeller diameter

cw

local chord of the main wing

dr

cw {D}

mean chord of the main wing

rhumb-line distance measured over the Earth’s surface along a path of constant bearing

d wp

great-circle distance to some waypoint, pg 927

E E

Euler axis vector, pg 872

control deflection vector in the generalized linear control problem, pg 848

{D} Laplace transform of control deflection vector in the generalized linear control problem, pg 848

D drag force, pg 2 ~ section drag force, pgs 2, 4 D Dadd additive drag, pg 191 Dc

drag on a forward canard

Dh

drag on either an aft horizontal tail or a forward canard

Di ~ Di

induced drag local section induced drag, pg 47

Dl,δ a dimensionless coefficient, pg 814 Dl,δ r dimensionless coefficient, pg 814 Dm,δ e dimensionless coefficient, pg 814 Dnac nacelle drag, pg 191 Dn,δ a dimensionless coefficient, pg 814 Dn,δ r dimensionless coefficient, pg 814 Dt

drag on an aft horizontal tail

Dv

drag on a vertical tail

Dw

drag on the main wing

Dx,δ e dimensionless coefficient, pg 814

magnitude of Euler axis vector

E

endurance or length of time an aircraft can fly without refueling

Emax maximum endurance or maximum time an aircraft can fly without refueling

Eij Eij′

Euler axis variable, pg 873

Ex

xb- and xf -component of Euler axis vector

Ey

yb- and yf -component of Euler axis vector

Ez

zb- and zf -component of Euler axis vector

{e}

Euler-Rodrigues quaternion

{e}

Euler-Rodrigues quaternion magnitude

Euler axis variable, pg 874

*

{e} {e&} e ec

Euler-Rodrigues quaternion conjugate time rate of change of the EulerRodrigues quaternion Oswald efficiency factor, pgs 224 Oswald efficiency factor for a forward canard

Nomenclature

973

eh

Oswald efficiency factor for either an aft horizontal tail or a forward canard

Fr

engine mount reaction force, pg 191

{e}r

Fr

rolling friction force

renormalized Euler-Rodrigues quaternion

FS

resultant surface force vector

et

Oswald efficiency factor for an aft horizontal tail

FSxb

xb-component of resultant surface force

FSyb

yb-component of resultant surface force

es

span efficiency factor, pgs 49, 51

FSzb

zb-component of resultant surface force

ew

Oswald efficiency factor for the main wing

Fxb

xb-component of pseudo aerodynamic force vector, including thrust

ex

xb- and xf -component of the EulerRodrigues quaternion

Fxb o

e&x

time rate of change of the xb- and xf component of the Euler-Rodrigues quaternion

equilibrium xb-component of pseudo aerodynamic force vector, including thrust

Fxb , p change in xb-component of pseudo

ey

yb- and yf -component of the EulerRodrigues quaternion

Fxb ,q change in xb-component of pseudo

e& y

time rate of change of the yb- and yf component of the Euler-Rodrigues quaternion

aerodynamic force vector, including thrust, with rolling rate aerodynamic force vector, including thrust, with pitching rate

Fxb ,r change in xb-component of pseudo

aerodynamic force vector, including thrust, with yawing rate

ez

zb- and zf -component of the EulerRodrigues quaternion

e&z

time rate of change of the zb- and zf component of the Euler-Rodrigues quaternion

e0

scalar-component of the EulerRodrigues quaternion

e&0

time rate of change of the scalarcomponent of the Euler-Rodrigues quaternion

F

pseudo aerodynamic force vector including thrust, pg 611

F

magnitude of force vector

F

uninstalled thrust, pg 191

Fa

resultant aerodynamic force vector

Fa

amplitude of sinusoidal forcing function

Fc

effective net force during transition, pg 319

Fyb

Fj

yb-component of pseudo aerodynamic force vector, including thrust

resultant force vector for a jet engine

Fp

resultant pressure force vector

Fyb o

Fp

pitch control force provided by pilot

equilibrium yb-component of pseudo aerodynamic force vector, including thrust

Fp ,n longitudinal control force per g Fp ,V control force gradient

Fxb ,u change in xb-component of pseudo

aerodynamic force vector, including thrust, with xb-component of airspeed

Fxb ,u& change in xb-component of pseudo

aerodynamic force vector, including thrust, with xb-component of aircraft acceleration

Fxb ,v change in xb-component of pseudo

aerodynamic force vector, including thrust, with yb-component of airspeed

Fxb ,w change in xb-component of pseudo

aerodynamic force vector, including thrust, with zb-component of airspeed

Fxb ,w& change in xb-component of pseudo

aerodynamic force vector, including thrust, with zb-component of aircraft acceleration

Fyb , p change in yb-component of pseudo

aerodynamic force vector, including thrust, with rolling rate

974

Nomenclature

Fyb ,q change in yb-component of pseudo

aerodynamic force vector, including thrust, with pitching rate

~ Fθ

propeller section circumferential force

f f

dimensionless force, pgs 303−304

f′ fL

dimensionless force derivative, pg 304

Fyb ,v change in yb-component of pseudo

f LO ′ f LO

dimensionless force, pg 305 dimensionless force, pg 305

Fyb ,w change in yb-component of pseudo

fS f S′

aerodynamic force vector, including thrust, with zb-component of airspeed

fT

Fzb

zb-component of pseudo aerodynamic force vector, including thrust

thrust fraction provided by a particular propeller, pg 451

[G ]

transfer-function matrix, pg 849

Fzb o

equilibrium zb-component of pseudo aerodynamic force vector, including thrust

G

dimensionless vortex strength vector

G

dimensionless vortex strength, pg 85

G

transfer function, pg 848

g

acceleration of gravity

go H H

angular momentum vector

He

aerodynamic elevator hinge moment

Hs

stabilator primary hinge moment

H xb

xb-component of angular momentum vector

H yb

yb-component of angular momentum vector

H zb

zb-component of angular momentum vector

h

angular momentum vector for all spinning rotors relative to the bodyfixed coordinate system

h

distance above the center of gravity in a direction normal to fuselage reference line

hc

distance above the center of gravity to aerodynamic center of forward canard

hh

distance above the center of gravity to aerodynamic center of either an aft horizontal tail or a forward canard

Fyb ,r change in yb-component of pseudo

aerodynamic force vector, including thrust, with yawing rate

Fyb ,u change in yb-component of pseudo

aerodynamic force vector, including thrust, with xb-component of airspeed aerodynamic force vector, including thrust, with yb-component of airspeed

Fzb , p change in zb-component of pseudo

aerodynamic force vector, including thrust, with rolling rate

Fzb ,q change in zb-component of pseudo

aerodynamic force vector, including thrust, with pitching rate

Fzb ,r change in zb-component of pseudo

aerodynamic force vector, including thrust, with yawing rate

Fzb ,u change in zb-component of pseudo

aerodynamic force vector, including thrust, with xb-component of airspeed

Fzb ,u& change in zb-component of pseudo

aerodynamic force vector, including thrust, with xb-component of aircraft acceleration

Fzb ,v change in zb-component of pseudo

aerodynamic force vector, including thrust, with yb-component of airspeed

Fzb ,w change in zb-component of pseudo

aerodynamic force vector, including thrust, with zb-component of airspeed

Fzb ,w& change in zb-component of pseudo

aerodynamic force vector, including thrust, with zb-component of aircraft acceleration

Prandtl’s tip loss factor, pg 143 local lift force vector per unit length measured along the quarter-chord line, pg 480 dimensionless force derivative, pg 305 dimensionless force derivative, pg 305

acceleration of gravity at sea level geometric altitude

Nomenclature

975

hj

distance above the aircraft center of gravity to the jet engine thrust axis

[i ]

identity matrix

hnp

ir

unit vector in the r-direction

distance above the center of gravity to the aircraft stick-fixed neutral point

ix

unit vector in the x-direction

hOC

FAR takeoff obstacle clearance altitude

i xb

unit vector in the xb-direction

hp

distance above the aircraft center of gravity to the propeller axis

ixf

unit vector in the xf -direction

iy

unit vector in the y-direction

hT

distance above the center of gravity to the center of thrust

i yb

unit vector in the yb-direction

hs

i yf

unit vector in the yf -direction

slipstream enthalpy, Chapter 2

ht

iz

unit vector in the z-direction

distance above the center of gravity to aerodynamic center of an aft horizontal tail

i zb

unit vector in the zb-direction

izf

unit vector in the zf -direction

hv

distance above the center of gravity to aerodynamic center of a vertical tail

iθ

unit vector in the θ-direction

hw

i∞

unit vector in the freestream-direction

distance above the center of gravity to aerodynamic center of the main wing

i [J ]

Jacobian matrix

J

propeller advance ratio, pg 145

K

propeller aerodynamic pitch-todiameter ratio, pg 145

Kc

propeller chord-line pitch-to-diameter ratio

Kd

proportionality constant, pg 353

KL

aeroelasticity coefficient, pg 517

Km

aeroelasticity coefficient, pg 517

KR

takeoff and landing coefficient, pg 304

KT

takeoff and landing coefficient, pg 303

KW

takeoff and landing coefficient, pg 303

K0

takeoff and landing coefficient, pg 303

hw

height of the wing above the ground, used for ground effect computations

hxb

xb-component of angular momentum vector for all spinning rotors relative to the body-fixed coordinate system

hyb

yb-component of angular momentum vector for all spinning rotors relative to the body-fixed coordinate system

hzb

zb-component of angular momentum vector for all spinning rotors relative to the body-fixed coordinate system

h∞ [I ]

freestream enthalpy, Chapter 2

I I

imaginary part of complex number local area moment of inertia

I xxb

moment of inertia, pgs 609−610

I xyb

product of inertia, pgs 609−610

I xzb

product of inertia, pgs 609−610

I yxb

product of inertia, pgs 609−610

I yyb

moment of inertia, pgs 609−610

I yzb

product of inertia, pgs 609−610

I zxb

product of inertia, pgs 609−610

I zyb

product of inertia, pgs 609−610

I zzb

moment of inertia, pgs 609−610

inertia tensor, pgs 609−610

square root of −1

K1

takeoff and landing coefficient, pg 303

K2

takeoff and landing coefficient, pg 303

k k

gain coefficient, pg 899

k k aa k ar kes k ra

number of propeller blades spring constant control system gain coefficient, pg 576 control system gain coefficient, pg 576 stabilator-elevator linkage coefficient, pg 569 control system gain coefficient, pg 576

976

Nomenclature

k rr

control system gain coefficient, pg 576

lr

kt

torsional spring constant

lref

reference length

L ~ L Lc Lh

lift force, pg 2

lt

distance aft of the center of gravity to aerodynamic center of an aft horizontal tail

ltn

distance aft of the aircraft stick-fixed neutral point to the aerodynamic center of an aft horizontal tail

lv

distance aft of the center of gravity to aerodynamic center of a vertical tail

lw

distance aft of the center of gravity to aerodynamic center of the main wing

lwn

distance aft of the aircraft stick-fixed neutral point to the aerodynamic center of the main wing

lwt

distance used to compute aerodynamic derivatives with respect to translational acceleration, pgs 667, 669

M

Mach number

section lift force, pgs 2, 4 lift on a forward canard lift on a either an aft horizontal tail or a forward canard

Lnll

minimum allowable negative lift

L pll Lt

lift on an aft horizontal tail

Lv

lift on a vertical tail

Lw

lift on the main wing

l l

source or vortex sheet length

l

propeller torque

l

rolling moment about the center of gravity excluding thrust, pgs 2, 442, 613

maximum allowable positive lift

distance aft of the center of gravity in a direction parallel to the fuselage reference line

global reference length

Mb

local bending moment

Mb

turbofan bypass exit Mach number

M cr

critical Mach number

Me

core nozzle exit Mach number

Mi

inlet Mach number

lc

distance aft of the center of gravity to aerodynamic center of a forward canard (always < 0)

lf

distance aft of the aircraft center of gravity to center of pressure of the fuselage

M∞

freestream Mach number

M

l Hs

pseudo aerodynamic moment vector including thrust effects, pg 612

stabilator hinge location

lh

[M ] coefficient matrix in rate equation for

distance aft of the center of gravity to aerodynamic center of a either an aft horizontal tail or a forward canard

lj

distance aft of the aircraft center of gravity to the jet engine inlet

lmp

distance aft of the center of gravity to the aircraft stick-fixed maneuver point

lnp

distance aft of the center of gravity to the aircraft stick-fixed neutral point

′ lnp

distance aft of the center of gravity to the aircraft stick-free neutral point

lp

distance aft of the aircraft center of gravity to the propeller

lp

propeller torque or rolling moment

the Euler-Rodrigues quaternion, pg 893

[M ] matrix of cofactors, pg 849 [M ]T transpose of matrix of cofactors, pg 849 Ma

resultant aerodynamic moment vector

MS

resultant surface moment vector

M Sxb xb-component of resultant surface moment vector

M Syb yb-component of resultant surface moment vector

M Szb zb-component of resultant surface moment vector

M xb

xb-component of pseudo aerodynamic moment vector, including thrust effects

Nomenclature

M xb o equilibrium xb-component of pseudo

M yb ,w change in yb-component of pseudo

M xb , p change in xb-component of pseudo

M yb ,w& change in yb-component of pseudo

aerodynamic moment vector, including thrust effects aerodynamic moment, including thrust effects, with rolling rate

M xb ,q change in xb-component of pseudo

aerodynamic moment, including thrust effects, with pitching rate

M xb ,r change in xb-component of pseudo

aerodynamic moment, including thrust effects, with yawing rate

M xb ,u change in xb-component of pseudo

aerodynamic moment, including thrust effects, with xb-component of airspeed

M xb ,v change in xb-component of pseudo

aerodynamic moment, including thrust effects, with yb-component of airspeed

M xb ,w change in xb-component of pseudo

aerodynamic moment, including thrust effects, with zb-component of airspeed

M yb

yb-component of pseudo aerodynamic moment vector, including thrust effects

aerodynamic moment, including thrust effects, with zb-component of airspeed

aerodynamic moment, including thrust effects, with zb-component of aircraft acceleration

M zb

aerodynamic moment vector, including thrust effects

M zb , p change in zb-component of pseudo

aerodynamic moment, including thrust effects, with rolling rate

M zb ,q change in zb-component of pseudo

aerodynamic moment, including thrust effects, with pitching rate

M zb ,r change in zb-component of pseudo

aerodynamic moment, including thrust effects, with yawing rate

M zb ,u change in zb-component of pseudo

aerodynamic moment, including thrust effects, with xb-component of airspeed

M zb ,v change in zb-component of pseudo

aerodynamic moment, including thrust effects, with yb-component of airspeed

M yb , p change in yb-component of pseudo

aerodynamic moment, including thrust effects, with rolling rate

M zb ,w change in zb-component of pseudo

aerodynamic moment, including thrust effects, with zb-component of airspeed

M yb ,q change in yb-component of pseudo

aerodynamic moment, including thrust effects, with pitching rate

M yb ,r change in yb-component of pseudo

m m

M yb ,u change in yb-component of pseudo

~ m m&

aerodynamic moment, including thrust effects, with yawing rate aerodynamic moment, including thrust effects, with xb-component of airspeed

M yb ,u& change in yb-component of pseudo

aerodynamic moment, including thrust effects, with xb-component of aircraft acceleration

M yb ,v change in yb-component of pseudo

aerodynamic moment, including thrust effects, with yb-component of airspeed

zb-component of pseudo aerodynamic moment vector, including all thrust effects

M zb o equilibrium zb-component of pseudo

M yb o equilibrium yb-component of pseudo

aerodynamic moment vector, including thrust effects

977

mass, in Sec. 7.2 and 8.1 only pitching moment about the CG excluding thrust, pgs 2, 442, 613 section pitching moment, pg 2 mass flow rate

m&

time rate of change of aircraft mass, in Sec. 7.2 only

mac

pitching moment about the aerodynamic center

m& b

turbofan mass flow rate bypassing the engine core

mc

pitching moment on a forward canard about its aerodynamic center

978 m& c

Nomenclature

nnll

negative load limit, pg 285

np

yawing moment for the propeller about the propeller center

n pll [P]

positive load limit, pg 285 panel coefficient matrix, pg 31

P

power input to a control volume

the aircraft center of gravity

PA

available propulsive power

m& e

exit mass flow rate

PA0

mh

pitching moment on either an aft horizontal tail or a forward canard about its aerodynamic center

full-throttle available power at standard sea level

Pb

brake power, torque multiplied by the angular velocity

m& i m& j ~ m

inlet mass flow rate

Pin

power input, Chapter 2

jet engine mass flow rate

Pm

power developed by a motor

leading-edge section pitching moment

PR

mt

aft horizontal tail pitching moment about its aerodynamic center

propulsive power required for steady level flight

PRmin minimum power required for steady

mv

vertical tail moment about its aerodynamic center

p

pressure

mw

wing pitching moment about its aerodynamic center

p

rolling rate (xb-component of angular rate vector ω xb ), pgs 69, 613

section pitching moment about point with axial coordinate x

p&

rolling acceleration (xb-component of angular acceleration vector)

N

summation index for finite series

p

dimensionless rolling rate, pgs 71, 558

N ~ N

upward normal force, pg 2

turbofan bypass exit pressure

section normal force, pgs 2, 4

pb pd

pressure just downstream of prop circle

Nj

jet engine upward normal force

pe

core nozzle exit pressure

turbofan mass flow rate passing through the engine core

mcg f pitching moment for the fuselage about the aircraft center of gravity

mcg j pitching moment for the jet engine about the aircraft center of gravity

mcg p pitching moment for the propeller about

le

~ m x

level flight

Np

propeller upward normal force

pi

inlet pressure

[n]

null matrix, pg 810

pl

pressure on lower surface of airfoil

n n n

unit outward normal

po

equilibrium rolling rate

load factor, lift divided by weight

ps pu

ultimate slipstream pressure

pu

pressure on upper surface of airfoil

p0

stagnation pressure

p0e

core nozzle exit stagnation pressure

yawing moment about the CG excluding thrust, pgs 2, 442, 613

n

dummy index for infinite series

ncg f

yawing moment for the fuselage about the aircraft center of gravity

ncg p

yawing moment for the propeller about the aircraft center of gravity

pressure just upstream of prop circle

p0i

inlet stagnation pressure compressor inlet stagnation pressure

nmax maximum load factor

p01 p02

nmin minimum load factor

p03

turbine inlet stagnation pressure

compressor outlet stagnation pressure

Nomenclature

979

residual

afterburner outlet stagnation pressure

R R

fan outlet stagnation pressure

RA

aspect ratio, pg 49

p0∞

freestream stagnation pressure

aspect ratio of a forward canard

p1

compressor inlet pressure

R Ac R Ah R At

aspect ratio of an aft horizontal tail

R Aw

aspect ratio of the main wing

p04

turbine outlet stagnation pressure

p05 p06

p2

compressor outlet pressure

p3

turbine inlet pressure

p4

turbine outlet pressure

p5

afterburner outlet pressure

p6

fan outlet pressure

p∞

freestream pressure

{Q} *

{Q}

turning or spin radius

aspect ratio of either an aft horizontal tail or a forward canard

Rb

turbofan bypass ratio

RDc

Dutch roll coupling ratio, pg 791

RDp

Dutch roll phase-divergence ratio, pg 791

arbitrary quaternion

RDs

Dutch roll stability ratio, pg 791

arbitrary quaternion conjugate

Rd

phugoid pitch-damping ratio, pg 745

RE

mean radius of the Earth

Req

equatorial radius of the Earth

RG

glide ratio, pg 270

RG 0

zero-wind glide ratio, pg 272

Rgx

dimensionless coefficient, pgs 559, 675

Rgy

dimensionless coefficient, pgs 559, 675

RL

lift residual

{Q} arbitrary quaternion magnitude Q& weight of fuel consumed per unit time Qx

x-component of arbitrary quaternion

Qy

y-component of arbitrary quaternion

Qz

z-component of arbitrary quaternion

Q0

scalar-component of arbitrary quaternion

Q& 2−3 combustion chamber heat addition rate Q& 4−5 afterburner heat addition rate

RL ,α change in the lift residual with α RL ,δ e change in the lift residual with δe

q

pitching rate (yb-component of angular rate vector ω yb ), pgs 505, 613

q&

pitching acceleration (yb-component of angular acceleration vector)

q

dimensionless pitching rate, pg 558

qb

Rl,δ a dimensionless coefficient, pg 675

brake-power-specific fuel consumption, pg 255

qo

equilibrium pitching rate

Rl,δ r dimensionless coefficient, pg 675 Rmax maximum range or total distance an

qP

propulsive-power-specific fuel consumption, pg 249

Rm

R

residual vector

R

Reynolds number

Rm,α change in the moment residual with α,

R

ideal gas constant

R

range or total distance an aircraft can fly without refueling

R

real part of complex number

Rl, p dimensionless coefficient, pg 675

Rl,r

dimensionless coefficient, pg 675

Rl,β

dimensionless coefficient, pg 675

aircraft can fly without refueling

moment residual

Rm,q dimensionless coefficient, pg 675 pg 402

Rm,α dimensionless coefficient, pg 675 Rm,αˆ dimensionless coefficient, pg 675 Rm,δ e change in the moment residual with δe, pg 402

980 Rm,δ e Rm,µ Rm,µˆ Rn, p Rn,r Rn,β Rn,δ a Rp Rn,δ r RP W Rs Rs RT RT W RTc RTh

RTt RTw RVhw Rx ,q Rx ,α Rx,αˆ Rx,δ e Rx , µ Rx,µˆ Ry, p R y ,r R y ,β R y ,δ a R y ,δ r Rz ,q Rz ,α Rz ,αˆ Rz ,δ e Rz ,µ

Nomenclature dimensionless coefficient, pg 675 dimensionless coefficient, pg 675 dimensionless coefficient, pg 675

Rz ,µˆ dimensionless coefficient, pg 675 R1 local lateral radius of curvature for the Earth, pg 923

R2

local longitudinal radius of curvature for the Earth, pg 923

r r r

position vector

r

yawing rate (zb-component of angular rate vector ω zb ), pgs 558, 613

dimensionless power-to-weight ratio, pg 236

r&

yawing acceleration (zb-component of angular acceleration vector)

dimensionless coefficient, pg 675 dimensionless coefficient, pg 675 dimensionless coefficient, pg 675 dimensionless coefficient, pg 675 phugoid phase-divergence ratio, pg 745 dimensionless coefficient, pg 675

position vector magnitude radial polar coordinate

outer radius of ultimate slipstream

r

dimensionless yawing rate, pg 558

phugoid stability ratio, pg 745

r

dimensionless variable, pg 378

taper ratio, pg 51

ro

equilibrium yawing rate

thrust-to-weight ratio, pg 230

rp

radial position of a streamline at the propeller outlet

rp

radius of curvature for the pull-up maneuver

rs

radial position of a streamline in the ultimate slipstream

rs

specific range, pg 257

S

planform area

S S

surface area

Sc

planform area of a forward canard

Se

planform area of elevator

Sf

maximum cross-sectional area of the fuselage

Sh

planform area of either an aft horizontal tail or a forward canard

dimensionless coefficient, pg 675

Sr

global reference area

dimensionless coefficient, pg 675

St

planform area of an aft horizontal tail

dimensionless coefficient, pg 675

Sv

planform area of a vertical tail

dimensionless coefficient, pg 675

Sw

planform area of the main wing

dimensionless coefficient, pg 675

Sθ

shorthand notation for sin(θ )

dimensionless coefficient, pg 675

Sθo

shorthand notation for sin(θ o )

dimensionless coefficient, pg 675

Sθ

dimensionless coefficient, pg 675

Sφ

taper ratio of a forward canard taper ratio of either an aft horizontal tail or a forward canard taper ratio of an aft horizontal tail taper ratio of the main wing headwind velocity ratio, pg 277 dimensionless coefficient, pg 675 dimensionless coefficient, pg 675 dimensionless coefficient, pg 675 dimensionless coefficient, pg 675 dimensionless coefficient, pg 675 dimensionless coefficient, pg 675 dimensionless coefficient, pg 675

shorthand notation for sin(Θ/ 2)

dimensionless coefficient, pg 675

2

shorthand notation for sin(θ / 2) shorthand notation for sin (φ )

Nomenclature

Sφo

shorthand notation for sin (φ o )

{T}

981

temporary quaternion, pg 880

shorthand notation for sin(φ / 2)

TA

available thrust

Sψ

shorthand notation for sin (ψ )

T A0

Sψ o

shorthand notation for sin (ψ o )

full-throttle available thrust at standard sea level

Tb

turbofan bypass exit temperature

Te

core nozzle exit temperature

Ti

inlet temperature

TLO

thrust at liftoff

TR

thrust required for steady level flight

Sφ

2

Sψ

2

shorthand notation for sin(ψ / 2)

SΩ t

shorthand notation for sin (Ω t )

s

Laplace transform variable, pg 848

s

spanwise coordinate

s

distance

s

dimensionless variable, pg 378

sa

takeoff acceleration distance

s BF

TS

static thrust

FAR balanced field length

sb

Tx

landing braking distance

x-component of temporary quaternion, pg 880

sc

distance from liftoff to obstacle clearance altitude

sef

Txb T,V

engine failure distance

sef g

Ty

ground roll distance with engine failure

y-component of temporary quaternion, pg 880

sf

landing free-roll distance

Tyb

yb-component of thrust vector

s f rr

failure recognition and reaction distance

Tz

sg

takeoff or landing ground roll distance

z-component of temporary quaternion, pg 880

sOC

FAR takeoff distance from brake release to obstacle clearance altitude

Tzb

zb-component of thrust vector

Tθ

shorthand notation for tan(θ )

sr

takeoff rotation distance

Tθo

shorthand notation for tan(θ o )

sx

sign of the x-component of the EulerRodrigues quaternion

shorthand notation for tan(φ )

sy

Tφ Tφo

sign of the y-component of the EulerRodrigues quaternion

Tψ

shorthand notation for tan(ψ )

sz

sign of the z-component of the EulerRodrigues quaternion

Tψ o

shorthand notation for tan(ψ o )

T0

experimental coefficient, pg 302

T0

scalar-component of temporary quaternion, pg 880

TRmin minimum thrust required for steady level flight

xb-component of thrust vector change in thrust with respect to airspeed

shorthand notation for tan(φ o )

s0

sign of the scalar-component of the Euler-Rodrigues quaternion

T

thrust vector

T0

stagnation temperature

T

temperature

T0b

T

turbofan bypass exit stagnation temperature

thrust

T ~ T T′

T0e

core nozzle exit stagnation temperature

average thrust

T0i

inlet stagnation temperature

T01

compressor inlet stagnation temperature

experimental coefficient, pg 302

T ′′

experimental coefficient, pg 302

T02

compressor outlet stagnation temperature

propeller section thrust force

982

Nomenclature

T03

turbine inlet stagnation temperature

Vc

rate of climb, pg 240

T04

turbine outlet stagnation temperature

Vc

canard volume ratio, pg 384

T05

afterburner outlet stagnation temperature

Vd

spin descent velocity vector

T06

Vd

design airspeed

fan outlet stagnation temperature

T0∞

Vd

spin descent velocity magnitude

freestream stagnation temperature

T1

Vd

velocity just downstream of prop circle

compressor inlet temperature

T2

exit velocity vector

compressor outlet temperature

Ve

T3

Ve

exit velocity magnitude

turbine inlet temperature

T4

turbine outlet temperature

Ve

propeller relative airspeed component, pg 179

T5

afterburner outlet temperature

Vef

engine failure airspeed

T6

fan outlet temperature

Veh

effective headwind, pg 259

T∞

freestream temperature

Vexb

xb-component of exit velocity vector

t t t tf

airfoil thickness, pg 23

Veyb

yb-component of exit velocity vector

time

Vezb

zb-component of exit velocity vector

dimensionless variable, pg 378

V f rr

failure recognition and reaction airspeed

landing free-roll time

Vg

ground speed vector

tp

period of oscillation

Vg

ground speed

tr

takeoff rotation time

horizontal velocity, pgs 271, 895

t0

Vh

dimensionless variable, pg 378

relative wind on a horizontal surface

t50

Vh

50% damping time

Vhw

headwind velocity

u u&

xb-component of airspeed vector (Vxb )

Vh

horizontal tail volume ratio, pg 357

xb-component of aircraft acceleration vector (V&xb )

ua

unit axial vector, pg 85

un

unit normal vector, pg 85

uo

equilibrium xb-component of airspeed

us

unit normal to airfoil section, pg 85

u∞

unit vector along a semi-infinite vortex

V

velocity or airspeed vector

V

velocity magnitude or airspeed

Var

aileron reversal airspeed

VBG

best glide airspeed

VBG 0 zero-wind best glide airspeed Vb

local propeller blade section relative airspeed, pg 137

Vc

spin circumferential velocity vector

Vi

inlet velocity vector

Vi

inlet velocity magnitude

Vj

jet engine exit velocity vector

Vj

jet engine exit velocity magnitude

VLO

liftoff airspeed for takeoff

VMD minimum drag airspeed VM

maneuvering speed, pg 288

VMDV minimum power airspeed VMS

minimum sink airspeed

Vmin minimum airspeed, airspeed at C L max VN

local relative normal velocity, pg 583

VOC

airspeed at obstacle clearance altitude

Vo

equilibrium airspeed magnitude

Vp

perturbation velocity vector, pg 95

Nomenclature

983

Vr

local relative wind vector, pg 583

Vθ

θ -component of velocity

Vr

r-component of velocity

Vθd

Vrs

r-component of slipstream velocity

θ -component of velocity just downstream of prop circle

Vs

sink rate, pg 269

Vθ i

Vs

θ -component of propeller induced velocity

ultimate slipstream velocity, Chapter 2

Vθ s

θ -component of slipstream velocity

V0

initial airspeed magnitude

V∞ V∞

freestream velocity vector

v v&

yb-component of airspeed vector (Vyb )

v ji

dimensionless velocity vector, pg 84

vi

dimensionless velocity vector, pg 86

vai

dimensionless axial velocity, pg 86

vni

dimensionless normal velocity, pg 86

vo

equilibrium yb-component of airspeed

v xb vx f

xb-component of arbitrary vector xf -component of arbitrary vector

v yb

yb-component of arbitrary vector yf -component of arbitrary vector

Vsmgw level-flight stall speed at maximum gross weight

Vstall stall speed, airspeed at C L max VTD

touchdown airspeed for landing

Vt

relative wind on an aft horizontal tail

Vtrim airspeed at trim

freestream velocity magnitude yb-component of aircraft acceleration vector (V&yb )

Vv

relative wind on a vertical tail

Vv

vertical velocity, pg 895

Vv

vertical tail volume ratio, pg 448

Vw

wind vector

Vw

wind speed

Vwxf

xf -component of wind vector

Vwy f

yf -component of wind vector

Vwz f

zf -component of wind vector

Vx

x-component of velocity vector

Vxb

explicit notation for xb-component of airspeed vector (u)

vy f v zb

V&xb

explicit notation for xb-component of aircraft acceleration vector (u& )

vz f

zf -component of arbitrary vector

W

weight vector

Vxd

x-component of velocity just downstream of prop circle

W

weight

Vxi

x-component of propeller induced velocity

We

gross weight with fuel tanks empty

Wf

gross weight with fuel tanks full

Vxs

x-component of slipstream velocity

Vy

y-component of velocity vector

V yb

explicit notation for yb-component of airspeed vector (v)

V&yb

explicit notation for yb-component of aircraft acceleration vector (v& )

Vz

z-component of velocity vector

Vzb

explicit notation for zb-component of airspeed vector (w)

V&zb

explicit notation for zb-component of &) aircraft acceleration vector (w

zb-component of arbitrary vector

Wmax maximum gross weight

Wxb

xb-component of weight vector

Wxbo equilibrium xb-component of weight W yb yb-component of weight vector W ybo equilibrium yb-component of weight

Wzb zb-component of weight vector Wzbo equilibrium zb-component of weight W&1−2 turbojet compressor shaft work rate

W&3−4 turbojet turbine shaft work rate w zb-component of airspeed vector (Vzb )

984

Nomenclature

& w

zb-component of aircraft acceleration vector (V&zb )

xo

dummy variable for x-integration, used in thin airfoil theory

wi

dimensionless velocity vector, pg 86

xo

wo {X}

equilibrium zb-component of airspeed

equilibrium xf -component of aircraft position vector

xT

xb-coordinate of the center of thrust for the complete aircraft, pg 655

xt

x-coordinate of the aerodynamic center of an aft horizontal tail

&} {X

state variable vector in the generalized eigenproblem, pg 703 time derivative of state variable vector in the generalized eigenproblem, pg 703

{X}

Laplace transform of the state variable vector in the generalized linear control problem, pg 848

X

xb-component of aerodynamic force vector, excluding thrust

x

aftward aerodynamic axial coordinate, pgs 2, 600

x

dimensionless aftward axial coordinate, pg 372

x

Laplace transform of x, pg 848

xu xw

x-coordinate of upper surface x-coordinate of the aerodynamic center of the main wing

Y

yb-component of aerodynamic force vector, excluding thrust

Yp

yb-component of propeller force (propeller side force)

y

upward aerodynamic normal coordinate, pgs 2, 600

y

dimensionless upward normal coordinate, pg 372

xa

atmosphere-fixed coordinate, pg 603

xac

axial coordinate of aerodynamic center

xb

forward body-fixed axial coordinate, pg 602

yˆ ya yb

xbh

xb-coordinate of the aerodynamic center of the horizontal tail or canard

ybp

xbv

xb-coordinate of the aerodynamic center of the vertical tail

spanwise distance from the center of gravity to the propeller axis, positive right, pg 451

xbw

xb-coordinate of the aerodynamic center of the main wing

yC

y-coordinate of control point

xC

x-coordinate of control point

xCG

x-coordinate of center of gravity

xcp

axial coordinate of center of pressure

xf

northward Earth-fixed coordinate, pg 602

x& f

xf -component of ground speed vector

xl

x-coordinate of lower surface

xmc

x-coordinate of maximum camber

xmp

x-coordinate of the aircraft stick-fixed maneuver point

xN

x-coordinate of nodal point

xnp

x-coordinate of the aircraft stick-fixed neutral point

yc yd yf y& f yl ymc yN yo yt yu Z Z

change of variables, pgs 97 atmosphere-fixed coordinate, pg 603 rightward body-fixed spanwise coordinate, pg 602

y-coordinate of camber line, pg 23 y-coordinate of deflected camber line eastward Earth-fixed coordinate, pg 602 yf -component of ground speed vector y-coordinate of lower surface maximum camber y-coordinate of nodal point equilibrium yf -component of aircraft position vector one-half the local airfoil thickness y-coordinate of upper surface geopotential altitude zb-component of aerodynamic force vector, excluding thrust

Nomenclature

z

leftward aerodynamic spanwise coordinate, pgs 2, 600

z′

leftward aerodynamic spanwise coordinate, pgs 463-464

z

dimensionless leftward aerodynamic spanwise coordinate, pg 372

z′

dimensionless leftward aerodynamic spanwise coordinate, pg 463

za

atmosphere-fixed coordinate, pg 603

z ar

z-coordinate of aileron root

z at

z-coordinate of aileron tip

zb

downward body-fixed normal coordinate, pg 602

zbv

985

α L0 h zero-lift angle of attack for either an aft horizontal tail or a forward canard

α L0t zero-lift angle of attack for an aft horizontal tail

α L0 w zero-lift angle of attack for the main wing

αo αp αT αT 0

equilibrium angle of attack angle of attack for the propeller axis thrust angle of attack, pg 223 thrust angle of attack at zero fuselage angle of attack, pg 655

αt

local angle of attack for an aft horizontal tail

zb-coordinate of the aerodynamic center of the vertical tail

α0 f

zf

downward Earth-fixed coordinate, pg 602

angle that the minimum drag axis of the fuselage makes with the fuselage reference line

α 0h

z& f

zf -component of ground speed vector

mounting angle for either an aft horizontal tail or a forward canard

zo

equilibrium zf -component of aircraft position vector

α0 p

angle that the propeller axis makes with the fuselage reference line

zT

zb-coordinate of the center of thrust for the complete aircraft, pg 655

mounting angle for an aft horizontal tail

zT 0

perpendicular offset between the thrust vector and the CG, pg 658

α 0t α 0w β

α

geometric angle of attack relative to the freestream (For a complete aircraft, this is defined relative to the fuselage reference line), pgs 3−4, 603

β

propeller aerodynamic pitch angle, pg 131

α& αb

βa

time rate of change of angle of attack

arctangent definition of sideslip angle commonly used for analytical estimation of aerodynamic forces and moments, pgs 603−609

α eff

local wing section angle of attack, including effects of downwash

βc

propeller chord-line pitch angle, pg 132

αf

angle of attack for the minimum drag axis of the fuselage

βe

αh

local angle of attack for either an aft horizontal tail or a forward canard

arcsine definition of sideslip angle commonly used for experimental determination of aerodynamic forces and moments, pgs 603−609

βp βt

sideslip angle for the propeller axis

αi αj α L0 α L0c

local propeller blade section angle of attack, including effects of downwash

induced angle of attack angle of attack for the jet engine axis zero-lift angle of attack zero-lift angle of attack for a forward canard

mounting angle for the main wing general linearized definition of sideslip angle commonly used for small angle of attack, pgs 442, 445, 603−609

aerodynamic pitch angle at the propeller blade tip

Γ

local section circulation vector, pg 480

Γ Γ

vortex strength wing dihedral angle, pg 475

986

Nomenclature

Γ

wing, airfoil, or propeller blade section circulation

Γ wt γ γ γ

wingtip vortex strength

vortex sheet strength per unit spanwise length

∆q

γ OC

climb angle at the obstacle clearance altitude

∆q ′

γt

strength of trailing vortex sheet per unit span

dimensionless time rate of change of disturbance in congruous dimensionless pitching rate, pg 811

∆r ∆r& ∆r

disturbance in yawing rate

climb angle, pg 239

∆q& ∆q

∆qˆ

specific heat ratio

∆Fxb disturbance in xb-component of pseudo aerodynamic force vector, including thrust

∆Fyb disturbance in yb-component of pseudo aerodynamic force vector, including thrust

∆Fzb disturbance in zb-component of pseudo aerodynamic force vector, including thrust

(

(

∆rˆ (

∆r

(

disturbance in pitching acceleration disturbance in dimensionless pitching rate, pg 673 dimensionless time rate of change of disturbance in dimensionless pitching rate, pg 674 disturbance in congruous dimensionless pitching rate, pg 811

disturbance in yawing acceleration disturbance in dimensionless yawing rate, pg 673 dimensionless time rate of change of disturbance in dimensionless yawing rate, pg 674 disturbance in congruous dimensionless yawing rate, pg 811

∆M xb disturbance in xb-component of pseudo

∆r ′

dimensionless time rate of change of disturbance in congruous dimensionless yawing rate, pg 811

∆M yb disturbance in yb-component of pseudo

∆u ∆u&

disturbance in xb-component of airspeed

∆V ∆V&

disturbance in velocity

∆v ∆v&

disturbance in yb-component of airspeed

∆w ∆w&

disturbance in zb-component of airspeed

∆Wxb ∆W yb ∆Wzb ∆x ∆x&

disturbance in xb-component of weight

∆xc

disturbance in aircraft position, pg 810

aerodynamic moment vector, including thrust effects aerodynamic moment vector, including thrust effects

∆M zb disturbance in zb-component of pseudo

aerodynamic moment vector, including thrust effects

∆mt

aerodynamic twisting moment generated by aileron deflection

∆p ∆p& ∆p

disturbance in rolling rate

∆pˆ (

∆p ( ∆p′

∆q

disturbance in rolling acceleration disturbance in dimensionless rolling rate, pg 673 dimensionless time rate of change of disturbance in dimensionless rolling rate, pg 674 disturbance in congruous dimensionless rolling rate, pg 811 dimensionless time rate of change of disturbance in congruous dimensionless rolling rate, pg 811 disturbance in pitching rate

disturbance in xb-component of aircraft acceleration vector time rate of change of disturbance in velocity disturbance in yb-component of aircraft acceleration vector disturbance in zb-component of aircraft acceleration vector disturbance in yb-component of weight disturbance in zb-component of weight disturbance in position time rate of change of disturbance in position

Nomenclature

987

∆x&c

time rate of change of disturbance in aircraft position, pg 810

∆ς y congruous dimensionless disturbance in

∆x f

disturbance in xf -component of aircraft position vector

∆ς ′y congruous dimensionless time rate of

∆x& f

disturbance in xf -component of ground speed vector

∆yc ∆y& c

disturbance in aircraft position, pg 810

∆y f

disturbance in yf -component of aircraft position vector

∆y& f

disturbance in yf -component of ground speed vector

∆z c ∆z&c

disturbance in aircraft position, pg 810

∆z f

disturbance in zf -component of aircraft position vector

∆z& f

disturbance in zf -component of ground speed vector

∆α ∆α&

disturbance in angle of attack, pg 673

∆αˆ

time rate of change of disturbance in aircraft position, pg 810

time rate of change of disturbance in aircraft position, pg 810

time rate of change of disturbance in angle of attack dimensionless time rate of change of disturbance in angle of attack, pg 673

∆α ′ congruous dimensionless time rate of change of disturbance in angle of attack, pg 811

∆β ∆βˆ

aircraft position, pg 811

change of disturbance in aircraft position, pg 811

∆ς z

congruous dimensionless disturbance in aircraft position, pg 811

∆ς ′z

congruous dimensionless time rate of change of disturbance in aircraft position, pg 811

∆θ ∆θ&

disturbance in Euler elevation angle

∆θˆ

dimensionless time rate of change of disturbance in Euler elevation angle, pg 674

∆µ

disturbance in dimensionless forward velocity, pg 673

∆µˆ

dimensionless time rate of change of disturbance in dimensionless forward velocity, pg 674

∆µ ′ congruous dimensionless time rate of change of disturbance in dimensionless forward velocity, pg 811

∆ξ x disturbance in dimensionless xf -component of aircraft position, pg 673

∆ξˆx

dimensionless time rate of change of disturbance in dimensionless xf -component of aircraft position, pg 674

disturbance in sideslip angle, pg 673

∆ξ y disturbance in dimensionless yf -com-

dimensionless time rate of change of disturbance in sideslip angle, pg 674

∆ξˆy

ponent of aircraft position, pg 673

∆β ′ congruous dimensionless time rate of ∆δ a ∆δ e ∆δ r ∆ς x

time rate of change of disturbance in Euler elevation angle

change of disturbance in sideslip angle, pg 811

∆ξ z

disturbance in aileron deflection

∆ξˆz

disturbance in elevator deflection disturbance in rudder deflection congruous dimensionless disturbance in aircraft position, pg 811

∆ς ′x congruous dimensionless time rate of change of disturbance in aircraft position, pg 811

∆φ ∆φ&

∆φˆ

dimensionless time rate of change of disturbance in dimensionless yf -component of aircraft position, pg 674 disturbance in dimensionless zf -component of aircraft position, pg 673 dimensionless time rate of change of disturbance in dimensionless zf -component of aircraft position, pg 674 disturbance in Euler bank angle time rate of change of disturbance in Euler bank angle dimensionless time rate of change of disturbance in Euler bank angle, pg 674

988 ∆ψ ∆ψ&

∆ψˆ

Nomenclature disturbance in Euler azimuth angle time rate of change of disturbance in Euler azimuth angle dimensionless time rate of change of disturbance in Euler azimuth angle, pg 674

δl

spatial vector, pg 87

δ δa δ ao δe δ e,n

flap deflection, pg 36

δ eo δ et δf δr δ ro δs δ so δ s,n δt

ε ε ε~a εb εd ε dj ε dp εd0

εd0 j εd0p

aileron deflection, pgs 69, 340, 489 equilibrium aileron deflection elevator deflection, pgs 340, 348 elevator angle per g, change in elevator deflection required to sustain each additional g of normal acceleration equilibrium elevator deflection stabilator elevator-trim setting, pg 569 local section flap deflection rudder deflection, pgs 340, 445 equilibrium rudder deflection stabilator deflection, pg 568 equilibrium stabilator deflection stabilator angle per g, change in stabilator deflection required to sustain each additional g of normal acceleration trim tab deflection, pg 526 eccentricity of the Earth, pg 923 orthogonality error, pg 899 local aileron section flap effectiveness, pgs 489-490 local propeller blade downwash angle, pg 136 downwash angle jet engine inlet downwash angle propeller downwash angle downwash angle at zero fuselage angle of attack jet engine inlet downwash angle at zero fuselage angle of attack propeller downwash angle at zero fuselage angle of attack

ε d ,α εe εf ε fi εi εr εs ε sp ε s0 ε s ,β εt εu ε u0

ε u ,α εΩ ε∞

downwash gradient, the change in downwash angle with angle of attack elevator effectiveness flap effectiveness, pg 39 ideal flap effectiveness, pg 37 local propeller blade induced angle, pg 136 rudder effectiveness sidewash angle propeller sidewash angle sidewash angle at zero sideslip angle sidewash gradient, the change in sidewash angle with sideslip angle small tolerance on the order of computer precision upwash angle upwash angle at zero fuselage angle of attack upwash gradient, the change in upwash angle with angle of attack washout effectiveness, pg 54−55 local propeller blade advance angle, pg 136

ζ

dimensionless length vector, pg 85

ζ ζ

damping ratio, pg 699

ζ η ηc

dummy variable for z-integration

ηd ηh ηh ηi ηO ηP

dimensionless propeller radial coordinate, pg 145 normal panel coordinate, pg 30 ratio of dynamic pressure on a forward canard to the freestream dynamic pressure flap deflection efficiency, pg 40 flap hinge efficiency, pg 40 ratio of dynamic pressure on either an aft horizontal tail or a forward canard to the freestream dynamic pressure ideal efficiency overall efficiency uninstalled propulsive efficiency

Nomenclature

ηp η pi ηT ηt

propulsive efficiency ideal propulsive efficiency thermal efficiency ratio of dynamic pressure on an aft horizontal tail to the freestream dynamic pressure (tail efficiency), pg 349

ηv

ratio of dynamic pressure on a vertical tail to the freestream dynamic pressure (vertical tail efficiency), pg 349

η xx η xy η xz η yx η yy η yz η zx η zy η zz Θ Θ Θ Θ wp

dimensionless coefficient, pg 813 dimensionless coefficient, pg 813 dimensionless coefficient, pg 813 dimensionless coefficient, pg 813 dimensionless coefficient, pg 813 dimensionless coefficient, pg 813 dimensionless coefficient, pg 813 dimensionless coefficient, pg 813 dimensionless coefficient, pg 813 complex phase angle, pg 708 Euler axis rotation angle angle, pg 872

ι zx ι zy κ κb

989

dimensionless coefficient, pg 675, 813 dimensionless coefficient, pg 813 Goldstein’s kappa factor, pg 142 vortex span factor in downwash computations, pgs 372−374

κD

planform contribution to the induced drag factor, pgs 49, 51, 55

κ DL

lift-washout contribution to the induced drag factor, pg 55

κ Do optimum induced drag factor, pg 58 κ DΩ washout contribution to the induced drag factor, pg 55

κL κl κ lp κp

lift slope factor, pgs 51, 55 dihedral factor, pgs 478-479 roll damping factor, pg 73 position factor in downwash computations, pgs 373−375

κs

wing sweep factor in downwash computations, pgs 376−379

κv

vortex strength factor in downwash computations, pgs 372−374 vortex sidewash factor, pg 465

θ θ

angular polar coordinate

κβ Λ Λ Λc

change of variables for the chordwise coordinate in thin airfoil theory, pg 25

Λh

θ

quarter-chord sweep angle for either an aft horizontal tail or a forward canard

change of variables for the spanwise coordinate in lifting-line theory, pg 48

Λt

θ θ&

quarter-chord sweep angle for an aft horizontal tail

Euler elevation angle, pgs 396, 619-621

Λw

quarter-chord sweep angle for the main wing

θf

λ λ

eigenvalue, pg 698

change of variables for the flap chord fraction, pg 37

θo ι xy ι xz ι yx ι yz

equilibrium Euler elevation angle

λ λc

source sheet strength per unit length

great-circle arc angle, pg 926 great-circle arc angle to some waypoint, pg 927

time rate of change of Euler elevation angle

dimensionless coefficient, pg 813 dimensionless coefficient, pg 675, 813 dimensionless coefficient, pg 813 dimensionless coefficient, pg 813

λDr λp

source strength quarter-chord sweep angle quarter-chord sweep angle for a forward canard

propeller aerodynamic pitch length, pg 132 propeller chord-line pitch length, pg 132 Dutch roll eigenvalue phugoid eigenvalue

990 λr λs λsp µ

µl µu µr ν ξ ξ ρ ρ0 ρ∞ σ σ σ Dr σp σr σs σ sp σ∞

τ τ τx

Nomenclature roll mode eigenvalue spiral mode eigenvalue short-period eigenvalue Mach angle, angle that constant potential lines make with the freestream, pg 102 lower surface Mach angle upper surface Mach angle coefficient of rolling friction kinematic viscosity

φmax φo φp φˆp φ∞ ϕ

ϕc ϕw

{χ}

surface panel coordinate, pg 30

χ

change of variables, pg 101

χ

density stagnation density freestream density damping rate, pg 698 spin axis offset angle, pg 581 Dutch roll damping rate phugoid damping rate roll mode damping rate spiral mode damping rate short-period damping rate Dutch roll damping rate with infinite roll damping throttle setting congruous dimensionless time, pg 811 dimensionless time for longitudinal motion, pg 673

τy

dimensionless time for lateral motion, pg 673

Φ Φ Φd Φ wp φ φ φ φ&

dimensionless variable, pg 21 Earth-fixed latitude, pg 922 destination latitude, pg 924 waypoint latitude, pg 927 Euler bank angle, pgs 281, 619-621 propeller aerodynamic angle, pg 180 velocity potential time rate of change of Euler bank angle

χp χq χr χα χβ χθ χµ χξ x χξ y χξ z χφ χψ

maximum bank angle equilibrium Euler bank angle perturbation velocity potential, pg 95 perturbation variable, pg 95 freestream velocity potential, pg 95 rotation angle between two body-fixed coordinate systems, pg 682 crab angle, pg 258 wind-track angle, pg 258 eigenvector, pg 703 eigenvector component normalized control surface distribution function, pg 70 eigenvector rolling rate component eigenvector pitching rate component eigenvector yawing rate component eigenvector angle of attack component eigenvector sideslip angle component eigenvector elevation angle component eigenvector axial velocity component eigenvector ξx-component eigenvector ξy-component eigenvector ξz-component eigenvector bank angle component eigenvector heading component

Ψ Ψ Ψ Ψ Ψd Ψ wp ψ

dimensionless variable, pg 21

ψ ψ&

propeller aerodynamic angle, pg 180

ψg

ground track or rhumb-line bearing, pgs 258, 924

Earth-fixed longitude, pg 922 phase angle, pg 702 relaxation factor, pg 87 destination longitude, pg 924 waypoint longitude, pg 927 Euler azimuth angle or heading, pgs 258, 619-621 time rate of change of Euler azimuth angle or heading

Nomenclature

ψ gc ψo ψw

wind direction, pg 258

Ω

vorticity vector

Ω

aircraft angular velocity vector

Ω

maximum total washout, geometric plus aerodynamic, pg 53

great-circle bearing, pg 926 equilibrium Euler azimuth angle

Ω turning or spin rate Ω max maximum turning rate Ω opt optimum total washout to minimize induced drag, pg 58

ωf ωm ωn ωnDr ωs ω xb

991

frequency of sinusoidal forcing function maximum response frequency, pg 702 undamped natural frequency, pg 699 Dutch roll undamped natural frequency ultimate slipstream angular velocity explicit notation for xb-component of aircraft angular rate vector ( p)

ω& xb

explicit notation for xb-component of aircraft angular acceleration vector ( p& )

ω yb

explicit notation for yb-component of aircraft angular rate vector ( q)

ω& yb

explicit notation for yb-component of aircraft angular acceleration vector (q& )

ω zb

explicit notation for zb-component of aircraft angular rate vector ( r)

ω

aircraft angular rate vector

ω ω ω

aircraft angular rate vector magnitude normalized washout distribution function, pg 53

ω& zb

explicit notation for zb-component of aircraft angular acceleration vector (r&)

ω ωd ωd Dr ωd p ωd sp

propeller angular velocity

ω0 ϖn

initial aircraft angular rate

control input frequency, pg 861

damped natural frequency, pg 698 Dutch roll damped natural frequency phugoid damped natural frequency short-period damped natural frequency

ϖ∞

dimensionless undamped natural frequency, pg 745 Dutch roll dimensionless undamped natural frequency with infinite roll damping