## NOMENCLATURE AND ABBREVIATIONS

This listing includes only the symbols used throughout the text or a chapter. Symbols limited to a few pages are defined when used and are not listed here.

ENGLISH NOMENCLATURE

a speed of sound; slope of lift curve, dCJda

a„ acceleration normal to flight path

a0 speed of sound at sea level; slope of lift curve, dCJda

a, slope of horizontal tail lift curve, dCLJda

av slope of vertical tail lift curve, dCLJda

a average acceleration

A projected frontal area; reference area; aspect ratio, b2/S; disc area

А в cooling baffle area

b wingspan; propeller section chord in Figure 6.11

b constant (Equation 8.32)

b2 constant (Equation 8.32)

b3 constant (Equation 8.37)

b’ span between rolled-up vortices

В (M2- 1),/2; number of propeller blades

c chord length

Cf flap chord

c0 midspan chord

*c, *tip chord

c mean aerodynamic chord or geometric mean chord

Cd section drag coefficient = D/qc

Са average section drag coefficient for propeller

CD drag coefficient for finite wing or airplane = DlqS

CDi induced drag coefficient

Cdj, parasite drag coefficient = CD for C, = 0

CDv drag coefficient for body based on volume to the two-thirds power

Cf skin friction coefficient = DlqSw

CF average skin friction coefficient for airplane

Ch hinge moment coefficient = HjqSc (S and c for control surface)

Ci section lift coefficient = Llqc rolling moment coefficient = L/qSb

Ci average section lift coefficient for propeller

CL wing or airplane lift coefficient = LlaS

CLa airplane lift coefficient at approach speed

С/ч| trim CL; CL for zero angle of attack

Cm section pitching moment coefficient = M/qc2

CM airplane pitching moment coefficient = MlqSc

Смя дСмІ dq

C„ normal force coefficient = FJqc

CN yawing moment coefficient = N/qSb

Cp pressure coefficient = (p – p«,)lq; specific heat at constant pressure

CP propeller power coefficient = Plpn3D5

Cp. induced power coefficient

Cs propeller speed-power coefficient = (pV5IPn2)il$

Ct propeller thrust coefficient = Tlpn2D4 Cv specific heat at constant volume Cx X force coefficient = XIqS CY side force coefficient = YlqS

Cz Z force coefficient = ZlqS

Cp jet momentum coefficient = mlqc or mlqS

D drag; propeller diameter; body diameter

Dc cooling drag

Df skin friction drag

Д induced drag

e Oswald’s wing efficiency factor (Equation 4.32); voltage

/ frequency, Hz; equivalent flat-plate area

fs rate of change of total energy with fuel weight, dhJdWf

F force, jet engine thrust; Prandtl’s tip loss factor (Equation 6.37)

Fe free elevator factor (Equations 8.42 and 8.46)

Fg gross jet engine thrust

Fn force normal to chord; net jet engine thrust

F0 turbojet static thrust

g acceleration due to gravity

G gain of operational amplifier; gearing (Equations 8.27 and 8.30)

h height; location of center of gravity aft of leading edge of c as a

fraction of c, height defined in Figure 2.16; propeller section thickness in Figure 6.11 /labs absolute ceiling

642 NOMENCLA TURE AND ABBREVIA TIONS he total energy of airplane per unit weight

hi location of horizontal tail aerodynamic center aft of leading edge of

c as a fraction of c

hn location of airplane neutral point aft of leading edge of c as a

fraction of c

hnw location of wing neutral point aft of leading edge of c as a fraction of c

h0 distance defined in Figure 2.2

H hinge moment

і current

ihs incidence angle of horizontal stabilizer, positive nose down

i, incidence angle of horizontal tail, positive nose down

ix dimensionless mass moment of inertia about x-axis (Equation 10.16)

ixz dimensionless mass product of inertia about x-z axes (Equation

10.16)

iy dimensionless mass moment of inertia about у-axis (Equation 10.16)

іг dimensionless mass moment of inertia about z-axis (Equation 10.16)

Ix mass moment of inertia about x-axis

Ixz mass product of inertia about x-z axes

Iy mass moment of inertia about у-axis

Iz mass moment of inertia about z-axis

J propeller advance ratio = VlnD

ke constant (Equation 8.33)

Kc correction factor (Figure 6.34a)

Kp see Equation 5.97 and Figure 5.38

Kv see Equation 5.97 and Figure 5.38

/ reference length

/ac distance defined in Figure 8.5

/, distance from center of gravity to horizontal tail aerodynamic center

l„ distance from center of gravity to vertical tail aerodynamic center

L lift; rolling moment

m airplane mass; mass flow rate; doublet strength

M pitching moment; Mach number

Mcr critical Mach number

n rotational speed, rps; load factor, LIW

N yawing moment, rpm

Np propeller yawing moment

Nj jet normal force

Nt low-pressure rotor rpm (forward compressor, aft turbine)

N2 high-pressure rotor rpm (aft compressor, forward turbine)

p static pressure; distance from leading edge of airfoil to Zmax; pro

peller pitch

p,2 total pressure at compressor inlet

ph total pressure in turbine exhaust

p dimensionless roll rate, pb/2V

рж free-stream static pressure

pa atmospheric pressure

p0 reservoir pressure; sea level atmosphere pressure

P stick force; power; roll rate

Pa power available

PB static pressure just ahead of cooling baffle

PE static pressure at engine cowling exit

Pi propeller-induced power

Pia static propeller-induced power

PN propeller normal force

Pr power required

ps excess specific power, dhjdt (Equation 7.61)

Puse useful power

Pxs excess power (Pa – Pr)

q dynamic pressure, pV2l2; source strength, point or distributed

q dimensionless pitch rate, Qcl2 V

Q volume flux; source strength; pitch rate; propeller torque

r pressure ratio for the Brayton cycle (Equation 6.69)

r0 sea level value of r

r dimensionless yaw rate, Rbl2V; radius vector from point P to

vortex element in Biot-Savart law

R universal gas constant, plpT; Reynolds number, VIIv; yaw rate;

electrical resistance; radius; radius of curvature; range Rx Reynold’s number based on x distance from leading edge

R/C rate of climb

s stick travel

sa airborne distance for takeoff or landing

S planform area; Strouhal number, fDIV; distance, reference area

Sw wetted area

t time; temperature, °С; airfoil thickness (sometimes denotes maximum

value or ratio of maximum value to c) te endurance time

t* air seconds (Equations 9.28 and 10.14)

T thrust, absolute temperature

TB temperature just ahead of cooling baffle

Tc thrust coefficient (Equation 6.22)

T0 static thrust

и x component of velocity; increment in same component above U0

й dimensionless perturbation velocity in x direction, u/U0

U0 trimmed airplane velocity; free-stream velocity

v у component of velocity

vr radial component of velocity

v„ tangential component of velocity

V local velocity; free-stream velocity

VA approach velocity

Vc velocity of climb

Vcai calibrated airspeed

Ve equivalent airspeed; resultant velocity (Figure 6.9)

VE velocity at engine cowling exit

Va ground speed

VH horizontal tail volume

V, indicated airspeed

Vlof liftoff speed

Vm volume

Vmc minimum control speed

V™ minimum unstick speed

V0 free-stream velocity

Vr resultant velocity (Figure 6.9)

VR takeoff rotation speed

Vs stalling speed

VS| stalling speed, one engine out

Vr propeller tip speed, wR

Vtr trim speed

V„ vertical tail volume

Vw wind velocity

V, critical engine failure calibrated airspeed

V2 airspeed over takeoff obstacle

V» free-stream velocity

w z component of velocity; downwash; propeller-induced velocity

wa axial component of propeller-induced velocity

w0 static value of propeller-induced velocity; impact velocity (Equation

6.60)

w, tangential component of propeller-induced velocity

W airplane weight

Wa airflow

WE airplane empty weight

Wf fuel flow rate

WP total fuel weight

Wi initial airplane weight

x cartesian coordinate, directed forward; relative radius along pro

peller blade, r/R

xh relative hub radius for propeller, rhIR

Xj distance of center of gravity aft of inlet (Figure 8.23)

x„ x-coordinate of point at which induced velocity is to be calculated

X resultant aerodynamic force on airplane in x direction

у right-handed, orthogonal coordinate directed to the right, spanwise

distance to right of airplane centerline yp у location of point at which induced velocity is to be calculated

Y resultant aerodynamic force on airplane in у direction

2 cartesian coordinate directed downward; airfoil camber (sometimes

denotes maximum value or ratio of maximum value to c) zp z location of point at which induced velocity is to be calculated

Z resultant aerodynamic force on airplane in z direction

Zj distance of jet thrust line below center of gravity

Zp distance of propeller thrust line above center of gravity

GREEK NOMENCLATURE

a angle of attack; angle defined in Biot-Savart law (Figure 2.16)

a, induced angle of attack

a0i angle of zero lift

/8 sideslip angle, angle defined in Biot-Savart law (Figure 2.16);

Prandtl-Glauert compressibility correction factor (1 — M2)l/2; blade section pitch angle

у ratio of specific heats (1.4 for air); vortex strength (point or dis

tributed)

Г wing dihedral angle; vortex strength

5 ratio of ambient pressure to sea level ambient pressure; flow

deflection angle that causes oblique shock wave; fractional increase in CD. above elliptic case; boundary layer thickness 8a aileron deflection, sum of left and right aileron angles, positive for

right aileron down, left aileron up <5e elevator angle, positive for down elevator

Sf flap angle, positive down

Sr rudder angle, positive to the left

8, trim tab angle, positive down

8* displacement thickness (Figure 4.2 and Equation 4.3)

Д denotes an increment

e wing twist (positive nose up); downwash angle; apex angle for delta

wing; drag-to-lift ratio eT wing twist at tip

ea де/da = rate of change of downwash angle with a

€p deldfi = rate of change of sidewash angle with /3

£ damping ratio

7j propeller efficiency = TV/P; correction to т (Figure 3.33)

t), ideal propeller efficiency

r), ratio of dynamic pressure at tail to free-stream g

в pitch angle; oblique shock wave angle; angle between thrust line and

horizontal; ratio of absolute ambient temperature to sea level value вс climb angle between velocity vector and horizontal

eD descent angle between velocity vector and horizontal

A taper ratio, c,/c0; also function in Figure 5.42; propeller advance

ratio, VIwR

A angle of sweepback

H coefficient of viscosity; Mach wave angle; dimensionless airplane

mass (Equations 9.31 and 10.16); coefficient of braking or rolling friction

v kinematic viscosity

p mass density

<7 ratio of mass density to sea level value; root of characteristic

equation; propeller section solidity, Bc/ttR t flap effectiveness factor (Equation 3.48 and Figure 3.32); dimension

less time, tit*; time constant (time for a damped system to reach 1/e of its initial displacement)

ф roll angle; velocity potential; resultant flow angle for propeller blade

section (Figure 6.9)

фс compressible velocity potential

фі incompressible velocity potential

фт helix angle at tip of propeller trailing vortex system

ф stream function; yaw angle

a) angular velocity or circular frequency, radians per second

at curl of velocity vector, V x V

шп undamped natural frequency, radians per second

SUBSCRIPTS

a ailerons

ac aerodynamic center

am ambient

В base; cooling baffle

c compressible; corrected

CLB climb

CR cruise

DES descent

e elevator

/ flap

HLD hold

і incompressible; index, induced, initial

jet; index

index

lower

maximum

minimum

reservoir, sea level, free-stream

optimum

horizontal tail

horizontal tail

vertical tail

winglet

wing

Any quantity may indicate differentiation with respect to quantity, for example, Cia = dCJda. quarter chord midchord

just upstream of shock wave

just downstream of shock wave

conditions far removed from body (free stream)

SUPERSCRIPTS

throat conditions where M = 1

derivative with respect to time, f, or dimensionless time, т

ABBREVIATIONS

aerodynamic center brake horsepower bypass ratio

brake specific fuel consumption |

center of pressure

center of gravity

cylinder head temperature

exhaust gas temperature

engine pressure ratio, p,7lp,2

effective shaft horsepower

Federal Aviation Administration

Federal Air Regulations

gallons per hour

in-ground effect

kt |
knots |

LE |
leading edge |

In |
natural logarithm |

MAP |
manifold absolute pressure |

NACA |
National Advisory Committee for Aeronautics |

NASA |
National Aeronautics and Space Administration |

OGE |
out-of-ground effect |

rpm |
revolutions per minute |

rps |
revolutions per second |

SFC |
specific fuel consumption |

shp |
shaft horsepower |

ТЕ |
trailing edge |

thp |
thrust horsepower |

TIT |
turbine inlet temperature |

TO |
takeoff |

TSFC |
thrust specific fuel consumption |

[1] L=f (pi —pu) dx (3.5)

J о

The moment about the leading edge, defined positive nose up, will be

MLE = -| x(pi – pu) dx (3.6)

Jo

In accord with Equation 2.12, the lift and moment can be expressed in terms of dimensionless coefficients.

**[2]** = 0.6328

Pi

[3] Taxi and takeoff allowance.

• Climb from sea level to 41,000 ft.

• Cruise at maximum cruise thrust.

• Descent to sea level.

• Land with 45-min reserve fuel.