C MO Pitching moment coefficient about aerodynamic centre of wing.. Centre of gravity position on reference chord.. hm Controls-fixed manoeuvre point position on reference chord.. 52 A
Trang 151 Symbols and notations
Table 3.4 Continued
b3 Elevator hinge moment derivative with respect
to
B Input matrix Number of blades on a propeller
c Wing chord Viscous damping coefficient Pitot tube coefficient
c0 Root chord
ct Tip chord
c y Local chord at spanwise co-ordinate y.
cg Centre of gravity
cp Centre of pressure
C Output matrix
CC Coefficient of contraction
C D Total drag coefficient
C DO Zero lift drag coefficient
Cf Frictional drag coefficient
C L Lift coefficient
C LW Wing lift coefficient
C LT Tailplane lift coefficient
C H Elevator hinge moment coefficient
C m Pitching moment coefficient
C MO Pitching moment coefficient about aerodynamic centre of wing
C n Yawing moment coefficient
C p Pressure coefficient Power coefficient for propellers
C R Resultant force coefficient
C v Coefficient of velocity
CP Centre of pressure
D Drag Propeller diameter
D' Drag in a lateral-directional perturbation
D Direction cosine matrix Direct matrix
Dc Camber drag
D f Friction drag
D p Pressure drag
D Incidence drag
f Coefficient of friction
F Aerodynamic force Feed-forward path transfer function Fractional flap chord
Fc Aerodynamic force due to camber
Fr Froude number
F Aerodynamic force due to incidence
F Elevator control force
g Acceleration due to gravity
G Controlled system transfer function
h Height Centre of gravity position on reference chord Enthalpy (specific)
h0 Aerodynamic centre position
hF Fin height co-ordinate above roll axis
hm Controls-fixed manoeuvre point position on reference chord
h' m Controls-free manoeuvre point position on reference chord
Trang 252 Aeronautical Engineer’s Data Book
Table 3.4 Continued
hn Controls-fixed neutral point position on reference chord
h' n Control-free neutral point position on reference chord
H Hinge moment Feedback path transfer function Total pressure Shape factor
HF Fin span measured perpendicular to the roll axis
H m Controls fixed manoeuvre margin
H" m Controls free manoeuvre margin
i x Moment of inertia in roll (dimensionless)
i y Moment of inertia in pitch (dimensionless)
i z Moment of inertia in yaw (dimensionless)
I" Normalized inertia
I x Moment of inertia in roll
I y Moment of inertia in pitch
I z Moment of inertia in yaw
J Propeller ratio of advance Moment of inertia
j (or i) The imaginary operator (–1)
k Spring stiffness coefficient Lift-dependent drag factor Interference factor
k cp Centre of pressure coefficient
k d Cavitation number
k Pitch rate transfer function gain constant
M
M
M
M
L
L
L
L
L
l
l
l
K
K
k
k
k
k q u Axial velocity transfer function gain constant
w Normal velocity transfer function gain constant
Pitch attitude transfer function gain constant Turbo-jet engine gain constant
K Feedback gain Circulation Bulk modulus
K Feedback gain matrix
0 Circulation at wing mid-section
n Controls-fixed static stability margin
K' n Controls-free static stability margin
l Lift per unit span
d Disc loading (helicopter)
f Fin arm
t Tail arm
L Lift Rolling moment Temperature lapse rate
c Lift due to camber
w Wing lift
F Fin lift
T Tailplane lift
Lift due to incidence
m Mass Strength of a source or sink (fluid mechanics) Hydraulic depth
m' Rate of mass flow
M Mach number
0 Free stream Mach number
crit Critical Mach number
M Pitching moment
0 Wing–body pitching moment
Tailplane pitching moment
Trang 353 Symbols and notations
Table 3.4 Continued
n Frequency Number of revs per second
Polytropic exponent
N Yawing moment
P
P
P
o
p
P
0
s
t
q
Discharge quantity
Q Dynamic pressure
r Yaw rate perturbation General response variable Radius vector
R Radius of turn Resultant force Characteristic gas constant
Re Reynolds number
s Wing semi-span Laplace operator Specific
U
U
T
T
S
S
S
S
B
F
T
t
T
r
s
u
u
U
e
E
V
V
v
v
V
e
E
V
V
V
V
V0
F
R
S
T
V
w
W
W
W
e
E
path earth axes
Trang 454 Aeronautical Engineer’s Data Book
Table 3.4 Continued
y
x
x
X
y
B
y
Y
z
ordinate
z Transformed state vector
Z Normal force component
Greek symbols
'
e
T
e
e
of vortex
Airfoil section camber Boundary layer thickness
m Mass increment
Throttle lever angle Downwash angle
Rudder angle perturbation Damping ratio
e
(polar) Propeller helix angle
Eigenvalue Wavelength Friction coefficient in a
µ
µ
µ
1
2
b
Trang 555 Symbols and notations
Table 3.4 Continued
Subscripts
0 Datum axes Normal earth-fixed axes
Straight/level flight Free stream flow conditions Sea level
1/4
2
∞
a
b
c
D
e
E
F
g
h
H
i
l
LE
L
m
n
n
p
p
q
r
r
s
Stagnation Surface
t Tangential
TE Trailing edge
T Tailplane
u Axial velocity
v Lateral velocity
V Vertical
w Normal velocity
x ox axis
y oyaxis
z ozaxis
Angle of attack or incidence
Throttle lever
Elevator
Pitch
Ailerons
Thrust
Trang 656 Aeronautical Engineer’s Data Book
3.5 The International Standard
Atmosphere (ISA)
The ISA is an internationally agreed set of assumptions for conditions at mean sea level and the variations of atmosphere conditions with altitude In the troposphere (up to
11 000 m), temperature varies with altitude at
a standard lapse rate L, measured in K (or °C)
per metre Above 11 000 m, it is assumed that temperature does not vary with height (Figure 3.1)
So, in the troposphere:
Temperature variation is given by:
T = T0– Lh
Pressure is given by:
where T
T2
T1
p2
p1 = 5.256
= temperature at an altitude h (m)
sea level (K)
L = lapse rate in K/m
p = pressure at an altitude
The lapse rate L in the ISA is 6.5 K/km
The ‘tropopause’
16
2
4
6
8
10
12
14
The stratosphere:
temperature does not
The troposphere:
temperature lapse rate L = 6.5˚C/km vary with height
Temperature, ˚C
Fig 3.1 The ISA; variation of temperature with altitude
Trang 757 Symbols and notations
In the stratosphere T = TS = constant so:
p2 2
where R is the universal gas constant: R =
287.26 J/kg K
Table 3.5 shows the international standard atmosphere (ISA) Table 3.6 shows the lesser used US (COESA) standard atmosphere
Table 3.5 International standard atmosphere (sea level conditions)
Property Metric value Imperial value Pressure (p) 101 304 Pa 2116.2 lbf/ft2 Density () 1.225 kg/m3 0.002378 slug/ft3
Temperature (t) 15°C or 288.2 K 59°F or 518.69°R
Speed of sound (a) 340 m/s 1116.4 ft/s
Viscosity (µ) 1.789 10–5 3.737 10–7
kg/m s slug/ft s Kinematic viscosity 1.460 10–5 1.5723 10–4
Thermal conductivity 0.0253 J/m s/K 0.01462 BTU/ft
h°F
Gas constant (R) 287.1 J/kg K 1715.7 ft
lb/slug/°R
Specific heat (Cp) 1005 J/kg K 6005 ft lb/slug/°R
Specific heat (Cv) 717.98 J/kg K 4289 ft lb/slug/°R Ratio of specific 1.40 1.40
heats (
Gravitational 9.80665 m/s2 32.174 ft/s2
acceleration (g)
Trang 8Table 3.5 Continued
Altitude Temperature Pressure ratio Density ratio Dynamic Kinematic a
(°C) (p/p o ) ( / o ) viscosity ratio viscosity ratio (m/s)
Trang 92438 8000 –0.6 0.7428 0.7860 0.9567 1.2172 330.8
Trang 10Table 3.5 Continued
Altitude Temperature Pressure ratio Density ratio Dynamic Kinematic a
(°C) (p/p o ) ( / o ) viscosity ratio viscosity ratio (m/s)
Trang 117924 26000 –36.3 0.3552 0.4325 0.8548 1.9766 308.4
Trang 12Table 3.5 Continued
Altitude Temperature Pressure ratio Density ratio Dynamic Kinematic a
(°C) (p/p o ) ( / o ) viscosity ratio viscosity ratio (m/s)
Trang 1315544 51000 –56.3 0.1091 0.1451 0.7947 5.4773 295.1
Trang 14Table 3.6 US/COESA atmosphere (SI units)
Alt
(km) /o p/p o t/t o temp
(K)
press
(N/m 2 )
dens
(kg/m 3 )
a (m/s)
µ (10 –6 kg/ms)
(m 2 /s)
–2 1.2067E+0 1.2611E+0 1.0451 301.2 1.278E+5 1.478E+0 347.9 18.51 1.25E–5
0 1.0000E+0 1.0000E+0 1.0000 288.1 1.013E+5 1.225E+0 340.3 17.89 1.46E–5
2 8.2168E–1 7.8462E–1 0.9549 275.2 7.950E+4 1.007E+0 332.5 17.26 1.71E–5
4 6.6885E–1 6.0854E–1 0.9098 262.2 6.166E+4 8.193E–1 324.6 16.61 2.03E–5
6 5.3887E–1 4.6600E–1 0.8648 249.2 4.722E+4 6.601E–1 316.5 15.95 2.42E–5
8 4.2921E–1 3.5185E–1 0.8198 236.2 3.565E+4 5.258E–1 308.1 15.27 2.90E–5
10 3.3756E–1 2.6153E–1 0.7748 223.3 2.650E+4 4.135E–1 299.5 14.58 3.53E–5
12 2.5464E–1 1.9146E–1 0.7519 216.6 1.940E+4 3.119E–1 295.1 14.22 4.56E–5
14 1.8600E–1 1.3985E–1 0.7519 216.6 1.417E+4 2.279E–1 295.1 14.22 6.24E–5
16 1.3589E–1 1.0217E–1 0.7519 216.6 1.035E+4 1.665E–1 295.1 14.22 8.54E–5
18 9.9302E–2 7.4662E–2 0.7519 216.6 7.565E+3 1.216E–1 295.1 14.22 1.17E–4
20 7.2578E–2 5.4569E–2 0.7519 216.6 5.529E+3 8.891E–2 295.1 14.22 1.60E–4
22 5.2660E–2 3.9945E–2 0.7585 218.6 4.047E+3 6.451E–2 296.4 14.32 2.22E–4
24 3.8316E–2 2.9328E–2 0.7654 220.6 2.972E+3 4.694E–2 297.7 14.43 3.07E–4
26 2.7964E–2 2.1597E–2 0.7723 222.5 2.188E+3 3.426E–2 299.1 14.54 4.24E–4
28 2.0470E–2 1.5950E–2 0.7792 224.5 1.616E+3 2.508E–2 300.4 14.65 5.84E–4
30 1.5028E–2 1.1813E–2 0.7861 226.5 1.197E+3 1.841E–2 301.7 14.75 8.01E–4
32 1.1065E–2 8.7740E–3 0.7930 228.5 8.890E+2 1.355E–2 303.0 14.86 1.10E–3
34 8.0709E–3 6.5470E–3 0.8112 233.7 6.634E+2 9.887E–3 306.5 15.14 1.53E–3
36 5.9245E–3 4.9198E–3 0.8304 239.3 4.985E+2 7.257E–3 310.1 15.43 2.13E–3
Trang 1538 4.3806E–3 3.7218E–3 0.8496 244.8 3.771E+2 5.366E–3 313.7 15.72 2.93E–3
40 3.2615E–3 2.8337E–3 0.8688 250.4 2.871E+2 3.995E–3 317.2 16.01 4.01E–3
42 2.4445E–3 2.1708E–3 0.8880 255.9 2.200E+2 2.995E–3 320.7 16.29 5.44E–3
44 1.8438E–3 1.6727E–3 0.9072 261.4 1.695E+2 2.259E–3 324.1 16.57 7.34E–3
46 1.3992E–3 1.2961E–3 0.9263 266.9 1.313E+2 1.714E–3 327.5 16.85 9.83E–3
48 1.0748E–3 1.0095E–3 0.9393 270.6 1.023E+2 1.317E–3 329.8 17.04 1.29E–2
50 8.3819E–4 7.8728E–4 0.9393 270.6 7.977E+1 1.027E–3 329.8 17.04 1.66E–2
52 6.5759E–4 6.1395E–4 0.9336 269.0 6.221E+1 8.055E–4 328.8 16.96 2.10E–2
54 5.2158E–4 4.7700E–4 0.9145 263.5 4.833E+1 6.389E–4 325.4 16.68 2.61E–2
56 4.1175E–4 3.6869E–4 0.8954 258.0 3.736E+1 5.044E–4 322.0 16.40 3.25E–2
58 3.2344E–4 2.8344E–4 0.8763 252.5 2.872E+1 3.962E–4 318.6 16.12 4.07E–2
60 2.5276E–4 2.1668E–4 0.8573 247.0 2.196E+1 3.096E–4 315.1 15.84 5.11E–2
62 1.9647E–4 1.6468E–4 0.8382 241.5 1.669E+1 2.407E–4 311.5 15.55 6.46E–2
64 1.5185E–4 1.2439E–4 0.8191 236.0 1.260E+1 1.860E–4 308.0 15.26 8.20E–2
66 1.1668E–4 9.3354E–5 0.8001 230.5 9.459E+0 1.429E–4 304.4 14.97 1.05E–1
68 8.9101E–5 6.9593E–5 0.7811 225.1 7.051E+0 1.091E–4 300.7 14.67 1.34E–1
70 6.7601E–5 5.1515E–5 0.7620 219.6 5.220E+0 8.281E–5 297.1 14.38 1.74E–1
72 5.0905E–5 3.7852E–5 0.7436 214.3 3.835E+0 6.236E–5 293.4 14.08 2.26E–1
74 3.7856E–5 2.7635E–5 0.7300 210.3 2.800E+0 4.637E–5 290.7 13.87 2.99E–1
76 2.8001E–5 2.0061E–5 0.7164 206.4 2.033E+0 3.430E–5 288.0 13.65 3.98E–1
78 2.0597E–5 1.4477E–5 0.7029 202.5 1.467E+0 2.523E–5 285.3 13.43 5.32E–1
80 1.5063E–5 1.0384E–5 0.6893 198.6 1.052E+0 1.845E–5 282.5 13.21 7.16E–1
82 1.0950E–5 7.4002E–6 0.6758 194.7 7.498E–1 1.341E–5 279.7 12.98 9.68E–1
84 7.9106E–6 5.2391E–6 0.6623 190.8 5.308E–1 9.690E–6 276.9 12.76 1.32E+0
86 5.6777E–6 3.6835E–6 0.6488 186.9 3.732E–1 6.955E–6 274.1 12.53 1.80E+0 65
Trang 16Section 4
Aeronautical definitions
4.1 Forces and moments
Forces and moments play an important part in the science of aeronautics The basic definitions are:
Weight force (W)
Weight of aircraft acting vertically downwards
Aerodynamic force
Force exerted (on an aircraft) by virtue of the diversion of an airstream from its origi nal path It is divided into three compo nents: lift, drag and lateral
Lift force (L)
Force component perpendicularly ‘upwards’
to the flight direction
Drag force (D)
Force component in the opposite direction
to flight Total drag is subdivided into
pressure drag and surface friction drag
Pressure drag
Force arising from resolved components of normal pressure Pressure drag is sub divided into boundary layer pressure or
form drag, vortex or induced drag, and wave
drag
Surface friction drag
Force arising from surface or skin friction between a surface and a fluid
Pitching moment (M)
Moment tending to raise the nose of an aircraft up or down It acts in the plane defined by the lift force and drag force
Trang 1767 Aeronautical definitions
Lift force (L)
D) Pitching moment (+M)
W
Drag force ( Aircraft climbing
L
Rolling moment (LR)
moment (N)
W
D Yawing
Lift (+L)
x
Nose yaws to right (+N)
Drag (+ Lateral (+
y
Left wing
up (+LR)
Nose pitches
up (+M)
Fig 4.1 Forces, moments and motions
Trang 1868 Aeronautical Engineer’s Data Book
Moment tending to roll an aircraft about its nose-to-tail axis (i.e to raise or lower the wing tips)
Yawing moment (N)
Moment tending to swing the nose of an aircraft to the left or right of its direction of flight
Figure 4.1 shows the basic sign conventions that are used Motions are often also referred to by
their relation to x-, y-, z-axes: See Table 4.1
Table 4.1 The general axis system
inertia displacement
Trang 19Aeronautical definitions 69
Vertical tail arm
Wheelbase
Wing leading edge Wing trailing edge
Tip chord
LE sweep angle
1 / 4 chord
sweep angle
Mean aerodynamic
chord (MAC)
LE sweep angle
Front fuselage
Mean aerodynamic tail chord (MAC)
Root chord Centre of gravity
Tail span
Wing dihedral Γ
Wheel track Upper surface
Chord line Camber line
Lower surface Leading edge
Trailing edge
Fig 4.2 Basic aircraft terminology
Trang 20
70 Aeronautical Engineer’s Data Book
4.2 Basic aircraft terminology
Table 4.2 Basic aircraft terminology (see also Figure 4.2)
Aspect ratio (A) A measurement of the
‘narrowness’ of the wing form Camber line A line joining the locus of points
situated midway between the upper and lower surfaces of a wing
Dihedral (2) Upward or downward (anhedral)
angle of the wing
Leading edge (LE) Front edge of the wing
Mean aerodynamic A chord parameter defined as:
chord (MAC) (c
c
)A
+s
2 dy –s
+s cdy –s
Root chord (cO) Chord length of the wing where
it meets the fuselage
Standard mean A chord parameter given defined chord (SMC) or as
Geometric mean c = SG/b or SN/b
chord (c)
+s cdy –s
= +s
dy –s
Sweepback ( or ) Lateral orientation of a wing
measured between the lateral
(y) axis and the wing leading
edge LE or LE), or the 1/4 chord position (1/4 or 1/4), or the wing trailing edge (TE or
TE)
Tip chord (ct) Chord length of the wing at its
tip
Trailing edge (TE) Rear edge of the wing
Wing (gross) area (SG) The plan area of the wing,
inclusive of the continuation within the fuselage
Wing (net) area (SN) The plan area of the wing
excluding any continuation within the fuselage
Wing plan form The shape of the plan view of the
wing
Wingspan (b) Distance between the extreme
tips of the wings
... 5.2158E? ?4 4.7700E? ?4 0.9 145 263.5 4. 833E+1 6.389E? ?4 325 .4 16.68 2.61E–256 4. 1175E? ?4 3.6869E? ?4 0.89 54 258.0 3.736E+1 5. 044 E? ?4 322.0 16 .40 3.25E–2
58 3.2 344 E? ?4 2.8 344 E? ?4 0.8763 252.5... 2.9328E–2 0.76 54 220.6 2.972E+3 4. 694E–2 297.7 14. 43 3.07E? ?4
26 2.7964E–2 2.1597E–2 0.7723 222.5 2.188E+3 3 .42 6E–2 299.1 14. 54 4.24E? ?4
28 2. 047 0E–2 1.5950E–2 0.7792 2 24. 5 1.616E+3... 3.962E? ?4 318.6 16.12 4. 07E–2
60 2.5276E? ?4 2.1668E? ?4 0.8573 247 .0 2.196E+1 3.096E? ?4 315.1 15. 84 5.11E–2
62 1.9 647 E? ?4 1. 646 8E? ?4 0.8382 241 .5 1.669E+1 2 .40 7E? ?4 311.5 15.55 6 .46 E–2
64