Mô tả:
Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
The Atmosphere,
Aerodynamic and Airplane
Nomenclatures
Ngô Khánh Hiếu
1
Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
Basic definitions (1/8)
Pressure:
- Is the normal force per unit area acting on the
fluid.
- Static pressure is the pressure of the air above
the elevation being considered.
- to distinguish it from the total and dynamic
pressures, the actual pressure of the fluid,
which is associated not with its motion but with
its state, is often referred to as the static
pressure, but where the term pressure alone is
used it refers to this static pressure.
- Bernoulli’s equation for incompressible fluids:
1
ρV 2 + p = pT
2
p : “free-stream pressure”, static pressure
- Standard atmospheric pressure at sea-level is
defined as the pressure that can support a
column of mercury 760 mm in length. So, its
value is 1.01325 105 N/m2 (or 2116.22 Ib/ft2).
- The ratio of the pressure P at altitude to sealevel standard pressure Po is:
δ=
- The equation of state:
P = ρ RT
where: R = 287 J/kgoK
- Many pressure gages indicate the difference
between the absolute pressure and the
atmospheric pressure existing at the gage
(gage presssure).
pT: total pressure (Stagnation pressure)
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P
P0
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Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
Basic definitions (2/8)
Temperature:
- Is an abstract concept but can be thought of as
a measure of the motion of molecular particles
within a substance.
- The temperatures are measured using the
absolute Kelvin or Rankin scales.
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TF = TC + 32
5
TK = TC + 273.15 =
TR = TF + 459.67
5
( TF + 459.67 )
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- The temperature of atmosphere varies
significantly with altitude. The ratio of ambient
temperature at altitude, T, to a sea-level
standard value, To, is denoted by :
θ=
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T
T0
The altitude (h) used in ISA standard
atmosphere is “Geopotential altitudes” (not
“Geometric altitudes”).
hgeometric =
hgeopotential Rearth
Rearth − hgeopotential
However, the difference between these two
altitudes at 30 km is about 0.5%.
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Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
Basic definitions (3/8)
Density:
Variation of density
with temperature for
water (ref. Wikipedia)
Mass
ρ=
Unit volume
From the equation of state, it can be seen that
the density of a gas is directly proportional to
the pressure and inversely proportional to the
absolute temperature.
For vehicles that are flying at approximately 100
m/s or less, the density of the air flowing past
the vehicle is assumed constant.
Variation of density
with temperature for
air (ref. Wikipedia)
The ratio of ambient air density ( ) to standard
sea-level air density ( o) is given by :
σ=
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ρ
ρ0
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Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
Basic definitions (4/8)
Viscosity:
- Viscosity can be thought of as the internal
friction of a fluid.
- In all real fluids, a shearing deformation is
accompanied by a shearing stress. The
shearing stress is proportional to the rate of
shearing deformation. The constant of
proportionality is called the coefficient of
viscosity ( , kg/m.s).
τ =µ
υ=
- Kinematic viscosity:
u
y
-
The unit of kinematic viscosity is stokes.
1 stokes = 100 centistokes = 0.00001
m2/s
1 centistokes = 1 mm2/s
: Dynamic viscosity
- For temperatures below 3000 K, the dynamic
viscosity of air is independent of pressure. So,
it can be calculated by the Sutherland’s
equation:
� T 2
�
−6
�
µ = 1.458 10 �
�T + 110.4 �
�
�
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µ
ρ
(ref. Wikipedia)
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Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
Basic definitions (5/8)
Mach number:
M=
V
a
- The speed of sound is established by the properties of the fluid. For a perfect gas:
a = γ RT
- The aerodynamic characteristics of an airplane depend on the flow regime around the airplane.
As the flight Mach number is increased, the flow around the airplane can be completely
subsonic, a mixture of subsonic and supersonic flow or completely supersonic.
- The flight Mach number is used to classify the various flow regimes. An approximate
classification of the flow regimes follows:
Incompressible subsonic flow
0 < M < 0.3
Compressible subsonic flow
0.3 < M < 0.8
Transonic flow
0.8 < M < 1.2
Supersonic flow
1.2 < M < 5.0
Hypersonic flow
5.0 < M
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6
Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
Basic definitions (6/8)
Pressure variation in a static fluid medium: If fluid particles are either all at rest or all moving with
the same velocity, the fluid is said to be a static medium. Since there is no relative motion between
adjacent layers of the fluids, there are no shear forces. The only forces acting on the surface of the
fluid elements are pressure forces.
- Consider the small fluid element whose center is defined by the coordinates x, y, z.
dP
gdz
=
−
�P �
RT
- For air, the earth’s mean atmosphere
temperature decreases almost linearly with z
up to an altitude of nearly 11000 m. We
obtain:
g / RB
� Bz �
P = Po �
1−
�
T
� o �
5.26
� Bz �
= Po �
1−
�
T
� o �
where: B = 0.0065 K/m; To = 288.15 K
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7
Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
Basic definitions (7/8)
The standard atmosphere: The basis for establishing a standard atmosphere is a defined variation
of temperature with altitude. In reality, variations would exist from one location on the earth to
another and over seasons at a given location. A standard atmosphere is a valuable tool that
provides engineers with a standard when conducting analyses and performance comparisons of
different aircraft design.
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Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
Basic definitions (8/8)
Bernoulli’s equation for a compressible fluid:
P = c.ρ γ
- If the flow can be assumed to be isentropic,
2
2
2
dP
VdV
=
−
− g�
dz
�
�
ρ
1
1
1
γ P 1 2
+ V + gz = constant
γ −1 ρ 2
- For perfect gas,
a 2 = γ RT = γ . P
ρ
1
� �
�2
�
2 �P0 �
�
V = a� �
− 1�
�
�
�
�
�
γ −1�
�P �
�
� �
�
γ −1
γ
γ −1
γ
P0: stagnation pressure
1
� �
�2
�
V
2 �P0 �
�
M = =� �
− 1�
�
�
�
�
a �
γ −1�
�P �
�
� �
�
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These two equations can be used with
M<1
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Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures
The atmosphere (1/2)
- Troposphere: h
θ=
11000 m
T
B
= 1+ h
T0
T0
P
−g
δ = = θ BR
P0
− ( 1+ g
ρ
BR )
σ=
=θ
ρ0
- Troposphere: 11000 m
h
20000 m
θ = θ1
δ = δ1.e
−( h − h1 ) g
RT1
�δ1 � −( h − h1 ) g RT1
σ =� �
.e
θ1 �
�
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