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its about aeroplanes
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Chapter - 4
1 by Shiva U Asst. Prof. AAE Dept.
Significance of speed of sound, Air speed and Ground
Speed, Properties of Atmosphere, Bernoullis Equation, Forces on the Airplane, Airflow over wing section, pressure
distribution over a wing section, Generation of lift, Drag,
Pitching moments, Types of Drag, Lift curve, Drag curve,
Lift/Drag Ratio curve, Factors affecting lift and Drag, center
of pressure and its effects, Airfoil Nomenclature, Types of
Aerofoil, Wing section-Aerodynamic center, Aspect ratio,
Effects of lift, Drag, Speed, Air Density on Drag.
2 by Shiva U Asst. Prof. AAE Dept.
Significance of Speed of Sound
The speed of "sound" is actually the speed of transmission of a small disturbance through a medium.
Sound itself is a sensation created in the human brain in
response to sensory inputs from the inner ear.
3 by Shiva U Asst. Prof. AAE Dept.
As a general rule Air is compressible Medium. When a disturbance producing an infinitesimal pressure change
is generates at some point in the flow, this disturbance
will be propagated throughout the air as a pressure
wave travelling at the speed of sound.
Knowing the magnitude of the speed of the sound is important. If the flow velocity exceeds the propagation
speed of disturbances, these disturbances will pile up
to form strong waves, called shock waves.
These shock waves in turn produce large changes in flow properties. One important consequence of all this
is an increase in drag.
4 by Shiva U Asst. Prof. AAE Dept.
Pressure-pulse or compression-type wave (longitudinal wave) confined to a plane. This is the only type of sound
wave that travels in fluids (gases and liquids)
5 by Shiva U Asst. Prof. AAE Dept.
Transverse wave affecting atoms initially confined to a plane. This additional type of sound wave (additional type
of elastic wave) travels only in solids, and the sideways
shearing motion may take place in any direction at right
angles to the direction of wave-travel (only one shear
direction is shown here, at right angles to the plane).
Furthermore, the right-angle shear direction may change
over time and distance, resulting in different types of
polarization of shear-waves
6 by Shiva U Asst. Prof. AAE Dept.
Wave Simulation
7 by Shiva U Asst. Prof. AAE Dept.
Airspeed Airspeed is the speed of an aircraft relative to the air.
Among the common conventions for qualifying airspeed are: indicated airspeed ("IAS"), calibrated airspeed ("CAS"), true airspeed ("TAS"), equivalent airspeed ("EAS") and density airspeed.
Indicated airspeed (IAS) is the airspeed indicator reading (ASIR) uncorrected for instrument, position, and other errors.
Calibrated airspeed (CAS) is indicated airspeed corrected for instrument errors, position error (due to incorrect pressure at the static port) and installation errors.
Equivalent airspeed (EAS) is defined as the speed at sea level that would produce the same incompressible dynamic pressure as the true airspeed at the altitude at which the vehicle is flying.
True airspeed (TAS) is the speed of the aircraft relative to the atmosphere.
8 by Shiva U Asst. Prof. AAE Dept.
9
Ground Speed Groundspeed is the speed of the aircraft relative to the
ground rather than through the air, which can itself be
moving.
by Shiva U Asst. Prof. AAE Dept.
10 by Shiva U Asst. Prof. AAE Dept.
Standard Atmosphere
What we call a Standard Atmosphere is a mathematical abstraction of the real atmosphere
A standard atmosphere can be thought of as the mean or average conditions of temperature, pressure and
density for given altitudes
This model allows engineers to estimate atmospheric conditions for use in design and analysis
There are different standard atmospheres in use: 1959 ARDC Model Atmosphere
U.S. Standard Atmosphere, 1962
ICAO Standard Atmosphere
11 by Shiva U Asst. Prof. AAE Dept.
Need to define what we mean by altitude first
Absolute Altitude, ha, is the height above the earths center
Geometric Altitude, hG, is the height above sea level.
Geopotential Altitude, h A mathematical definition: the altitude for a given condition
(T, p and ), if the gravitation acceleration was constant at the sea level value.
By hydrostatics: dp = - g dhG or dp = - go dh
Knowing the variation of g with hG yields the relation
h= (r/ (r + hG)) hG Very little difference at normal airplane altitudes
We will use geopotential altitude almost exclusively!!
12 by Shiva U Asst. Prof. AAE Dept.
Figure of standard atmosphere variation
13 by Shiva U Asst. Prof. AAE Dept.
Mathematical Model
The standard atmosphere defines the temperature variation
with altitude as shown
Now need to find pressure and density as functions of either T or h
Begin with the hydrostatic equation, divided by the equation of state for a perfect gas
dp / p= -godh/RT
Can integrate this equation for pressure when we know the P relationship between T and h
14 by Shiva U Asst. Prof. AAE Dept.
Gradient Layers, T varies linearly with h
Define a lapse rate, a, by: dT/dh = a
Define the conditions at the layer base by h1, p1, 1, and T1 In previous equation, replace dh with dT/a and integrate
w.r.t. temperature to get:
P/P1= (T/T1)-g
o/aR
And since p/p1 = (T)/(1T1)
/1=(T/T1)-[(g
0/aR)+1]
15 by Shiva U Asst. Prof. AAE Dept.
Isothermal Layers, T is constant
Start at the base of the layer where we will define the conditions as h1, p1, 1, and T
Integrate the previous equation W.R.T. h holding T Constant
P/P1= e (go/RT)( hh
1) = /1
16 by Shiva U Asst. Prof. AAE Dept.
Other Altitudes
Most flight instruments do not directly measure altitude -they measure pressure and deduce altitude.
If we know the local air pressure and use the standard atmosphere tables to look up the corresponding altitude, we call this the pressure altitude.
Similarly, knowing the local density, we could look up the density altitude, or knowing the temperature, the temperature altitude.
Remember, however, that since the local air rarely matches the standard atmosphere model, these altitudes rarely equal the geometric altitude - or even each other.
17 by Shiva U Asst. Prof. AAE Dept.
Daniel Bernoulli (1700 -1782) Bernoulli's Principle is a physical phenomenon
that was named after the
Swiss scientist Daniel
Bernoulli who lived
during the eighteenth
century. Bernoulli studied
the relationship of the
speed of a fluid and
pressure.
18
Bernoullis Principle
by Shiva U Asst. Prof. AAE Dept.
Bernoulli's Principle (top) says that increased air velocity produces decreased pressure.
Lift (bottom) is produced by an airfoil through a combination of decreased pressure above the airfoil and increased pressure beneath it.
Flow Over an Airfoil
19
Flow over an Airfoil
by Shiva U Asst. Prof. AAE Dept.
Bernoulli's Equation
20 by Shiva U Asst. Prof. AAE Dept.
Forces on the Airplane
21 by Shiva U Asst. Prof. AAE Dept.
During flight the four forces acting on the airplane are:
Lift is the upward force created by the effect of airflow as it passes over and under the wings. It supports the
airplane in flight.
Weight is a downward force caused by the pull of gravity. It opposes lift.
Thrust is the forward force generated by the propeller and engine which propels the airplane through the air.
Drag is the rearward force that limits the speed of the airplane.
22 by Shiva U Asst. Prof. AAE Dept.
Airfoil Geometry
23
An airfoil is the 2D cross-
section shape of the wing,
which creates sufficient lift
with minimal drag
by Shiva U Asst. Prof. AAE Dept.
HOW DOES AN AIRFOIL GENERATE LIFT?
Lift due to imbalance of pressure distribution over top and bottom surfaces of airfoil (or wing) o If pressure on top is lower than pressure on bottom surface, lift is generated
o Why is pressure lower on top surface?
We can understand answer from basic physics: o Continuity (Mass Conservation)
o Newtons 2nd law (Euler or Bernoulli Equation)
24
Lift = PA
by Shiva U Asst. Prof. AAE Dept.
HOW DOES AN AIRFOIL GENERATE LIFT?
1. Flow velocity over top of airfoil is faster than over bottom surface
o Streamtube A senses upper portion of airfoil as an obstruction
o Streamtube A is squashed to smaller cross-sectional area
o Mass continuity rAV=constant: If A THEN V
25
Streamtube A is squashed
most in nose region
(ahead of maximum thickness)
A B
by Shiva U Asst. Prof. AAE Dept.
HOW DOES AN AIRFOIL GENERATE LIFT?
2. As V p
o Incompressible: Bernoullis Equation
o Compressible: Eulers Equation
o Called Bernoulli Effect
3. With lower pressure over upper surface and higher pressure over bottom surface, airfoil feels a net force in upward direction Lift
VdVdp
Vp
r
r
constant2
1 2
26
Most of lift is produced
in first 20-30% of wing
(just downstream of leading edge)
by Shiva U Asst. Prof. AAE Dept.
Ty
p
i
c
a
l
S
t
r
e
a
m
l
i
n
e
s
27
Angle of Attack
chord lineV
by Shiva U Asst. Prof. AAE Dept.
Pressure Distribution
99500
99550
99600
99650
99700
99750
99800
99850
99900
99950
100000
0 0.2 0.4 0.6 0.8 1
Chordwise Distance, x, m
Su
rfa
ce
Pre
ss
ue
, P
, N
/sq
m
Net Normal Force
Upper Surface Pressure
Lower Surface Pressure
n P P dxlc
u ( )0
28 by Shiva U Asst. Prof. AAE Dept.
29 by Shiva U Asst. Prof. AAE Dept.
Pressure Coefficient Distribution
02
2
1
V
ppcp
r
2
2
1
V
ppcp
r
12
2
1
2
2
1
2
2
1
0
0
V
V
V
ppcp
r
r
r
30
In free-stream:
At stagnation point (V=0):
Positive Cp means the pressure is higher than the free-
stream (atmospheric) pressure, and negative Cp means
suction relative to free-stream pressure. The maximum,
which occurs at the stagnation point, is always 1. by Shiva U Asst. Prof. AAE Dept.
Pressure Distribution on
Cambered Airfoil
31 by Shiva U Asst. Prof. AAE Dept.
by Shiva U Asst. Prof. AAE Dept. 32
Computation Fluid Dynamics Simulation
33 by Shiva U Asst. Prof. AAE Dept.
CFD Simulation: Near stall
34 by Shiva U Asst. Prof. AAE Dept.
CFD Simulation: Fully Stalled
35 by Shiva U Asst. Prof. AAE Dept.
by Shiva U Asst. Prof. AAE Dept. 36
Evolution of
Airfoil Design
Laminar boundary
layer creates less skin
friction drag
37 by Shiva U Asst. Prof. AAE Dept.
Airfoils
1- Geometric characteristics of the airfoils.
2- Aerodynamic characteristics of the airfoils.
Airfoil Geometric Characteristics
38 by Shiva U Asst. Prof. AAE Dept.
39 by Shiva U Asst. Prof. AAE Dept.
40
Airfoil geometric characteristics include:
1- Mean camber line : The locus of points halfway between
the upper and lower surfaces as measured perpendicular
to the mean camber line.
2- Leading & trailing edges: The most forward and rearward
points of the mean camber line.
3- Chord line: The straight line connecting the leading and
trailing edges.
by Shiva U Asst. Prof. AAE Dept.
4- Chord C : The distance from the leading to trailing edge
measured along the chord line.
5- Camber : The maximum distance between the mean
camber line and the chord line.
6- Leading edge radius and its shape through the leading
edge.
7- The thickness distribution: The distance from the upper
surface to the lower surface, measured perpendicular
to chord line
41 by Shiva U Asst. Prof. AAE Dept.
NACA Airfoil Series
1- NACA 4-digit series
2- NACA 5-digit series
3- NACA 1-series or 16-series
4- NACA 6- series
42 by Shiva U Asst. Prof. AAE Dept.
NACA Four-Digit Series
Example: NACA 2412
NACA 2 4 12
43
Camber in
percentage of chord
yc = 0.02 C
Position of camber
in tenths of chord xc = 0.4 C
Maximum thickness (t )
in percentage of chord
(t/c)max = 0.12
xc yc C
by Shiva U Asst. Prof. AAE Dept.
44 by Shiva U Asst. Prof. AAE Dept.
NACA Five-Digit Series
Example: NACA 23012
NACA 2 30 12
45
When multiplied by 3/2
yields the design lift
coefficient Cl in tenths.
Cl = 0.3
When divided by 2, gives
the position of the
camber in percent of
chord xc = 0.15 C
Maximum thickness
(t ) in percentage of
chord (t/c)max = 0.12
by Shiva U Asst. Prof. AAE Dept.
way2v_000Sticky NoteNational Advisory Committee for Aeronautics (NACA)
NACA Six- Series
Example: NACA 64-212
NACA 6 4 - 2 12
46
Series
designation 6
Location of minimum
pressure in tenths of
chord (0.4 C)
Design lift
coefficient in
tenths (0.2)
Maximum thickness (t )
in percentage of chord
(t/c)max = 0.12
Note that this is the series of laminar airfoils .
by Shiva U Asst. Prof. AAE Dept.
47 by Shiva U Asst. Prof. AAE Dept.
48 by Shiva U Asst. Prof. AAE Dept.
The component of the total aerodynamic force that acts at right angles to the resultant relative wind
The two factors that most affect the coefficient of lift and the coefficient of drag are:
1. Shape of the airfoil &
2. Angle of Attack
49
LIFT
by Shiva U Asst. Prof. AAE Dept.
L= CL 1/2 S V2
L ~ Lift force
CL ~ Coefficient of lift
~ density of the air in slugs S ~ total wing area in square feet
V ~ airspeed (in feet per second)
50 by Shiva U Asst. Prof. AAE Dept.
D= CD 1/2 S V2
D ~ Drag force
CD ~ Coefficient of lift
~ density of the air in slugs
S ~ total wing area in square feet
V ~ airspeed (in feet per second)
51 by Shiva U Asst. Prof. AAE Dept.
Mcg = CM,cg1/2 S V2c
Mcg ~Moment about center of gravity
~ density of the air in slugs
S ~ total wing area in square feet
V ~ airspeed (in feet per second)
c ~ chord length
52 by Shiva U Asst. Prof. AAE Dept.
Types of Drag
53 by Shiva U Asst. Prof. AAE Dept.
54 by Shiva U Asst. Prof. AAE Dept.
Form or pressure drag is caused by the
separation of air that is flowing over the aircraft
or airfoil.
55 by Shiva U Asst. Prof. AAE Dept.
Flow over flat plate
by Shiva U Asst. Prof. AAE Dept. 56
Flow over Cylinder
Flow over Airfoil
The leading edge of a wing will always produce a certain amount
of friction drag.
57 by Shiva U Asst. Prof. AAE Dept.
Induced drag is a byproduct of lift.
58 by Shiva U Asst. Prof. AAE Dept.
Aspect Ratio
59 by Shiva U Asst. Prof. AAE Dept.
60 by Shiva U Asst. Prof. AAE Dept.
Center of Pressure
Center or pressure : The point of intersection
between the chord line and the line of action of
the resultant aerodynamic force R.
61 by Shiva U Asst. Prof. AAE Dept.
Moment on an Aircraft
62 by Shiva U Asst. Prof. AAE Dept.
63
Aerodynamic Center
by Shiva U Asst. Prof. AAE Dept.
Aerodynamic Center The aerodynamic center is the point at which the
pitching moment coefficient for the airfoil does not
vary with lift coefficient i.e. angle of attack.
64 by Shiva U Asst. Prof. AAE Dept.
Lift Curve
65 by Shiva U Asst. Prof. AAE Dept.
66 by Shiva U Asst. Prof. AAE Dept.
Drag Curve
67 by Shiva U Asst. Prof. AAE Dept.
Lift/Drag Ratio Curve
68 by Shiva U Asst. Prof. AAE Dept.
Factors Affecting Lift & Drag
69 by Shiva U Asst. Prof. AAE Dept.
Effect of lift, drag, Speed & Air Density
on Drag
70 by Shiva U Asst. Prof. AAE Dept.
71 by Shiva U Asst. Prof. AAE Dept.