Mechanics of Flight/Fundamentals of Flight COURSE NOTES

1
Mechanics of Flight/Fundamentals of
FlightCOURSE NOTES

• John Baird

2
MILESTONES IN FLIGHT

• GEORGE CAYLEY (1773 - 1857) WAS THE FIRST TO
  EXPLAIN HOW THE FORCE ON THE WIN CAN BE RESOLVED
  INTO TWO COMPONENTS OF

LIFT
PERPENDICULAR TO THE FLIGHT DIRECTION
DRAG
PARALLEL TO THE FLIGHT DIRECTION
LIFT
WING SURFACE
DRAG
CAYLEY ALSO UNDERSTOOD THE FIRST PRINCIPLES OF
STABILITY AND CONTROL
3
WE TRY TO ANSWER THE THREE BASIC QUESTIONS

• 1. WHY AN AEROPLANE FLIES?

AERODYNAMICS
2. WHY DOES IT FLY - SO FAST? SO
FAR? SO HIGH?
PERFORMANCE
3. WHY DOES IT BEHAVE THE WAY IT DOES AND HOW
TO CONTROL IT?
STABILITY CONTROL
4
Visualisation Examples
5
VISCOSITY

• TWO FEATURES OF LIQUIDS AND GASES ARE RESPONSIBLE
  FOR EXISTENCE OF

VISCOSITY
COHESIVE OR ATTRACTIVE FORCES DOMINATE OVER
INERTIA FORCES AND LARGER THE COHESIVE FORCES
(MORE CLOSELY PACKED MOLECULES, GREATER THE
VISCOSITY.
LIQUIDS
THE BASIS OF VISCOSITY IS THE INTERNAL RESISTANCE
DUE TO COLLISION AND TRANSFER OF MOMENTUM.
GASES
Fast molecules exchange with slow ones and vice
versa. Slowing of fast molecules and vice versa
is viscosity.
Fast drift
Slow drift
6
FOR LIQUIDS

• VISCOSITY WITH TEMP. BECAUSE BONDS
  BETWEEN MOLECULES WEAKEN OR CAN EVEN BREAK IN
  OTHER WORDS, COHESIVE FORCES WEAKEN.
• VISCOSITY WITH TEMP. BECAUSE INCREASE IN
  TEMPERATURE CAUSES INCREASED MOLECULAR ACTIVITY
  WHICH IN TURN LEADS TO MORE COLLISIONS AND MORE
  TRANSFER OF MOMENTUM, THEREFORE MORE VISCOSITY.

DECREASES
FOR GASES
INCREASES
7
NEWTONS LAW OF VISCOSITY

• THIS ESTABLISHES THE RELATION BETWEEN SHEAR FORCE
  (FRICTION FORCE) AND THE VISCOSITY.
• IT STATES
• SHEARING FORCE
• A AREA OF INTERFACE
• ?u VELOCITY DIFFERENCE BETWEEN ADJACENT
• LAYERS OF FLUID.
• ?h SEPARATION DISTANCE BETWEEN LAYERS OF
• FLUID
• ? PROPORTIONALITY CONST. CALLED THE
• COEFFICIENT OF VISCOSITY.

u2
Fs
?h
u1
?u u2- u1
Fs
8
DEFINITION OF VELOCITY GRADIENT
Moving plate
u
A
A
Couette or channel flow
?h
B
B
?u
?
Fixed plate
gradient
u0
Flow
velocity gradient
Boundary layer flow
y
B
A
Fixed plate
velocity profile
9

• UNITS OF SHEAR STRESS ??ARE N/m2 in SI.
• FLUIDS OBEYING NEWTONS LAW, ARE CALLED Newtonian
  Fluids
• EXAMPLES AIR, WATER, ALL FLUIDS WHICH HAVE
  SIMPLE MOLECULAR STRUCTURE.
• THINK OF SOME FLUIDS WHICH ARE NOT NEWTONIAN!

10
International Standard Atmosphere
30
Balloons
Ozone Layer
Mesosphere
U2 Spyplane
20
Concorde
Stratosphere
Altitude (km)
Large Jet Liners
Tropopause
10
Troposphere
General Aviation
Helicopters
Birds
Sea Level
Insects
-56.5
Temperature (degrees Centigrade)
11
SPEED OF SOUND

• THE SPEED OF SOUND IS RELATED TO THE PRESSURE
  DENSITY BY THE ISENTROPIC RELATION
• WHERE ? IS THE RATIO OF SPECIFIC HEATS IN AIR
  (CP/ CV) AND IS EQUAL TO 1.4
• NOTE THAT THE SPEED OF SOUND IS A FUNCTION OF
  TEMPERATURE. THE SPEED OF SOUND DECREASES WITH
  INCREASING ALTITUDE (IE DECREASING TEMPERATURE)
• R IS THE GAS CONSTANT FOR AIR AND IS 287.05 J/kg K

12
PROPERTIES OF FLUIDS

• FLUIDS CAN BE CLASSIFIED AS OR
• .
• IN A COMPRESSIBLE FLUID, PRESSURE VELOCITY
  CHANGES ARE ACCOMPANIED BY SIGNIFICANT DENSITY
  CHANGES.
• IN AN INCOMPRESSIBLE FLUID, PRESSURE VELOCITY
  CHANGES DO NOT CAUSE ANY APPRECIABLE CHANGES IN
  DENSITY.
• LIQUIDS ARE GENERALLY INCOMPRESSIBLE (Eg. WATER).
• GASES ARE GENERALLY COMPRESSIBLE (Eg. AIR).

COMPRESSIBLE
INCOMPRESSIBLE
13
PROPERTIES OF FLUIDS

• THE FLOW PARAMETER THAT BECOMES IMPORTANT UNDER
  SUCH CIRCUMSTANCES IS THE MACH NO. DISCUSSED
  EARLIER.
• AT HIGH SPEEDS THEREFORE, WE CAN TALK IN TERMS
  OF
• SUBSONIC 0.3 lt M lt 0.7
• TRANSONIC 0.7 lt M lt 1.4
• SUPERSONIC 1.4 lt M lt 5
• HYPERSONIC M gt 5

14
FLOW REGIMES IN AIR
TERMINOLOGY
Subsonic
Transonic
Supersonic
Hypersonic
0
1 2 3 4 5 6
7 8 9 10
Non Linear
Oxygen dissociates (Chemical reactions important)
Incompressible
Linear
Compressible
0
1 2 3 4 5 6
7 8 9 10
15
BOUNDARY LAYERS

• IN VISCOUS FLOWS THE EFFECTS OF VISCOSITY (WHICH
  PRODUCE FRICTIONAL OR SHEAR STRESSES) ARE
  CONFINED TO A VERY THIN LAYER OF FLUID CLOSE TO
  THE SURFACE. THIS THIN LAYER NEAR THE SURFACE IN
  WHICH VISCOSITY EFFECTS ARE CONFINED IS CALLED
  BOUNDARY LAYER, BECAUSE OF INTERNAL FRICTION DUE
  TO VISCOSITY, THE LAYER OF AIR CLOSEST TO THE
  BODY STICKS TO THE SURFACE AND THE VELOCITY
  GRADUALLY INCREASES TILL AT THE EDGE OF THE
  BOUNDARY LAYER, IT IS EQUAL TO THE VELOCITY IN
  THE ADJACENT EXTERNAL FLOW.

BOUNDARY LAYER DETAIL
Flow
BOUNDARY LAYER
velocity gradient
y
B
A
Fixed plate
velocity profile
16
BOUNDARY LAYERS

• BECAUSE THE EFFECTS OF VISCOSITY ARE CONFINED TO
  THE BOUNDARY LAYER, IT HAS OFTEN BEEN POSSIBLE TO
  ANALYSE AERODYNAMIC PROBLEMS BY TREATING THE AIR
  AS IDEAL FLUID AND THIS HAS YIELDED QUITE
  ACCEPTABLE RESULTS ESPECIALLY AS REGARDS
• .
• FOR TREATING THE PROBLEM OF AERODYNAMIC DRAG,
  HOWEVER, WE NEED TO CONSIDER THE
• WE ALSO NOTE THAT IN AN IDEAL FLUID, THAT HAS NO
  VISCOSITY, THE FLUID EXHIBITS NO SHEAR FORCES AND
  THERE WOULD BE NO RELATIVE MOTION BETWEEN
  ADJACENT LAYERS OF FLUID. SUCH A FLUID IS SAID
  TO
• PAST THE SURFACE.

AERODYNAMIC LIFT
BOUNDARY LAYER
SLIP
17
BOUNDARY LAYERS

• WITH REAL FLUIDS, ON THE OTHER HAND, THERE IS NO
  RELATIVE MOTION AT THE SURFACE. IN OTHER WORDS,
  AT THE SURFACE WE HAVE
  CONDITION.
• THE CONCEPT OF THE BOUNDARY LAYER WAS FIRST
  PROPOSED BY THE GERMAN AERODYNAMICIST LUDWIG
  PRANDTL (1875 - 1953) IN 1905.
• IT WAS TRULY A MILESTONE IN AERODYNAMICS

NO SLIP
Zero velocity at wall, the no slip condition
18
TYPICAL BOUNDARY LAYER PROFILE
Free stream velocity, U
0.99U
?
Boundary layer thickness
Velocity gradient
Velocity Profile
Surface
19
BOUNDARY LAYER BEHAVIOUR

• WHEN THE BOUNDARY LAYER IS SUBJECTED TO
• INCREASING PRESSURE IN THE FLOW DIRECTION, IT
• BECOMES MORE AND MORE SLUGGISH AS IT HAS TO FLOW
• AGAINST AN ADVERSE PRESSURE GRADIENT. IT
• EVENTUALLY COMES OFF THE SURFACE. THE BOUNDARY
• LAYER IS THEN SAID TO BE SEPARATED.
• WHEN THE BOUNDARY LAYER ON AN AEROFOIL OR WING
• SEPARATES, WE SAY THAT THE AEROFOIL OR WING HAS
• ONCE THE BOUNDARY LAYER SEPARATES THE DRAG
• INCREASES DRAMATICALLY AND WE CAN NO LONGER
• ASSUME THAT FLOW OVER. THE AEROFOIL IS SMOOTH
• (IDEAL).

STALLED
20
A Separated Boundary Layer
21
B.L. BEHAVIOUR IN ADVERSE PRESSURE GRADIENT
Pressure force
Flow decelerating
Flow separated
Point of separation
Increasing Pressure
22
PRESSURE DISTRIBUTION ON AN AEROFOIL
Negative pressure
Adverse Pressure Gradient
23
STALL ON AN AEROFOIL
NOTE RECIRCULATION REGION
Negative Pressure
24
NATURE OF DRAG
DRAG ARISES DUE TO
PRESSURE DISTRIBUTION OVER BODY
SKIN FRICTION ON SURFACE OF BODY
SKIN FRICTION DRAG
PRESSURE DRAG
(ALSO CALLED FORM DRAG)
25
REAL FLOWS AND AERODYNAMIC DRAG
INCISCID FLOW
VISCOUS FLOW
26
Pressure Drag on a Cylinder
???degrees?
27
Skin Friction Drag
y
Skin Friction Drag Area x Shear Stress at wall
28
Total Drag
DRAG ON A TWO DIMENSIONAL OBJECT (PROFILE DRAG)
IS A COMBINATION OF PRESSURE DRAG (ALSO CALLED
FORM DRAG) AND SKIN FRICTION DRAG
PROFILE DRAG PRESSURE DRAG SKIN FRICTION DRAG
29
Stream Tube

• VELOCITY IS INVERSELY PROPORTIONAL TO THE CROSS-
• SECTIONAL AREA. IN OTHER WORDS,
• WHENEVER THERE IS ACCELERATION OF FLUID FLOW, THE
• CROSS-SECTION IS NARROW AND THE STREAMLINES
• CONVERGE.
• WHEN THERE IS A DECELERATION, THE CROSS-SECTION
  IS
• WIDER AND THE STREAMLINES DIVERGE.

30
Bernoullis Equation

• BERNOULLIS EQN. RELATES CHANGES IN VELOCITY TO
• CHANGES IN PRESSURE IN STEADY INCOMPRESSIBLE
• INVISCID FLOW ALONG A STREAM LINE. IT IS THE MOST
  IMPORTANT EQUATION IN FLUID MECHANICS.

where p is the (static) pressure ? is the
density, V is the local velocity and p0, the
constant, is called the total pressure. The term
is sometimes called the dynamic pressure.
31
Applications of Bernoullis Equation
One way of writing Bernoullis equation is Total
pressure static pressure dynamic pressure.
A PITOT TUBE
If the velocity is zero the pressure is equal to
the total pressure
4d
d
To differential pressure gauge
p
32
Measurement of Velocity

• FROM BERNOULLIS EQN. WE HAVE

THEREFORE, BY MEASURING THE DIFFERENCE
BETWEEN THE TOTAL PRESSURE (Po) AND STATIC
PRESSURE (?), WE CAN CALCULATE THE VELOCITY IN A
FLOW.
33
PITOT TUBE USED IN A WIND TUNNEL TO MEASURE
VELOCITY
Test Section
po
V
Pitot-static tube
To micromanometer
34
PITOT TUBE USED TO MEASURE BOUNDARY LAYER PROFILE
V
Boundary layer velocity profile
Pitot tube fixed to manometer traverse
Static orifice
To manometer
35
ALTERNATIVE VIEW OF BERNOULLIS EQUATION
pressure energy per unit volume
Total energy per unit volume
kinetic energy per unit volume
36
Pressure and Velocity
37
Using Bernoullis Equation to Measure Velocity of
Aircraft

• THEREFORE, BY NOTING THE EQUIVALENT AIRSPEED FROM
• ASI AT ANY ALTITUDE, WE CAN DETERMINE THE TRUE
  AIR
• SPEED BY THE KNOWLEDGE OF RELATIVE DENSITY ?.
• USUALLY, THE AIRSPEED INDICATOR IS CALIBRATED SO
• THAT IT READS DIRECTLY THE SPEED EITHER IN KNOTS
  OR
• km/hr.
• Static pressure measured by port on fuselage

Dynamic pressure measured by pitot probe
38
Flow Examples
Dividing streamline pp0 at stagnation point
Flow accelerates and pressure reduced
39
Flow Examples
All objects in a flow have a stagnation point
40
Flow Examples
s
T
s
Free stream V????p?
V????p?
F
F
s
s
Pressure and Velocity
V?
V?
p?
p?
Distance along aerofoil
41
TRANSITION TO TURBULENCE
Osborne Reynolds in the 1880s investigated the
behaviour of flow that was either direct
(laminar) or sinuous (turbulent).
42
Transition to Turbulence

• Whether the flow is turbulent or laminar depends
  on the relative magnitude of the viscous forces
  and the kinetic forces (momentum) of the flow.
• When viscous forces are large, small
  irregularities are removed by viscous damping.
  This is characterised by slow flow, and/or high
  viscosity.
• When the flow has sufficient momentum such that
  the viscous forces are relatively small, it
  becomes turbulent.

43
Example of a Turbulent Boundary Layer
44
Stability of Shear Flow
V P
p,V1
V P
V P
p,V2
V P
Dividing stream line
Splitter Plate
Consider the flow above in which viscosity is
very small. Consider what happens if the
dividing stream line is disturbed a small
amount. Note that, if the velocity difference is
high enough the pressure differences will act to
increase the divergence of the streamline. IT
WILL BECOME TURBULENT
45
Stability of Shear Flow
U P
p,U1
U P
D
U P
p,U2
U P
IF VISCOUS FORCES DOMINATE, DISTURBANCE ENERGY
WILL DISSIPATE. IF KINETIC FORCES DOMINATE THE
DISTURBANCES WILL GROW AND FLOW WILL BECOME
TURBULENCE. WHETHER A FLOW IS TURBULENT OR NOT
DEPENDS ON
REYNOLDS NUMBER
46
REYNOLDS NUMBER
? FLUID DENSITY V A VELOCITY - USUALLY THE
FREE STREAM VELOCITY D A REPRESENTATIVE LENGTH
SCALE ? THE FLUID VISCOSITY
EXAMPLES
U
D
CHORD C
For a given configuration and definition the Re
determines when the transition to turbulence
occurs.
47
LAMINAR AND TURBULENT FLOW

• LAMINAR FLOW
• SMOOTH STEADY SMALLER
• SHEAR STRESS
• TYPICALLY STREAMLINED
• BODIES
• LESS SKIN
• FRICTION DRAG. MORE
  PRESSURE DRAG

Laminar profile
Turbulent mean profile
48
LAMINAR AND TURBULENT FLOW

• TURBULENT FLOW
• HIGHLY DISORGANISED BASICALLY LARGE
• UNSTEADY SHEAR STRESS
• MORE SKIN
• FRICTION DRAG.
• LESS PRESSURE
• DRAG
• TYPICALLY
• BLUFF BODIES

Laminar profile
Turbulent mean profile
49
Transition to Turbulence
Smoke visualisation of a boundary layer. The
laminar boundary layer on the left is tripped
by a grid and becomes turbulent
50
Boundary Layer Profiles
Laminar Profile
Y
Streamlines
Turbulent Profile
Momentum exchange by viscous forces only
U
Momentum exchanged more effectively by mass
transport into lower layers
51
(a)
(b)
The laminar boundary layer (a) encourages
separation and leads to a wide wake and high form
drag. In (b) a trip is used to cause transition
to turbulence in the boundary layer, separation
is delayed, the wake narrows and the form drag
decreases.
52
Turbulent Boundary Layer on a Flat Plate
Free stream velocity V
turbulent eddies
Boundary layer edge
?t
?L
?t
?L
?s
Laminar
Transition
Turbulent
Vertical dimension exaggerated
53
Four Fluid Phenomena Number 1
Pressure force
Flow decelerating
Flow separated
Point of separation
1. Adverse pressure gradients cause separation
(Separation cannot occur in favourable gradients)
54
Four Fluid Phenomena Number 2
Pressure force
Flow separated
Point of separation
Laminar flow
Energy deep in boundary layer is resistant to
separation
Turbulent flow
2. Turbulence inhibits or delays separation
55
Four Fluid Phenomena Number 3
Pressure force
3. In a certain Re range adverse pressure
gradients can encourage turbulence, and
favourable gradients can relaminarise flow.
56
Four Fluid Phenomena Number 4
4. In a certain Re range surface roughness
encourages turbulence.
57
Cricket Ball Swing
Polished Side
Laminar Flow
Asymmetric wake
Roughened side
Turbulent Flow tripped by seam and maintained by
rough surface
1/2 ? V2
Turbulent
Laminar
Pressure
LIFT
0
180
Angle (degrees)
58
REYNOLDS NUMBER ITS SIGNIFICANCE

• WE HAVE SEEN THAT THE TURBULENT MOTION IS MORE
• VIGOROUS AND ENERGETIC. ALSO, THE VELOCITY
• FLUCTUATIONS IN TURBULENT FLOW IMPOSE STRESSES
• ADDITIONAL TO THOSE SHEAR STRESSES THAT RESULT
• FROM MOLECULAR MOTIONS. THESE ADDITIONAL
• STRESSES ARISING PURELY OUT OF TURBULENT
• FLUCTUATIONS ARE CALLED OR
• SOMETIMES REFERRED TO AS EDDY STRESSES.
• THEREFORE
• TOTAL SHEAR STRESS VISCOUS SHEAR
  STRESS
• IN TURBULENT FLOW
• REYNOLDS STRESSES

REYNOLDS STRESSES
59
More on Reynolds Number and Scaling
IN FLUID MECHANICS IT IS MORE CONVENIENT TO USE
NON-DIMENSIONAL NUMBERS SUCH AS THE REYNOLDS
NUMBER IN DESCRIBING FLOW. LET US FIND A
NON-DIMENSIONAL NUMBER RELATED TO DRAG. DRAG IS
A FORCE WHICH, IN MANY CASES, IS RELATED TO THE
KINETIC ENERGY OF THE FLOW (SEE BELOW)
Gauge pressure near zero
IN THE CASE SHOWN, THE DRAG IS LIKELY TO BE
PROPORTIONAL TO THE DYNAMIC PRESSURE 1/2
?U2 THEREFORE WE DEFINE THE DRAG COEFFICIENT AS
U
DRAG
Area A
Gauge pressure of 1/2 ?U2
60
More on Reynolds Number and Scaling
SIMILARLY THE LIFT COEFFICIENT IS
WHERE L IS THE LIFT GENERATED BY AN AEROFOIL OF
PLAN AREA A
Air Flow (V)
Wing Planform (A)
Span (b)
Chord (c)
61
WHY USE COEFFICIENTS ?
IMAGINE THAT YOU HAVE MEASURED THE LIFT ON AN
AEROFOIL IN A WIND TUNNEL AT VARIOUS VELOCITIES
NOW WE VARY THE SIZE OF THE AEROFOIL
U4
C4
U3
C3
LIFT
LIFT
U2
C4
C1
U1
ANGLE OF ATTACK
ANGLE OF ATTACK
THE RESULTS ARE FAR TOO COMPLEX
62
WHY USE COEFFICIENTS ?
IF WE PLOT NON-DIMENSIONAL NUMBERS SUCH AS LIFT
COEFFICIENT VS ANGLE OF ATTACK ALMOST ALL DATA
COLLAPSES TO ONE LINE
SLIGHT VARIATION CAUSED BY CHANGING REYNOLDS
NUMBER
LIFT COEFFICIENT
ANGLE OF ATTACK
THE RESULTS ARE NOW SIMPLIFIED
63
ANOTHER EXAMPLE
DRAG ON A CYLINDER
VARIABLE DIAMETERS
DRAG
Log (DRAG COEFFICIENT)
VELOCITY
Log (REYNOLDS NUMBER)
ON A NON-DIMENSIONAL PLOT OF APPROPRIATE
PARAMETERS ALL DATA COLLAPSES TO ONE GRAPH
64
SCALING LAWS DIMENSIONAL ANALYSIS

• IN FLUID FLOWS, WE CAN ALWAYS IDENTIFY A
• CHARACTERISTIC DIMENSION FOR A BODY OVER OR
• THROUGH WHICH FLUID FLOWS. THIS CAN BE, FOR
• EXAMPLE, THE CHORD OF AN AEROFOIL, DIAMETER OF A
• PIPE, HEIGHT OF A CHANNEL, ETC.
• IN A SIMILAR VEIN, WE CAN DEFINE A CHARACTERISTIC
• VELOCITY SCALE WHICH IS TYPICAL FOR A GIVEN
  PROBLEM.
• FOR EXAMPLE, THE FLIGHT SPEED OF AN AIRCRAFT, OR
• TEST SECTION VELOCITY IN A WIND TUNNEL, OR FREE-
• STREAM VELOCITY EXTERNAL TO THE BOUNDARY LAYER.

65
REYNOLDS NUMBER
REYNOLDS NUMBER IS THE MOST IMPORTANT PARAMETER
IN AERODYNAMICS. ? is the density of the
fluid U is a characteristic velocity, typically
free stream velocity L is a characteristic
dimension, typically the diameter of a cylinder
or pipe or the chord of an aerofoil ? is the
fluid viscosity.
66
Drag Lift Coefficients
The main aim of aerodynamics is to predict drag
and lift. Drag has the units of
The drag is likely to be related to the pressure
experienced by the aerofoil which is typified by
the Stagnation Pressure 1/2 ?U2
We can multiply by an area ( L2) to get the same
units as Force
is dimensionless and is called the Drag
Coefficient
67
DRAG ON A CYLINDER
Re lt 1 Viscous flow, drag is proportional to
velocity, skin friction drag dominates
10 lt Re lt 5x105 Viscous flow, drag is
proportional to the square of velocity, pressure
drag dominates.
Re gt 5x105 Boundary layer is turbulent and
separation is delayed. Thus the wake is narrower
and there is a greater area of pressure recovery
on the rearward surfaces. Thus drag is reduced.
68
1000
jet transports
general aviation
1.0
0.5
sailplanes
100
0.2
0.1
birds bats
0.05
10
hang
gliders
0.01
insects
Series1
Speed (m/s)
human
-
dirigibles
Mach number
powered
1
aircraft
0.001
models
dust particles
0.1
0.0001
0.01
1
2
3
4
5
6
7
8
9
log
(
Reynolds
number)
10
Approximate Reynolds number ranges of aerodynamic
objects in nature and technology.
69
M - 0.3
0.8
1.2
5
Compressible
Supersonic
Low Speed
Hypersonic
Transonic
Subsonic
US SST L 32 m
Hypersonic Aircraft L 32m
Large Jet transport
Concorde L 20 m
Cruise
Take-off
IRBM
RL
Space Ferry L 10.7 m
ICBM
L 4 m
Vstol, cargo.
Gemini GT-3 L 2.1 m
Velocity (km/s)
Reynolds number and speed (Mach number) regimes
for various vehicles (Poisson-Quinton, 1968)
70
How does Streamlining work?
Relt1
Consider two bodies of revolution A and B. At
low Re, skin friction drag is much larger than
pressure drag. Viscous forces dominate. Note
that B has a much larger surface area than A.
A
B
The drag on B will be much larger than the drag
on A. Streamlining will not work.
71
How does Streamlining work?
Regt100
Pressure drag dominates.
1/2 ? V2
Pressure
A
0
180
Angle (degrees)
1/2 ? V2
Pressure
Distance from leading edge
B
The drag on A will be much larger than the drag
on B. Streamlining reduces the drag substantially
72
The Effect of Streamlining
Thickness
Wire
NACA 64-421 airfoil compared with a circular wire
having the same drag. The diameter of the wire
is one tenth of the thickness of the aerofoil.
73
MORE ON REYNOLDS NUMBER
If we want to model the flow over an object we
should try to get the Reynolds number of the
model and the full size object as close as
possible.
Lmodel
Lfull size
74
MORE ON REYNOLDS NUMBER
IF (Re )model (Re )full size Then (Cd )model
(Cd )full size and (CL )model (CL )full size
IN PRACTICE THIS CAN RARELY BE ACHIEVED
75
L
AF
V
T
D
W
Primary forces acting on an aircraft in steady
level flight.
76
L
L/D3.3
D
V
L
?
L/D4
Lift to drag ratio for a flat plate, a cambered
plate and an aerofoil at incidence.
D
V
?
77
(No Transcript)
78
Air Flow (V)
Leading edge
A
Wing Planform (S)
Chord line
Span (b)
Chord (c)
Leading edge radius
Thickness
Trainling edge
Camber
A
Camber line
Air Flow
AoA(?)
Trailing edge
Chord (c)
Wing and aerofoil nomenclature
Section A-A
79
Rectangular wing
Swept wing
Sweep angle (??
cr
c
?
Elliptic wing
Delta wing
cr
c
Tapered wing
Ogive wing (Concorde)
Tip cord (ct)
Root cord (cr)
b
b
Figure 8.4a Typical wing planforms
80
Conventional low speed aerofoil
Transoinc supercritical aerofoil
Low speed symmetric aerofoil
Thin supersonic biconvex aerofoil
Laminar flow aerofoil
Multi-element high lift aerofoil
Typical aerofoil sections
81
Cp
x/c
Pressure loss due to viscosity
Pressure distribution on a lifting aerofoil
82
(No Transcript)
83
Ways of Plotting Aerofoil Performance
Lift Coefficient
Drag Coefficient
Angle of Attack
Angle of Attack
Lift Coefficient
or
Drag Coefficient
Polar Plot
84
Lift and Drag Curves
Shape of curve indicates sudden stall or gentle
stall
CLmax
Drag Coefficient
Lift Coefficient
CDmin
Angle of Attack
Angle of Attack
Offset indicates asymmetric aerofoil
85
Polar Plots
CLmax
Lift Coefficient
Drag Coefficient
86
Measurement of Profile Drag
Up till now we have been talking about the
behaviour of infinitely long aerofoil sections
(or profiles). These are measured in an wind
tunnel with the aeorfoils being terminated in the
walls. Real wings are not infinite
Wing Tip Vortex
Testing Aerofoil Profiles
Testing three dimensional wings
87
Induced Drag
Note that a downwards velocity is generated
Low Pressure
Wing Tip
High Pressure
Wing Tip Vortex
88
Induced Drag
Lift
Induced Drag
Airspeed
Drag
Induced downwards airflow
Local Lift
Two Dimensional Flow (infinite aspect ratio)
Drag
Local Airspeed
Three Dimensional Flow (finite aspect ratio)
89
Induced Drag
Induced Drag is proportional to the square of the
Lift Coefficient.
Infinite wing
the Induced Drag
Finite wing
CL
the wing area
the aspect ratio, span divided by chord
?
Note, curves cross at zero lift point
90
Basic Flight Mechanics
Note that for steady level flight, the Lift L is
equal to the Weight W (mg). If we assume that
the lift is generated entirely by the wing, we
can write
L
AF
V
T
D
W
To maintain steady level flight at low speeds the
CLmust be increased (by increasing angle of
attack). In high speed flight CL must be
decreased (by decreasing angle of attack).
91
Basic Flight Mechanics
L
L
T
D
D
W
W
Angle of attack Large ( 20-25 degrees)
Angle of attack Small ( 3-4 degrees)
Note an aircrafts minimum speed (landing speed)
is determined by CLmax and the wing area.
92
Total Drag on an Aircraft
The total drag on an aircraft is a combination of
drag caused by appendages, skin friction drag,
pressure drag (collectively called parasite drag)
and induced drag. Induced drag is high at low
speeds (high CL) and low at high speeds ( low CL).
Drag
Velocity (steady and level)
93
Total Drag on an Aircraft
Induced Drag
Total Drag
Parasite Drag Includes profile drag, (pressure
drag and skin friction drag on wing), skin
friction and pressure drag on fuselage,
empennage, engine necelles, landing gear etc.
94
High Lift Devices

• The minimum controllable speed at which an
  aircraft can fly determines the landing speed.
  From the above equation, the landing speed can be
  reduced by increasing CLmax ( ie by delaying
  stall) or by increasing the wing area. Most
  modern high lift devices work on a combination
  of
• Delaying stall by increasing camber,
• Delaying stall by re-energising the boundary
  layers inhibiting separation,
• Increasing the total effective wing area.

95
The Effect of Flaps
CLmax increases with??
?30
?15
CL
?0
?
?
Modern aerofoils have a CLmax of 1.4.
Multi-element flaps can increase that to 3.2
Zero lift point changes with camber
96
Elementary Flight Mechanics
97
Power and Drag
P
Stall Speed
D
Vmp
VmD
Velocity
98
As Weight Increases
Stall Speed
Weight W2
D
Drag
Weight W1
VmD
Velocity
99
Increasing Weight

• WL and as W increases L increases
• If CL and the AoA are unchanged V must increase
  as W1/2
• At a given AoA, L/D is constant and D is
  proportional to W
• At a given AoA, Preq DV and is proportional to
  W3/2

100
Power Requirements
Stall Speed
Pavail
Max climb rate
Max speed
Preq
Power
Take-off and Landing speed
Velocity
101
Maximum Payload
Preq
Pavail
Drag
Minimum workable manoevre range
Velocity
102
Pitching Moment
Pitching Moments CmM/(1/2 r V2Sc)Cm0 k
CL (Nose up is positive)
Aft point of reference
Cm
CL (or AoA)
Aerodynamic Centre ref point
Forward point of reference
103
Aerodynamic Centre
L
L
M
Centre of Pressure
O
A
O
C
A
C
L
Position of C varies with a
M0 constant
O
A
C
Position of Aerodynamic Centre(A) remains fixed
104
Stability of Wing Alone
Highly unstable
Unstable
Pitching Moment
CL
Neutrally stable
CG moving aft
Stable (desirable)
Unresponsive
105
Longitudinal Stability
Lw
LT
G
C
W
Lw
M0 constant
LT
G
A
W
106
Stability of Wing and Tailplane
Tail Alone
Wing Alone
CL
Aircraft
Pitching Moment
Trim Point

• Movement aft of CofG makes aircraft less stable.
• Neutral point is point of CofG where aircraft is
  neutrally stable (Cm constant)
• Static margin is distance CofG is ahead of
  neutral point