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Physical Laws
Lecture 1

Formula sheet
∑F = ma
T-D-f = ma
V = V2 + a t
KE = ½ mV2
HP= T*V /325
1 kt = 1
...
2 ft/sec2
F

I

VF = Final speed or Takeoff speed
VI = Initial speed
a = Acceleration
s = Takeoff distance
Start with zero velocity
Velocity is always in Feet per Second unless stated
...
69 ft/s
Velocity (mph) 1 kt = 1
...
305 meters
1 Nautical mile = 1851 meters
1 Statue mile = 1609 meters
1 kg = 2
...
225 lbforce

Newton’s First Law
• A body at rest will remain at rest and a body in
motion will remain in motion, in a straight line,
unless acted upon by an unbalanced force
...

• The same holds true while flying straight and
level flight
...
Either of these will change the
balance of forces
...


Newton’s Third Law
• For every action there is an equal and
opposite reaction force
...


1ST LAW:
Every object in a state of uniform motion tends to remain in that state
of motion unless an external force is applied to it
...


AT CRUISE CONSTANT ALTITUDE

Forces
• On takeoff roll there is an unbalance of forces (thrust is
greater than drag) causing the airplane to accelerate
• The faster the aircraft goes, greater lift is created and
eventually there is enough lift on the wing to take off
• During ascending flight, if the aircraft is maintaining a
constant true airspeed, all the forces are balanced
...

• No change is airspeed means no acceleration
...

The airplane is moving through the air at an airspeed which is
the hypotenuse of
this triangle
...

TAS ≠ GS in a climb or descend,
assuming ideal conditions

Rate of Climb (ROC) have to
be converted from Feet per
Minute (FPM) to knots
...
69 to
convert to Knots
...
5 • m • v2
– potential energy (pressure)

14

Gas Laws,
Atmosphere
Lecture 2

Density Altitude

• Air density given as a height above mean sea level
• Is pressure altitude (altimeter) corrected for
nonstandard temperature
• As OAT increases, air density decreases and DA
increases
• DA affects

– lift (reduction in air density reduces the wing's lift)
– efficiency of propeller or rotor (an airfoil) similar to lift on
wing
– power output of engine (less oxygen at altitude)
which is reduced at altitude and influenced by
moisture in air
See Exercise 2, Question 5 on how
to calculate Density altitude!

Exercise 2, Question 5

Humidity
• Increase in humidity

– decreases density of air
– increases density altitude

• Usually, not a major factor in density altitude
computation
– little effect on aerodynamic efficiency
– more a factor regarding engine performance
(moisture displaces air molecules)

The Venturi Tube and Bernoulli’s Principle
Giovanni Battista Venturi (late 1700’s), Italian physicist

kinetic energy
(velocity)
potential energy
(pressure)

velocity
increases
pressure
decreases

Bernoulli’s principle states that when the velocity of
airflow INCREASES, it’s pressure DECREASES
...
g
...
92 – Current barometric setting) x 1000 + current field elevation]

δ (delta) Pressure ratio:

θ (theta) Temperature ratio:

σ (sigma) Density ratio:

Pactual / Pssl
Actual pressure at current
altitude / Pressure at sea level
(29
...
g
...

Piper
...

• The pitot-static system comprises one or
more pitot probes (or tubes) facing the oncoming air flow to measure pitot pressure (also
called stagnation, total or ram pressure) and one
or more static ports to measure the static
pressure in the air flow
...


Pitot Static System

• The pitot tube is mounted facing forward with static pressure
detected at ports on one or both sides of the aircraft
...


Total pressure = Static pressure + Dynamic pressure
Static pressure: Static ports
Dynamic pressure: Pitot tube

Airspeed
• Airspeed is the speed of an aircraft relative to
the air
...

• EASA definition: Indicated airspeed means the
speed of an aircraft as shown on its pitot static
airspeed indicator calibrated to reflect
standard atmosphere adiabatic compressible
flow at sea level uncorrected for airspeed
system errors
...
Up to 200 knots CAS
and 10,000 ft (3,000 m), the difference is negligible,
but at higher speeds and altitudes CAS must be
corrected for compressibility error to determine EAS
...

• EAS is closely related to IAS shown by the airspeed
indicator
...


About EAS
• EAS is also called the “perfect IAS”
• If the airspeed system worked perfectly, it
would always display EAS
• The only difference between EAS and TAS is
density (temperature)
– Sophisticated systems use the Rosemont
temperature probe and computer to calculate
temperature ram rise friction (without
temperature input, there is no TAS reading)

True Airspeed
• TAS is speed of the aircraft relative to the
atmosphere
• TAS and heading of an aircraft constitute its
velocity relative to the atmosphere
...
4788 k nots)
= mach number
= Temperature ( kelvin )
= Standard sea level temperature (288
...
g
...
They use impact and static pressures as
well as a temperature input
...

• The result is the true physical speed of the aircraft
relative to the surrounding body of air
...


Continuity Equation

• The equation states that mass air flow, Q, is constant
...

• In transonic and supersonic flight, air density is compressed
and is regarded as dynamic
...

The width of the wing is greatest where it meets the fuselage at
the wing root and progressively decreases toward the tip
...
The average length of the chord is known as the mean
aerodynamic chord (MAC)
...
Pitch attitude (angle of fuselage relative to the
horizontal)
2
...
Angle of incidence (angle of wing relative to the
fuselage)
• AOA =Pitch attitude + incidence - angle of climb
Note: Pitch attitude does not equal AOA

Angle of Attack
Angle of Attack (AOA or α): Angle between the average relative
wind and chord line of the airfoil
– The angle of attack is the angle between the chord line and the average
relative wind
...


Center of Pressure: Point on the chord line where the Aerodynamic
Force acts
total lift

Lift Coefficient

SAMPLE DATA: SYMMETRIC AIRFOIL

Angle of Attack, a
A symmetric airfoil generates zero lift at zero a

Lift Coefficient

SAMPLE DATA: CAMBERED AIRFOIL

Angle of Attack, a
A cambered airfoil generates positive lift at zero a

SAMPLE DATA



Lift coefficient (or lift)
linear variation with angle
of attack, a

Lift (for now)







Cambered airfoil has
lift at a=0
At negative a airfoil
will have zero lift

Cambered airfoils have
positive lift when a = 0
Symmetric airfoils have
zero lift when a = 0

At high enough angle of
attack, the performance
of the airfoil rapidly
degrades → stall

NACA 4412 vs
...

AF comes from two components, lift and drag:
– Lift (L) is the component of the AF acting perpendicular to the relative wind
...
Point along the chord line around which all
changes in the aerodynamic force take place
2
...


Aerodynamic Force acts
through the center of
pressure
...
Lift from Wings / Elevator
in pitching aircraft, nose down)
Negative Lift: When it acts downward
(Eg
...
Rudders)
Thrust: When lift force moves forward (Eg
...

In normal flight circumstances, the relative wind is the opposite direction of the aircraft flight
path
...
If the flight path is forward then the relative wind is backward
...
If the flight path is forward and upward, then the relative wind is backward and
downward
...
If the flight path is forward and downward, then the relative wind is backward and
upward
...

Also relative wind can created by a
stationary object and the motion of the air
around it, as when an aircraft is pointed
down a runway for take-off
...

(Eg
...

• Newton’s third law of motion: to every action there is an equal
and opposite reaction
...


relative low pressure

upwash

downwash

Coefficients of Lift and Drag
• q = dynamic pressure
• V= TAS

ρ = density

• Aerodynamic force is the combination of lift and
drag, and is expressed similarly

Factors Affecting Lift
• There are eight factors that affect lift, and the first
three are readily apparent:
– Density (ρ)
– Velocity (V)
– Surface area (S)

• The remaining five factors are accounted for in the
coefficient of lift and influence production of lift
– Angle of attack (α)
– Camber

• The remaining three factors are not so easily
discernable
...
Leading Edge Stall
(abrupt departure,
boundary layer dissipates)

Trailing Edge Stall …
...


(no air attaches to
upper airfoil)

Stall
• Wing tip stall
increases with wing
taper or sweep

• Deep Stall:
T-tail is more at risk

High Lift Devices
• Two Types

– Delay boundary layer separation
(Blown flaps, that blows bleed air over the top of the wing to
re-energise boundary layer & Leading edge slats)
– Increase camber (Trailing edge Flaps)

• Increase CL at high AOA
• Reduce takeoff and landing speeds (reduces stall speed)
Example:
20,000 lb a/c at 250 kt develops 20,000 lb of lift
Slowing to 125 kt, lift devices increase CL so 20,000
lb is still produced at lower velocity

Flaps
•
•
•
•
•

Method to increase CLmax is to increase camber (flaps)
Stall AOA decreases
Visibility on takeoff/landing improves (lower pitch α)
Increase drag which enables steeper glide slope
Allows higher power setting without increasing
airspeed on landing (go-around)

Flaps
•
•
•
•
•
•

Deflecting flaps causes a twisting action to wing
Flap design determines amount (split is least)
Elevator used to compensate
First half of flap deflection increases lift
Second half of deflection increases drag
High structural load on aircraft (use at slower
airspeeds)
• Leading edge flaps operate similarly to trailing edge
flaps (increase wing area and camber)

Got Lift? Flaps
• Flaps increase
the wing’s
camber
...


• Almost all jet
transports also
have leading
edge flaps
...
3 and 1
...


Slats and Slots

• Slots allow high static pressure air under the wing to
accelerate through a nozzle and inject boundary layer
in upper airfoil
• As air accelerates, it converts from potential to
kinetic energy
• Added kinetic energy overcomes adverse pressure
gradient and adheres to airfoil
• AOA increases and Clmax increases

Slats and Slots
• Slats are movable leading edge sections that form slots
• Some deploy aerodynamically at high AOA
• Others deploy mechanically , hydraulically, or
electrically
• Camber is unchanged, so no change in CL due to area

Vortex

Vortex (Swept Wing)

•
•
•
•
•

Vortex Generator

Vortex generators modify the boundary layer
Flow in the boundary layer can be laminar or turbulent
Surface air adheres and slows, added layers slow less
Laminar air flows freely and is orderly and stable
Back from the leading edge is a transition region
where boundary layer becomes turbulent
• Despite the turbulence, on the wing surface, there is
still a thin laminar sub-layer with no turbulence
• This is due to the dampening effects of viscosity
• The sub-layer slows and becomes the cause of
separation and reverse flow, causing the wing stall

Vortex Generator
• A simple form of boundary layer control is achieved by
vortex generators
• A vortex generator (VG) may be a small vane
(aerodynamic device) attached to an airfoil)
• When the airfoil is in motion relative to the air, the VG
creates a vortex
• This removes part of the slow-moving boundary layer in
contact with the airfoil surface, energizes the flow to reestablish the laminar sub-area, which delays local flow
separation and aerodynamic stalling

Vortex Generator

• They affect boundary layer in the flow around a
airfoil
• Turbulent boundary layer is more resistant to
separation
• In this way it is possible to fly at a slower speed and
higher angles of attack
• Vortex Generators on stabilizers act similarly
improving the effectiveness of control at low speeds
and with high deflections of control surfaces

Boundary Layer Control Devices
Vortex generator
mounted on C-182 wing

vortex generators are small plates about an
inch deep standing on edge in a row
spanwise along the wing
...

These tend to prevent or delay the
breakaway of the boundary layer by reenergizing it

Wingtip Vortices

• High pressure air at stagnation point (leading edge) flows
spanwise (toward tip)
• At tip, flows around and to upper surface and adds to
downwash
• Downwash doubles
• Circular motion results in wingtip vortices

Winglets
No winglet compared with
blended winglet
Wingtip vortices reduce the aircraft performance by
reducing the effective angle of attack of the wing
through the induction of downwash
• Impact on fuel burn
• Vortices from large aircraft are dangerous for small
aicraft
• To prevent leakage of higher pressure air from
underneath the wing

Planform effects and
Induced drag,
Lecture 7

DRAG
THREE TYPES OF DRAG:
– TOTAL (Induced + Parasite)
– INDUCED
• Is a byproduct of lift
...

External fuel tanks, missile rack control surface drag)

DRAG

D= CD 1/2p S V2
D ~ Drag force
CD ~ Coefficient of lift
p(rho) ~ density of the air in slugs
S ~ total wing area in square feet
V ~ airspeed (in feet per second)
This is similar to the equations for lift and
aerodynamic perforce

Total Drag
• Induced and Parasite =
Total Drag
Can plot AOA for Clmax
v

^
As speed increases, parasitic
drag increases exponentially
As speed decreases, induced
drag increases exponentially
This is the drag curve

Lift to Drag Ratio
• Lift to drag ratio (L/D) is used to determine efficiency
of an airfoil
• A high ratio indicates a more efficient airfoil
• It is calculated by dividing lift by drag (all terms
except Cl and CD cancel out)

Drag: Total Drag (Power Required) Curve
1,400
1,200

max
...
2x, 20 Knots to 40 Knots), drag
or lift will be quadrupled (4x)
...


• In contrast, the relationship between lift or drag
and air density is a direct relationship
– an increase or decrease in air density will cause an
increase or decrease in both drag and lift

Planform Shapes
**Aspect Ratio:
Ratio of length to breadth (chord)**
High AR = long, narrow wings
Low AR = short, stubby wings

Characteristics that reduce induced drag:

Aspect ratio
Wing span
Wing area
Aspect Ratio: Span2/Area
** Wing span is the distance of the Wingtip to Wing root (For swept
wings) **
**Whereas for rectangular wings, the span is from Wingtip to Wingtip * *

Span
• Selecting span is a basic decision in design of a wing
• Span may be constrained by contest rules, hangar
size, or ground facilities
• **Best to use the largest span consistent with
structural dynamic constraints (flutter) which directly
reduces induced drag**
• As span increases, wing structural weight also
increases and at some point weight increase offsets
induced drag savings

Optimum Span
• This point is rarely reached, for several reasons:
– the optimum span is quite flat and must stretch a great deal to
reach the actual optimum
– concerns about wing bending as it affects stability and flutter
compound as span is increased
– cost of the wing increases as structural weight increases
– volume of the wing in which fuel can be stored is reduced
– it is more difficult to locate the main landing gear at the root of
the wing
– the Reynolds number of wing sections is reduced, increasing
parasite drag and Lmax

Surface Area
• Wing area, like the span, is chosen based on a wide
variety of considerations including:
–
–
–
–
–

cruise drag
stalling speed
field length requirements
wing structural weight
fuel volume

• These considerations often lead to a wing with the
smallest area allowed by the constraints
• However, sometimes wing area must be increased to
obtain reasonable CL at cruise conditions

Cruise Conditions

• Selecting cruise conditions is an integral part of the wing
design process
• Cruise altitude affects fuselage structural design and
engine performance as well as aircraft aerodynamics
• The best CL for the wing is not the best for the aircraft as
a whole
• An example of this is seen by considering a fixed CL, fixed
Mach design
– to fly higher, wing area must be increased correspondingly for
drag
– fuselage drag decreases, though
– So we can minimize drag by flying very high with very large
wings, but this is not feasible because of engine performance

Twist
Wing twist is calculated so cruise drag is not excessive
Twist changes structural weight by modifying the moment
distribution over the wing
Twist on swept-back wings produces a positive pitching
moment which has a small effect on trimmed drag
Amount of twist is a tradeoff
in cruise drag, drag in
second segment climb,
and wing structural weight
CATIA 6A - (Computer Aided
Three-dimensional Interactive
Application) by Dassault

Wing Sweep
•

*Is the angle between the line of 25% chord points and the longitudinal axis*
25% 25%

•

Vortex forms on a swept wing all
along the span (more induced
drag)
Note: Swept wing configuration
causes earlier stall, so takeoff
distance must be increased

Swept Wing Span
•
•
•

Span in a straight wing is the distance between two wing tips parallel to
the aircraft’s lateral axis (y-axis)
With a swept wing, span is twice the distance between one wing tip to the
fuselage center line parallel to the 50 % sweep chord line
Wing sweep angle alters wing span to an effective span which is smaller

Wing Sweep
• Sweep is chosen almost exclusively for its desirable effect on
transonic wave drag
• It permits higher cruise Mach number, or greater thickness/CL
at a given Mach number without drag divergence
• It increases additional loading at the tip and causes spanwise
boundary layer flow, exacerbating the problem of tip stall
which reduces CLmax or increases required taper ratio for
good stall
• It increases structural weight - because of increased tip
loading and increased structural span
• It stabilizes the wing aeroelastically but is destabilizing to the
aircraft
• Too much sweep makes it difficult to accommodate the main
gear in the wing

Taper Ratio
Rectangular wing (taper ratio of 1
...
0)

Ultimate taper ratio (but will
stall at wing tip vs
...
low pressure on aft portion)
– Also known as wake or form drag (proportional to size of wake
produced)

• Interference (restricts smooth flow, e
...
, fuselage -wing root
junction or external stores)
• Wave (behind a shockwave is an adverse pressure gradient
due to increase in static pressure as velocity slows)
• Ram (due to compression aft of jet engine compressor)
• Roughness (fasteners, joints)
• Trim (from use of horizontal tail download)

Parasite Drag
• Drag that is produced by non-lifting
portions of the airframe (i
...
, not the wings
or tail)
• There are 3 components of parasitic drag:
» Form Drag
» Skin Friction Drag
» Interference Drag

Form Drag
• The portion of drag that is generated because
of the shape of the aircraft
• Generated in the turbulent areas of airflow
where slipstream does not conform to aircraft
shape
• Varies directly with the airspeed

Skin Friction Drag
• The boundary layer air creates a stagnant
layer of air molecules
• Drag is created when the slipstream comes in
contact with this stagnant flow
• Varies directly with the airspeed

Interference Drag
• Created by the collision of airstreams
• Generated by mixing of streamlines between aircraft
components
• Example:

– air flowing around fuselage mixing with air flowing around an external fuel
tank
– we know drag of the fuselage and fuel tank individually
– total drag after attaching fuel tank will be greater than the sum of the
fuselage and fuel tank separately

• Causes eddy currents, restrictions, and turbulence to
smooth flow
• Varies directly with the airspeed

Drag at Zero Lift
• Reflects total drag coefficient for a given
power, speed, and altitude
• Is the drag area (f) which is the product of
zero-lift drag coefficient and aircraft's wing
area
• Is total drag minus induced drag

Parasite Drag

• Total parasite drag (DP) can be found by multiplying
dynamic pressure by an area
• Equivalent parasite area (f) is the area of a flat plate
perpendicular to the relative wind that would
produce the same amount of drag as form drag,
friction drag and interference drag combined
• It is not the cross-sectional area of the airplane
• DP will increase in direct proportion to V2

• q = dynamic pressure

Reducing Parasite Drag
• DP is the sum of form, friction and interference
• Some approaches to reducing drag:

– Form drag is reduced in the design phase by streamlining
– Skin friction is difficult to reduce, but can be smoothed,
machined, or coated
– Interference drag can be minimized by proper fairing and
filleting, which allows streamlines to meet gradually rather
than abruptly

• Parasite drag is not caused by lift or compressibility

Streamlining

• Shape of an object is a major factor
• Profile drag (skin + pressure) of an object increases as the
square of the velocity
– so, doubling airspeed (2x) increases drag four times (4x) at
subsonic speeds

Drag Noise

• Noise produced by induced and parasite drag can be
addressed with:
– Mid fuselage engine placement (Boeing 27)
– Over the wing (engine nacelles above leading edge of
wing)
– High aspect ratio wing (lower approach speed = less noise)
– Continuous flap trailing edge (reduces edge interference)
– Advanced exhaust duct liner (reduces fan noise)
– High bypass ratio engine (reduces jet noise)
– Krueger Slat
(B-737)

Ground Effect
• Occurs within several feet from the ground
surface, typically about one wing span in
height
• Change in three-dimensional flow pattern
around aircraft because the vertical
component of airflow around wing is
restricted by ground surface
• Alters wing’s upwash, downwash, and
wingtip vortices
• Reduction of wingtip vortices due to
ground effect alters spanwise lift
distribution and reduces the induced angle
of attack and induced drag
• Wing will require a lower AOA in ground
effect to produce the same lift coefficient
or, if a constant angle of attack is
maintained, an increase in lift coefficient
will result

Ground Effect
• Will alter the thrust required vs
...
4 percent

– however, when the wing is at a height equal to one-fourth its span,
reduction in induced drag is 23
...
6 percent

• So, a large reduction in induced drag will take place only when the wing
is very close to the ground
• Because of this variation, ground effect is most usually recognized
during the ground separation during takeoff or just prior to touchdown

Ground Effect
• These general effects point out the possible danger in attempting take off
prior to achieving the recommended takeoff speed
• Due to reduced drag in ground effect, the aircraft may seem capable of
taking off well below the recommended speed, however, as the aircraft
rises out of ground effect (OGE) with a deficiency of speed, the greater
induced drag may result in very marginal initial climb performance
• With high GTOW, high density altitude, or high temperature, a deficiency
of airspeed during takeoff may permit the aircraft to become airborne
but is incapable of flying OGE
– the aircraft may become airborne initially then settle back to the runway
– no attempt should be made to force the aircraft airborne because required
takeoff speed is necessary for initial climb performance
– for this reason, it is imperative that a definite climb be established before
retracting landing gear or flaps

Drag Bucket
Frequently associated with gliders
Refers to ratio of an aircraft's forward motion to its descent
when flown at constant speed
Is numerically equal to the aircraft's L/D ratio
Is in the low AOA regime for laminar airfoils

Laminar Flow
• Smooth, uninterrupted flow of air over the contour of the
wings, fuselage, or other parts of an aircraft in flight
• Is most often found at the front of a streamlined body
and is an important factor in flight
• If the smooth flow of air is interrupted over a wing
section, turbulence is created which results in a loss of
lift and a high degree of drag
• An airfoil designed for minimum drag and uninterrupted
flow of the boundary layer is called a laminar airfoil

Laminar Flow
• Laminar flow theory began with development of a
symmetrical airfoil section which had the same curvature
on both the upper and lower surface
• The design was relatively thin at the leading edge and
progressively widened to a point of greatest thickness as far
aft as possible
• The theory in using an airfoil of this design was to maintain
adhesion of the boundary layers of airflow which are
present in flight as far aft of the leading edge as possible
• The term laminar is derived from the lamination principle
involved with multiple overlaying steams of air

Laminar Flow
• Viscous drag (friction between air and surface) is much
larger in the turbulent boundary layer
• Energy to overcome this force is substantial
• A subsonic transport aircraft in cruise uses one-half of the
powerplant energy to overcome skin friction and boundary
layer drag
• The usual definition of a laminar flow airfoil is that the
favorable pressure gradient ends somewhere between 30
and 75% of chord

Laminar Flow

• Laminar flow is an inherently unstable condition
easily upset
• Two techniques are available to delay transition
from laminar to turbulent flow
– Passive: across leading edges of wing/tail with sweep
angle LT 18 deg so local pressure decreases over the
surface from leading edge to trailing edge; known as
natural laminar flow (NLF)
– Active: Uses surface cooling or removal of small amount
of boundary layer via suction on porous materials,
surface slots or small perforations; for high subsonic and
supersonic wings only suction can control sweep-induced
crossflow; known as laminar flow control (LFC)

Hybrid Laminar Flow

• Begun in the 1980s (with the B-767) laminar air flow has been
investigated to find ways to delay separation due to turbulence
working forward from trailing edge
• Similar innovation now used on 787-9
• Tiny holes covering unpainted leading
edge of 787-9’s vertical tail used to
control airflow over the surface
• Turbulent airflow is reduced using
suction as air pulls turbulent layer
through the small holes
• Technique used by NASA on F-16XL
and recently by Airbus on A320
test aircraft in the late 1990s
• By ingesting the turbulent layer of air
through the tiny holes, overall drag
over the tail surface is reduced

Jet Aircraft
Performance
Lecture 9

Thrust Available
• Engine Pressure Ratio

Thrust Available
• Result of airframe and powerplant characteristics
• Depicted in thrust and power curves
• Used to find
–
–
–
–
–
–

maximum endurance
range
angle of climb
rate of climb
glide endurance
glide range

Thrust
• Relates to Newton’s Second law (F = ma)
• Formula for Thrust
T = Q (V2 - V1)
Q = mass Flow
V2 = exhaust gas exit velocity
V1 = inlet air velocity

Or,

Q = p AV
So,
T = p AV1 (V2-V1)

Thrust
Thrust can be produced directly from
engines (turbojet, ramjet, rocket)
Power can be produced from propellers or rotors
Thrust is directly proportional to density
As density increases, so does available thrust (Fig
...
7)
Thrust is constant with airspeed – as airspeed increases,
change in V increases, so thrust remains the same
High by-pass engines (turbofans) lose available thrust as
airspeed increases (Because air is compressed at the front
and pushing against the compressor blades)
...
0, velocity air pressure is very high
No compressor or turbine is needed
Fewer components and higher tolerance for heat
Does not work at subsonic speeds
At Mach 6
...
6
...
g
...
These forces are:

DRAG
&
FRICTION

PERFORMANCE FACTORS
TAKEOFF & LANDING

For a given altitude and RPM, the thrust
from a propeller-driven airplane
decreases as velocity increases during
the takeoff roll
...


• Takeoff velocity is a function of stalling speed
...
2 x Vso
To find takeoff speed, find
stall speed first, and
multiply stall speed by 1
...
This is overcome
with:

REVERSE THRUST

PERFORMANCE FACTORS
TAKEOFF & LANDING
HYDROPLANING SPEED

TP (9)

INCREASE LANDING

DECREASE LANDING

• NO WINDS

• HEADWIND

• NO FLAPS

• FULL FLAPS

• NO BRAKES

• FULL BRAKING

• NO REVERSE

• FULL REVERSE

• HYDROPLANING

• DRY RUNWAY

• HIGH WEIGHT

• LOW WEIGHT

PERFORMANCE FACTORS
TAKEOFF & LANDING

For a given altitude and RPM, the thrust
from a propeller-driven airplane
decreases as velocity increases during
the takeoff roll
...
e
...
e
...
e
...


“Torque Reaction”
• Newton’s 3rd – airplane turns propeller, propeller turns airplane
• A left-banking
tendency causes
roll to left
• On ground, wheel
friction increase t
• Counter with
offset engine and
rudder in TO/flight

Corkscrew effect (spiraling slipstream)
•
•
•
•

Propwash spirals around fuselage
During TO, strong sideward force on tail
Vertical stabilizer is on the top of the airplane, not the bottom
A left-yawing
tendency
• Causes rolling
moment (long ax)
• With a/s, spiral
elongates and is
less effective
• Counteracting torque and spiral

“P-factor”
• Downward moving blade takes a bigger “bite” of air than
upward moving blade (asymmetric loading)
• Difference in rotation
(and relative wind)
• Left yawing tendency

Gyroscopic precession
• “90 degrees ahead in
the direction of
rotation”
• Occurs during pitching
(e
...
rotation about the
lateral axis)
• Right-yaw tendency
when the nose is rising
• Left-yaw tendency when
the nose is falling

Gyroscopic precession
• A left-turning tendency during takeoff in
taildragger aircraft only
...

Pitching = Lateral axis (Longitudinal Stability)
Rolling = Longitudinal axis (Lateral Stability)
Yawing = Vertical axis (Directional Stability)

Center of Gravity
• Most aircraft are designed so the wing center of lift (CL) is rear of CG
(makes a/c nose heavy and downward force used on horizontal stabilizer to
balance)
• Conventional designs (horizontal stabs on fuselage), wing downwash
produces negative lift on stab
• So, as speed decreases, downward flow is reduced, and nose will pitch
down
• As nose lowers, AOA is reduced, airspeed increases, downflow is restored,
etc
...

257

• Effect of CG

More on Stability

– Forward CG

• Stronger tail load
• Less efficient
• Outside limits

– May not be able to
land aircraft properly

– Aft CG

• Lighter tail load
• Decreases stability

– Stall recovery difficult

down lift

lift

Aside: CG and Center of Pressure
Location

• Aft CG increases speed:

– the tail creates less lift (less drag);
– the tail creates less down force (wings need to create less lift)
...

259

Longitudinal Static Stability
• The wing contribution to longitudinal static stability
depends mainly location of wing AC with respect to CG
• Straight wing aircraft have AC forward of CG, causing
longitudinal static instability

Wing Sweep
• When wings are swept to forward position they exert
strong longitudinal destabilizing effect
• Because AC is forward of CG, it increases
maneuverability
• As wings move aft, AC moves aft making aircraft
more longitudinally stable

Fuselage
• Fuselage acts as an airfoil and produces lift
• Fuselage AC is located fwd of CG
• With increased AOA fuselage produces lift
(destabilizing effect)
• So, the fuselage is a negative contributor to
longitudinal stability

Moment
• A body free to rotate will turn about the center of gravity – called
moment in aeronautics
• Moment = force applied x distance at which applied
• Moment arm = distance from datum point to applied force
• Moment is expressed in terms of distance of the arm x aircraft
weight (in inch pounds)
• Often located at the 20% point of mean aerodynamic chord
• Designers prefer to keep the moment small
• Pilots use controls to counteract forces acting to destabilize the
aircraft
• Trimming devices are used to offset forces set up by fuel
burnout, passenger and cargo load changes, AoA
• Elevator trim tabs and adjustable horizontal stabilizers are the
most common

Horizontal Stabilizer
• Is a symmetric airfoil designed to stabilize aircraft around
lateral axis
• Contribution to longitudinal static stability is from moment it
produces around CG
• Since it’s CG is well behind aircraft CG, the horizontal stab
has greatest effect on longitudinal static stability
• Larger horizontal stab increases pitching moment so is used
on shorter aircraft
• Tail-mounted engine nacelles will increase longitudinal
stability

Neutral Point

• Longitudinal static stability provided by horizontal stab must
overcome wing and fuselage instability
• Note several points of AC, and calculated point where entire
aircraft CG is located
• As CG moves aft, static stability decreases
• NP defines farthest aft CG position without negative stability
• Beyond that the a/c becomes unstable and pilot has difficulty
controlling flight

Dynamic Stability
• Represented as variations of controlled functions versus time

• There are two dynamic longitudinal oscillatory modes
– Phugoid (If one cycle exceeds 10 seconds)
– Short-period (1 – 2 seconds for each cycle)

• If the time unit for one cycle is above 10 seconds duration, it
is called a long-period oscillation (phugoid) and is easily
controlled
• In a longitudinal phugoid oscillation, AOA remains constant
when airspeed increases and decreases
• A convergent phugoid is desirable but not required
• The phugoid can be determined only on a statically stable
aircraft and greatly affects trimming qualities

Short-Period
• If the time period for one cycle is 1 or 2 seconds, it is called
a short-period oscillation and is very difficult to control
(often the pilot gets in phase with the oscillation and
reinforces it)
• A neutral or divergent, short-period oscillation is dangerous
because structural failure results if the oscillation is not
damped immediately
• Short-period oscillations affect control surfaces and reveal
themselves as porpoising in the aircraft or as buzz or flutter
in the control surfaces
• A short-period oscillation is a change in AOA with no change
in airspeed
• Short-period oscillation of a control surface is of high such
frequency the a/c does not have time to react

Dynamic Stability
• Dynamic stability – long-term characteristics
of the airplane
– Positive dynamic
stability:
– Assume positive
static stability

– Damped oscillations

Dynamic Stability
• Neutral dynamic stability
– Persistent
(phugoid)
oscillations

Dynamic Stability
• Negative dynamic stability

– Increasing (divergent) oscillations
– Never returns to
equilibrium
– Avoid at all costs

Dynamic Stability
• If no positive static stability, cannot have positive
dynamic stability
• So, to return to equilibrium, aircraft must have both
positive static and dynamic stability
• Thus, if positive static stability and negative
dynamic stability, aircraft returns to trim but has
diverging oscillations

Lateral and Directional
Stability
Lecture 13

Stability - how do we get it?
• Lateral (roll stability)
– Keel effect

Stability – how do we get it?
• Lateral (roll) stability
– Dihedral

– “When the airplane is banked
without turning, it tends to
sideslip or slide downward
toward the lowered wing
...
”

Lateral Stability
• If one wing is lowered (e
...
by turbulence), the
airplane sideslips
...

– This raises the lower wing
...
g
...

– The airplane turns to the right
...
F18, to
be able to fit into aircraft carrier hangar)

Directional Divergence
• Condition of flight in which reaction to small sideslip results in
an increase in sideslip angle
• Caused by negative directional static stability
• Could result from tail damage
• If aircraft experiences negative directional stability at high AoA,
result will be nose-slice directional divergence

Spiral Divergence
• Strong directional stability and weak lateral stability
• Disturbance causes wing to dip which starts roll to left
• With weak lateral stability it cannot correct and flight path
arcs to left
• A/C responds to new RW and yaws into it
• Right wing is advancing and increased airflow causes more roll
to left

Dihedral Effect

• This is roll due to sideslip and is a cross coupling effect
• Yaw produces roll
• Dihedral effect can be created several ways
–
–
–
–

Sweep the wings (design)
Place wings high on fuselage
Attach a high vertical tail
Tilt wings up geometrically

• The stronger the dihedral effect, the more powerful
the roll-off response is to sideslip excursions
• Gliders have no dihedral, so nose will yaw but not roll

Anhedral Effect
Highly maneuverable fighter planes have no dihedral
and some fighter aircraft have wing tips lower
than the roots, giving the aircraft a high roll rate
A negative dihedral angle is called anhedral

The AV-8B Harrier II above has a negative dihedral (anhedral) effect

Control – Aircraft Types
• Stabilization

– maintaining aircraft equilibrium re aerodynamics, propulsion, gravity,
and moment
– a compensatory control

• Regulation

– control against disturbances (e
...
, from atmospheric forces)
– a compensatory control

• Maneuvering

– equilibrium of the aircraft is being changed intentionally
– a compensatory and precognitive control

Control - Positions

• Direct -- (yoke) ………………………
...

• Indirect velocity

(variable joystick or cursor key)

Open and Closed Loop Feedback
• Closed loop
–
–
–
–

provides continuous information to the operator
can be manipulated at will
employs slow movement accuracy
HOTAS

• Open loop

•

– involves higher level motor programs
– operator must re-enter the system and decide on action
required and degree of motor activity
– operator does not receive continuous feedback
– release direct controls and reorient to other tasks, monitor
systems and situation (autopilot)
– often found in automated flight control systems

Closed-Loop
• Characteristics are that the system
– Is limited by the amount of available bandwidth
(frequencies)
– Is used to explain slow movement
– requires about 200 msec to perceive action and
movement

Open-Loop
• Characteristics are that the system
– Is used with higher-level motor programs
– Is applied in systems where thinking is required
BEFORE movement begins
– is NOT based on feedback

Dynamic Lateral Stability

• Lateral and directional stability are interrelated
• This is called cross-coupling
• Motions of an a/c are such that rolling motion causes
yawing motion and v/v

Dynamic Directional Stability

• Defined as the amount of oscillations and the time to
return to steady state condition, when disturbed
• Affected by yaw damping, also called yaw moment due
to yaw rate (Nr)
• Both parameters are affected by size of vertical tail and
how far located from CG (known as “tail volume”)
• Bigger and farther away the tail is, stronger the static and
dynamic directional stability
• Other features to strengthen
directional stability are ventral fins
• Controlled by yaw damper system that
senses yaw rate and provides
rudder response to oppose the rate

Modes
• The three modes are coupled, in two axes
• Dutch Roll, is a second order response defined by
oscillations in yaw and roll when disturbed with
sideslip from steady flight
• Spiral mode (sometimes called lateral stability) is a
first order response (no oscillations) to a
disturbance in angle of bank
• Roll mode (a control mode) is a first order response
defined as how quickly an aircraft reaches steady
state roll rate with a lateral control input

Dutch Roll
• Term taken from ice skating (left to right using outer
edges)
• Type of aircraft motion consisting of an out-of-phase
combination of "tail-wagging" and rocking from
side to side (yaw-roll coupling)
• Heavily influenced by:
–
–
–
–
–

Static directional stability or yaw due to sideslip
Yaw damping or yaw due to yaw rate
Dihedral effect or roll due to sideslip
Roll damping or roll due to roll rate
Adverse and proverse yaw

Dutch Roll
• When a sideslip excursion occurs

– Dihedral effect causes roll opposite the sideslip
– Then static directional stability returns aircraft back into relative
wind
– Depending on Nr and LP , a/c will oscillate in yaw and roll
– If dynamically stable, a/c will return to steady state flight

• If dihedral effect is strong, oscillations will be more roll than
yaw
• If dihedral is weak, oscillations will be mostly yaw
• Typical airliner with swept wings will exhibit angle of
bank oscillations twice those in sideslip
• Adverse and proverse yaw can initiate Dutch roll

Spiral Mode
• First order motion with respect to angle of bank

– If a/c continues to roll off after AOB established and hands off, it is
said to be divergent
– If a/c rolls out, then is said to be convergent
– If a/c remains in same AOB, is said to be neutral
– These are felt in the flight controls

• Main parameters of spiral mode are
directional stability and dihedral effect
• If strong directional stab and weak dihedral,
a/c will tend toward divergent spiral
mode (and v/v)
• The text is misleading here, as well,
(states all a/c must have lat
...
g
...
g
...
g
...
0) is due to
low lift coefficients at the tip and high lift coefficients at the
root
• Since area of highest lift coefficient will stall first, the
rectangular wing has a strong root stall tendency
• This pattern provides adequate stall warning and aileron
effectiveness
• The planform is limited to low speed, light-weight airplanes
where simplicity of construction and favorable stall
characteristics are the predominating requirements
• A highly tapered wing (λ = 0
...
5) have a lift distribution and
stall pattern that is similar to the elliptical wing

Stalls
• Stalls cannot be eliminated, but can be made more
predictable by having the wing stall gradually
• Since most airplanes do not have rectangular wings, they
tend to stall with little or no warning
• Wing tailoring techniques are used to create a root to tip
stall progression and give the pilot some stall warning
while ensuring that the ailerons remain effective up to
a complete stall
• Trailing edge flaps decrease stalling angles of attack in their
vicinity, causing initial stall in the flap area
• Boundary layer control devices and vortex generators are
used to delay BL air separation and to inhibit stall near
wing tips
• Propeller a/c may have a tip stall tendency during poweron stalls due to the increased airflow over wing root

Wing Twist
• Geometric twist is a decrease in angle of incidence from
wing root to wingtip
• Root section is mounted at an angle to the longitudinal
axis, and the leading edge of the remainder of the
wing is gradually twisted downward
• This results in a decreased AoA at the wingtip due to its
lower angle of incidence
• The root stalls first because of its higher AoA
• A typical wing twist might be 3º

Aerodynamic Twist

• Aerodynamic twist (section variation) - gradual
change in airfoil shape that increases CLmax AoA
to higher value near the tip than at the root
• Accomplished by decrease in camber from root to
tip or decrease in relative thickness of wing (as
compared to chord) from root to tip
• Since thicker and more positively cambered airfoils
stall at lower angles of attack, wing root stalls
before wingtip

Aerodynamic Twist

• Spanwise flow on a swept wing is not accelerated over the
wing and does not contribute to the production of lift
– Instead, it induces a strong tip stall tendency

– Stall fences redirect airflow along the
chord, delaying tip stall and enabling
wing higher AoA without stalling

– A sharply angled piece of metal (stall strip) is mounted on
the leading edge of the root section to induce a stall at the
wing root
– Since subsonic airflow cannot flow
easily around sharp corners, it
separates the boundary layer at
higher angles of attack, ensuring
that the root section stalls first

Stall Pattern
• Most desirable stall pattern on a wing is one that begins at
the root
• Primary reason for a root first stall pattern is to
maintain aileron effectiveness until wing is fully
stalled
• Local stall patterns near wing tips result in loss of lateral
control
• Also, turbulent airflow from wing root may buffet the
empennage, providing an aerodynamic warning of
impending stall
• Different planforms have characteristic stall patterns

Stall
• Laminar vs
...
8G

Stall speed
increases
accordingly
345

Stall Recovery
• To produce required lift at slow speeds, must fly at high AoA
• Flying slow at high AoA is a critical phase of flight, so pilots
practice recovering from several types of stalls
• Steps in a stall recovery involve simultaneously adding power,
relaxing back stick pressure and rolling wings level (“max,
relax, level”)
– Add power to increase airspeed, break descent (especially at low
altitudes) and restore a V greater than VS
– Decrease the AoA to recover from a stalled condition
– Initial reaction is to pull nose up, however, exact opposite must be done
– Control must be moved forward to decrease AoA and allow wing to
provide sufficient lift to fly once again
– By lowering nose, AoA is decreased and boundary layer separation point
moves back toward trailing edge, restoring lift
– Pilot rolls out of bank to wings level to decrease stall velocity and use all
available lift to break any further descent

Spin
•
•
•
•

Early in aviation, a spin usually ended in a fatality (airmail)
Once understood, pilots have practiced recovering from spins
The spin itself, however, has no practical value as a maneuver
There are three reasons for teaching spins
– every aircraft that is capable of stalling has the potential for entering a
spin (in high performance aircraft, many maneuvers are flown near the
stall region)
– spin training builds confidence in ability to handle an aircraft should it
inadvertently enter a spin
– spin training improves a pilot’s ability to remain oriented and still
make appropriate control inputs

• Aircraft have different spin characteristics and recovery
techniques
• Therefore, the pilot must know the flight manual procedures
for spin prevention and recovery for aircraft they fly

Spin
A spin is a stall that is aggravated with a turning and
yawing condition

Aggravated Stall
• A spin is an aggravated stall that results in autorotation

– Autorotation is a combination of roll and yaw that propagates itself
and progressively gets worse due to asymmetrically stalled wings

• For an aircraft to spin, it must reach stalled AoA and have
excessive yaw
• If an aircraft is not stalled, it will not spin
• If either the stall or yaw is removed, the aircraft will not
continue to spin

– A yawing moment can be induced with the rudder, by adverse yaw,
gust wing loading, etc
...
5 degrees per
second

364

Formulas
Radius of Turn:

Rate of Turn:

Turning Flight
• A/C turn by rotating lift vector and applying an
increased normal force (G)
• With lift rotated (in AOB), effective lift perpendicular
to weight decreases so normal force increases
• Greater force = turn and climb
• Lesser force = descend and turn
• Text uses examples of level turns
• In vertical loop, there is no AOB, yet a/c has turn rate
and radius
• Note: normal acceleration is also notated as NZ

Slips and Skids

•
•

•

•

Normal turn
– Horizontal lift equal centrifugal force
Slipping turn
– Horizontal lift greater than centrifugal force
– Need more rudder (is opposite turn direction)
Skidding turn
– Horizontal lift greater than centrifugal force
– Need less rudder (high risk of stall)
The greater the angle of bank, the greater the load placed on the aircraft

Lift Vector
Change direction of a/c flight path by reorienting lift vector in
desired direction
Lift vector divided into 2 components - horizontal and vertical
Horizontal (centripetal force) accelerates a/c toward inside of turn
In level flight lift = wt, but in turn only vertical component opposes wt

If no increase in total lift vector, a/c will lose altitude because wt
is greater than LV
Increased lift is obtained by increasing AoA
Load factor (n) is the ratio of total lift to the airplane’s weight
Ex: 3,000 lb a/c in 60º AOB turn needs 3,000 lb of vertical lift to
maintain altitude
...
g
...

The airplane’s wings are supporting only the
weight of the plane
 Turning increases load factor (G’s) b/c you are
accelerating around a corner

Load Factor
• Load factor results from two
forces - centrifugal force
and gravity
• For any given bank angle, rate of
turn varies with airspeed higher the speed, slower
the rate of turn
• Load factor increases
significantly after bank r
eaches 45°or 50°
• Load factor for any a/c in 60°bank
is 2 G’s
• Load factor in 80°bank is 5
...
2 ft/s2
• An a/c at 2 Gs is experiencing twice the acceleration
forces of gravity
• When wing is loaded (elevated G), it requires greater
AoA to maintain airspeed at increased wt (load)
• Therefore, is closer to stall than if unloaded (true
whether aerodynamic loading or physical loading)

• VS with AoB

Accelerated Stall

• Shown for AoB in level flight, although relationship
between G and VS remain same regardless of AoB
Use AOB to
determine
normal load
factor (G)
...
g
...
attack a/c)

Maneuvering Airspeed
• Maximum speed at which a/c may be stalled safely is
determined for all new designs
• This speed is the “design maneuvering speed” (VA)
• VA is fastest airspeed a/c can travel when full
deflection of controls is possible
• Airspeed where aerodynamic lift limit curve meets load
limit factor (LLF) line (structure damage)
• If fly faster, possible structural damage if a/c exceeds
LLF (excess G in turn or severe turbulence)
• As a/c burns fuel, becomes lighter, so VA becomes less
(reduced weight, same as with stall)

Maneuvering Envelope
• Used in KIAS, KCAS, KEAS where unaffected by
density
• Use IAS to gauge approach speed, thunderstorm
penetration, and max gear and flap speeds
• Curve from origin to load limit factor is aerodynamic
lift limit - √G
• Airspeed limits are
– VNE (never exceed)
– VMO (max operational)
– MMMO (max operational Mach)

VG Diagram
• When a/c is operated outside of envelope, permanent
deformity of a/c structure may occur or high rate of fatigue
damage
• Operation above limit load factor must be avoided in normal
operation
• There are two other points of importance on the VG diagram
• First, is intersection of the positive limit load factor and
the line of maximum positive lift capability
– Airspeed at this point is the minimum airspeed at which limit
load can be developed aerodynamically
– Any airspeed greater than this provides a positive lift capability
sufficient to damage the a/c
– Any airspeed less does not provide positive lift capability sufficient
to cause damage from excessive flight loads

• This is “maneuvering speed”

•
•
•
•

VG / VN Diagram
Graph where scales are based on velocity
vs
...

The borders of this flight regime are called
flight envelope or manoeuvring envelope
...
g
...

• Although supporting load at 150% of max, parts of
a/c may bend or twist
• This 1
...
g
...
g
...
5 X 2/3) X 2/3) = 2
...
5 to 9 G

Forward CG
• Forward CG location increases the need for greater back
elevator pressure, however, may no longer be able to
oppose increase in nose-down pitching
• Higher elevator control forces normally exist with forward
CG due to increased stabilizer deflection
• Nose-up trim involves setting the tail surfaces to produce
greater down load on aft portion of fuselage, which adds
to wing loading and total lift required from wing if
altitude is to be maintained
• Requires a higher AoA which results in more drag and
produces a higher stalling speed
• With forward loading, “nose-up” trim is required to maintain
level cruising flight
• It is required that the trimming device be capable of holding
a/c in a normal glide with power off

Aft CG
• A/C becomes less stable as CG moves aft which causes
increase in AoA and wing contribution to stability
decreases
• With aft loading and “nose-down” trim, the tail surfaces will
exert less down load, relieving wing of that much wing
loading and lift required to maintain altitude
• Recovery from stall becomes more difficult as CG moves aft
• Important in spin recovery, due to point in rearward loading
of a/c at which flat spin will develop
• A zero indication on the trim tab control is not the same as
“neutral trim” because of the force exerted by
downwash from wings and fuselage on tail

CG
• Maneuvering a/c in turbulent air requires application of
greater control forces when load is dispersed
• Longer moment arms to positions of heavy fuel and cargo
loads must be overcome by control surface actions
• A/C with full outboard wing tanks are sluggish in roll while a/c
with full nose and aft cargo bins are less responsive to
elevator controls
• Requirements for type certificate specify a/c at certain speed
will dampen out vertical displacement of nose within
certain number of oscillations

High speed Flight
Lecture 16

Compressibility
• At speeds below 260 knots, air is incompressible
(altitude with density constant and varied P)
• Compressibility effects become more important as
speed increases
• Compressibility (and viscosity) is very important at
speeds approaching speed of sound
• In these speed ranges, compressibility causes a
change in density of air around a/c

Mach Number
• Mach is the ratio of true airspeed to the
speed of sound
– Speed of sound decreases with temperature
– Temperature decreases with altitude
– At higher altitudes, same IAS leads to higher
Mach numbers
– Conversely: at higher altitudes, a certain Mach
number can be achieved at a lower IAS

• IAS increases with altitude compressibility
(descending)

High Speed Flight
• Subsonic (Mach ~0
...
7 to ~1
...
3 to 5
...
0)
– Aircraft speeds above Mach 5
...
g
...
0), but does not
exceed it
• Actual MachCrit varies among a/c, however sweepback and
thicker airfoils wing will delay and lower MachCrit because wing
will accelerate airflow faster than a thinner one (Thick
sweptback wings reaches its critical Mach faster than
thinner wings)
• Possible to have both supersonic and subsonic airflow at same
time
• Acceleration results in compressibility effects (e
...
, shock wave
formation, drag increase, buffeting, stability, and control
difficulties

MachCrit
• Flight in transonic and supersonic ranges are common for
military a/c, however, civilian jet a/c normally operate in
cruise at Mach 0
...
90
• MachCrit is the boundary between subsonic and transonic
flight and point of reference for all compressibility effects
in transonic flight
• Shock waves, buffet, and airflow separation take place above
critical MachCrit

MachCrit
• A/C is most efficient when cruising at or near MachCrit
• At speeds 5 – 10 % above MachCrit , compressibility effects
begin and drag rises sharply (with buffet, trim, stability
changes, and decrease in control surface effectiveness)
• This is the point of drag divergence, and is typically the speed
chosen for high-speed cruise operations
• At some point beyond high-speed cruise are turbine powered
a/c max operating speeds: VMO and MMO

Speed Ranges
• VMO is max operating speed in kts (limits ram air pressure
acting against structure and prevents flutter)
• MMO is max operating speed in Mach number and should not
be exceeded (possible loss of control)
• MachCrit and MMO for a/c occur at a given Mach number
• TAS, however, varies with OAT, so TAS corresponds to a specific
Mach number
• When a/c cruising at constant Mach number enters area of
higher OAT, TAS and required fuel increases, and range
decreases

Speed Ranges
• Unlike operations in lower altitudes, IAS at which jet a/c stalls
increases significantly with altitude due to TAS increase
• At high TAS, air compression causes air flow distortion over
wings and in pitot system
• At same time, IAS representing MMO decreases with altitude
• Eventually, a/c can reach altitude where there is no difference
between IAS and TAS

Subsonic Flight
• When at subsonic speeds, “pressure warning” is transmitted
at speed of sound ahead of a/c
• Air ahead moves aside before a/c arrives and is prepared to
let it pass easily
• When a/c reaches speed of sound, pressure change can no
longer warn because a/c is at front of own pressure
waves
• Air piles up in front of a/c causing sharp decrease in flow
velocity (corresponds with increase in air pressure and
density)

High Subsonic Flight
(Below MCrit )
•

Local airflow speed over wing is greater than a/c speed (due to continuity
or AV = K)

(At MCrit )
•

As a/c speed increases so does maximum speed of airflow over wing

Shockwave
•
•
•

At high subsonic speeds, high camber portions of the wing can induce
supersonic airflow (MCrit)
Where the airflow slows to subsonic speeds behind that point, a shockwave
forms
The shockwave causes boundary layer separation

– High-speed buffet, “aileron snatch”, “Mach tuck”
– Mach tuck is caused by the center of pressure moving rearward to 50% of chord on the
wing
...
0 and decreases after
transition into supersonic regime above Mach 1
...
0
• Gave rise to notion of unbreakable sound barrier, because
seemed no a/c would have the force to overcome it

it

Supersonic Flight
• Normal shock waves move aft to trailing edge
– Increase in size and strength
-- AC shifts from 25% MAC to 50% MAC
AC = aerodynamic center

MAC = mean aerodynamic chord

Supercritical Airfoils
(Circular Arc or Bi-convex)

• **Allows normal shock wave where upper surface
pressure gradient is favorable**
• **Is designed with less curvature on upper surface **
• Avoids some of the poor low speed problems
associated with the double-wedge airfoil

Sweep
• Delaying wave induced separation improves performance
• On straight wing, air strikes leading edge at 90° to produce lift
• Sweepback concept is that only airflow perpendicular to wing
affects pressure distribution and shock waves
– Swept wing is struck by airflow at smaller than 90°

• Has effect of wing flying slower and delays shock wave forming
• Advantage of sweep is increase in MachCrit and force divergence
• **If wings swept back on TO roll, a/c would have greater stall
speed for same wing area and speed/distance for TO
would be greater**

Supersonic Engine Inlets
(Well Above Mach 1)

• To reduce energy loss from a strengthening
normal shock, use a “spike” inlet
• **Spike produces oblique shock waves which
weaken normal shock wave and reduce
compressibility drag**

Rotor Aerodynamics
Lecture 17

Rotor Systems
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Semi-rigid (Bell-205)
Articulated (AS-330)
Intermeshing (Kaman K-Max)
Tandem (Boeing 46)
Coaxial (Kamov Ka-50)
Hingeless (BK-117)
Bearingless (EC-145)
Transverse (AW 609)
Hybrid (ABH-X3)

Semi-Rigid Rotor System
• Normally two bladed systems
• Teetering “see-saw” or underslung
• Blades move in two directions
– Feather
– Flap

• Bell UH-1 Huey

Fully Articulated Rotor System
• **3 or more blades that lead, lag, and flap**
• Blades travel independently of each other
through full range of motion
• Anti-flap bushings
• Dampers
• Sikorsky H-60

Rigid Rotor System
• Mechanically simple, structurally complex
• Smaller, simpler helicopters
• Minimal blade movement
– Blades absorb most movement
– Feather only (pitch)

• MBB Bo 105

Blade Twist
• **Helicopter blades are designed with a twist in
order to prevent uneven lift distribution**
• Twist offsets differential lift caused by blade speed
• Twisted blades generate more lift near the root
and less lift at the tip than untwisted blades

Ground Effect
• Less than 1 rotor disk diameter hover height results in
surface friction
• **When hovering, effective lift is increased and induced
drag is reduced**
• Lower blade AoA for same lift
• Restricts generation of blade tip vortices

Out of Ground Effect
• Induced flow no longer restricted
• Blade tip vortices increase with decreased outward
airflow
• Drag increases
• More power required

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Aerodynamic Considerations Unique to
Rotorcraft
Translating tendency
Coning
Translational lift
Dissymmetry of lift
Retreating blade stall (VNE)
Autorotation
Vortex ring state (settling with power)
Dynamic rollover

Blade Coning
• Centrifugal force causes the rotor blades to
“pull” from the center of the rotor hub
– Provides strength to support helo

• Lift generated from blade AoA
• Coriolis Effect
Lift

Hover

Flat Pitch
(On the Ground)

C Effect
Center of Mass

Retreating Blade Stall
•

“Retreating” blade stalls in forward flight
due to insufficient lift capability
AoA increase required on retreating blade
to compensate for increased airspeed
Generates VNE speed
– VNE = point where retreating blade will
stall
– Retreating blade is incapable of
producing enough lift to suspend
weight of aircraft
Stall limits fixed wing slow speeds and
rotary wing maximum speed

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**When approximately 25% of
rotor disk becomes stalled**

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Rolling tendency
Nose pitch up
Vibrations

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STALL
REGION

Autorotation
• Powered flight - rotor drag overcome by engine
• Loss of engine - RPM must be maintained using upward
airflow
• Altitude = potential energy
– Potential energy converted to kinetic energy

• Dissymmetry of lift minimized

Autorotation - Entry
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Loss of engine power
Rapid rotor RPM decay
Trim considerations
Quick initial collective reduction
Slow to best airspeed
Horizontal flow of air changes to vertical flow

Autorotation - Steady State Decent
• **While descending, upward relative wind
counteracts induced flow*
• Rotational relative wind slower near blade
root
(hub)
– Increases toward blade tips

• 3 blade regions in a steady state auto
– Driven
– Driving
– Stall

Driven/Driving/Stall Regions
• Driven - nearest to blade tips
– Total aerodynamic force inclined slightly behind rotating axis,
resulting in drag force which slows blade rotation

• Driving - between 25 -70 percent of blade radius
– Total aerodynamic force is inclined slightly forward of axis of
rotation, supplying thrust to accelerate blade rotation

• Stall region - inboard 25 percent of blade radius
– Operates above the stall angle of attack, causing drag which slows
blade rotation



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