- •Textbook Series
- •Contents
- •1 Overview and Definitions
- •Overview
- •General Definitions
- •Glossary
- •List of Symbols
- •Greek Symbols
- •Others
- •Self-assessment Questions
- •Answers
- •2 The Atmosphere
- •Introduction
- •The Physical Properties of Air
- •Static Pressure
- •Temperature
- •Air Density
- •International Standard Atmosphere (ISA)
- •Dynamic Pressure
- •Key Facts
- •Measuring Dynamic Pressure
- •Relationships between Airspeeds
- •Airspeed
- •Errors and Corrections
- •V Speeds
- •Summary
- •Questions
- •Answers
- •3 Basic Aerodynamic Theory
- •The Principle of Continuity
- •Bernoulli’s Theorem
- •Streamlines and the Streamtube
- •Summary
- •Questions
- •Answers
- •4 Subsonic Airflow
- •Aerofoil Terminology
- •Basics about Airflow
- •Two Dimensional Airflow
- •Summary
- •Questions
- •Answers
- •5 Lift
- •Aerodynamic Force Coefficient
- •The Basic Lift Equation
- •Review:
- •The Lift Curve
- •Interpretation of the Lift Curve
- •Density Altitude
- •Aerofoil Section Lift Characteristics
- •Introduction to Drag Characteristics
- •Lift/Drag Ratio
- •Effect of Aircraft Weight on Minimum Flight Speed
- •Condition of the Surface
- •Flight at High Lift Conditions
- •Three Dimensional Airflow
- •Wing Terminology
- •Wing Tip Vortices
- •Wake Turbulence: (Ref: AIC P 072/2010)
- •Ground Effect
- •Conclusion
- •Summary
- •Answers from page 77
- •Answers from page 78
- •Questions
- •Answers
- •6 Drag
- •Introduction
- •Parasite Drag
- •Induced Drag
- •Methods of Reducing Induced Drag
- •Effect of Lift on Parasite Drag
- •Aeroplane Total Drag
- •The Effect of Aircraft Gross Weight on Total Drag
- •The Effect of Altitude on Total Drag
- •The Effect of Configuration on Total Drag
- •Speed Stability
- •Power Required (Introduction)
- •Summary
- •Questions
- •Annex C
- •Answers
- •7 Stalling
- •Introduction
- •Cause of the Stall
- •The Lift Curve
- •Stall Recovery
- •Aircraft Behaviour Close to the Stall
- •Use of Flight Controls Close to the Stall
- •Stall Recognition
- •Stall Speed
- •Stall Warning
- •Artificial Stall Warning Devices
- •Basic Stall Requirements (EASA and FAR)
- •Wing Design Characteristics
- •The Effect of Aerofoil Section
- •The Effect of Wing Planform
- •Key Facts 1
- •Super Stall (Deep Stall)
- •Factors that Affect Stall Speed
- •1g Stall Speed
- •Effect of Weight Change on Stall Speed
- •Composition and Resolution of Forces
- •Using Trigonometry to Resolve Forces
- •Lift Increase in a Level Turn
- •Effect of Load Factor on Stall Speed
- •Effect of High Lift Devices on Stall Speed
- •Effect of CG Position on Stall Speed
- •Effect of Landing Gear on the Stall Speed
- •Effect of Engine Power on Stall Speed
- •Effect of Mach Number (Compressibility) on Stall Speed
- •Effect of Wing Contamination on Stall Speed
- •Warning to the Pilot of Icing-induced Stalls
- •Stabilizer Stall Due to Ice
- •Effect of Heavy Rain on Stall Speed
- •Stall and Recovery Characteristics of Canards
- •Spinning
- •Primary Causes of a Spin
- •Phases of a Spin
- •The Effect of Mass and Balance on Spins
- •Spin Recovery
- •Special Phenomena of Stall
- •High Speed Buffet (Shock Stall)
- •Answers to Questions on Page 173
- •Key Facts 2
- •Questions
- •Key Facts 1 (Completed)
- •Key Facts 2 (Completed)
- •Answers
- •8 High Lift Devices
- •Purpose of High Lift Devices
- •Take-off and Landing Speeds
- •Augmentation
- •Flaps
- •Trailing Edge Flaps
- •Plain Flap
- •Split Flap
- •Slotted and Multiple Slotted Flaps
- •The Fowler Flap
- •Comparison of Trailing Edge Flaps
- •and Stalling Angle
- •Drag
- •Lift / Drag Ratio
- •Pitching Moment
- •Centre of Pressure Movement
- •Change of Downwash
- •Overall Pitch Change
- •Aircraft Attitude with Flaps Lowered
- •Leading Edge High Lift Devices
- •Leading Edge Flaps
- •Effect of Leading Edge Flaps on Lift
- •Leading Edge Slots
- •Leading Edge Slat
- •Automatic Slots
- •Disadvantages of the Slot
- •Drag and Pitching Moment of Leading Edge Devices
- •Trailing Edge Plus Leading Edge Devices
- •Sequence of Operation
- •Asymmetry of High Lift Devices
- •Flap Load Relief System
- •Choice of Flap Setting for Take-off, Climb and Landing
- •Management of High Lift Devices
- •Flap Extension Prior to Landing
- •Questions
- •Annexes
- •Answers
- •9 Airframe Contamination
- •Introduction
- •Types of Contamination
- •Effect of Frost and Ice on the Aircraft
- •Effect on Instruments
- •Effect on Controls
- •Water Contamination
- •Airframe Aging
- •Questions
- •Answers
- •10 Stability and Control
- •Introduction
- •Static Stability
- •Aeroplane Reference Axes
- •Static Longitudinal Stability
- •Neutral Point
- •Static Margin
- •Trim and Controllability
- •Key Facts 1
- •Graphic Presentation of Static Longitudinal Stability
- •Contribution of the Component Surfaces
- •Power-off Stability
- •Effect of CG Position
- •Power Effects
- •High Lift Devices
- •Control Force Stability
- •Manoeuvre Stability
- •Stick Force Per ‘g’
- •Tailoring Control Forces
- •Longitudinal Control
- •Manoeuvring Control Requirement
- •Take-off Control Requirement
- •Landing Control Requirement
- •Dynamic Stability
- •Longitudinal Dynamic Stability
- •Long Period Oscillation (Phugoid)
- •Short Period Oscillation
- •Directional Stability and Control
- •Sideslip Angle
- •Static Directional Stability
- •Contribution of the Aeroplane Components.
- •Lateral Stability and Control
- •Static Lateral Stability
- •Contribution of the Aeroplane Components
- •Lateral Dynamic Effects
- •Spiral Divergence
- •Dutch Roll
- •Pilot Induced Oscillation (PIO)
- •High Mach Numbers
- •Mach Trim
- •Key Facts 2
- •Summary
- •Questions
- •Key Facts 1 (Completed)
- •Key Facts 2 (Completed)
- •Answers
- •11 Controls
- •Introduction
- •Hinge Moments
- •Control Balancing
- •Mass Balance
- •Longitudinal Control
- •Lateral Control
- •Speed Brakes
- •Directional Control
- •Secondary Effects of Controls
- •Trimming
- •Questions
- •Answers
- •12 Flight Mechanics
- •Introduction
- •Straight Horizontal Steady Flight
- •Tailplane and Elevator
- •Balance of Forces
- •Straight Steady Climb
- •Climb Angle
- •Effect of Weight, Altitude and Temperature.
- •Power-on Descent
- •Emergency Descent
- •Glide
- •Rate of Descent in the Glide
- •Turning
- •Flight with Asymmetric Thrust
- •Summary of Minimum Control Speeds
- •Questions
- •Answers
- •13 High Speed Flight
- •Introduction
- •Speed of Sound
- •Mach Number
- •Effect on Mach Number of Climbing at a Constant IAS
- •Variation of TAS with Altitude at a Constant Mach Number
- •Influence of Temperature on Mach Number at a Constant Flight Level and IAS
- •Subdivisions of Aerodynamic Flow
- •Propagation of Pressure Waves
- •Normal Shock Waves
- •Critical Mach Number
- •Pressure Distribution at Transonic Mach Numbers
- •Properties of a Normal Shock Wave
- •Oblique Shock Waves
- •Effects of Shock Wave Formation
- •Buffet
- •Factors Which Affect the Buffet Boundaries
- •The Buffet Margin
- •Use of the Buffet Onset Chart
- •Delaying or Reducing the Effects of Compressibility
- •Aerodynamic Heating
- •Mach Angle
- •Mach Cone
- •Area (Zone) of Influence
- •Bow Wave
- •Expansion Waves
- •Sonic Bang
- •Methods of Improving Control at Transonic Speeds
- •Questions
- •Answers
- •14 Limitations
- •Operating Limit Speeds
- •Loads and Safety Factors
- •Loads on the Structure
- •Load Factor
- •Boundary
- •Design Manoeuvring Speed, V
- •Effect of Altitude on V
- •Effect of Aircraft Weight on V
- •Design Cruising Speed V
- •Design Dive Speed V
- •Negative Load Factors
- •The Negative Stall
- •Manoeuvre Boundaries
- •Operational Speed Limits
- •Gust Loads
- •Effect of a Vertical Gust on the Load Factor
- •Effect of the Gust on Stalling
- •Operational Rough-air Speed (V
- •Landing Gear Speed Limitations
- •Flap Speed Limit
- •Aeroelasticity (Aeroelastic Coupling)
- •Flutter
- •Control Surface Flutter
- •Aileron Reversal
- •Questions
- •Answers
- •15 Windshear
- •Introduction (Ref: AIC 84/2008)
- •Microburst
- •Windshear Encounter during Approach
- •Effects of Windshear
- •“Typical” Recovery from Windshear
- •Windshear Reporting
- •Visual Clues
- •Conclusions
- •Questions
- •Answers
- •16 Propellers
- •Introduction
- •Definitions
- •Aerodynamic Forces on the Propeller
- •Thrust
- •Centrifugal Twisting Moment (CTM)
- •Propeller Efficiency
- •Variable Pitch Propellers
- •Power Absorption
- •Moments and Forces Generated by a Propeller
- •Effect of Atmospheric Conditions
- •Questions
- •Answers
- •17 Revision Questions
- •Questions
- •Answers
- •Explanations to Specimen Questions
- •Specimen Examination Paper
- •Answers to Specimen Exam Paper
- •Explanations to Specimen Exam Paper
- •18 Index
Chapter
5
Lift
Aerodynamic Force Coefficient . . . . . . . . . . . . . . . . . . . |
. . |
. . |
. |
71 |
The Basic Lift Equation . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
. |
72 |
Review: . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
|
.75 |
The Lift Curve . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
|
.76 |
Interpretation of the Lift Curve . . . . . . . . . . . . . . . . . . . |
. . |
. . |
. |
76 |
Velocity - Dynamic Pressure Relationship . . . . . . . . . . . . . . . . |
. . |
. . |
|
.79 |
Density Altitude |
|
|
|
79 |
Aerofoil Section Lift Characteristics . . . . . . . . . . . . . . . . . . |
. . |
. . |
|
.79 |
Introduction to Drag Characteristics |
|
|
|
80 |
Lift/Drag Ratio . . . . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
. |
80 |
Effect of Aircraft Weight on Minimum Flight Speed . . . . . . . . . . . . |
. . |
. . |
|
.82 |
Condition of the Surface . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
|
.82 |
Flight at High Lift Conditions |
|
|
|
82 |
Three Dimensional Airflow |
|
|
|
85 |
Wing Terminology . . . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
|
.85 |
Wing Tip Vortices . . . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
. |
86 |
Wake Turbulence: (Ref: AIC P 072/2010) . . . . . . . . . . . . . . . . |
. . |
. . |
|
.88 |
Ground Effect . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
|
.91 |
Conclusion |
|
|
|
96 |
Summary |
|
|
|
98 |
Answers from page 77 . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
. |
99 |
Answers from page 78 . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
. 100 |
|
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
101 |
|
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . |
. . |
108 |
69
5 Lift
Lift 5
70
Lift 5
Aerodynamic Force Coefficient
The aerodynamic forces of both lift and drag depend on the combined effect of many variables. The important factors are:
• |
Airstream velocity (V) |
} Dynamic Pressure ( ½ ρ V2) |
||
• |
Air density (ρ) |
|||
• Shape or profile of the surface |
} |
Pressure Distribution (CL or CD) |
||
• |
Angle of attack |
|
||
|
|
•Surface area (S)
•Condition of the surface
•Compressibility effects (to be considered in later chapters)
Dynamic Pressure
The dynamic pressure (½ ρ V2) of the airflow is a common denominator of aerodynamic forces and is a major factor since the magnitude of a pressure distribution depends on the energy given to the airflow (KE = ½ m V2).
Pressure Distribution
Another major factor is the relative pressure distribution existing on the surface. The distribution of velocities, with resulting pressure distribution, is determined by the shape or profile of the surface and the angle of attack (CL or CD).
Surface Area
Since aerodynamic forces are the result of various pressures distributed on a surface, the surface area (S) is the remaining major factor - the larger the surface area for a given pressure differential, the greater the force generated.
Thus, any aerodynamic force can be represented as the product of three major factors:
•The dynamic pressure of the airflow (½ρ V2 )
•The coefficient of force determined by the relative pressure distribution (CL or CD),
and
• The surface area of the object (S)
The relationship of these three factors is expressed by the following equation:
F = Q CF S
where
F = aerodynamic force (Lift or Drag)
Q = dynamic pressure (½ρ V2)
CF = coefficient of aerodynamic force (CL or CD)
S = surface area
Lift 5
71
5 Lift
Lift 5
The Basic Lift Equation
Lift is defined as the net force generated normal (at 90°) to the relative airflow or flight path of the aircraft.
The aerodynamic force of lift results from the pressure differential between the top and bottom surfaces of the wing. This lift force can be defined by the following equation:
L = 1/2 ρ V2 CL S
Correct interpretation of the lift formula is a key element in the complete understanding of Principles of Flight.
Figure 5.1
Note: For the sake of clarity; during this initial examination of the lift formula it is stated that CL is determined by angle of attack. This is true, but CL is also influenced by the shape or profile of the surface and other factors which will be amplified in later sections.
•An aircraft spends most of its time in straight and level flight.
•How much lift is required? The same as the weight.
•Consider that at any moment in time weight is constant, so lift must be constant.
•While generating the required lift force, the less drag the better because drag has to be balanced by thrust, and thrust costs money.
•The value of lift divided by drag is a measure of aerodynamic efficiency. This has a maximum value at one particular angle of attack. For a modern wing this is about 4°. If this “optimum” angle of attack is maintained, maximum aerodynamic efficiency will be achieved. Note: Maximum CL and minimum CD are not obtained at best L/D.
•Lift is generated by a pressure differential between the top and bottom surface of the wing. Pressure is reduced by the air accelerating over the top surface of the wing. The wing area must be big enough to generate the required lift force.
72
Lift 5
•Air gets thinner as altitude increases. If the speed of the aircraft through the air is kept constant as altitude is increased, the amount of air flowing over the wing in a given time would decrease - and lift would decrease.
•For a constant lift force as altitude is increased, a constant mass flow must be maintained. As air density decreases with altitude, the speed of the wing through the air (the true airspeed (TAS) must be increased.
If you refer to the ICAO Standard Atmosphere chart on page 27, the air density at 40 000 ft is only one quarter of the sea level value. We can use this as an example to illustrate the relationship between the changes in TAS that are required as air density changes with altitude.
TO KEEP LIFT CONSTANT AT 40 000 ft,
TAS MUST BE DOUBLED
× 4
× 2
|
|
|
KEEP CONSTANT TO |
|
|
|
|
MAINTAIN L/D MAX |
|
L = ½ |
V2 |
CL S |
|
FIXED AREA |
|
CONSTANT
CONSTANT DYNAMIC PRESSURE (IAS)
1 4
Figure 5.2
For this example we will assume the optimum angle of attack of 4° is maintained for aerodynamic efficiency and that the wing area is constant.
At 40 000 ft the air density is 1/4 of the sea level value, so the speed of the aircraft through the air must be doubled to maintain dynamic pressure (hence lift) constant. TAS is squared because essentially we are considering the kinetic energy of the airflow (KE = ½ m V2).
Lift 5
73
5 Lift
Lift 5
The lift formula can also be used to consider the relationship between speed and angle of attack at a constant altitude (air density).
IF SPEED IS DOUBLED, CL MUST BE REDUCED
TO ¼ OF ITS PREVIOUS VALUE
× 4 |
1 |
|
× 2 |
4 |
|
|
|
|
|
|
|
L = ½ |
V2 |
CL S |
FIXED AREA |
CONSTANT |
|
|
DYNAMIC PRESSURE |
|
|
|
|
|
|
|
FOUR TIMES GREATER |
CONSTANT |
|
|
(IAS DOUBLED) |
|
|
|
|
ALTITUDE |
|
|
|
Figure 5.3
As speed is changed, angle of attack must be adjusted to keep lift constant.
As an example: if IAS is doubled, TAS will double, and the square function would increase dynamic pressure (hence lift) by a factor of four. As the aircraft is accelerated, the angle of attack must be decreased so that the CL reduces to one quarter of its previous value to maintain a constant lift force.
It is stated on page 27 that IAS will vary approximately as the square root of the dynamic pressure. The proportionality between IAS and dynamic pressure is:
I AS Q
For the sake of simplicity and to promote a general understanding of this basic principle (though no longer true when considering speeds above M 0.4), it can be said that TAS will change in proportion to IAS, at constant altitude, (double one, double the other, etc).
The lift formula can be transposed to calculate many variables which are of interest to a professional pilot. For example: if speed is increased in level flight by 30% from the minimum level flight speed, we can calculate the new CL as a percentage of CLMAX :
74