405: Theory of Flight

405.01 Introduction

Definitions:

Aircraft: any machine capable of deriving support in atmosphere from reactions of air

Airplane: power-driven, heavier-than-air aircraft that derives lift in flight from aerodynamic reactions on surfaces that remain fixed under given conditions of flight

Airframe: complete structure of airplane, includes fuel tanks + lines, without instruments and engine installed

Definitions - Wings:

Camber: curvature of upper + lower surfaces, usually upper surface has greater camber (curvature) than lower

Chord: imaginary straight line joining leading and trailing edges of wing

Span: maximum distance from tip to tip of airfoil, wing, or stabilizer

Mean Aerodynamic Chord (MAC): average chord of wing

Area: wing are = length (span) x width (chord)

Aspect Ratio: relationships between length and width of wing, determines how much lift + drag is created, wings with higher AR generate more lift and less drag, gliders have wings with high AR

• Aspect Ratio = span/MAC

Wing Planform: shape of wing as seen from directly above (shapes can be rectangular, swept, etc) (can also be tapered from wing root to tip, can be on leading edge, trailing edge, or both)

Angles:

• Angle of Incidence: angle the wing is permanently inclined to longitudinal axis of plane, affects flight visibility, takeoff and landing characteristics, and amount of drag created during level flight 

• Angle of Attack: angle where airfoil meets relative airflow

• Relative Airflow: describes direction of airflow with respect to wing

• Flight path and relative airflow are always parallel, but travel in opposite directions

• Relative airflow is affected by wing speed and direction on ground and during takeoff + landing

• Relative airflow unaffected by wing speed and direction once aircraft is airborne

• Increasing angle of attack = increases difference of pressure between upper + lower surfaces of wing (more lift created), increases amount of downwash resulting in more lift until stall stage is reached (after stall angle reached, downwash and pressure differential decrease resulting in less lift)

Axes:

Longitudinal Axis: extends lengthwise through fuselage from nose to tail

Lateral Axis: extends crosswise from wing tip to wing tip

Vertical/Normal Axis: passes vertically through center of gravity

• All axes pass through center of gravity (point that is the center of plane’s total weight)

Aircraft Movements:

• Caused by control surfaces and occur around axes of aircraft

• Three types: roll, pitch, and yaw

  • Roll: movement of aircraft around longitudinal axis 

  • Pitch: movement of aircraft around lateral axis

  • Yaw: movement of aircraft around vertical/normal axis

• Roll and yaw are related

  • Rolling changes relative airflow over wings →causes aircraft to yaw

  • Yawing changes presentation of wings to relative airflow →causes aircraft to roll

Controls:

• Ailerons

• Located on trailing edge of each wing, close to tip

• Controls movement around longitudinal axis (roll)

• Movement of control stick to right: right aileron goes up, spoils lift and causes wing to descend (left aileron goes down, increases camber = more lift and left wing rises) →aircraft rolls to right

• Elevator

• Located on horizontal stabilizer of tail, at trailing edge

• Controls movement around lateral axis (pitch)

• Movement of control stick forwards: elevator goes down = increased camber of horizontal tail surface = increased lift on tail section (tail rises and nose descends)

• Pulling back on control stick: decreases lift →elevator goes upwards, tail descends and nose rises

• Rudder

• Located on trailing edge of vertical stabilizer

• Controls movement around vertical axis (yaw)

• Pressure applied to left rudder pedal: rudder moves left, pressure of airflow against rudder moves tail right, nose yaws left

• Opposite occurs when pressure applied to right pedal

405.02 Laws and Forces

Newton’s Laws

• Newton’s First Law (aka law of inertia)

  • A body persists in this state of rest or of uniform motion unless acted upon by an external unbalanced force

  • Air is a gaseous fluid →possesses inertia, so when air is in motions, it will stay in motion

• Newton’s Second Law

  • The net force on an object is equal to the mass of the object multiplied by its acceleration

  • Force = mass x acceleration

  • To change the state of an object, a force must be applied

  • To alter the uniform state of air, introducing an airfoil into the airflow alters the uniform flow of air

• Newton’s Third Law

  • Whenever a particle A exerts a force on another particle B, B simultaneously exerts a force on A with the same magnitude in the opposite direction

  • To every action, there is an equal and opposite reaction

  • Lift is created by the airfoil moving through the air, and the downward force of air creates lift, which is a force that created an equal and opposite reaction

Lift, Weight, Drag, Thrust

• Lift

  • The upward force which sustains the aircraft in flight

  • The wings are designed to create a vertical reaction as they move horizontally through the air, and both the upper and lower surfaces of the wing deflect air downwards, also known as downwash

  • Bernoulli’s Principle explains the pressure differences with the lower pressure over the wing, and the higher pressure below the wing

• Weight

  • The downward force on an aircraft due to gravity

  • The weight of an aircraft is the force that acts vertically downward towards the center of the earth due to gravity

• Drag

  • The resistance of the aircraft moving forward, which is directly opposed to thrust

  • It is the resistance of an aircraft moving forwards through the air

• Thrust

  • The force exerted by the engine and propellers which pushes air backwards that causes a reaction/thrust forwards

  • No thrust in gliders →glide angle determines airspeed (steeper gliding angle = greater airspeed)

  • Equilibrium is then achieved by the remaining forces of lift, weight, and drag

• State where opposing forces are balanced

• Refers to steady motion (not rest)

• When all four forces are in equilibrium, result is steady state of motion at constant speed with constant altitude

• When forces not in equilibrium: thrust>drag = aircraft accelerates, thrust<drag = aircraft decelerates, lift>weight = aircraft climbs, lift<weight = aircraft descends

Aerodynamic Coupes

• Two forces that don’t pass through same point, but are parallel + equal + opposite, which causes turning moment of aircraft

• In most aircrafts, weight ahead of lift, drag above thrust to ensure that if engine power lost, aircraft will assume nose-down attitude to avoid possibility of stall and allow for better gliding characteristics

• Weight ahead of lift = nose down, lift ahead of weight = nose up, thrust above drag = nose down, drag above thrust = nose up

405.03 Lift and Drag

Bernoulli’s Theorem

• Total amount of energy in any system remains constant

• If one element of an energy system increases, the other must decrease

• Water and air both have energy in the form of pressure and speed

• High speed = low pressure, low speed = high pressure

• Airflow over wing

  • Airfoil: any surface designed to obtain reaction from air which moves, to obtain lift (includes wings, horizontal stabilizer, propeller blades, etc)

  • Air travels faster over the upper surface of the wing, creating lower pressure

  • Air travels slower under the wing, creating higher pressure

Center of Pressure and Pressure Distribution

• Pressure distribution changes with angle of attack (measured using center of pressure)

• If all distribution pressures equivalent to single force, force will act through a straight line (point where line cuts chord) called center of pressure

• Center of pressure is the point where all distributed pressures are equivalent to a single force

  • Center of pressure moves forwards as angle of attack increases up to stall point

  • Center of pressure moves backwards beyond stall angle, potentially causing instability

• Pressure distribution around wing changes with different angles of attack

  • Angle of attack increases, difference in pressure between upper and lower parts of wings (along with amount of downwash) both increase

Primary Factors Relating to Lift and Drag on a Wing

• Wing shape also affects lift and drag

  • Wings with deep camber create high lift

• Lift and drag vary with angle of attack

  • Lift increases (angle of attack increases), drag also increases

Lift and Drag Ratio

• Describes relationship between lift and drag

• Lift and Drag Ratio = coefficient of lift/coefficient of drag

• Maximum lift and drag ratio occurs at the angle of attack with the most lift for the least amount of drag

• Coefficients depend on airfoil shape and angle of attack

  • Reflects how the angle of attack is related to lift and drag

• Lift and drag ratios differ for every aircraft

Lift and Drag Curves

• Lift increases, drag increases

• Stalling angle of attack is highest point on the lift and drag curve

• Maximum lift and drag ratio for a wing is the angle of attack at which we obtain the most lift for the least amount of drag

Types of Drag

• Drag: the resistance the aircraft experiences when moving forward through the air

• Parasite Drag

  • Caused by all parts of aircraft that don’t contribute to lift (fuselage, landing gear, struts, antennae, cowl openings)

  • Can’t ever be fully eliminated, but can be reduced

  • Two components: form drag and skin friction

• Induced Drag

  • Caused by parts of aircraft that produce lift

  • Can never be eliminated

  • Increases with increased angle of attack, and decreases as angle of attack decreases

  • Caused by disturbed air that exerts resistance against forward motion of wing

  • Heavier, slower, and aircraft with clean configuration creates more of it

  • Aircraft design can affect induced drag (wings with high aspect ratio, winglets decrease wing tip vortices →swirling air patterns on tips of wing when lift generated)

  • Aircraft flight can affect induced drag (induced drag decrease with increase of airspeed, less when aircraft is flown near ground due to ground effect)

• Form Drag

  • Drag created by shape of body as it resists motion through air

  • Depends on longitudinal section of aircraft

  • Having sleeker body profile is important for having a drag coefficient

  • Transport Canada refers to form drag as Profile Drag

• Skin Friction

  • Caused by the tendency of air flowing over a surface to cling to surface

  • Can be reduced by removing dust, dirt, mud, ice, etc

  • Important to clean and de-ice aircraft while also removing parts of aircraft that cause drag (introduction of retractable landing gear, streamlining aircraft, etc)

• Streamlining

  • When aircraft’s body designed and shaped so drag is minimized as body moves through air

  • Aircraft that isn’t streamlined produces more eddies (swirls of air) since smooth air flow is disrupted and require more energy

  • Design features that increase streamlining (retractable landing gear, cantilevered wings, streamlined fuselage, frise and differential ailerons)

Additional Factors Relating to Lift and Drag on a Wing

• Characteristics of a wing that affects total lift and drag on an aircraft:

  • Angle of attack

  • Shape of airfoil

  • Area of wing

  • Density of air

  • Square of the true airspeed (actual speed of aircraft relative to air it’s going through)

Aircraft Performance

• Best glide speed (aka Best L/D, optimum distance  lids, gliding for range, gliding for distance)

  • Airspeed that allows aircraft to glide furthest distance for least amount of altitude lost

  • Airspeed that results in an angle of attack that gives maximum lift and drag ratio

  • Should be used when trying to cover maximum distance

  • Faster descent, furthest distance

• Minimum Sink Speed (aka best gliding speed for endurance)

  • Airspeed used to remain in air for longest period of time

  • Should be used when trying to maximize flight time

  • Slower descent, less distance

• Best Rate of Climb

  • Rate of climb that will gain most altitude in least amount of time

  • Should only be used during takeoff

• Best Angle of Climb

  • Angle that will gain most altitude in given distance

  • Speed depends on total weight of aircraft

  • Should be used where aircraft needs to climb over obstacle

  • Could overheat engine

• Approach Speed Calculation

  • 1.3 x stall speed + full wind speed = approach speed

  • Best L/D + ½ wind speed (including gusts) = approach speed

  • 1.3 x Vso (minimum steady flight speed of aircraft while landing) = approach speed

Laminar Flow

• Flow of air over wing forms boundary layer (thin sheet of air lying over surface) and air tends to stick to wing

• As wing moves, boundary layer begins to flow smoothly over wing

• Near center of wing, boundary layer begins to flow slowly because of skin friction, and air becomes turbulent and thick

• Transition Point: where boundary layer becomes turbulent

• Separation Point:where air is no longer flowing over wing

• Increase of speed and increased angle of attack tends to move transition point forwards

Features Affecting Transition Point

• Suction Method: thin slots that run wing root to tip

• Laminar Flow Airfoil: having the thickest part of chord at 50% increases laminar air flow

• Vortex Generators: small plates about 1in high and sit on edge of wing, increases energy of airflow (prevents boundary layer from breaking)

• Slats: attached to leading edge of wing that move ahead of wing at high angles of attack, decrease eddy formation over wing

• Slots: passageways built into wing, air flows through slots →increases smooth flow of air and decreases eddy formation

405.04 Stability

Definitions

Stability: tendency of an aircraft in flight to remain straight, level, upright, and to return to this altitude, if displaced without corrective action by the pilot

Inherent Stability: due to aircraft design features, the aircraft may overall be considered stable as long as it’s within proper CoG

Static Stability: initial tendency of an aircraft, when disturbed, to return to OG position

Dynamic Stability: overall tendency of aircraft to return to its position, following a series of damped out oscillations

Positive Stability: once displaced, aircraft will develop forces/moments, which tend to restore it to its OG position

Negative Stability (aka instability): once displaced, aircraft will develop forces/moments which tend to move it further away from OG position 

Neutral Stability: once displaced, aircraft will neither return to its OG position nor move further away

Longitudinal Stability

• Stability around lateral axis

• Pitch stability

• Most aircrafts designed to be nose heavy (if engine failed, aircraft would assume normal glide attitude)

• Affected by 2 factors:

  • Size and position of horizontal stabilizer (when aircraft pitches up, horizontal stabilizer meets air at greater angle of attack →more lift produced, bringing tail back up and restoring balance)

  • Center of Gravity (CoG too far aft = nose high attitude →difficult to control, CoG too far forward = aircraft will easily recover from stall, but difficult to maintain level flight)

Lateral Stability

• Stability around longitudinal axis

• Roll stability

• Affected by 4 factors:

  • Dihedral (angle that each wing makes with horizontal axis, wing drops = ow wing produces more lift and aircraft tends to roll back to proper position)

  • Sweepback (leading edge of wing slopes backwards, wing drops = low wing’s leading edge meets relative airflow at angle that’s perpendicular to relative airflow →lift is created and wing rises back to proper position)

  • Keel Effect (high wing aircraft, weight of aircraft is low = aircraft is disturbed and wing drops →aircraft acts like pendulum)

  • Proper Weight Distribution (having the aircraft loaded improperly can cause a rolling motion)

Directional Stability

• Stability around vertical axis

• Yaw stability

• Affected by 1 factor:

  • The Fin (if aircraft yaws away from intended direction, air hits vertical stabilizer and pushes aircraft back towards intended line of flight)

405.05 Stalls

Theory of a Stall

• Stall: when wing cannot produce lift to counteract the weight of the aircraft, and aircraft no longer flies, aircraft is falling due to gravity

• Up to the point of the stall:

  • Angle of attack increases

  • Laminar flow starts to separate

  • Transition point moves forward

  • Flow of air over wing becomes disturbed and air cannot follow camber of airfoil, airflow separates from wing and air becomes turbulent

  • Called Critical Angle of Attack

Centre of Pressure

• As angle of attack increases, centre of pressure moves forward

• At point of stall, centre of pressure moves rapidly back towards trailing edge of wing 

Symptoms and Characteristics of a Stall

• Nose high altitude with low airspeed

  • Most noticeable when about to stall from a straight glide altitude

  • Often a lack of wind noise

• Sloppy controls

  • Effectiveness of ailerons decrease as airspeed decreases due to lack of airflow over surfaces

  • Large movements of control column not effective when stalled

• Buffeting

  • Shaking of glider when turbulent air flows around glider

• Mushy controls

• Sinking sensation

• High rate of descent

• Wing and/or nose drop

• Recovery only possible by moving control column forward (lowers nose, increases amount of air moving over wings, creates enough lift to return aircraft to flight)

Stall Speed Factors

• Weight

  • When weight is added to aircraft, more angle of attack needed to produce enough lift to counteract additional weight

  • Critical angle of attack will stay the same, reached at higher airspeed

  • Weight increases, stall speed increases

• Center of Gravity

  • As CoG moves forward, stall speed increases

  • If CoG moves outside designed allowable CoG range, stability is negatively affected

• Turbulence

  • Upward vertical gusts can cause increase in angle of attack

  • Turbulence can result in stall if airspeed of aircraft is low

• Turns

  • Increase in angle of bank requires more lift due to increase of load factor

  • Lift always acts 90 degrees to wingspan, so in a turn lift doesn’t act straight up

  • As angle of bank (angle of aircraft when turning) increases, amount of lift required to sustain flight increases

• Flaps

  • Decrease stall speed by increasing lift due to increasing camber

• Snow, ice, frost, and heavy rain

  • Accumulates on aircraft and interferes with laminar air flow and boundary layer, decreases lift and increases stall speed

Spin Theory

• Spin: stalled condition that starts to auto-rotate

• When wing is stalled, attempt to increase angle of attack will increase induced drag →further decrease lift and stall wing

• Low wing will have greater angle of attack to relative airflow, receive less lift and drop more rapidly

• Nose will drop and auto-rotation will start

405.06 Secondary Control and Effects

Stick Trim

• Uses series of bungees/springs to maintain control column in particular location

• Alleviates pressure that pilot requires on controls

• Elevator trim helps maintain desired attitude (airspeed)

• More points on trim = more accurate in holding desired attitude

• In cockpit: trim forward = hold higher airspeed, trim aft = hold lower speed 

Trim Tab

• Found on trailing edge of control surface

Spoilers and Dive Breaks

• Spoilers

  • Disrupts laminar airflow over wing →decreases lift

• Dive Breaks

  • Disrupts airflow under wing, increases drag

• Deploying these two increases stall speed and increases drag

• Utilizing them allow pilots to control rate and descent and descent angle on final approach and landing

Flaps

• Found on trailing edge of wing

• Used to minimize need for increasing angle of attack to maintain lift at slow speeds

  • Will be lowered so front section of wing still meets air at same angle

• Lowering flaps increases camber of wing →allows aircraft to fly at slower airspeed and decreases stall speed

• Retracting flaps increases stall speed due to decreased camber

• Flaps effectively increase area of wing

• When thermalling (soaring and using rising currents of warm air to gain altitude), having flaps deployed can be helpful, but close them while travelling to new thermal

• Takeoff

  • Allow better angle of climb

  • Allow slower takeoff speed

  • Increase visibility

• Approach and landing

  • Allow slower approach speed

  • Reduce stall speed providing more room for error

  • Significantly improves visibility

  • Allows for steeper approach

Secondary Effects of Control

• Adverse Yaw

  • In a turn, if ailerons are used in isolation, adverse yaw will be produced due to induced drag created by down-going aileron (aileron drag)

  • Nose of aircraft will yaw opposite direction of turn 

  • Prevented by coordinated use of rudder

  • Can increase rate of descent

• Roll

  • In a turn, if rudders are used in isolation, they can produce roll →as aircraft yaws, outside wing moves through air faster than inside wing which is moving slower

  • Creates more lift over fast moving wing = aircraft rolls

405.07 Spins, Spiral Dives, Slips

Spins

• Autorotation that develops after aggravated stall

• Steep nose low attitude

• Rolling motion around longitudinal axis

• Constant airspeed

• Low airspeed

• Load Factor (G) is constant

• Descent rate is constant

• Stalled condition

• Primary cause: when one wing exceeds critical angle of attack when in a turn with insufficient rudder control

  • Can only enter spin when aircraft is fully stalled

• Types of Spins:

  • Incipient Spin: portion of spin between aircraft stalling and rotation starting

  • Fully Developed Spin: when rotation begins

  • Flat Spin: in a spin where aircraft has level pitch and roll attitude (VERY DANGEROUS)

• Spin Recovery

1. Apply full opposite rudder while centralizing control column

2. When rotation stops, centralize rudder

3. Pull out of the dive and return to level flight
   
   

Spiral Dives

• Steep, descending turn

• Excessively nose low attitude

• Excessive angle of bank

• Excessive load factors which gets higher

• Rapidly increasing airspeed

• Rapidly increasing rate of descent

• Aircraft is NOT stalled

• Spiral dive recovery

1. Coordinated roll level

2. Pull out of dive

Spin vs Spiral Dive

Slips

• Deliberate uncoordinated condition that’s used to lose excess height or correct for wind drift on final approach

• When used with spoilers, very high rate of descent is accomplished 

• Aircraft is in banked attitude

• Airspeed Indicator will not read correctly due to angle of pitot tube to relative airflow

• Forward slips

  • Used to lose altitude

  • Longitudinal axis not aligned with flight path 

  • Entry: simultaneously banking glider with aileron and applying enough opposite rudder to move longitudinal axis off desired track over ground and away from down-going wing

  • Recovery: release rudder to allow glider to return to its original heading, level wings with aileron, adjust pitch attitude with elevator to maintain desired airspeed

• Side Slip

  • Maintain a correct heading when there is a crosswind (wind blowing across direction of travel) or to move laterally over ground

  • Longitudinal axis aligned with flight plan

  • Entry: bank glider and simultaneously apply sufficient opposite rudder to prevent glider from turning, amount of bank and rudder required will depend on either how quickly you want to move laterally or how strong crosswind is

  • Recovery: level wings with aileron and release rudder at a rate that will ensure longitudinal axis does not change

• Side Slip vs Forward Slip

• Slipping Turns

  • Used to lose height while turning

  • Entry: can be started from straight glide, coordinated turn, or forward slip

  • Recovery: level the wings, release rudder and adjust pitch attitude to maintain desired airspeed