Lesson Two: Theory of Flight I
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Don’t read:
o Every other section within this chapter is testable, so far. Will cover ToF II the
week after.
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Four forces acting on an airplane in flight:
o Thrust: force exerted by the engine and propeller which forces air back, and
moves the plane forward
o Drag: resistance to forward motion, opposite
o Lift: force upward which sustains airplane in flight
o Weight: downward force due to gravity, F=mg.
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When thrust/drag, lift/weight are in balance, plane is in a state of equilibrium, and is
not accelerating. When the forces are not in balance, the plane is accelerating.
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Newton’s Three Laws
o A body in motion will tend to stay in motion (inertia). If you roll a ball across an
icy, frictionless surface, it would go on forever.
o F = ma. A mass will accelerate when subjected to a force. If you push something
hard enough, it moves. If you slam on the brakes to increase “friction” on the
tires, it slows down.
o For every action there is an equal and opposite reaction. If you punch me, your
fist would hurt afterwards because my face would’ve exerted an equivalent force
on your hand. Plus you’ll be demoted.
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Lift
o Airfoil
 Any surface designed to obtain a reaction from the air through which it
moves, to obtain lift
 Includes wings, horizontal stabilizer, etc.
 Camber is the curvature of the upper and lower surfaces of an airfoil;
upper surface typically has a greater curve than the lower surface
o Newton’s Third Law (Downwash)
 Air flowing over top surface passes over the wing towards the trailing
edge, where it’s forced down (cause it’s trying to stick to the curve of the
wing)
 Air flowing under bottom surface passes under the wing, hits the trailing
edge, and is forced down
 Newton’s Third Law  air moves down, plane moves up
o Bernoulli’s Principle (Conservation of Energy)
 Total energy of any system remains constant.
 Imcompressible fluids  has energy in both pressure and speed. If
pressure decreases, speed must increase, and vice-versa.
 Air is considered imcompressible  air flowing over top of wing is flows
through a “Venturi” tube, speeds up, and decreases in pressure.
 Air moving under bottom of wing moves at a relatively slower speed, and
so is at a higher pressure than up above.
 Air tends to flow from high pressure to low  results in wing being
forced upwards.
o Relative Airflow
 Direction of airflow with respect to wing…always opposite/parallel to
direction of motion of wing
 If wing is moving down and to the left, relative airflow is going up and to
the right.
 Direction/speed of wind have no effect on relative airflow in flight.
o Angle of Attack and Centre of Pressure
 Angle at which airfoil meets the relative airflow is called the angle of
attack.
 Just cause a wing is angled a certain way DOES NOT mean that it is
flying in that direction!
 As AoA is increased, the amount of downwash and pressure change
between the upper and lower surfaces is increased up to the stalling
angle (critical angle of attack), at which point, they decrease
 Sum of distributed pressure acting through a single line intersecting the
chord of an airfoil called centre of pressure
 As AoA is increased up to the point of stall, the CoP moves forward.
Beyond this point, it will move back. Movement of CoP causes plane to
become unstable.
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Weight
o F = mg. Sum of all weight acting through a point called centre of gravity.
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Thrust
o Forward force forcing a plane forward. Typically caused by forcing a mass of air
backwards, thus pushing the plane forward via Newton’s Third.
o Engines/propulsion systems cause thrust.
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Drag
o For an airplane to maintain steady flight, there must be sufficient lift to balance
weight of airplane, and sufficient thrust to overcome drag.
o The force of lift always acts perpendicularly to the relative airflow. However, the
resultant force between lift and drag acts perpendicularly to the chord.
o Parasite Drag
 Drag caused by parts of airplane which DON’T cause lift
 Fuel tanks, undercarriage, etc.
1. Form drag
 Drag created from the shape of a body as it resists motion
through the air
2. Skin friction
 Tendency of air flowing over a body to cling to its surface
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Reduced by eliminating unnecessary parts of airplane sticking out (i.e.
retractable gears, cantilever wings vs. strutted wings, etc.), streamlining,
and cleaning
 Interference drag: resistance caused by the effect of one part on another
(at attachment points)
o Induced Drag
 Drag caused by parts of airplane which DO cause lift
 Can’t be removed.
 Increases as the AoA increases, decreases as AoA decreases.
 Can only be reduced during initial design
 High aspect ratio (ratio of span to chord) produces less induced
drag (hence why gliders have long, narrow wings)
 Responsible for wing-tip vortices
 Airflow over top surface is at a lower pressure than the ambient
air; forced inwards towards the trailing edge
 Airflow over bottom surface is at a higher pressure than the
ambient air; forced outwards towards the trailing edge
 When two airflows unite at trailing edge, bottom air flow moves
up and over, resulting in the curling of air to form vortices.
 The heavier the airplane and the higher the span loading on the
wing, the more air will be displaced downwards -> the greater the
circulation of air -> the greater the magnitude of the wing tip
vortex created -> the greater the induced drag
 Induced drag does not increase as the speed increases  greatest when
airplane is flying slowly (max lift, min speed, esp. with high AoA)
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Vortices near the ground disrupted; can’t form properly because of the
surface. This is called ground effect (and hence “penetration
approaches” are sometimes used by glider pilots to fly a further distance
when running out of altitude)
Winglets disrupt wing-tip vortices
Induced Drag
Parasite Drag
Drag
Speed
o Read “Lift and Drag Curves” and “Thrust Available and Drag”
o Streamlining
 Design device by which a body is shaped so drag is minimized as the body
moves forward through the air
 Ball vs. Thin plate
o Aileron drag
 In a bank, one aileron is depressed while the other is up.
 Downed wing has up aileron (less lift = less drag), up wing has down
aileron (more lift = more drag)
 Banked left = right aileron down  greater drag on right wing  right
wing moves backwards slightly
 Countered by implementing frise and/or differential ailerons
 Frise
 Downgoing aileron streamlined into wing, lessening the increase
in drag; upgoing aileron protrudes into airstream, increasing its
drag
 Differential
 Downgoing aileron moves through smaller angle, lessening the
increase in drag; upgoing aileron moves through large angle,
increasing its drag
o Boundary layer
 Very thin sheet of air lying over the surface of the wing
 Air has viscosity, tends to stick to its surface
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As air moves over the leading edge, it clings smoothly to the surface,
resulting in smooth laminar flow
As air moves to the centre of the wing, it loses speed due to skin friction
and becomes thicker and turbulent. The point where laminar flow
becomes turbulent flow called transition point  turbulent flow
increases drag
As speed increases, transition point tends to move forward
As AoA increases, transition point moves forward.
Countered by the suction method, laminar flow airfoil or vortex
generators
Read about the above methods to cause the transition point to not
appear so close to the front. Laminar flow airfoil is the most important!
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Couples
o Formed when two forces, like thrust and drag, are equal and opposite but
parallel
o Couple will cause a turning moment about a given axis
o If weight is ahead of lift, couple will turn nose of airplane down. If thrust is above
drag, couple will turn nose down.
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Read “Conventional Airfoils” and “Laminar Flow Airfoils”
Planform
o Refers to shape of wing as seen from directly above.
o Can be rectangular, elliptical, delta, swept-back, swept-forward, etc.
o Aspect ratio = span/MAC
o High aspect ratio = more lift, less drag
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Angle of Incidence
o Angle at which wing is permanently inclined to the longitudinal axis of the
airplane
o Choosing right AoI can improve flight vis., and enhance T/O and landing
performance
Read “Wing Tip Design”
Wash-out/Wash-in
o Used to reduce tendency of the wing to stall suddenly as critical AoA is
approached
o Wing is twisted so that the AoI at the wing tip is less than that at the root of the
wing
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o Causes the wing root to stall before the wing tip; prevents premature loss of
aileron control
o Increasing AoI called wash-in and increases lift; decreasing AoI called wash-out
and it decreases lift
Wing Fences
o Vertical fin-like surfaces attached to the upper surface of the wing to control
airflow
o Give better slow speed handling and stall characteristics
Slots, Slats and Leading Edge Flaps
o Slats  airfoils fitted to LE of wing; at high AoA, they move out ahead of wing.
The AoA of the slat is less than that of the wing, so smooth air flow over slat
smooths out eddies forming over wing. Improves lateral control.
o Slots  passageways built into wing a short distance from the LE, so at high AoA
airflow flows through the slots, smoothing the ar.
o LE Flaps  increases camber of the wing and increases the lift coefficient at high
angles of attack. Found on large transport planes.
Spoilers
o Increase drag, decreases lift.
o Found on gliders to assist with landing and other purposes.
o Long, narrow strip of metal arranged span-wise along top surface of airfoil.
o Some airplanes have spoilers in place of ailerons.
Speed brakes
o Found on some high-perf. Airplanes
o Facilitates optimum descent without decreasing power to dramatically cool
engines
Flaps
o Increases lift, increase drag.
o Gives better T/O performance, and steeper approach angles and lower approach
and landing speeds.
o Increases upper camber of the wing when deployed, increasing lift and induced
drag.
o 10o flaps = more lift increase than drag increase
o 40o flaps = more drag increase than lift increase
o Read up on types of flaps
 Fowler: slides out and down, very common and considered most
advantageous
o Changes in flap affect trim
 As flaps are lowered, CoP moves rearward, creating a nose-down
moment. But the flaps can change airflow over empennage on some
planes, screwing up empennage lift  causing nose to come up, so will
have to trim nose down.
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Axes of an Airplane
o Three axes around which the airplane moves.
o All pass through plane’s C.G.
o Longitudinal axis
 Extends lengthwise through fuselage from nose to tail
 Movement about the longitudinal axis called roll
o Lateral axis
 Extends crosswise, from wing tip to wing tip
 Movement about the lateral axis called pitch
o Vertical/normal axis
 Passes vertically through C.G.
 Movement about the normal axis called yaw
 Yawing right  left wing moves faster than right wing, gets more relative
airflow  gets more lift, and left wing is lifted slightly  induces a roll
right (“adverse roll”)
 Aileron drag causes adverse yaw
 Dynamic yaw is movement or rotation about the normal axis
 Static yaw is when the airplane is flying with some angle of sideslip, so
nose is not aligned in flight path
Balanced Controls
o Controls sometimes dynamically balanced to assist pilots to move them
(compare with trim)
o Having some control surface in front of hinge, air striking front portion helps
move control surface in required direction (dynamic balance)
o Helps to counteract adverse yaw when applied to ailerons
o Mass balance is resultant when a control surface is fitted with a mass (i.e. lump
of lead) in front of hinge
 Helps prevent flutter
o Static balance describes a plane’s balance without any airflow
**Stability (this generally kills a lot of people; pay extra attention to this section!!)
o Tendency of an airplane in flight to remain in straight, level, upright flight and to
return to this attitude after being displaced, without corrective action by the
pilot.
o Displacement from normal attitude frequently caused by turbulence, thermals,
etc.
o Static stability is the initial tendency of an airplane, when disturbed, to return to
its original position
o Dynamic stability is the overall tendency of an airplane to return to its original
position.
o Positive stability  plane tends to return to its original attitude after being
displaced.
 Great for transport planes and recreation/easy-flying planes. But this
usually means that the plane isn’t very maneuverable, although it makes
for a pleasant ride.
o Neutral stability  plane tends to remain in its displaced position after being
displaced
o Negative stability  plane tends to be displaced even further after a force is
exerted on it
 Great for fighter planes and planes requiring high maneuverability. But
every little bump will be amplified, and you’ll feel everything!
o Planes which have a certain sign of static stability may not have the same sign of
dynamic stability, depends on design.
o Longitudinal stability
 Stability about the lateral axis
 Also called pitch stability
 Affected by:
 Size and position of the horizontal stabilizer
o Something forces nose up, tail down; HS meets airflow at a
higher AoA, obtains more lift, tail up, nose back down.
o Proper AoI important in design.
 Position of C.G.
o If C.G. too far aft, plane will have a permanent nose up
tendency.
o Lateral stability
 Stability about the longitudinal axis
 Also called roll stability
 Affected by:
 Dihedral
o Angle that each wing makes with the horizontal 
typically refers to an upward tilt of wings.
o Found mainly on low-wing planes
o If a disturbance causes one wing to drop, unbalanced force
produces sideslip in direction of downgoing wing. Leads to
air striking lower wing at higher AoA, increasing its lift and
lifting it back up.
o Negative dihedral called anhedral.
o
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Keel effect
o Found mainly on high wing airplanes
o Wings attached in a high position on fuselage, and so
weight is low in the fuselage
o When plane is disturbed and when one wing dips, the
weight acts as a pendulum and rocks the plane back to
original position.
 Sweepback
o Leading edge slopes backward
o Similar to dihedral; dipped wing meets air at higher AoA,
low wing gets more lift, and rises back to original position
 Proper distribution of weight
o Direction stability
 Stability about the vertical axis
 Affected by fin
 Airplane has tendency to fly ahead into relative airflow
 If airplane yaws left due to some external force, more airflow
would hit the right sit of the fin  would push nose back to
original straight-flying attitude
 Also affected a little bit by keel effect and sweepback
 Sweepback: when the plane is yawed to the left, more airflow
strikes right wing, increasing its drag and yawing the plane back to
original attitude