Aerodynamics and Principles of Flight

Module 2 · Aerodynamics and Principles of Flight · Lesson 1 of 8

The Atmosphere and How a Wing Makes Lift

Lift starts with the air itself: its weight, its pressure, and what happens when it speeds up over a curved surface.

The atmosphere is 78 percent nitrogen, 21 percent oxygen, and 1 percent other gases. Air has mass and weight, and most of the atmosphere's oxygen is below 35,000 feet. PHAK 4-1

Air is a fluid. It flows, it fills its container, and it has a small resistance to flow called viscosity. Air molecules right at the wing surface stick to it because of friction and have a relative velocity near zero. That thin layer is the boundary layer. PHAK 4-2 to 4-3

The Standard Atmosphere

Because the real atmosphere changes all the time, aircraft instruments and performance charts are built on one reference: the International Standard Atmosphere. PHAK 4-3 to 4-4

• Sea level: 59 °F (15 °C) and 29.92 "Hg (1,013.2 mb). That is about 14.70 psi.
• Temperature drops about 2 °C (3.5 °F) per 1,000 feet up to 36,000 feet.
• Pressure drops about 1 "Hg per 1,000 feet up to 10,000 feet.
• At 18,000 feet the atmosphere weighs half what it does at sea level.

Excerpt from PHAK Figure 4-3, Properties of standard atmosphere.

Density Altitude

Pressure altitude is the altitude on the altimeter with 29.92 set. Density altitude is pressure altitude corrected for nonstandard temperature. The airplane performs as though it were at the density altitude, whatever the altimeter says. PHAK 4-4

Thin air reduces three things at once: engine power (less air into the engine), thrust (a less efficient propeller), and lift (less force on the wings). PHAK 4-4

High elevation, low pressure, high temperature, and high humidity all raise density altitude and cut performance. PHAK 4-4 Module 5 builds on this with the density altitude chart.

Newton, Bernoulli, and the Airfoil

Newton's third law says every action has an equal and opposite reaction. The wing is shaped and inclined to force air downward, and the air forces the wing upward. PHAK 4-6 to 4-7

Bernoulli's principle says that as the velocity of a moving fluid increases, its pressure decreases. A venturi tube shows it: the air speeds up at the narrow throat, and the pressure there drops. Air moving over the curved top of a wing speeds up the same way, which lowers the pressure above the wing. PHAK 4-6 to 4-7

Know the parts of the airfoil by name. The chord line is the straight line from the leading edge to the trailing edge. Camber is the curvature of the upper and lower surfaces. The mean camber line runs halfway between the two surfaces. PHAK 4-6 to 4-7

Pressure Above, Pressure Below

Air flowing over the wing makes regions of negative pressure (less than atmospheric) and positive pressure (more than atmospheric). The negative pressure on top makes a larger force than the positive pressure underneath. PHAK 4-8

The average of all that pressure acts through one point, the center of pressure. It moves forward as angle of attack increases and aft as angle of attack decreases. That travel changes the airplane's balance and controllability. PHAK 4-8

Near the leading edge there is a stagnation point where the airflow nearly stops. The air under the wing is slowed, which raises its pressure. The downwash leaving the trailing edge pushes air down and back, and the reaction pushes the wing up and forward. PHAK 4-8

The pressure difference alone does not account for all of lift. Symmetrical airfoils and even a flat paper airplane make lift because they turn the airflow. PHAK 4-8 to 4-9 At the wingtip, high-pressure air below spills around to the low-pressure top and forms a tip vortex. Lesson 2.7 covers what that means for you. PHAK 4-9

Module 2 · Aerodynamics and Principles of Flight · Lesson 2 of 8

The Four Forces, Drag, and Lift-to-Drag Ratio

Thrust, drag, lift, and weight are always there. How they balance decides whether you speed up, slow down, climb, or descend.

In steady flight the forces cancel. The sum of all upward forces equals the sum of all downward forces, and the sum of all forward forces equals the sum of all rearward forces. That holds level, climbing, or descending. It does not mean all four forces are equal: lift and weight are much larger than thrust and drag. PHAK 5-2

Angle of attack is the acute angle between the chord line of the airfoil and the direction of the relative wind. PHAK 5-2

The Lift Equation

The PHAK writes lift as L = C_L × ½ ρ V² × S: the coefficient of lift (set by the airfoil and angle of attack), air density, velocity squared, and wing area. PHAK 5-4 to 5-5

• Lift is proportional to the square of velocity. At 200 knots an airplane has four times the lift it has at 100 knots, at the same angle of attack. PHAK 5-4
• Lift and drag vary directly with air density. At higher altitude, or on a hot humid day, you need a higher true airspeed for any given angle of attack. PHAK 5-5
• Lift varies directly with wing area. A 200 sq ft wing lifts twice as much as a 100 sq ft wing of the same shape at the same angle of attack. PHAK 5-5

In the PHAK's example wing (Figure 5-5), the coefficient of lift peaks at 20°, which is that wing's critical angle of attack. The lift-to-drag ratio peaks at 6°, the angle where the wing gets the most lift for the least drag. PHAK 5-5

Two Kinds of Drag

Parasite drag is any drag not associated with making lift. Induced drag is the price of making lift. PHAK 5-6

Parasite drag increases as the square of airspeed. Induced drag varies inversely with the square of airspeed. So as you slow toward the stall, total drag rises because of induced drag, and as you approach VNE it rises because of parasite drag. Somewhere between, total drag is at its minimum. PHAK 5-8

At L/D max, the thrust needed to overcome drag is at its minimum, which matters for maximum range. Minimum power and maximum endurance happen at a different point. PHAK 5-8 The examiner may also ask how thrust changes the picture: add power in level flight and the airplane speeds up and starts to climb unless you lower the angle of attack to keep lift equal to weight. PHAK 5-3

Module 2 · Aerodynamics and Principles of Flight · Lesson 3 of 8

Stability

A stable airplane tends to put itself back where it was. Where you load it decides how strongly.

The airplane rotates about three axes, all through the center of gravity. Roll is about the longitudinal axis, pitch is about the lateral axis, and yaw is about the vertical axis. Ailerons control roll, the elevator controls pitch, and the rudder controls yaw. PHAK 5-12 to 5-13

Stability is the airplane's built-in tendency to correct a disturbance and return to, or continue on, its original flight path. It is mainly a design characteristic. PHAK 5-14

PHAK 5-14 to 5-15, Figures 5-21 and 5-22.

Longitudinal Stability (Pitch)

Longitudinal stability is about the lateral axis. It depends on where the wing is relative to the CG, where the horizontal tail is relative to the CG, and how big the tail is. PHAK 5-15

Most airplanes put the center of lift behind the CG. That makes them nose-heavy, so the horizontal tail makes a small downward force to hold the nose up. Picture a lever: lift pushes up in the middle, weight at the CG pulls down in front, and tail-down force pulls down at the back. PHAK 5-16

Slow down and the downwash on the tail weakens, so the nose drops and the airplane picks up speed. Speed up and the tail-down force grows, so the nose rises. After a few smaller and smaller oscillations the airplane settles at its trimmed speed. PHAK 5-16 to 5-17 You can test it in flight: trim for hands-off, push the nose down briefly, and watch whether the oscillations die out, continue, or grow. PHAK 5-17

CG Position and Handling

PHAK 5-25, 5-43. A forward CG needs more nose-up trim, which adds tail-down load, so the wing must fly at a higher angle of attack. An aft CG past the limit can leave the elevator unable to lower the nose.

Lateral Stability (Roll)

Lateral stability is about the longitudinal axis. The PHAK names four design features that provide it: dihedral, sweepback, keel effect, and weight distribution. It explains the first three, below. PHAK 5-17

• Dihedral. The wingtips sit higher than the roots. When a gust rolls the airplane, it sideslips. The wing slipping into the wind gets a higher angle of attack and more lift, which rolls the airplane back. PHAK 5-18
• Sweepback. The low wing presents its leading edge more squarely to the airflow and gains lift. About 10° of sweepback gives about 1° of effective dihedral, and a high wing gives about 5° more effective dihedral than a low wing. PHAK 5-18
• Keel effect. On a high-wing airplane the fuselage hangs below the wing like a pendulum and rolls the airplane back to level. PHAK 5-18 to 5-19

Directional Stability (Yaw)

Directional stability is about the vertical axis. The vertical fin and the fuselage side area behind the CG act like the feathers on an arrow and point the nose into the relative wind. It is the easiest kind of stability to design in. The airplane stops yawing, but it does not return to its old heading by itself; you do that. PHAK 5-19

Dutch Roll and Spiral Instability

Dutch roll is a coupled roll-and-yaw oscillation. The nose traces a figure eight on the horizon. In most light airplanes it dies out in a few cycles. PHAK 5-20

Spiral instability happens when directional stability is strong compared with the dihedral effect. After a gust, the nose yaws into the relative wind, the outside wing speeds up and gains lift, and the bank steepens. The nose drops and a slow descending spiral begins. That is why an airplane cannot be flown hands-off indefinitely. PHAK 5-20

Pulling back in a spiral only tightens the turn and adds load factor. Improper recovery from spiral instability has probably caused more general aviation fatalities than any other factor. Loss of horizon reference is a common cause. PHAK 5-20 AFH Chapter 5 gives the spiral dive recovery; Module 12 covers it.

Module 2 · Aerodynamics and Principles of Flight · Lesson 4 of 8

Turns, Load Factor, and the V-g Diagram

Bank the airplane and part of lift goes sideways. The wing has to work harder, and the stall speed goes up with it.

An airplane is not steered like a car. It turns because you bank it. In a bank, lift splits into a vertical component that opposes weight and a horizontal component that pulls the airplane toward the center of the turn. The horizontal component of lift is what turns the airplane, not the rudder. PHAK 5-22 to 5-23

Banking does not create more lift. With part of lift now pointing sideways, less is left to hold up the weight, so you add back pressure to increase angle of attack until the vertical component again equals weight. More angle of attack means more induced drag, so you lose airspeed unless you add power. PHAK 5-23

Load Factor

Load factor is the ratio of the load on the wings to the airplane's weight, measured in G. At 3 G you are pressed into the seat with three times your weight. PHAK 5-33 In a coordinated level turn the load factor is 2 G at 60° of bank and 5.76 G at 80°. It climbs at a terrific rate past 45° to 50°. PHAK 5-34

Rate and Radius of Turn

At a given airspeed, more bank means a faster rate of turn and a smaller radius. At a given bank, more airspeed means a slower rate and a larger radius. The PHAK's example: at 120 knots and 30° of bank the rate is 5.25° per second and the radius is about 2,215 feet. At 240 knots and the same bank the rate halves and the radius is four times larger, about 8,861 feet. PHAK 5-38 to 5-40

Slips, Skids, Climbs, and Descents

• Slipping turn. Too much bank for the rate of turn. The horizontal lift component is greater than centrifugal force. Fix it by decreasing bank, increasing the rate of turn, or both. PHAK 5-23
• Skidding turn. Too much rate of turn for the bank. Centrifugal force is greater than the horizontal lift component. Fix it by reducing the rate of turn, increasing bank, or both. PHAK 5-23
• Climbs. In a steady climb, lift is about the same as in level flight at the same airspeed. Part of weight acts rearward along with drag, so you need more power to hold airspeed. A 10° climb needs thrust equal to drag plus 17 percent of weight. PHAK 5-23 to 5-24
• Descents. Part of weight acts forward along the flight path, so you reduce power to descend at the same airspeed. PHAK 5-24 to 5-25

Category Limits and Maneuvering Speed

PHAK 5-34. For airplanes over 4,000 lb the limit is reduced. The structure must carry 1.5 times the limit load without failure; that 1.5 is the factor of safety (PHAK 5-33).

Design maneuvering speed, VA, is the speed below which you can move a single flight control, one time, to full deflection, about one axis, in smooth air, without risk of damage. It does not protect against multiple full inputs in one axis or full inputs in more than one axis at once. PHAK 5-35 Below VA the wing stalls before it can make a damaging load. PHAK 5-37 In rough air, slow to VA. PHAK 5-37

Stall speed rises with the square root of load factor. An airplane that stalls at 50 knots in level flight stalls at 100 knots at 4 G. PHAK 5-34 to 5-35 For older airplanes, VA is about 1.7 times the normal stall speed, and a stall at that speed produces about 2.89 G. PHAK 5-35

The V-g Diagram

The V-g diagram shows which combinations of airspeed and load factor are safe. Each airplane has its own, valid at a certain weight and altitude. PHAK 5-37 The curved lines are maximum lift capability: above them the wing stalls before it can make more G. The horizontal limit lines are the limit load factors. Where the positive stall line meets the positive limit is maneuvering speed. The vertical line at the right is the never-exceed speed. PHAK 5-37 to 5-38

Module 2 · Aerodynamics and Principles of Flight · Lesson 5 of 8

Stalls, Angle of Attack, and Spins

A stall is about angle of attack, not airspeed and not attitude. Get that right and the recovery makes sense.

A stall is a rapid decrease in lift caused by airflow separating from the wing when the critical angle of attack is exceeded. It can happen at any pitch attitude or airspeed. The wing does not stop making lift entirely; it can no longer make enough to sustain level flight. PHAK 5-25

The stall speed changes with weight, load factor, and other conditions, but a given airplane always stalls at the same angle of attack. That critical angle is about 16° to 20°, depending on the design. PHAK 5-25

Three Ways to Exceed the Critical Angle

Why the Wing Root Stalls First

Most training airplanes are built so the wing root stalls before the tip. The stall moves outward, which keeps the ailerons working longer. Designers do it with washout (twist that gives the root a higher angle of attack than the tip) or with stall strips on the inboard leading edge. PHAK 5-25; AFH 5-15

Even so, reduce the angle of attack before you use aileron. If a wing drops at the stall and you roll against it with aileron, the down aileron raises that wing's angle of attack and can deepen its stall. AFH 5-15

Most training airplanes drop the nose at the stall because the center of lift is behind the CG. That nose-down tendency recovers the wing, which is why an aft CG beyond the limit is so dangerous. PHAK 5-25 to 5-26 Ice, snow, and frost also lower the stalling angle: as little as 0.8 millimeter of ice on the upper wing surface increases drag and reduces lift by 25 percent. PHAK 5-26

Recognizing the Stall

Stall warning comes from a horn, light, or stick shaker, or from the airplane's own pre-stall buffet. You also have feel (controls get soft and less effective), vision (pitch awareness, though a stall can happen in any attitude), hearing (the sound of the airflow changes), and kinesthesia (the seat-of-the-pants sense). AFH 5-13

The published 1 G stall speed is valid only in unaccelerated 1 G flight, in coordinated flight, at one weight, and at one CG. Change any of those and the stall speed changes. An angle of attack indicator shows how close you are to the critical angle directly. AFH 5-13; PHAK 5-27

Stall Recovery

The AFH gives a six-step template. In a training airplane with no autopilot or speedbrakes, four steps apply. Always follow the manufacturer's procedure when there is one. AFH 5-15 to 5-16

1. Disconnect the autopilot or wing leveler
   If equipped. Manual control is essential.
   if equipped
2. Pitch nose-down
   Reduce angle of attack until the stall warning stops. Trim nose-down if the elevator alone is not enough.
   first action
3. Roll wings level
   Points the lift vector up. Use rudder to cancel yaw so the stall does not become a spin.
   after AOA
4. Add thrust/power
   As needed. Power reduces altitude loss but does not break the stall by itself.
   as needed
5. Retract speedbrakes/spoilers
   If equipped.
   if equipped
6. Return to the desired flightpath
   Smooth, coordinated inputs. Avoid a secondary stall.
   last

AFH 5-15 to 5-16, Figure 5-10. The AFH recommends practicing stalls high enough to recover no lower than 1,500 feet AGL in a single-engine airplane.

Stalls the Examiner Will Ask About

• Secondary stall. Happens after a recovery when you pull the nose up too abruptly, or try to break the stall with power alone, and exceed the critical angle again. AFH 5-18
• Accelerated stall. Any stall at more than 1 G, as in a steep turn, a pull-up, or an overshot base-to-final turn. It happens at a higher indicated airspeed than the published stall speed and tends to be more aggressive. AFH 5-19 to 5-20
• Cross-control stall. Aileron one way, rudder the other. The classic case is a skidding base-to-final turn where the pilot adds inside rudder to tighten the turn, holds off the bank with opposite aileron, and pulls back. It can roll the airplane toward inverted and into a spin with little warning. The safest fix for an overshoot is a go-around. AFH 5-20
• Elevator trim stall. Full power applied for a go-around with nose-up trim set for the approach. The nose rises sharply and turns left. Hold the nose down with forward pressure and retrim. AFH 5-20 to 5-21

Spin Awareness

A spin is an aggravated stall that results in autorotation: the airplane follows a downward corkscrew path. In every spin at least one wing is stalled. A spin needs two things, a stall and yaw. Yaw can come from rudder, adverse yaw from aileron, the left-turning tendencies, or wake turbulence. AFH 5-22

AFH 5-23 to 5-24. The first turn of a spin loses about 1,000 feet and each turn after that about half as much (AFH 5-23).

Use the turn indicator, not the ball, to tell spin direction. The ball's position depends on where the instrument is mounted. AFH 5-24 Many normal-category airplanes were only required to show recovery from a one-turn spin. If your airplane is placarded against spins, there is no assurance it will recover from a developed spin. AFH 5-25

Module 2 · Aerodynamics and Principles of Flight · Lesson 6 of 8

Left-Turning Tendencies

Four separate effects of the spinning propeller all push the nose the same way. That is why your right foot works hard on takeoff.

Pilots lump these together as "torque." Most U.S. engines turn the propeller clockwise as seen from the pilot's seat; everything here assumes that. PHAK 5-30 to 5-31 Designers offset some of the effect for cruise, the speed where the airplane spends most of its time, so at other speeds you correct with rudder and trim. PHAK 5-31

The Four Elements

• Torque reaction. The engine and propeller turn one way, so the airplane tries to roll the other way: to the left. On the takeoff roll this puts more weight on the left main wheel, more friction on the left tire, and a turn to the left. PHAK 5-31
• Corkscrewing slipstream. The propeller spirals the slipstream around the fuselage, and it strikes the left side of the vertical fin, yawing the nose left. The spiral is tight and strong at high power and low speed, as in takeoff and power-on stalls, and stretches out as speed increases. It also makes a rolling moment to the right. PHAK 5-31, Figure 5-48
• Gyroscopic precession. A force on a spinning rotor takes effect 90° ahead in the direction of rotation. Raising the tail of a tailwheel airplane on the takeoff roll is like pushing forward on the top of the propeller disc; the result is a yaw to the left. Any yaw makes a pitching moment and any pitch makes a yawing moment. PHAK 5-31 to 5-32
• P-factor (asymmetric loading). At a high angle of attack the descending blade, on the right side seen from behind, meets the air at a higher resultant velocity than the ascending blade. It makes more thrust, so the center of thrust moves right and the nose yaws left. PHAK 5-32

Module 2 · Aerodynamics and Principles of Flight · Lesson 7 of 8

Ground Effect and Wingtip Vortices

Near the runway the ground changes how your wing flies. Behind a heavy airplane, its vortices can roll yours.

How Vortices Form

When the wing makes lift, pressure below it is higher than pressure above. Air flows outward along the bottom, spills around the tips, and rolls up into a vortex behind each wingtip. Viewed from behind, the vortices turn counterclockwise at the right tip and clockwise at the left tip. PHAK 5-7 to 5-8

Vortex strength is directly proportional to weight and inversely proportional to wingspan and speed. They are strongest when the generating airplane is heavy, clean, and slow, which is the takeoff, climb, and landing phases. PHAK 5-9

Avoiding Wake Turbulence

• Avoid flying through another airplane's flight path. PHAK 5-9
• Taking off behind another airplane, rotate before the point where it rotated. PHAK 5-9
• Taking off after a larger airplane has landed, lift off beyond the point where it touched down; its wake ends there. PHAK 5-9
• Avoid following another airplane on a similar path within 1,000 feet below it. Vortices sink several hundred feet per minute, nominally to 500 to 1,000 feet below the flight path. PHAK 5-9, Figure 5-13
• Landing behind another airplane, stay above its approach path and touch down after the point where its wheels touched. PHAK 5-9
• Stay at least three rotor diameters from a hovering helicopter, and avoid the strong vortices of a helicopter in slow forward flight. PHAK 5-9
• If you are unsure where the other airplane took off or landed, about 3 minutes gives the wake time to dissipate. PHAK 5-9 to 5-11

Vortices drift with the wind. A 10-knot wind moves them about 1,000 feet per minute. Near the ground (within 100 to 200 feet) they also spread sideways at 2 to 3 knots. A light crosswind of 1 to 5 knots can cancel the upwind vortex's outward drift and leave it sitting in the touchdown zone. PHAK 5-9 to 5-10, Figure 5-15

Ground Effect

Within about one wingspan of the surface, the ground restricts the vertical part of the airflow around the wing. Upwash, downwash, and wingtip vortices all shrink, so induced drag drops. PHAK 5-11 The effect is small until you are very close.

The trap: the airplane can lift off below the recommended speed in ground effect, then climb out of it and settle back to the runway, or fail to climb, especially when heavy, hot, and high. Do not force it off with a deficiency of speed, and establish a positive rate of climb before you retract gear or flaps. PHAK 5-12 The soft-field takeoff uses this on purpose: lift off at the lowest possible airspeed and stay in ground effect while you accelerate to Vx or Vy. ACS PA.IV.C.S9

Module 2 · Aerodynamics and Principles of Flight · Lesson 8 of 8

Flight Controls and Trim

Each primary control changes the camber of one surface, which changes its lift and rotates the airplane about one axis.

The ailerons, elevator (or stabilator), and rudder are the primary flight controls. Flaps, leading edge devices, spoilers, and trim are secondary controls: they improve performance or relieve you of control pressure. PHAK 6-2 At low airspeed the controls feel soft and the airplane responds slowly; at high airspeed they firm up and the response is quicker. PHAK 6-3

Ailerons and Adverse Yaw

Turn the control wheel right: the right aileron goes up and the left aileron goes down. The up aileron decreases camber and lift on the right wing; the down aileron increases camber and lift on the left wing; the airplane rolls right. PHAK 6-3

The wing with the down aileron makes more lift and more drag, so it slows slightly and the nose yaws toward it: opposite the direction of the turn. That is adverse yaw. It is worse at low airspeed, high angle of attack, and with large aileron deflections, and you correct it with rudder in the direction of the turn. PHAK 6-3 to 6-4

Designers reduce adverse yaw with differential ailerons, Frise-type ailerons, rudder-aileron interconnect springs, and flaperons. None removes it completely. PHAK 6-4 to 6-5

Elevator, Stabilator, and Rudder

• Elevator. Pull the control column aft and the elevator's trailing edge goes up. That makes more downward force on the tail, so the tail goes down and the nose pitches up about the CG. PHAK 6-5
• T-tail. Sits above most of the propeller downwash, so at slow speed you need more elevator travel and force to raise the nose. With a high angle of attack, low airspeed, and aft CG it can be more susceptible to a deep stall. PHAK 6-6
• Stabilator. A one-piece horizontal tail that pivots. It is very sensitive, so an antiservo tab moves in the same direction as its trailing edge to add feel and resist overcontrolling. PHAK 6-7
• Rudder. Push the left pedal and the rudder moves left, the tail moves right, and the nose yaws left. It is more effective at higher speed and in the propeller slipstream. PHAK 6-8

Flaps and Other High-Lift Devices

Flaps increase both lift and induced drag at a given angle of attack, so you can fly a slower approach. PHAK 6-8

On the leading edge, fixed slots and movable slats delay separation to a higher angle of attack, and leading edge flaps and cuffs add camber and raise the maximum lift coefficient. Spoilers do the opposite: they destroy lift and add drag, for descent, roll control, or braking. PHAK 6-9 to 6-10

Trim

Trim relieves you of holding constant pressure. On most small airplanes a trim tab on the elevator's trailing edge moves opposite to the elevator: roll in nose-down trim and the tab goes up, the airflow pushes the elevator's trailing edge down, the tail rises, and the nose drops. If you are holding back pressure, you need nose-up trim. Set power, pitch, and configuration first, then trim. PHAK 6-10 to 6-11

Module 2 · Aerodynamics and Principles of Flight · Module Exam

Module 2 Exam

Twenty questions drawn from all eight lessons, in the three-option format of the FAA knowledge test. Pass mark: 80 percent.

Module 2 · Aerodynamics and Principles of Flight · Oral Scenario

Oral Scenario: A Hot Afternoon Departure

The examiner starts from a planned flight and follows your answers. Say each answer out loud before you open it.

"It's 3 p.m. in July, 34 °C at the field, and you'll have two friends and bags aboard, close to maximum weight with the CG near the aft limit. The runway is short and a Boeing 757 is landing ahead of you. Walk me through the aerodynamics of this departure."