Aerodynamics & Principles of Flight
PHAK Ch 5 • Four Forces, Lift, Drag, Stalls, Stability
Principles
Dynamics
Key Takeaways
- In unaccelerated flight the four forces are in equilibrium: Lift = Weight and Thrust = Drag.
- Lift acts perpendicular to the relative wind; weight acts straight down through the CG.
- Climb needs excess thrust (Thrust > Drag); in a constant-speed turn Lift > Weight.
- Lift increases with airspeed², wing area, air density, and AoA up to the critical AoA.
The Four Forces of Flight
In unaccelerated flight, the four forces are in equilibrium. How they interact is the foundation of all flight.
- Steady flight is equilibrium: Lift = Weight and Thrust = Drag.
- Lift acts perpendicular to the relative wind; drag acts parallel, opposing motion.
- Weight always acts straight down, toward the center of the earth.
- Excess thrust climbs or accelerates; tilting the lift vector is what turns the airplane.
Lift
Upward force from airflow over the wings. Acts perpendicular to the relative wind.
- Generated by pressure differential (lower pressure on top, higher on bottom)
- Increases with airspeed², wing area, air density, and angle of attack (up to critical AoA)
- Acts perpendicular to the relative wind, NOT straight up
- In a turn, lift tilts — vertical component decreases, requiring back pressure or more speed
Weight
Gravity pulling the aircraft toward the center of the Earth. Acts through the center of gravity (CG).
- Always acts straight down toward the center of the Earth
- Includes aircraft empty weight + fuel + passengers + cargo
- Changes during flight as fuel burns off
- CG position affects stability and controllability
Thrust
Forward force from the engine-driven propeller. Acts parallel to the direction of flight.
- Produced by the propeller converting engine power to forward force
- In level cruise: Thrust = Drag
- Increasing thrust (adding power) accelerates the aircraft or allows climb
- Propeller efficiency decreases at very high and very low speeds
Drag
Rearward force opposing the aircraft's motion through the air. Acts parallel to and opposite the relative wind.
- Parasite drag: increases with airspeed² (form, skin friction, interference)
- Induced drag: byproduct of lift, decreases with airspeed (highest at slow speeds)
- Total drag = parasite + induced; minimum at L/D max speed
- L/D max speed = best glide speed (Vg) — refer to your POH for the specific value
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Force Relationships in Flight
- Straight & Level (unaccelerated) — Lift = Weight, Thrust = Drag
- Climb (constant speed) — Lift = Weight, Thrust > Drag (excess thrust)
- Descent (constant speed) — Lift = Weight, Drag > Thrust
- Constant-speed turn — Lift > Weight (vertical component = weight), Thrust = Drag
- Acceleration (level) — Lift = Weight, Thrust > Drag
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Key Takeaways
- Lift comes from Bernoulli (lower pressure over the top) and Newton (downwash) working together.
- AoA is the angle between the chord line and relative wind; exceeding the critical AoA (~16-18°) stalls the wing.
- Parasite drag rises with airspeed²; induced drag is greatest at low speed / high AoA.
- Total drag is minimum at L/D max = best glide speed (Vg); weight changes the speed, not the ratio.
- In the region of reversed command (below L/D max), flying slower needs MORE power, not less.
Bernoulli's Principle & Newton's Third Law
- Bernoulli: As air velocity increases over the curved upper wing surface, static pressure decreases
- Newton: The wing deflects air downward (downwash), and the equal/opposite reaction pushes the wing up
- Both principles work together to generate lift — neither alone fully explains it
- Camber helps but isn't required — symmetric airfoils and flat plates also produce lift at a positive AoA (ignore the "equal-transit-time / longer-path" myth the FAA cautions against)
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Angle of Attack (AoA)
- AoA = angle between the chord line and the relative wind
- AoA is NOT the pitch attitude — an airplane can stall at any attitude
- Increasing AoA increases lift (and drag) up to the critical AoA
- Critical AoA for most GA aircraft: ~16-18°
- Beyond critical AoA: airflow separates, lift drops sharply = STALL
- AoA is the ONLY factor that determines stall — not airspeed alone
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Coefficient of Lift (CL) Curve
- CL increases approximately linearly with AoA up to critical AoA
- At critical AoA, CL reaches maximum (CL max) then drops sharply
- Flaps increase CL max — allowing slower flight before stall
- Adding flaps shifts the CL curve up and to the left (stall at lower AoA)
- Contamination (ice, frost, bugs) decreases CL max and moves stall to lower AoA
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Types of Drag
- Parasite Drag — Non-lift-producing drag from moving through the air Form drag (shape), skin friction (surface roughness), interference drag (where components meet) (Increases with speed² — doubles speed = 4× parasite drag)
- Induced Drag — Byproduct of lift — caused by wingtip vortices Wingtip vortices create downwash, tilting the lift vector backward (Greatest at LOW speed / HIGH AoA. Decreases as speed increases)
- Total Drag — Sum of parasite + induced drag Minimum at L/D max speed (best glide) (L/D max: where parasite = induced drag curves cross)
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Lift-to-Drag Ratio (L/D)
- L/D max = the speed where you get the most lift for the least drag
- L/D max = best glide speed (Vg) — refer to your POH for the specific value
- At L/D max: maximum range in glide, most efficient cruise
- L/D ratio for typical trainer: about 9:1
- Weight does NOT change L/D max ratio, but changes the SPEED at which it occurs
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Region of Reversed Command
- Below L/D max speed, induced drag dominates — slowing down actually INCREASES total drag
- More power is needed to fly slower — counterintuitive but critical to understand
- This is the "back side of the power curve" where the normal throttle/speed relationship reverses
- In this region: reducing power causes a descent, and pulling back on the yoke (slowing further) makes it worse
- Slow flight, approach, and traffic pattern operations all occur in or near this region
- Active power management is essential — pitch controls airspeed, power controls altitude
- Failure to add power in slow flight turns is a classic cause of unintended stalls in the traffic pattern
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Excess Thrust & Climb Performance
- An airplane climbs because thrust exceeds drag — the "excess thrust" is what goes into climbing
- Anything that increases drag directly reduces climb performance: high AOA from over-rotation, extended flaps, poor technique
- Vy (best rate of climb) = speed where excess POWER is maximized — most altitude per minute (Vx, best angle, is where excess THRUST is maximized)
- Vx (best angle of climb) = speed where the ratio of climb to forward distance is greatest — most altitude per ground distance
- Over-rotating on takeoff creates high induced drag that kills climb rate — even though you left the ground sooner
- Density altitude degrades climb in three ways: less engine power, less propeller bite, less wing lift per airspeed
- High gross weight demands more lift (more drag) and leaves less excess thrust for climbing
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Common Gotcha
"Why does slow flight require more power, not less?" The answer is the region of reversed command: at high AOA, induced drag is enormous, so the only way to hold altitude at slow speed is to add power. Pitch controls airspeed; power controls altitude.
Key Takeaways
- A stall is exceeding the critical AoA — it can happen at any airspeed, attitude, or power setting.
- Stall recovery: reduce AoA (lower the nose) first, then add power and clean up flaps.
- Stall speed rises with load factor: Vs(new) = Vs(1G) × √(load factor) — ~41% higher at 60° bank.
- Spin = stall + yaw; recover with PARE (Power idle, Ailerons neutral, Rudder opposite, Elevator forward).
- The base-to-final skidding cross-control stall is the #1 fatal GA scenario — never steepen past 30° in the pattern.
Stall Fundamentals
- A stall occurs when the wing exceeds the CRITICAL ANGLE OF ATTACK
- Stalls can occur at ANY airspeed, attitude, or power setting
- The critical AoA is constant for a given wing configuration (~16-18°)
- Stall speed increases with: weight, load factor (turns), forward CG, ice/frost
- Stall speed decreases with: flaps extended, lower weight
- Stall warning: horn/light activates 5-10 knots above stall
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Types of Stalls
Power-Off Stall
- Configuration: Landing configuration — flaps as desired, idle power
- Purpose: Simulates approach-to-landing stall
- Recovery: Reduce AoA (lower nose), add full power, retract flaps incrementally, climb Vy
Power-On Stall
- Configuration: Takeoff configuration — 0-10° flaps, full or climb power
- Purpose: Simulates departure stall — most dangerous (high pitch, torque)
- Recovery: Reduce AoA (lower nose), hold full power, level wings, climb Vy
Accelerated Stall
- Configuration: Any configuration — from an abrupt pull-up or steep turn
- Purpose: Stall at HIGHER than normal speed due to increased load factor
- Recovery: Reduce AoA, reduce load factor (shallow bank), add power
Cross-Control Stall
DANGER
- Configuration: Uncoordinated flight — ailerons opposing rudder (skidding turn)
- Purpose: Most dangerous — leads to snap roll/spin entry, common base-to-final
- Recovery: Coordinated flight, reduce AoA — PREVENTION is key
Secondary Stall
- Configuration: During recovery from the initial stall
- Purpose: Caused by too-aggressive pitch-up during recovery
- Recovery: Reduce AoA again — recover smoothly, do not pull back too fast
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Stall Speed Formula
Vs (new) = Vs (1G) × √(load factor)
| Bank Angle | Load Factor | Stall Speed ↑ |
|---|---|---|
| 30° | 1.15 G | +~7% |
| 45° | 1.41 G | +~19% |
| 60° | 2.0 G | +~41% |
| 75° | 3.86 G | +~96% (nearly doubled!) |
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Spin Entry & Recovery
- Spin = autorotation after stall with yaw — one wing deeper in stall than the other
- Spin entry: stall + yaw (rudder input or uncoordinated flight)
- Most trainers (Normal category) are NOT approved for intentional spins — check your POH
- Recovery: PARE — Power idle, Ailerons neutral, Rudder opposite spin, Elevator forward
- After rotation stops: neutralize rudder, gently pull out of dive
- Altitude loss during spin recovery: 500-1,000+ feet per turn
PARE RecoveryPARE
- PPower idle
- AAilerons neutral
- RRudder opposite
- EElevator forward
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Base-to-Final: The #1 Fatal GA Scenario
- More pilots die from base-to-final stall/spin accidents than almost any other single cause in GA
- The setup: turning base to final, you overshoot the centerline and the runway starts sliding behind you
- The temptation: add bottom rudder to tighten the turn while holding opposite aileron to keep wings level
- This creates a skidding, cross-controlled turn at low altitude and low airspeed — the textbook spin entry
- The stalled wing drops sharply, the airplane autorotates, and there is ZERO altitude for recovery
- Most of these accidents happen below 1,000 ft AGL — the spin is unrecoverable
- Prevention: NEVER steepen bank past 30° in the pattern. If you overshoot, go around — no exceptions
- If the ball is off-center in the pattern, you are one control input away from a fatality
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Common Gotcha
"At what airspeed does the wing stall?" is a trap. The wing stalls at the critical angle of attack, not at any fixed airspeed. Weight, load factor, bank angle, and density altitude all shift the indicated stall speed. Answer AOA first, then explain that published Vs / Vs0 comes from 1-G level flight at max gross.
Ask Kit
Drill the relationship:
“Explain why a 60° level bank turn produces 2 G and makes indicated stall speed jump about 41%. Include the formula and a worked example from the Cessna 172.”
Key Takeaways
- Load factor (n) = Lift / Weight, measured in G’s; straight-and-level flight is 1G.
- In a bank, load factor = 1 / cos(bank angle) — it rises steeply past 45°.
- The Vg (V-n) diagram shows the safe envelope between the stall curve and the structural limit load factors.
- Maneuvering speed (Va) is where the stall curve meets the positive limit load — below it the wing stalls before structural failure.
- Va DECREASES as the aircraft gets lighter; slow to Va or below in turbulence.
Load Factor Basics
- Load factor (n) = Lift / Weight, measured in G's
- Straight and level flight = 1G
- In a bank, load factor = 1 / cos(bank angle)
- Load factor increases stall speed: Vs = Vs₁ × √n
- Excessive load factor causes structural damage or failure
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Load Factor in Turns
| Bank Angle | Load Factor | Stall Speed × |
|---|---|---|
| 0° | 1.0 G | 1.00× |
| 15° | 1.04 G | 1.02× |
| 30° | 1.15 G | 1.07× |
| 45° | 1.41 G | 1.19× |
| 60° | 2.0 G | 1.41× |
| 75° | 3.86 G | 1.96× |
60°+ bank = structural concern for Normal category (+3.8G limit)
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Vg (V-n) Diagram Explained
- Normal Operating Range — Between the +1G line and positive limit load factor, between Vs and Vne. Where you fly.
- Positive Limit Load Factor — Normal category: +3.8G. Exceeding it risks structural failure.
- Negative Limit Load Factor — Normal category: -1.52G. Negative G from pushover or inverted flight.
- Stall Region (left side) — Below and left of the curve — the airplane stalls before reaching that load factor. Aerodynamic protection.
- Structural Damage (above positive limit) — Wing may bend or fail. Avoid.
- Maneuvering Speed (Va) — Where the stall curve meets the positive limit load factor line. Below Va, the wing stalls before structural limits.
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Maneuvering Speed (Va)
- Va = maximum speed for full/abrupt control input without exceeding structural limits
- Below Va: wing stalls before structural failure — aerodynamic protection
- Above Va: full deflection can exceed structural limits before stall
- Va DECREASES with weight: lighter aircraft = lower Va
- Va varies with weight — check your POH for the specific range at different gross weights
- In turbulence: slow to Va or below. Reduce power, maintain attitude.
- Va is NOT a "safe" speed — you can still overstress with rapid successive inputs
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Ask Kit
Connect it to your aircraft:
“My Cessna 172's maneuvering speed (Va) changes with weight. Walk me through why Va decreases as the airplane gets lighter, with the physics.”
Key Takeaways
- Four left-turning tendencies (TPSG) affect single-engine props, all worst at low speed, high power, high AoA.
- Torque rolls the airplane left; P-factor, spiraling slipstream, and gyroscopic precession yaw it left.
- The fix for the yawing tendencies is right rudder — most needed on takeoff and climb.
- Adverse yaw initially yaws the nose OPPOSITE the turn; counter it with coordinated rudder — “step on the ball.”
Left-Turning Tendencies
Four left-turning tendencies affect single-engine prop aircraft — most pronounced at low speed, high power, high AoA.
Torque
Newton's Third Law: engine rotates propeller clockwise, so the airplane tends to roll LEFT
- When worst: High power, low speed (takeoff, climb)
- Correction: Right aileron / right rudder trim. Most single-engine trainers run slightly left wing-heavy at high power.
- The reaction to the clockwise-spinning propeller (seen from the cockpit) rolls the airplane left. Most noticeable on takeoff.
P-Factor (Asymmetric Thrust)
At high AoA, the descending blade (right side) has a higher AoA and produces more thrust than the ascending blade
- When worst: High AoA — slow flight, climb, takeoff rotation
- Correction: Right rudder to counteract left yaw
- With the propeller disc tilted up (high AoA), the descending right blade takes a bigger "bite" of air. The thrust center shifts right, creating a left-yawing moment.
Spiraling Slipstream
The propeller spins the air into a corkscrew over the fuselage. It strikes the left side of the vertical stabilizer, pushing the tail right and nose left.
- When worst: Low speed, high power — dissipates at higher speeds
- Correction: Right rudder. At cruise, the spiral expands and has less effect.
- Picture the propwash as a helix around the fuselage. At the tail it hits the left side of the vertical stabilizer, yawing the nose left.
Gyroscopic Precession
A force applied to a spinning gyroscope (the propeller) takes effect 90° later in the direction of rotation.
- When worst: Pitch changes — especially tail-raising on takeoff (tailwheel), or pitch-up
- Correction: Anticipate with rudder during pitch changes
- Raising the tail (nose-down force) is felt 90° clockwise as left yaw. Lowering the tail (nose-up force) produces right yaw. Most noticeable in tailwheel aircraft.
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Memory Aid: "TPSG"
TPSG
- TTorque (roll LEFT)
- PP-Factor (yaw LEFT at high AoA)
- SSpiraling slipstream (yaw LEFT)
- GGyroscopic precession (yaw LEFT when pitching up)
All four cause LEFT yaw/roll — counteract with RIGHT rudder!
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Adverse Yaw
- When you bank, the lowered aileron (rising wing) creates more lift AND more induced drag
- That extra drag on the rising wing pulls it backward, yawing the nose OPPOSITE to the intended turn
- This is adverse yaw — the airplane initially yaws away from the turn before the vertical stabilizer corrects it
- Counteract with coordinated rudder pressure INTO the turn — "step on the ball"
- More pronounced at slow speeds — ailerons deflect more, creating a larger drag differential
- Some aircraft use differential ailerons (up aileron deflects more than down) or Frise ailerons (leading edge projects into airflow) to reduce adverse yaw
- The inclinometer (ball) is your coordination gauge — centered ball means coordinated flight
- At slow speed in the traffic pattern, adverse yaw + poor rudder = skid — a dangerous setup for a cross-control stall
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Common Gotcha
"Why do you need rudder in a turn?" Adverse yaw. The lowered aileron creates more drag than the raised one, yawing the nose away from the turn. Without coordinated rudder, you get a skid — and at slow speed, a skid is a spin waiting to happen.
Key Takeaways
- Longitudinal (pitch) stability is set primarily by CG position — forward CG is more stable.
- Lateral (roll) stability comes mainly from wing dihedral; directional (yaw) stability from the vertical stabilizer.
- Forward CG raises stall speed and makes flaring harder; aft CG lowers stall speed but can become uncontrollable.
- Ground effect (within ~one wingspan) reduces induced drag — it causes float on landing, not extra lift.
Three Axes of Stability
Longitudinal StabilityLateral axis (pitch)
Tendency to return to original pitch attitude after disturbance
- CG position is the PRIMARY factor — forward CG = more stable
- Horizontal stabilizer provides a tail-down force to balance the nose-heavy airplane
- If CG too far forward: heavy nose, hard to flare, higher stall speed
- If CG too far aft: light nose, easy to over-rotate, may become uncontrollable
Lateral StabilityLongitudinal axis (roll)
Tendency to return to wings-level after disturbance
- Dihedral (upward wing angle) is the primary design feature
- High wing placement also contributes (pendulum effect)
- Sweepback provides some lateral stability
- Keel effect of fuselage side area
Directional StabilityVertical axis (yaw)
Tendency to weathervane into the relative wind (nose into wind)
- Vertical stabilizer (fin) is the primary design feature
- Acts like a weathervane — side area behind CG exceeds area ahead
- Sweepback also contributes to directional stability
- Insufficient directional stability leads to Dutch roll
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Forward CG
- More longitudinally stable (nose-heavy)
- Higher stall speed (tail-down force adds to weight)
- Greater fuel consumption (more trim drag)
- Harder to flare for landing
- More elevator authority needed
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Aft CG
- Less stable — may become uncontrollable
- Lower stall speed (less tail-down force)
- Better fuel efficiency (less trim drag)
- Easier to over-rotate on takeoff
- Possible inability to recover from stall/spin
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Ground Effect
- Occurs within approximately one wingspan of the surface
- Reduces induced drag by disrupting wingtip vortex formation
- Reduces downwash angle behind the wing
- Aircraft "floats" during landing — may overrun runway
- During soft-field takeoff: used to accelerate in ground effect before climbing
- Does NOT significantly increase lift — it reduces DRAG (especially induced drag)
- Transition out of ground effect requires more power/speed
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