reSource Course · Commercial Pilot · Module 2

Aerodynamics for Commercial Maneuvers

The physics behind every commercial maneuver, worked out with real numbers.

Private pilot aerodynamics told you that bank adds load and that stalls happen at a critical angle of attack. The commercial checkride expects you to put numbers on it and explain the reasons: why a 50° steep turn raises stall speed by a quarter, why maneuvering speed drops when you fly solo, why turn radius grows with the square of airspeed, how a chandelle trades airspeed for altitude, and how an accelerated stall turns into a spin. This module covers the aerodynamics knowledge in ACS Area I Task F and Areas V and VII.

6Lessons
9Interactive labs
39Check questions

What Each Maneuver Asks of the Wing

Interactive
Bank (ACS)50°
Load factor1.56 G
Stall speed71 kt

Example airplane: a 1-G clean stall speed of 57 KIAS at maximum gross weight. Load factors are for a coordinated, level turn at the steepest bank.

Module 2 · Aerodynamics for Commercial Maneuvers · Lesson 1 of 6

Lesson 2.1

Load Factor and Stall Speed

Why a level turn needs more lift than the airplane weighs, and why stall speed goes up with the square root of the extra load.

CA.I.F.K3CA.V.A.K2dCA.VII.D.K1PHAK pp. 5-33 to 5-37 · ACS pp. 36, 48

Load factor is the total lift the wing makes divided by the weight of the airplane. It is measured in G. In straight-and-level flight the wing makes lift equal to weight, so the load factor is 1 G. Anything that makes the wing carry more than the airplane weighs raises the load factor: banking, pulling out of a dive, or a gust that suddenly raises the angle of attack.

In a level turn, the lift vector tilts with the wings. Only the vertical part of the lift holds the airplane up; the horizontal part turns it. To keep the vertical part equal to weight, total lift has to grow as the bank steepens. In a coordinated level turn that works out to:

Load Factor

n = 1 ÷ cos(bank)

30° gives 1.15 G, 45° gives 1.41 G, 60° gives 2.0 G. By 75° the load factor is 3.86 G, above the normal category limit.

Stall Speed

VS turn = VS × √n

At 2 G the stall speed is √2, or 1.41 times the 1-G stall speed: 41% higher. At 50° bank it is 25% higher.

Independent of Speed

Bank Sets the G

In a level turn the load factor depends only on bank angle. A 60° bank is 2 G at 80 knots or at 180 knots.

Why Stall Speed Rises

Lift depends on angle of attack and on dynamic pressure, which goes with the square of airspeed. If the wing must make twice the lift at the same airspeed, it needs a higher angle of attack. It reaches the critical angle of attack, and stalls, at a higher airspeed than it would wings level. Because lift goes with airspeed squared, doubling the required lift raises the stall speed by √2, not by 2. This is the root of every accelerated stall in Lesson 2.5.

Bank, Load and Your Margin Above the Stall

Interactive · F04
Load factor1.41 G
Stall speed now68 kt
Increase+19%
Margin22 kt
Steepest level bank at this speed66°

Example airplane: 1-G clean stall speed 57 KIAS, normal category (+3.8 G limit). The amber dot on the chart is your bank; the blue line is your airspeed. Where the line crosses the curve is the steepest level turn you can hold at that airspeed before the wing stalls.

Limit Load Factors by Category

The structure is certificated to a limit load factor for its category. Above the limit load, the airframe may be permanently bent. Certification adds a safety factor of 1.5, so the structure should not fail until the ultimate load factor, 1.5 times the limit. That margin is for gusts and errors, not for flying.

CategoryPositive LimitNegative LimitTypical Use
Normal+3.8 G−1.52 GNon-acrobatic flight; bank up to 60°
Utility+4.4 G−1.76 GLimited acrobatics, often including spins, at reduced weight
Acrobatic+6.0 G−3.0 GAcrobatic flight as listed in the AFM

Values from PHAK p. 5-35. Many airplanes are certificated in more than one category; the limits that apply depend on how the airplane is loaded. Check the POH limitations section.

Remember

Bank sets the G. The G sets the stall speed.

Learn four numbers cold: 30° is 1.15 G and +7%, 45° is 1.41 G and +19%, 50° is 1.56 G and +25%, 60° is 2 G and +41%.

Check Yourself

Module 2 · Aerodynamics for Commercial Maneuvers · Lesson 2 of 6

Lesson 2.2

Maneuvering Speed and Weight

The placarded VA is right only at maximum gross weight. Lighter, the safe speed is lower.

CA.V.A.K2cCA.V.C.K2cCA.I.F.R2PHAK p. 5-36 · AFH p. 10-1 · ACS pp. 36–37

Design maneuvering speed, VA, is the speed at which the wing reaches the limit load factor and the stall at the same moment. Below VA, a full, abrupt pull on the elevator stalls the wing before it can load the structure past its limit. The stall relieves the load. Above VA, the same pull can reach the limit load before the wing stalls.

From Lesson 2.1, the stall speed at the limit load factor is VS × √nlimit. That speed is VA. For a normal category airplane, VA ≈ VS × √3.8, about 1.95 times the 1-G stall speed.

Why VA Goes Down With Weight

A lighter airplane needs less lift for 1 G, so it stalls at a lower speed. Because VA is tied to stall speed, it drops too, by the square root of the weight ratio:

Formula

VA new = VA × √(W new ÷ W max)

At 81% of max gross, VA is 90% of the placarded value (√0.81 = 0.9).

Rule of Thumb

Half the Weight Change

Reduce VA by about half the percentage of weight removed. 20% lighter means about 10% slower.

The Trap

The Placard Is Heavy

The placard or POH value is usually for maximum gross weight. Solo with low fuel, flying at the placarded VA is flying above your real VA.

A lighter airplane is also hurt more by turbulence. The same vertical gust changes the wing's angle of attack by the same amount, so it adds the same amount of lift. That extra lift is spread over less weight, so the load factor jumps more. Slowing down reduces both the gust load and the speed at which the wing will stall to relieve it.

Unload the Airplane, Then Hit a Gust

Interactive · F05
Weight3,024 lb
VA now110 kt
Gust load2.3 G

Example airplane: empty weight 1,900 lb, pilot and front passenger 340 lb, rear passengers 170 lb each, maximum gross 3,100 lb, placarded VA 111 KIAS. Gust load uses the standard sharp-edged gust formula with an alleviation factor. It shows the trend, not POH data.

What VA Does Not Protect You From

  • VA covers one full, abrupt deflection of one control. It does not cover full deflections in more than one axis at once, or rapid back-and-forth inputs such as rudder reversals. Those can exceed structural limits below VA.
  • VA is not marked on the airspeed indicator. Find it in the POH limitations section or on a placard, often listed for several weights.
  • VA is not VNO. VNO, the top of the green arc, is the maximum structural cruising speed for smooth air. In turbulence, slow to VA for your weight, or to the POH turbulence penetration speed if it gives one.

The ACS steep turn and chandelle Tasks both ask you to explain maneuvering speed, including the effect of weight. The steep turn is flown at the manufacturer's recommended speed or, if none, a speed not above VA (CA.V.A.S2). In a light airplane, that means VA for today's weight.

Remember

Lighter airplane, lower VA.

Before a steep turn, a chandelle or a turbulent descent, work out VA for today's weight: placard × √(weight ÷ max gross).

Check Yourself

Module 2 · Aerodynamics for Commercial Maneuvers · Lesson 3 of 6

Lesson 2.3

Rate and Radius of Turn; Overbanking

Bank and airspeed together set how fast you turn and how much room you need. Bank alone sets the load factor.

CA.V.A.K2aCA.V.A.K2bCA.V.A.K2eCA.V.C.R7PHAK pp. 5-38 to 5-39 · AFH pp. 10-1 to 10-3 · ACS pp. 36–37

The horizontal part of lift turns the airplane. A steeper bank gives a bigger horizontal part, so a tighter, faster turn. A higher airspeed means the airplane has more momentum to redirect, so at the same bank the turn is wider and slower. The formulas show how strongly each one matters:

Radius

R (ft) = V² ÷ (11.3 × tan bank)

V is true airspeed in knots. Radius grows with the square of airspeed: double the speed, four times the radius.

Rate

Rate (°/s) = 1,092 × tan bank ÷ V

Rate falls in direct proportion to airspeed: double the speed, half the rate of turn.

Confined Areas

Slow and Steep

The tightest turn comes from a low airspeed and a steep bank. The limit is the stall speed, which rises with the bank.

The 11.3 in the radius formula is the same constant as in the pivotal altitude formula you will use for eights on pylons in Module 13. Both come from the same physics of a coordinated turn.

Rate and Radius, Drawn to Scale

Interactive · F06
Radius898 ft
Rate11.8 °/s
Time for 360°30 s
Load factor1.56 G

The amber circle is your turn; the dashed circle is a commercial steep turn (50° at 110 KTAS) for comparison. The airplane moves at the real rate of turn. The view rescales so both circles fit; read the scale bar.

The Overbanking Tendency

In any turn, the outside wing flies a bigger circle than the inside wing in the same time, so it moves faster through the air. Lift grows with the square of airspeed, so the outside wing makes more lift. That difference tries to roll the airplane further into the turn.

Bank (PHAK)What the Airplane DoesWhat You Do
Shallow, below about 20°Lateral stability is stronger than the speed difference; the airplane tends to roll back toward levelHold a little aileron into the turn
Medium, about 20° to 45°The two roughly balance; the bank tends to stay where you put itNeutralize the ailerons
Steep, more than 45°The outside wing wins; the bank tends to keep steepeningHold some aileron opposite the turn, with coordinated rudder, to keep the bank from increasing

Why the Outside Wing Wins

Interactive
Outer wingtip112.2 kt
Inner wingtip107.8 kt
Extra tip lift+8.3%

Wingspan 36 ft. Extra tip lift compares the lift on equal sections at each wingtip, using lift ∝ airspeed². The speed difference is set only by the turn radius, so it grows quickly as the radius shrinks.

Coordination in Steep Banks

Holding opposite aileron to stop the overbanking creates adverse yaw away from the turn. That is why a steep turn often needs more rudder into the turn than you expect, with the ball centered. A skid (too much rudder) raises the inside wing's angle of attack and sets up the cross-control stall in Lesson 2.5. A slip (too little rudder) costs altitude and makes the turn sloppy.

Climbing and descending turns add one more effect. In a climbing turn, the outside wing travels a longer, shallower path, so it meets the air at a slightly higher angle of attack, which adds to the overbanking. In a descending turn, the inside wing has the higher angle of attack. That matters in the steep spiral and in a gliding turn to final: if the airplane stalls in a descending turn, the inside wing tends to stall first.

Remember

Speed squared sets the radius. Bank sets the G.

A 50° steep turn at 110 knots is a circle about 1,800 ft across. At 160 knots, the same bank needs about 3,800 ft.

Check Yourself

Module 2 · Aerodynamics for Commercial Maneuvers · Lesson 4 of 6

Lesson 2.4

Energy Management

Think of the airplane as an energy account. The throttle changes the balance; the elevator moves energy between airspeed and altitude.

CA.V.C.R6CA.V.D.R6CA.IV.M.K1AFH Chapter 4, pp. 4-1 to 4-19 · ACS pp. 33, 37–38

An airplane in flight holds two kinds of mechanical energy. Altitude is potential energy. Airspeed is kinetic energy. You can add them into one number, the energy height: the altitude you would reach if you traded all your airspeed for altitude with no drag.

Energy Height

H = altitude + V² ÷ 2g

At 120 knots the airspeed is worth about 640 ft of altitude. At 60 knots it is worth only about 160 ft.

Throttle

Changes Total Energy

Power above what is needed to fly at the current speed adds energy; less takes it away. Drag from gear, flaps or a slip also takes energy away.

Elevator

Distributes the Energy

Pitch moves energy between airspeed and altitude. It cannot add energy. Pull up and you buy altitude with airspeed; push over and you buy airspeed with altitude.

Kinetic energy goes with the square of airspeed, so knots are worth more at high speed. Slowing from 120 to 90 knots, with power unchanged, buys roughly 280 ft. Slowing from 90 to 60 knots buys only about 200 ft. This is why a chandelle gains most of its altitude early, while the airspeed is still high.

Throttle Versus Elevator: The Energy Account

Interactive · F07

Elevator moves energy between speed and height. Throttle changes how much energy you have.

Try the elevator only
Try the throttle only
Altitude you have3,000 ft
Airspeed120 kt
Speed is worth637 ft
Energy height3,637 ftsame as start
Vertical speed0 fpm
Energy rate0 fpm
Challenges
  1. Without touching the throttle, climb at least 200 ft by trading airspeed.
  2. Slow to 80 kt and stay within 50 ft of 3,000 ft. You will need the throttle.
  3. At idle, find the airspeed that gives the lowest sink rate, then pitch up to 62 kt and watch the sink get worse.

Energy height is the altitude you could reach if you pulled up and traded every knot for height until the airspeed reached zero, with no drag: altitude + V² ÷ 2g. At 120 kt your speed is worth about 637 ft, so at 3,000 ft your energy height is about 3,637 ft. Example airplane model, treating indicated airspeed as true airspeed: power required has the usual U shape, with minimum sink near 72 KIAS and a steep rise below about 68 KIAS. Energy rate is the climb or descent the throttle setting would give if airspeed stayed constant. The elevator slider sets the airspeed you are pitching for; the airplane takes a few seconds to get there.

Two Speed Regimes

Above the speed for minimum power required, the airplane behaves the way you expect: slowing down needs less power. Below it, in the region of reversed command (the back side of the power curve), slowing down needs more power, because induced drag is rising fast. There, raising the nose without adding power makes the airplane sink faster, not climb. Close to the ground, low and slow, the elevator has no energy left to give you. Only power, or altitude you no longer have, can fix it.

Energy in the Commercial Maneuvers

ManeuverThrottleElevatorEnergy Story
ChandelleSet at entry (full or as recommended), then fixedPitch rises through the first 90°, then held constantKinetic energy is traded for altitude; airspeed ends just above the stall (CA.V.C.K4, S5–S7)
Lazy eightFixedPitch, bank and airspeed change constantlyA continuous, symmetric exchange: altitude and airspeed at the 180° point return to entry values within ±100 ft and ±10 kt
Steep spiralIdle, with periodic clearingControls airspeedAltitude is spent at a controlled rate to hold a constant radius over a point
Power-off 180°Idle from abeamControls glide airspeedA fixed energy budget must reach a point; drag (flaps, slip) is the only way to spend extra (CA.IV.M.K1)
Remember

Throttle for total energy. Elevator for where it goes.

If you are high and fast, you have too much energy: reduce power or add drag. If you are low and slow, you have too little: add power. Pitch alone fixes only a mismatch between the two, high and slow or low and fast.

Check Yourself

Module 2 · Aerodynamics for Commercial Maneuvers · Lesson 5 of 6

Lesson 2.5

Angle of Attack and Accelerated Stalls

The wing stalls at its critical angle of attack. Airspeed, attitude and power only change when you get there.

CA.VII.D.K1CA.VII.D.K3CA.VII.D.R5CA.V.A.K2dAFH pp. 5-8, 5-12 to 5-16 · PHAK pp. 5-26 to 5-28 · ACS p. 48

A wing stalls when its angle of attack, the angle between the chord line and the relative wind, exceeds the critical angle of attack. For a given wing and flap setting, that angle does not change. The airplane can stall at any airspeed, in any attitude and at any power setting. The published stall speed is only the speed at which a 1-G, wings-level airplane at a stated weight reaches the critical angle.

What Moves the Stall Speed

FactorStall SpeedWhy
Load factor up (bank, pull-up, gust)Higher, × √nMore lift needed at the same speed means a higher angle of attack
Weight upHigher, × √(W ratio)More lift needed for 1 G
CG forwardHigherThe tail pushes down harder, so the wing carries the weight plus the tail load
Power onLowerPart of the thrust holds the airplane up when the nose is high, and the propeller blows air over the wing roots
Flaps extendedLowerThe wing makes more lift at a given angle, though the stall comes at a lower angle of attack
Frost, ice, contaminationHigherThe critical angle of attack drops and the maximum lift falls

Read the Angle of Attack, Not the Airspeed

Interactive
Weight
CG
AOA used23%
Stall speed now57 kt
Margin63 kt

Example airplane: 1-G stall 57 KIAS at 3,100 lb with an aft CG; a forward CG adds about 2%. AOA used is the share of the critical angle of attack the wing needs right now, the way most general aviation AOA indicators show it. The wing section's angles are drawn larger than life.

The Accelerated Stall

An accelerated stall is a stall at a load factor above 1 G, and so at an airspeed above the published stall speed. It usually comes from pulling too hard in a turn or a pull-up. It tends to be more sudden than a 1-G stall, and if the airplane is not coordinated one wing usually stalls first and drops. In the ACS Task, you roll into a coordinated 45° bank at no more than VA, then increase back pressure smoothly and firmly until the stall is impending, and recover no lower than 3,000 ft AGL (CA.VII.D.S2–S5).

Recovery is the same as every stall: first reduce the angle of attack with forward elevator pressure. Once the wing is flying again, level the wings with coordinated aileron and rudder, add power as needed, and return to the desired flight path without a secondary stall. Rolling the wings level first, while still stalled, can deepen the stall on the down-going wing.

The Cross-Control Stall

The classic case is the turn from base to final. The pilot overshoots the centerline, often with a tailwind on base, and tries to tighten the turn with inside rudder without steepening the bank. The rudder makes the airplane overbank, so the pilot holds opposite aileron, and pulls back to keep the nose up. Now the airplane is skidding, cross-controlled, at a load factor above 1 G, and low. The down aileron on the inside wing raises that wing's angle of attack further. If it stalls, the inside wing drops sharply and the airplane can roll inverted and spin with little warning, too low to recover. Prevent it: fly a normal pattern, keep the bank to a reasonable angle, stay coordinated, and go around rather than tighten the turn.

Angle of Attack Indicators

An AOA indicator shows how much of the critical angle of attack you are using, whatever the weight, load factor, bank or flap setting. That makes it a direct stall warning in exactly the cases where the airspeed indicator is misleading: a steep turn, a pull-up, a heavy airplane. Stall warning horns also sense angle of attack, so they work in accelerated stalls, but they give only a single warning point. Buffet varies by airplane and may come late. Know the range and limits of the warnings in your airplane (CA.VII.D.R2).

Remember

The wing does not know your airspeed. It knows its angle of attack.

To unstall a wing, reduce the angle of attack first. Everything else comes second.

Check Yourself

Module 2 · Aerodynamics for Commercial Maneuvers · Lesson 6 of 6

Lesson 2.6

Spins and Upset Prevention

How a stall becomes a spin, how to tell a spin from a spiral dive, and how weight and CG decide whether you can recover.

CA.VII.E.K1CA.VII.E.K2CA.VII.E.K3CA.VII.E.R1AFH pp. 5-1 to 5-7, 5-22 to 5-27 · RMH pp. 3-3, G-2 · ACS p. 49

A spin is an aggravated stall that results in autorotation. Both wings are stalled, but one more deeply than the other. The less-stalled wing makes more lift and less drag, so the airplane rolls and yaws toward the more-stalled wing and descends in a steep corkscrew. A spin needs two things: a stalled wing and yaw. Remove either and there is no spin. That is why coordination at high angles of attack matters so much.

Loss of control in flight is the leading cause of fatal general aviation accidents, and many of those accidents are the result of stalls, spins or accelerated maneuvers (RMH pp. 3-3, G-2). Most happen in the traffic pattern or during maneuvering at low altitude, where there is no height to recover.

The Four Phases of a Spin

  1. Entry
    The pilot provides, or fails to stop, a stall with yaw: uncoordinated flight at a high angle of attack.
    Phase 1
  2. Incipient
    From the stall until the spin is fully developed. In a light airplane, about 4–6 seconds and roughly the first two turns. Recovery is quickest here.
    Phase 2
  3. Developed
    Rotation rate, airspeed and vertical speed settle and stay steady from turn to turn. Airspeed stays low, near the stall.
    Phase 3
  4. Recovery
    The angle of attack comes below critical and rotation stops. It may take a quarter turn to several turns, depending on the airplane.
    Phase 4

Spin Recovery

Use the procedure in your POH first. Where the POH gives none, the AFH general recovery procedure is:

  1. Reduce power to idle. Power flattens the spin and increases the rate of rotation.
  2. Put the ailerons in neutral. Aileron in a spin can make it worse.
  3. Apply full rudder opposite the direction of rotation. Use the turn needle or turn coordinator to tell which way you are turning; the ball is not reliable in a spin.
  4. Apply a positive, brisk forward movement of the elevator to break the stall, just after the rudder reaches its stop.
  5. When rotation stops, neutralize the rudder. Holding it can start a spin the other way.
  6. Return to level flight with smooth back pressure, without a secondary stall and without exceeding VNE or the load limit.

Weight, CG and Spins

  • Aft CG makes the spin flatter and the nose higher. The elevator has less authority to lower the nose, so recovery can take longer or become impossible.
  • Forward CG makes the airplane harder to stall and spin, and generally easier to recover.
  • Higher weight means more inertia, so rotation is slower to start and slower to stop.
  • Uneven loading, such as fuel imbalance between the tanks, can change spin behavior and make one direction worse.
  • Many airplanes are approved for intentional spins only in the utility category, which limits the weight and keeps the CG forward, often meaning no rear passengers or baggage. A normal category placard reading "intentional spins prohibited" means the airplane was not tested for them, not that it cannot spin.

Spin or Spiral Dive?

A spiral dive is not a stall. The wing is flying, the airplane is in a steep, descending, banked turn, and airspeed and load factor are climbing fast. The two need opposite recoveries. Spin recovery uses opposite rudder and forward elevator. Spiral recovery is: reduce power, level the wings with coordinated aileron and rudder, then raise the nose gently to level flight without exceeding the load limit. Pulling back in a spiral only tightens it and raises the G load.

Spin or Spiral Dive? Read the Instruments

Interactive

For each case, decide what the airplane is doing.

    The key is airspeed. In a spin it is low and steady; in a spiral it is high and rising.

    Upsets and the Startle Response

    The AFH defines an airplane upset as an unintended pitch attitude more than 25° nose up or 10° nose down, a bank of more than 45°, or flight within those limits at an airspeed that is wrong for the conditions. A sudden, unexpected upset can trigger a startle response. For several seconds, the pilot may freeze or make a strong, instinctive input, usually pulling back, which is the wrong move in a stall or a spiral. Training to a short, practiced sequence is what shortens that delay.

    Nose-Low Upset: Put the Recovery in Order

    Interactive

    The airplane is 30° nose low in a 70° bank and the airspeed is rising. Tap the steps in the order you would do them.

      The sequence follows the AFH nose-low upset recovery. In a real upset, follow your POH and your training.

      Remember

      Spin: speed low and steady. Spiral: speed high and rising.

      In either one, the first move is never to pull. Unload, then fix the roll.

      Check Yourself

      Module 2 · Aerodynamics for Commercial Maneuvers · Knowledge Check

      Knowledge Check

      Module 2 Knowledge Check

      Fifteen questions in the style of the CAX test and the oral exam, each tagged with its ACS element. Pass mark: 80% (12 of 15).

      Score0 / 15