10.1 Load Factor, Bank Angle, and Stall Speed

ACS PA.V.A.K2 (steep-turn aerodynamics) and PA.VII stall knowledge share one number the Private Pilot Airplane test will keep asking: load factor. PHAK Chapter 5 defines load factor as the ratio of the aerodynamic load on the airplane to its weight — n = Lift / Weight — expressed in g. Sitting on the ramp you already feel 1g. Any time you force the flight path to curve — a level turn, a pull-up, a gust — lift must exceed weight and n rises.

Level-turn formula

In a coordinated, constant-altitude turn, the lift vector tilts. Only the vertical component of lift holds the airplane up; the horizontal component provides the centripetal force that turns you. For the vertical component to still equal weight,

n = 1 / cos(bank)

Bank is the only variable in that sentence. Airspeed, weight, and airplane type do not change the g of a given level bank. A Cessna and a jet both feel 2g in a coordinated 60° level turn. What does change with speed is turn rate and radius — not n.

PHAK’s own figure shows load factor staying modest through 30°–45° and then rising rapidly after about 50°. That is why a “steep” turn is not just a bigger version of a standard-rate turn. From 45° to 60° you add only 15° of bank and almost 0.6g. From 60° to 75° you add another 15° and almost another 1.9g.

A 75° level turn sits at about 3.86g. The Airplane Flying Handbook is blunt: a standard-category (normal-category) airplane is certificated to +3.8g, so a level 75° bank exceeds the limit load. Do not treat 60° as “halfway to 90° and still comfortable.” Cosine collapses in that last third of the quadrant.

Worked example — Vs 50 at 60°

A trainer stalls at 50 KIAS in 1g, coordinated, flaps-up, the configuration painted at the bottom of the green arc.

1. Level 60° bank → n = 1 / cos(60°) = 1 / 0.5 = 2.00 g.
2. Accelerated stall speed Vs_acc = Vs_1g × √n = 50 × √2.
3. √2 ≈ 1.414, so Vs_acc ≈ 70.7 KIAS — call it 71 KIAS, about 41 percent higher than the 1g number.

The wing did not change its critical angle of attack. You asked it to make twice the lift, so it reached CL-max at a higher dynamic pressure. If you pull to hold altitude at 65 KIAS in that bank, you are already below the new stall speed. The horn, if it sounds, is late relative to the 50-knot folklore you memorized.

Same airplane, 45°: n ≈ 1.41, √n ≈ 1.19, stall ≈ 59 KIAS. Same airplane, 70°: n ≈ 2.92, √n ≈ 1.71, stall ≈ 85 KIAS. Write those three rows until they are automatic. The knowledge test loves the 60° / 2g / 1.41× triplet and the “stall speed rises with the square root of load factor” wording.

Another PHAK classic: an airplane that stalls at 35 knots in 1g stalls at 70 knots in a 4g pull (√4 = 2). Same square-root rule, different n.

Limit load — normal versus utility

PHAK Chapter 5 splits maneuvering load factors by certification category:

• Normal: +3.8g to −1.52g
• Utility: +4.4g to −1.76g
• Acrobatic: +6.0g to −3.0g

Those are limit loads — the highest loads the structure is expected to see in service without permanent deformation. Regulations require a 150 percent factor of safety, so ultimate load (where failure is expected) is 1.5 × limit. For a normal-category airplane that is +5.7g. PHAK is equally blunt that the reserve is not a playground. Limit load already means the airplane may take a permanent set if you go past it; ultimate is where parts separate.

Most PAR trainers live in the normal category at typical training weights, even if the same airframe has a utility envelope at a reduced weight and more-forward CG (often the only envelope that permits intentional spins). Read the AFM/POH placard for this flight, not a generic “Cessnas are utility” memory.

VA — and the weight trap

Design maneuvering speed (VA) is the speed at which, in smooth air, you can move a single flight control one time to its full stop and the wing will stall before the limit load is exceeded. Stall at high AOA dumps the lift, so the structure never sees the full n the control deflection would otherwise produce. Above VA, the same abrupt input can bend metal before the wing stalls.

Three traps sit on that sentence:

1. One control, one time, smooth air. VA is not a license for full and opposite aileron, or for full elevator plus full rudder, or for the same input in a gust. After structural accidents the FAA has been explicit about the “single control” part. In turbulence you slow to VA or below and fly smoothly; you do not start yanking.
2. VA is not a painted constant. It is published at a weight — usually maximum gross. VA decreases as weight decreases. A lighter airplane stalls at a lower speed, so at a given indicated airspeed it is farther from the stall and can generate a higher load factor before the wing quits. If you use the gross-weight VA when you are light, you can exceed limit load before you stall. Many modern POHs publish two or three VA values. If yours publishes one, treat it as the heavy number and reduce it when you are light.
3. VA is not VNO or the top of the green arc. VNO is the maximum structural cruising speed (top of the green / bottom of the yellow). VA is usually below VNO and moves with weight. Rough-air penetration is about VA (or a published VB / turbulent-air speed), not “anywhere in the green.”

PHAK notes that on many older light airplanes VA is roughly 1.7 × the 1g stall. That is a historical rule of thumb, not a substitute for the AFM/POH.

The Vg (V-n) diagram plots airspeed against load factor and is the picture behind all of this: the stall curve on the left, limit-load lines top and bottom, VNE on the right. VA sits at the corner where the stall curve meets the positive limit-load line. Lighten the airplane and that corner slides left — a lower VA.

Overbanking tendency

In a steep turn the outside wing travels a larger radius, so it has a higher true airspeed and produces more lift than the inside wing. The airplane wants to keep rolling into the bank. Below about 30° the airplane’s lateral stability (dihedral effect) usually wants to roll you out. Past that, overbanking wins unless you hold opposite aileron. That is an ACS steep-turn knowledge item, not a curiosity. Combined with the 2g stall-speed rise at 60°, it is why a sloppy steep turn becomes an accelerated stall.

You also add back-pressure (higher AOA, more total lift) and usually power (induced drag rose with CL). Those control pieces belong with the maneuver in 10.4; the physics that make them necessary is this section.

Scenario: Priya’s 65-knot “safe” turn

Priya’s flaps-up 1g stall is 50 KIAS. On a base-to-final overshoot she banks past 50° and pulls to keep the runway in the windscreen at 65 KIAS — “fifteen knots above stall.” At 60° the wing’s stall is about 71 KIAS. She is not “a little slow.” She is already in the accelerated-stall band, and opposite aileron to hold bank is the last thing that will save her if she keeps pulling. Recovery is reduce AOA, then roll wings level. The 50-knot green-arc number was never a promise once she loaded the wing.