Private Pilot · Unit 2 · 30 min

Load Factor and Turns

The stalls lesson noted that a steep turn raises the stall speed and attributed the increase to load factor. This lesson develops the idea in full: what load factor is, why every turn creates it, how it multiplies both stall speed and structural stress, and the two airspeeds that keep you inside the airplane's limits.

What load factor is

Load factor is the ratio of the lift the wings are producing to the weight of the airplane, and it is spoken of in Gs. In steady, wings-level flight the wings carry exactly the airplane's weight, so the load factor is 1G. Pull 2 Gs and the wings are making twice the lift they need to hold the airplane up, the structure carries twice the airplane's weight, and you feel twice your own weight pressing into the seat. Load factor is the number behind that pressure, and it climbs the moment you do anything other than fly straight and level.

PHAK Ch 5, "Loads and Load Factors"

Why a turn creates load factor

Load factor in a turn is a consequence of the fact that lift is a force. In The Four Forces of Flight you saw that a force is a vector: it has a magnitude and a direction, drawn as an arrow. You also saw that any vector can be decomposed, split into two perpendicular arrows that add up to it, one vertical and one horizontal. Lift acts perpendicular to the relative wind, and in steady, wings-level flight the relative wind streams horizontally past the airplane, so the lift arrow points straight up and only has to balance weight.

Roll into a bank and the airplane tilts, lift vector included: lift remains perpendicular to the relative wind, but it now leans toward the inside of the turn instead of pointing straight up. Decompose that tilted arrow the way the vectors section showed, and the single lift force resolves into two components doing two different jobs: a vertical component still pointing up, and a horizontal component pointing toward the inside of the turn. The lift did not split into two forces; it is one force, and these are the two directions it is now pulling in at once.

The vertical component of lift still has to hold the airplane up against weight, while the horizontal component pulls the airplane around the turn. Because the vertical component must stay equal to weight to hold altitude, the total lift has to grow to cover the horizontal component on top of it. That larger total lift is the load factor climbing above 1G.

The steeper the bank, the larger the horizontal component the wing has to supply, and the more total lift it takes to keep the vertical component equal to weight. So load factor grows with bank angle, and it does not grow evenly.

Load factor rises steeply with bank

Up to about 45 degrees of bank the load factor climbs gently. Past that it rises fast. At 30 degrees it is about 1.15 Gs; at 45 degrees about 1.41 Gs; at 60 degrees it reaches 2 Gs, where the wings carry twice the airplane's weight; and at 80 degrees it is 5.76 Gs. The curve never reaches 90 degrees, because a truly 90-degree-banked turn cannot hold altitude at all.

For a typical general aviation airplane, about 60 degrees of bank is the practical limit for a coordinated level turn, because holding altitude there already demands close to full power. Every additional 10 degrees of bank beyond that adds roughly another G, climbing quickly toward the airplane's structural limits.

PHAK Ch 5, "Load Factors in Steep Turns"

Load factor and stall speed

Load factor connects directly back to Stalls and Spins. Because lift grows with the square of airspeed, the airspeed at which the wing reaches its critical angle, the stall speed, rises with the square root of the load factor. Double the load and the stall speed goes up by the square root of two, about 41 percent.

In practice, a wing can be stalled at any airspeed if you pull hard enough. An airplane that stalls at 50 knots wings-level will stall at 100 knots if you pull 4 Gs. This is the accelerated stall the stalls lesson named, now with numbers behind it. In a 60-degree-bank level turn at 2 Gs, the stall speed is already about 41 percent higher than the number in the handbook, and a steeper turn raises it further.

PHAK Ch 5, "Load Factors and Stalling Speeds"

Load factor and structure: the limit load and maneuvering speed

The other thing load factor threatens is the airframe. Every airplane is designed to a limit load factor, the most G it can take without bending something permanently. Beyond it lies the ultimate load, where the structure actually fails; certification requires a 50 percent margin between the two. Airplanes are certified in categories by how much they can take: normal category to 3.8 Gs, utility to 4.4 Gs, and acrobatic to 6.0 Gs, each with a negative limit as well.

You are kept clear of those limits by an airspeed: the maneuvering speed, or V_A. Below V_A, a full, abrupt deflection of a single control makes the wing stall before the load factor can build past the limit load, so the wing gives way harmlessly instead of the structure. Above V_A, that same input can overstress the airplane. Two things about V_A matter in the cockpit. It is lower at lighter weights, so a lightly loaded airplane has a lower maneuvering speed. And it protects against a single full input on one axis, not against repeated, combined, or reversing control inputs, which can break an airplane even below V_A. So in turbulence, or before any abrupt maneuvering, slow to V_A.

PHAK Ch 5, "Load Factors and Flight Maneuvers"

The Vg diagram

All of this fits on a single chart of the airplane's flight envelope, called the Vg diagram: airspeed along the bottom, load factor up the side. It shows every combination of speed and G the airplane can survive.

Each boundary on the diagram carries a specific meaning. The curved lines on the left are the maximum lift the wing can make: fly to the left of them and the wing stalls, so no higher load factor is available there. The horizontal lines top and bottom are the limit load factors, the structural ceiling and floor. Where the stall line meets the top limit-load line is the maneuvering speed: below it the airplane stalls before it can be overstressed, above it the structure is at risk. The right edge is the never-exceed speed (V_NE), the redline beyond which flutter or structural failure can occur. The enclosed area is the envelope, and safe flying stays inside it.

PHAK Ch 5, "Vg Diagram"

Turning: rate and radius

Because this lesson is also about turns, it is worth seeing how bank and speed set the turn itself. The rate of turn is how fast the heading changes, in degrees per second, and the radius of turn is how much ground the circle covers. Two relationships are worth carrying:

• At a given airspeed, steepening the bank turns the airplane faster and tighter: higher rate, smaller radius. It also raises the load factor, which is the price of the tighter turn.
• At a given bank angle, flying faster turns the airplane slower and wider: lower rate, larger radius. This is why fast airplanes need a lot of room to come around.

One rate has a name you will use constantly once you fly on instruments: the standard-rate turn, 3 degrees per second, which takes two minutes to go all the way around. Holding a standard rate takes more bank as you fly faster, which is one more place the speed-and-bank relationship shows up.

PHAK Ch 5, "Rate of Turn" and "Radius of Turn"

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