Load Factor and Flight Envelope

Load factor measures how hard the wing is working compared with straight and level flight. Whenever an aeroplane turns, pulls up or meets a vertical gust, the wing must produce more lift than the aeroplane weighs, and the structure, the occupants and the stall speed all feel the difference.

The flight envelope sets the limits. Plotted as the V-n diagram, it shows the speeds and load factors at which the aeroplane can fly without stalling and without damaging its structure. From it come the design manoeuvring speed, the never-exceed speed and the rules for flying in turbulence.

Load factor defined

The load factor, written n, is the ratio of lift to weight: n = L ÷ W. It is usually quoted in g. In steady straight and level flight lift equals weight and n = 1. A load factor of 2 means the wing is producing twice the aeroplane's weight in lift, and everything on board, pilot included, presses down with twice its normal weight. The aeroplane's mass has not changed; only the load on it has. The cockpit accelerometer, or g-meter, displays it.

Load factor matters for two reasons. The structure must carry n times the weight, so there is a structural limit. And the stall speed rises with the square root of the load factor, VS × √n, so the wing reaches its critical angle of attack at a higher speed. That is the accelerated stall described in stall.

Load factor in turns and pull-ups

In a level, co-ordinated turn the vertical component of lift must still equal the weight, so the total lift must rise as the bank increases. The load factor depends only on the bank angle: n = 1 ÷ cos(bank angle), whatever the aeroplane's type or weight (see turning flight).

The load factor climbs steeply beyond 60°: at 75° it is nearly 4 g. At a constant speed the induced drag rises with the square of the load factor, so a level 60° turn needs four times the induced drag of wings-level flight and extra power to hold speed.

In a pull-up the wing must supply the centripetal force for the curved path as well as support the weight. At the bottom of a pull-out of radius r the load factor is n = 1 + V² ÷ (g × r), so a faster or tighter pull-out produces more g. Over the top of a push-over the load factor falls below 1, and at zero g the wing produces no lift at all. The pilot feels the effect too: grey-out typically begins at around 3 to 4 g in a relaxed pilot.

At high altitude, airline crews keep a buffet margin of 1.3 g, the load factor of a level turn at about 40° of bank, between the cruise condition and the onset of buffet (see high-speed flight).

Limit and ultimate loads

The limit load is the highest load the aeroplane is expected to meet in service. The structure must carry it without permanent deformation, and the pilot must never deliberately exceed it. The ultimate load is the limit load multiplied by a factor of safety of 1.5, and the structure must carry it for at least three seconds without failing. The ultimate load factor is therefore 1.5 times the limit load factor: 3.75 g for an aeroplane designed to 2.5 g. Between limit and ultimate load the structure may be permanently deformed and needs inspection; beyond the ultimate load it may fail. The margin is for the unforeseen, not for routine use, and exceeding the limit load is a maintenance event even if nothing visibly breaks.

The limit load factors depend on the certification category:

For both transport and normal category aeroplanes the positive manoeuvring limit comes from the same formula, n = 2.1 + 24,000 ÷ (W + 10,000), with W the design maximum weight in pounds, and need not exceed 3.8; for transport aeroplanes it may not be less than 2.5. A light aeroplane up to about 4,100 lb therefore gets 3.8, and any transport aeroplane above 50,000 lb gets 2.5. With flaps extended the positive limit falls to +2.0 g in both codes.

Fly-by-wire aeroplanes enforce the limits themselves. In normal law the A320 limits the load factor to +2.5 g and -1 g clean, and to +2 g and 0 g with slats or flaps extended (see fly-by-wire).

The V-n (V-g) diagram

The V-n diagram, called the V-g diagram in FAA material, plots load factor vertically against airspeed, normally equivalent or indicated airspeed, horizontally. Its boundaries are:

• The stall curves. Lift at CLmax rises with the square of the speed, so the greatest load factor the wing can produce is n = (V ÷ VS)². This parabola passes through n = 1 at the 1 g stall speed, VS, and rises to meet the limit load line. A similar curve bounds the negative side. To the left of them the wing cannot produce the load factor: it stalls first.
• The limit load lines, horizontal at the positive and negative limit load factors. Above them the structure is overloaded.
• The design dive speed VD, the vertical line at the right. On light aeroplanes VNE, the red line, is set at no more than 0.9 VD to leave a margin for speed upsets. FAA handbook versions of the V-g diagram simply draw VNE as this right-hand boundary.

The design cruising speed VC lies between. On the airspeed indicator of a light aeroplane the green arc runs from VS1 to VNO, the yellow arc from VNO to VNE is for smooth air only, and the white arc from VS0 to VFE is the flap range, within which the flaps-extended envelope applies.

The envelope changes with weight: a heavier aeroplane stalls at a higher speed, so the stall curve moves right. At high altitude the low-speed and high-speed buffet boundaries narrow it further.

Manoeuvring speed and corner speed

Where the positive stall curve meets the positive limit load line is the design manoeuvring speed, VA. At that speed the wing reaches its critical angle of attack exactly at the limit load factor, so VA = VS × √n(limit). Below VA a full, abrupt deflection of a single control, or a sharp gust, stalls the wing before the limit load factor is reached; above it, the same input can overload the structure. An aeroplane with a 1 g stall speed of 60 kt and a limit of 2.5 g has a VA of about 95 kt.

Because stall speed varies with the square root of weight, so does VA. A published VA applies at maximum weight, and a lighter aeroplane needs a lower one: an aeroplane 20 % below maximum weight has a VA about 10 % lower. An aeroplane with a VA of 110 kt at 3,000 lb has one of about 98 kt at 2,400 lb. Flying the heavy-weight VA when light allows the limit load to be exceeded before the wing stalls.

VA protects against one full input in one direction on one axis. It does not protect against rapid reversals or full inputs on several axes at once. In 2001 American Airlines Flight 587, an Airbus A300-600, lost its vertical stabiliser after large alternating rudder inputs below VA. Since 2010, 14 CFR 25.1583 has required transport aeroplane flight manuals to state that such inputs may cause structural failure at any speed, even below VA.

The point where the stall curve meets the limit load line is also called the corner speed, a name FAA material sometimes gives to VA. There the aeroplane can turn at its highest rate and smallest radius: below it the stall limits the load factor, and above it the structure does.

Gust loads and the gust envelope

A vertical gust changes the angle of attack. An upward gust of velocity U met at true airspeed V raises the angle of attack by an angle whose tangent is U ÷ V, so lift and load factor jump without any pilot input. The gust load factor increment grows with airspeed, with gust velocity and with the lift-curve slope, and falls with wing loading. A high wing loading or a swept wing, which has a shallower lift-curve slope, therefore gives a smoother ride.

Designers draw a gust envelope from lines radiating from n = 1 at zero speed, with slopes set by the design gust velocities. Exam texts quote the classic values of 66 ft/s at VB, the design speed for maximum gust intensity, 50 ft/s at VC and 25 ft/s at VD, all vertical and in equivalent airspeed; the CS-23 gust envelope of a normal category aeroplane uses the VC and VD values at low altitude. A smaller gust is assumed at VD because the load a gust produces rises with airspeed. The design flight envelope combines the manoeuvre and gust envelopes, and the structure is designed for whichever is more critical at each speed.

In turbulence the answer is speed. Light aeroplanes slow to VA or below, where a strong gust stalls the wing before it can overload the structure; above VNO, the top of the green arc, the aeroplane is no longer protected even against the design gust. Transport aeroplanes fly the rough air speed VRA or MRA from the flight manual, and the crew holds attitude and accepts altitude changes rather than chasing them (see turbulence).

Unloading the wing

Unloading means reducing the angle of attack and the load factor, by relaxing back pressure or pushing. It is the first action in most recoveries. Unloading moves the stall speed back towards its 1 g value, removes the risk of an accelerated stall, restores roll authority and relieves the structure. With the wings unloaded, a steeply banked aeroplane can be rolled level before any pull is made.

The reverse is a common trap. Pulling while steeply banked adds load factor without raising the nose, which is how a spiral dive tightens and how aeroplanes are overstressed during recovery (see spins and spiral dives). In upset prevention and recovery the rule is to push to unload, roll to level the wings, and only then pull.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.