When Lift Fails

When it comes to aerodynamics, student pilots are taught about stalls early on. They are told that an airfoil stalls at one critical angle of attack, when air no longer flows over the upper surface in an organized pattern but instead separates or burbles away. Students are also told that an airfoil can be stalled at any attitude and at any air speed. At this point, the discussion of stalls is generally over, except for the admonition to "keep your air speed up and don't let this happen to you." But there's actually a lot more to learn. This paper will examine the aerodynamics behind a stalled airfoil, with the hope that the reader will come away with a better understanding of the physics of airfoil stall and with increased knowledge of how to avoid a stall.

Before we begin, it should be noted that the word "stall" as it applies to airplanes is a bit of a misnomer, since it makes one think of an automobile engine stalling -- a completely different problem. The term was probably coined because an airplane climbing at a steep incline is reminiscent of a car stalling as it attempts to climb a hill that is too steep. The word has remained in the aviation lexicon even though it causes confusion in aircraft accident reports.

In the flight training of stalls, students may think they are going aloft to practice losing control. In fact, they are learning how to maintain control. The goal in stall practice is not to get good at stalling an aircraft -- many dead pilots achieved that -- but to be able to recognize a stalled condition and then to recover with minimal loss of altitude. Another objective of stall practice is to make students aware of slow flight. Failure to attain or maintain a safe flying speed is the cause of a significant number of mostly fatal accidents.

To understand the stall, or lack of sufficient lift, one must understand how an airfoil creates lift in the first place. The camber, or curvature, of the airfoil increases the airflow over the upper wing surface, and the lowered pressure creates the upward force called lift. The pilot controls the amount of lift by adjusting the wing's angle of attack. The angle is measured between the chord line and the relative wind. As the angle of attack is increased, the coefficient of lift increases to the maximum coefficient of lift (Cl_max). The Cl_max is attained at the critical or stalling angle of attack. This stalling angle of attack is constant. That is, a given airfoil will always stall at the same angle of attack. (For a further discussion of this topic, see "Lift" in the January/February 1999 issue of Woman Pilot.)

The pressure on the upper surface of the wing is lowest at a point known as the center of pressure (CP). The exact location of this point depends on the airfoil, but is usually located between 30% to 50% of chord (the line connecting the leading and trailing edges). In other words, the CP is typically found roughly one-third to one-half of the way between the leading and trailing edges. A high-pressure stagnation point develops on the leading edge of the wing while a lower-pressure stagnation point develops at the trailing edge. A pressure gradient is determined by dividing the pressure difference between two points by the distance between them. The higher the difference in pressure and the closer the points, the greater the pressure gradient. A favorable pressure gradient is from high pressure to lower pressure, the natural direction of airflow. Due to a wing's pressure distribution, the pressure gradient is favorable from the leading edge to the CP and unfavorable from the CP to the trailing edge.

As the angle of attack increases, the pressure at the CP decreases. The lower the pressure at the CP, the greater the adverse pressure gradient to the trailing edge. At a particular angle of attack the adverse gradient becomes so great that the airflow begins to move from the trailing edge forward to the CP. As this forward-moving air meets the rearward-flowing relative wind, the air stream has nowhere to go but up and away from the airfoil. This burbling, felt by the pilot as a buffet, is the first indication of an imminent stall. As the stalled area of the wing increases forward from the trailing edge to the leading edge, the center of lift moves forward. When the entire wing is fully stalled, the loss of this forward upward force results in a nose-down tendency.

All airfoil-stall progression is from the trailing edge forward to the leading edge.The reason for this progression is the pressure gradient mentioned previously. The planform, or top-down view of the wing, plays an important role in the stall-progression pattern.

The most common design for light trainers is the rectangular planform. The use of wash-in and wash-out creates a stall pattern that starts at the trailing-edge root and develops forward and outward as the angle of attack is increased beyond the critical angle of attack. Wash-in and wash-out refer to the decreasing angle of incidence (angle between the chord line and the aircraft's longitudinal axis) as one moves from the wing root to the wingtip. The advantage of this pattern is that the ailerons are effective (not stalled) up to the most fully developed stall condition. The rectangular planform also has a lift load distribution advantage, with most of the lift created inboard, reducing the bending moment on the wing spar. The inboard stall initiation warns the pilot as the burbling air flows rearward onto the horizontal stabilizer and elevator. This creates a buffeting that can be felt on the control yoke, providing a natural stall warning. The use of stall strips on the leading-edge section of the wing can also induce stall initiation at the inboard sections of the wing.

The tapered wing is another kind of planform. In this wing the chord (the distance between the leading and trailing edge) decreases as one moves from the wing root to the wingtip. Tapering allows the inboard lift distribution, described earlier, that is desirable for spar-bending moment reasons. The taper causes the stall to initiate along the entire trailing edge, moving forward as the angle of attack is increased. The problem with this progression is that the ailerons begin to stall at the same time as the root. As soon as any buffet is felt, lateral control is reduced by the stalled ailerons. The shorter the chord (as at the trailing edge), the sooner the stall begins, because as the chord is decreased the distance also decreases between the CP and the higher pressure at the trailing edge. The shortened distance increases the adverse pressure gradient. Thus, the decreased chord at the wingtip would tend to stall first if it were not for the wash-out. Overall, the wash-out of the wingtips cancels the decreasing chord and the entire wing trailing edge stalls at once. This stall-progression pattern is similar to that of an elliptical airfoil.

The most unfavorable stall characteristics are found with the swept wing, which is used in transonic aircraft to reduce wave and parasite drag at cruise speeds. The sweep causes high induced drag and stall conditions at low speed. The sweep creates an induced upwash angle of the relative wind at the leading edge that increases from wing root to tip. This means that the wingtip is flying at a higher angle of attack than the root. Thus, it will reach its critical angle of attack first. The wingtip is the worst possible location for an initial stall, since loss of aileron control is the result. The burbling airflow off the wingtips does not encounter the tail assembly and thus does not give the pilot a natural stall buffet warning.

Another disadvantage of the swept wing is that as the stall progresses the area producing lift shrinks forward and the center of lift load has a pronounced forward shift. As this upward force shifts forward, the aircraft develops a nose-up tendency. The upward pitching moment can make stall recovery difficult. The moral of this story, of course, is that swept-wing aircraft should not be allowed to stall. To counteract the poor natural stall warning on a swept wing, an angle-of-attack sensor activates a "stick shaker" to give the pilot the simulated sensation of a stall buffet. Other airliners have a computerized fly-by-wire system that prohibits pilots from exceeding the critical angle of attack. Control inputs from the pilot that would result in a stall are simply ignored. It reminds one of the HAL 9000 computer in the movie 2001: A Space Odyssey:
"Pitch up higher, HAL!"
"I can't do that, Dave."

High-performance aircraft also use laminar-flow airfoils. In this design, drag is reduced by maximizing smooth air streams called laminar flow. This smooth airflow tends to separate more abruptly from the wing at high angles of attack, resulting in a full stall that occurs immediately after exceeding the critical angle of attack. Like the swept wing, this design improves high-speed efficiency at the expense of low-speed performance.

Pilots know that an airfoil can be stalled at any attitude and at any air speed. The part of this statement referring to attitude is easy to understand. Because the relative wind is opposite to flight path, the relative wind comes from beneath the airfoil when an aircraft is in descending flight. Even with a pitch attitude level with the horizon, the stalling angle of attack can be exceeded with a steep angle of descent. The air speed part of the statement is a bit more complicated. If the stalling angle of attack is always the same, why isn't the stalling air speed always the same? It's because four factors affect the stalling air speed: gross weight, load factor, altitude, and location of the center of gravity.

First let's examine the lift equation L = Cl S Greek letter sigma V_ktas²/295, where L = lift in pounds, Cl = coefficient of lift, S = wing area in square feet, Greek letter sigma = air density ratio to that of standard sea level, and V_ktas = true air speed in knots.

If the aircraft is in straight and level flight, lift is equal to weight and the equation becomes L = W = Cl S Greek letter sigma V_ktas²/295.

Solving for velocity, the equation is arranged as V_ktas²295 W / Greek letter sigma S Cl and V_ktas = the square root of 295W / Greek letter sigma S Cl.

As the air speed is decreased, the Cl must be increased by increasing the angle of attack to keep the lift equal to weight. As the critical angle of attack is reached, the Cl has reached the maximum Cl_max and the air speed is at the minimum speed, or stall speed. This speed is abbreviated as V_s.

When calculating an aircraft's stall speed the equation is V_s (knots true air speed) = the square root of 295W / Greek letter sigma S Cl_max. From this equation, each factor affecting the stall speed can be evaluated.

As the weight of an aircraft increases, so do the stall speed and the required angle of attack. If a heavy aircraft and a light one are both flying at the same speed, the heavy aircraft is at a higher angle of attack. If both aircraft decrease their air speed at the same rate, the heavy aircraft will reach the critical or stalling angle of attack first, at a higher air speed than the lighter aircraft. As the center of gravity is shifted forward, the greater nose-down moment must be offset by a greater tail-down force. This tail-down force increases the effective gross weight of the aircraft, increasing the stall speed as described previously.

The extension of flaps has a pronounced effect on stall speed. Some flaps, such as Fowler flaps, will increase the wing area (S) and thus decrease the stall speed. The extension of flaps also increases the maximum coefficient of lift by increasing the wing camber (curvature), and, with some flaps, the boundary layer energy. The lowering of the trailing edge with the extension of the flaps will increase the angle of attack for a given pitch attitude by increasing the angle of the chord line to the relative wind. (For a further explanation of flaps see "High Lift Devices" in the May/June 1998 issue of Woman Pilot.)

As altitude increases, the density ratio (Greek letter sigma) decreases. The higher the altitude, the higher the true air speed of the stall. The indicated stalling air speed remains the same (as does the calibrated and equivalent air speed) with increasing altitude, but the actual speed through the air mass (TAS) increases.

An aircraft's bank angle in a turn has an important effect on stall speed. As an aircraft banks, the lift vector is displaced away from the vertical. The horizontal component of this deflected lift vector acts to horizontally accelerate (turn) the aircraft. As the lift vector is deflected, less of it remains in the vertical direction. To maintain level flight, the vertical component of lift must remain equal to the aircraft's weight. To accomplish this, the entire lift vector must be increased by increasing the angle of attack. Pilots learn that banking an aircraft requires an increased back pressure on the control yoke. As the bank angle is increased in level flight, the angle of attack is increased, and will eventually reach a stall, no matter how high the air speed. Hence, the aircraft can be stalled at any air speed.

Load factor is the ratio of the lift the aircraft is producing to its weight. In level coordinated flight, the load factor is equal to the inverse of the cosine of the bank angle (1/cos Greek letter theta). In wings-level flight, the load factor is 1 (cos 0 = 1). As the bank angle increases, the load factor increases. At a bank angle of 60 (cos 60 = 0.5) the load factor is 2. The stall speed increases with the square root of the load factor as it does with weight. At low speeds, an increasing load factor will result in a stall. At high speeds, structural damage may occur before the stall. For example, normal-category aircraft are designed to withstand a load factor of 3.8 g's. If attempting to turn with a 75 bank, the stall speed is approximately doubled. If flying at an air speed that is less than twice the normal stall speed (V_s x 2), the aircraft will stall. If flying above this speed, structural damage may occur because a load factor in excess of 3.8 would be experienced. This is why the speed of an aircraft must be reduced to a value known as maneuvering speed (V_a) before attempting maneuvers that might possibly exceed the maximum load factor.

A spin is an aggravated stall in which one wing is more fully stalled than the other and thus experiences less lift and more drag. In the resulting autorotation, the aircraft yaws and rolls while descending. A spin requires a significant amount of altitude to recover, and some aircraft can become unrecoverable in a fully developed spin. Pilots should practice spins only in an aerobatic aircraft with a certified flight instructor.

To summarize, an airfoil stalls when it exceeds its critical angle of attack. To recover from a stall, the angle of attack must be decreased, usually by lowering the pitch attitude. As the pitch attitude is being adjusted, full power is added to minimize altitude loss. The proper stall recovery technique can make the difference between life and death. That's why competent pilots routinely practice stall recoveries in various configurations. It also helps if pilots understand the aerodynamics of the stall. In this case, an inch of prevention is definitely worth hundreds of feet of cure.

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