Chapter 14
Longitudinal Stability and Control

In addition to adequate performance, an aircraft must have satisfactory handling qualities. An aircraft must be able to maintain uniform flight and be able to recover from the effects of disturbing influences, such as gusts. This ability is called the stability of an aircraft. Adequate stability is necessary to minimize the workload of the pilot. In some cases, such as helicopter flight, it is necessary to provide artificial stabilization by use of automatic stabilization equipment (ASE). The mission of the aircraft is very important to the manufacturer when considering the design of the aircraft. A single‐engine Cessna trainer has a completely different mission than an F/A‐18 Super Hornet, and thus must be designed for the role that aircraft will play once in use.

Control is the response of an aircraft in flight path and attitude to the directions of a pilot, specifically when maneuvering the aircraft. For an aircraft to respond to the controls, its stability must be overcome. Stability and control are often compared to a seesaw, with stability at one end and control at the other. The more stability an aircraft has, the less controllability it has, and vice versa.

Stability also affects the maneuverability of an aircraft. Maneuverability allows an aircraft to be maneuvered easily and withstand the stresses we discussed in the previous chapter. This design characteristic is a function of the weight, structural strength, flight control design, and power plant, among other items. Modern, complex, high‐performance aircraft have complicated stability problems that are beyond the scope of this book. Our discussion here is basic and simple. Some simplifying assumptions are made to keep the discussion from getting too involved.

DEFINITIONS

Equilibrium

An aircraft is said to be in a state of equilibrium if the sum of all moments and forces at its center of gravity are equal to zero. This means that there is no pitching, yawing, or rolling, nor is any change of velocity taking place.

Static Stability

Static stability is the initial tendency of an aircraft to move once it has been displaced from its equilibrium position. If it has the tendency to return to its equilibrium position, it is said to have positive static stability. A trimmed aircraft in level flight, disrupted by thermal turbulence that initially has a tendency to return to its original condition, is said to have this type of stability.

This is illustrated by the ball/cone on the far left in Fig. 14.1. The bottom of the bowl is the equilibrium position of the ball. If the ball is moved to one side, it has the tendency to return toward the bottom. It has positive static stability. Note that for the ball to have positive static stability it is not important that the ball actually returns to the bottom, only that it has the tendency to return. The situation for the cone is the same on the far left; a force is applied and the natural tendency of the cone is to return to equilibrium.

Figure 14.1 Types of static stability.

U.S. Department of Transportation Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, 2008

If an aircraft that has been disturbed from its equilibrium position has the initial tendency to move farther away from its equilibrium position, it is said to have negative static stability. This is illustrated by the ball/cone on the far right of the image in Fig. 14.1. The ball has been displaced from its equilibrium position on the left (at the top of the bowl) and moved to the right by a force. The initial tendency of the ball is to move farther away from its original position, so the ball has negative static stability. The cone on the right of the image exhibits the same natural tendency as the ball when a force is applied; it moves farther away from the original point of equilibrium.

If an aircraft is disturbed from its equilibrium position and has the tendency neither to return nor to move farther away from its equilibrium position, it is said to have neutral static stability. This is illustrated by the ball/cone on a flat surface, as shown in the middle of the image in Fig. 14.1. If the ball/cone is displaced by a force it does not have a tendency to return to its original position, nor does it have a tendency to move away from its original position. This is neutral static stability.

For an aircraft to have positive stability, it must first have positive static stability.

Dynamic Stability

Dynamic stability is the movement of an aircraft with respect to time (Fig. 14.2). If an aircraft has been disturbed from its equilibrium position and the maximum displacement decreases with time, it is said to have positive dynamic stability. If the maximum displacement increases with time, it is said to have negative dynamic stability. If the displacement remains constant with time, it is said to have neutral dynamic stability.

Figure 14.2 Dynamic stability.

U.S. Department of Transportation Federal Aviation Administration, Glider Flying Handbook, 2013

OSCILLATORY MOTION

Aircraft motions are oscillatory in nature. Therefore, let us consider the possibilities of these oscillations. As we just mentioned, an aircraft must have positive static stability, but this does not ensure that it will have positive dynamic stability as well.

Consider the graph of aircraft displacement versus time shown in Fig. 14.3. The first reaction to the displacement is to return toward the equilibrium position. This is positive static stability. The subsequent oscillations, however, are divergent, so the dynamic stability (over time) is negative. This is a case of positive static and negative dynamic stability, and it is unacceptable.

Figure 14.3 Positive static and negative dynamic stability.

Another possibility is that of positive static stability and neutral dynamic stability, shown in Fig. 14.4. No damping of the oscillations occurs. This is also unacceptable.

Figure 14.4 Positive static and neutral dynamic stability.

The desired combination of positive static and positive dynamic stability is called a damped oscillation. An airplane will return to its equilibrium condition when this occurs. This is shown in Fig. 14.5.

Figure 14.5 Positive static and positive dynamic stability.

AIRPLANE REFERENCE AXES

To better envision the forces and moments acting on an airplane, we assign three mutually perpendicular reference axes, all intersecting at the CG. These are shown in Fig. 14.6. The longitudinal axis is assigned the letter X, and the aircraft experiences rolling motion around this axis using the ailerons. The lateral axis is the Y axis, and can be considered for our discussion the axis from wingtip to wingtip through the CG. The aircraft experiences pitching moments around the lateral axis by using either the elevator or stabilator primary flight controls. The vertical axis is the Z axis, and the aircraft experiences yawing motion around the vertical axis by use of the rudder. Again, all three imaginary axes pass through the aircraft's CG.

Figure 14.6 Airplane reference axes.

U.S. Department of Transportation Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, 2008

As seen in Fig. 14.7, the positive direction of the axes is determined by positioning the thumb, index finger, and middle finger of the right hand so that they are at right angles to each other. Point the thumb in the forward direction of the X axis, and the other fingers point to the positive directions of the Y and Z axes.

Figure 14.7 Establishing positive moment direction.

Three moments are possible about the three axes. These are given three identifying letters that occur in sequence in the alphabet. The rolling moment is L (to avoid confusion with lift we will call this L′), the pitching moment is M, and the yawing moment is N. The positive direction of these moments is determined by using the right‐hand rule, shown in Fig. 14.7. The right thumb points to the positive axis, and the curvature of the fingers shows the direction of the positive moments. The completed axes and moment illustration is shown in Fig. 14.8.

Figure 14.8 Airplane axes and moment directions.

Longitudinal stability and control refer to the behavior of the airplane in pitch, that is, movements of the longitudinal axis about the lateral axis as controlled by the elevator or stabilator. This movement is illustrated in Fig. 14.9. In the pure pitching case, no rolling or yawing of the aircraft takes place.

Figure 14.9 Movement of the longitudinal axis in pitch.

STATIC LONGITUDINAL STABILITY

An airplane is said to have positive static longitudinal stability if it tends to maintain a constant AOA in flight once it has been trimmed to that angle. If an airplane is trimmed so that it has zero pitching moments at some AOA and is in a state of equilibrium, and is then disturbed in pitch and tends to return to the trimmed AOA, it is said to have positive static longitudinal stability. The amount of longitudinal stability an aircraft has depends upon many factors. As you might expect the position of the CG plays an important part in the stability around the lateral axes, particularly when considering the distance of the tail from the CG and the location of the wing. Since we are dealing with moments, not only does the location of the tail influence the longitudinal stability, but also the magnitude (and direction) of the force on the tail. So, the area or size of the tail surface is important.

An airplane that has negative static longitudinal stability, on the other hand, will continue to pitch away from the trimmed AOA. If an airplane has neutral static longitudinal stability, it will remain at whatever AOA the disturbance has caused.

It is important for an airplane to have positive static longitudinal stability. A stable airplane is easy and safe to fly. It can be trimmed at any desired speed and will tend to maintain that speed. An airplane with negative static longitudinal stability will be impossible to trim and will require the pilot's attention at all times. A tendency to dive or initiate a climb when upset is possible, even to the point of a stall, which in extreme situations may be unrecoverable depending on the adverse condition.

The Pitching Moment Equation

The pitching moment about the aircraft CG is

(14.1)

where

MCG	=	pitching moment about the CG (ft‐lb)
CM(CG)	=	coefficient of pitching moment about CG
q	=	dynamic pressure (psf)
S	=	wing area (ft2)
C	=	mean aerodynamic chord, MAC (ft)

Rearranging Eq. 14.1 gives

(14.2)

Because the values of q, S, and c are always positive, it follows that for a nose‐up (+) pitching moment, the value of C_M(CG) must also be positive; for a nose‐down (−) pitching moment, the value of C_M(CG) must be negative.

Graphic Representation of Static Longitudinal Stability

A plot of the variation of C_M(CG) at different values of C_L (different AOAs) for an airplane with positive static longitudinal stability is shown in Fig. 14.10. The trim point is the value of C_L where the aircraft has no pitching moment. At all values of C_L above the trim point, such as point y, the aircraft will have a nose‐down (−) pitching moment. If the aircraft is disturbed by an up‐gust, the AOA (and C_L) will be increased. For stability, a nose‐down pitching moment is required, so this is a stabilizing condition. If the airplane is disturbed by a down‐gust, the AOA and value of C_L will be reduced. This is represented by point X in Fig. 14.10.

Figure 14.10 Positive static longitudinal stability.

The value of C_M(CG) at point X is positive, and a nose‐up pitching moment results. This is what is required for static stability. Thus, a negative slope on this graph represents an aircraft with positive static stability. Conversely, a positive slope would indicate an unstable aircraft, and a zero slope would represent an aircraft with neutral stability. These are shown in Fig. 14.11.

Figure 14.11 Types of static longitudinal stability.

There are different degrees of stability. Some aircraft tend to return to their equilibrium positions faster than others. Again, using the analogy of the ball/cone in the curved container, the degree of stability can be illustrated as shown in Fig. 14.12. Degrees of stability are shown on the plot by the slope of the curve. Steeper slope of the stable curve shows more stability, and steeper slope of the unstable curve shows more instability.

Figure 14.12 Degrees of positive static stability.

An airplane can be stable at lower angles of attack but may be unstable at higher angles of attack. This would indicate a pitch‐up problem at high AOA. This is shown in Fig. 14.13.

Figure 14.13 Aircraft static longitudinal stability.

Contribution of Aircraft Components to Pitch Stability

Wings

The static stability contribution of the wings depends on the relative position of the aerodynamic center AC and the center of gravity CG of the airplane. Consider a tailless (flying wing) airplane with a symmetrical airfoil section as shown in Fig. 14.14. We will consider two possibilities of CG and AC location:

1. CG is located forward of the AC (Fig. 14.14a).
2. CG is located behind the AC (Fig. 14.14b).

Figure 14.14 Effect of CG and AC location on static longitudinal stability.

If the airplane in Fig. 14.14a experiences an up‐gust, the AOA will be increased and the lift at the AC will increase. The airplane will then rotate about the CG (a free body will rotate around the CG), and this nose‐down moment will tend to rotate the airplane and return it to its equilibrium AOA. This is the stable condition. The greater the distance the AC is located behind the CG, the more nose‐down moment that will be experienced for a respective up‐gust.

If the airplane in Fig. 14.14b experiences an up‐gust, the increase in lift at the AC will rotate the airplane about its CG and create a nose‐up pitching moment and rotate the airplane away from its equilibrium position. This is the unstable condition. The CG must be ahead of the AC for a stable flying wing.

The airplane in Fig. 14.14a is stable in pitch, but it is not in equilibrium. The conditions for equilibrium require that there be no unbalanced forces or unbalanced moments acting on the airplane. The first requirement is easily satisfied by adjusting the AOA so that lift equals weight. The second requirement, however, has not been met. The forces of lift and weight create a nose‐down pitching moment because the AC is behind the CG and the aircraft naturally rotates around the CG. Therefore the unbalanced force must be canceled out by an opposing nose‐up pitching moment.

In our discussion of pressure distribution on airfoils in Chapter 3, we saw that the forces acting on the top and bottom surfaces of a symmetrical airfoil were located in the same position along the chord and that no pitching moment resulted from their location (see Fig. 3.19). The pressure location on cambered airfoils, on the other hand, was found not to be located at the same chordwise position, and so a nose‐down pitching moment resulted from positive camber (Fig. 3.20). A negatively cambered airfoil, again with the AC positioned behind the CG, produces a nose‐up pitching moment. Aircraft manufacturers not only design an airfoil with the correct position of AC to give the correct amount of nose‐up moment when in cruise flight, but also attach the airfoil in certain cases with a given negative AOA to provide the necessary nose‐up force. The correct amount of force for a given aircraft is what we need to cancel the nose‐down moment caused by the lift and weight vectors. This is shown in Fig. 14.15. Delta‐wing airplanes use reflexed (negatively cambered) trailing edges to create the nose‐up pitching moments required for equilibrium.

Figure 14.15 Static longitudinally stable flying wing in equilibrium.

The overall contribution of the wings of an aircraft to the static longitudinal stability depends on the location of the AC and the CG of the aircraft. If the AC is behind the CG, the contribution is stabilizing. If the AC is ahead of the CG, the contribution is destabilizing. The trend in recent years is to locate the wings farther back on the fuselage, thus increasing the aircraft's pitch stability.

There is one disadvantage in doing this. Consider the vertical forces acting on the aircraft if the AC is located behind the CG as shown in Fig. 14.16. In order to maintain flight in equilibrium, the tail must provide enough down force to compensate for the rotation around the CG. This tail‐down force must be accounted for by the total lift.

Figure 14.16 Airplane with static longitudinal stability.

It is assumed that this airplane has a symmetrical airfoil so it has no pitching moment due to the pressure distribution on the airfoil. For balance, the airplane must have a download on the tail (LIFT_T). The lift on the wing (LIFT_W) must equal the weight of the aircraft plus the lift on the tail. Thus, it must operate at a higher AOA than if the lift on the tail acted upward. Higher angles of attack produce more drag. One of the newer concepts is to reduce the static stability by moving the CG backward, and thus reduce the drag. This may require automatic stabilization devices. A rearward CG can reduce drag and increase airspeed, but caution is warranted as CG too far aft may impact nose‐down authority, and in worse case scenarios prevent the proper recovery from a stall/spin.

Fuselage

A streamlined fuselage has a pressure distribution similar to that of a body of revolution when placed in an airstream. The pressure distribution about such a body is shown in Fig. 14.17. It can be seen that no net lift is developed by the pressure distribution, but a nose‐up pitching moment is developed by an up‐gust, so the pitching moment is destabilizing. Thus, the fuselage is a destabilizing component.

Figure 14.17 Pressure distribution about a body of revolution.

Engine and Engine Nacelles

The amount of power and position of the thrust line also can impact longitudinal stability. A high thrust line can be seen in Fig. 14.18 to rotate the aircraft around the CG in a nose‐down moment, where a low thrust line below the CG introduces a pitching up moment. Power changes in our single‐engine aircraft example also influence longitudinal stability (Fig. 14.19). If full power is introduced a nose‐up rotation around the CG is experienced, and vice‐versa. At cruise power no moment is realized due to power adjustments.

Figure 14.18 Thrust line and longitudinal stability.

U.S. Department of Transportation Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, 2008

Figure 14.19 Power changes and longitudinal stability.

U.S. Department of Transportation Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, 2008

The direction of the airflow through a propeller disk or through a turbojet engine is not changed if the axis of the engine is in line with the aircraft's flight path. If the engine axis is at an angle with the relative wind, however, the airflow is turned so that it flows in the direction of the engine axis. When this happens, a side force is developed on the propeller shaft or on the side of the jet engine intake, in accordance with Newton's third law. This is shown on the aircraft in Fig. 14.20 and is a destabilizing force when in front of the CG.

Figure 14.20 Engine nacelle location contribution to pitch stability.

The axes of the aircraft are at a positive AOA to the relative wind and the resulting force creates a nose‐up pitching moment. This is a destabilizing moment. If the engines are mounted so that the propellers or jet intakes are behind the CG and the axis of the engine makes a positive angle with the relative wind, the resulting upward side force produces a nose‐down moment. This is a stabilizing moment. Propellers or jet engine intakes located forward of the CG are destabilizing components, and propellers or jet engine intakes located behind the CG are stabilizing components (tail mounted).

Horizontal Stabilizer

As the name implies, the horizontal stabilizer is a strongly stabilizing influence on static longitudinal stability. It is usually a symmetrical airfoil because it must produce both upward and downward airloads, and it may be in a fixed position as designed by the manufacturer to provide the best stability during cruise flight. The contribution of the horizontal stabilizer to the pitch stability of the aircraft can be seen in Fig. 14.21. Figure 14.21a shows that if an up‐gust causes the aircraft to pitch up, then an upward lift is developed by the horizontal tail. This creates a nose‐down moment, which is stabilizing. In Fig. 14.21b the opposite effect is achieved when the aircraft is pitched downward by a down‐gust. A nose‐up moment is developed in this case.

Figure 14.21 Lift of horizontal stabilizer produces a stabilizing moment.

A similar effect can be seen when analyzing the effect of airspeed and tail‐down force of a single‐engine, propeller aircraft (Fig. 14.22). In cruise flight the forces are balanced between the tail‐down force (nose‐up moment) and the nose‐down moment due to the rotation around the CG by the rearward AC and weight of the engine. This is the regime of flight where most pilots spend their time, and thus forces required to trim the airplane are usually designed to be minimal at this point. If the aircraft were pitched up around the lateral axis to a nose‐high position, airspeed would decrease and so would the respective tail load. As a result the nose would fall, the airspeed would increase, and so would the air going over the tail resulting in a nose‐up force. Eventually the aircraft would return to the original trimmed airspeed. If the aircraft was in a nose‐low attitude, the airspeed would increase, the air over the tail would increase, and the tail‐down force would increase, thus raising the nose back toward equilibrium flight.

Figure 14.22 Effect of speed on tail‐down force.

U.S. Department of Transportation Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, 2008

The degree of stability produced by the tail is determined by the tail size and the moment arm to the aircraft's CG. The tail area (ft²) multiplied by the moment arm (ft) equals the dimension of ft³, called the “tail volume.” It is an indication of the stabilizing effectiveness of the horizontal stabilizer. An increase in either the size of the surface or the distance between the CG of the airplane and the AC of the stabilizer will increase the tail volume and thus the stability of the aircraft. A smaller tail area located farther from the CG can have the same effect as a larger tail area closer to the CG. Of course many other factors in aircraft design must be accounted for when calculating tail volume.

Total Airplane

Figure 14.23 shows a typical buildup of wing with its AC forward of the CG, the wing plus the fuselage, the horizontal tail alone, and the total airplane. The horizontal stabilizer has enough stability to overcome the negative stability of the wing and fuselage combined. Stability of the engine location is not shown in this figure.

Figure 14.23 Typical buildup of aircraft components.

Effect of CG Position

Varying the CG position has a great effect on the longitudinal static stability of an airplane as shown in Fig. 14.24. Forward positioning of the CG results in increased pitch stability, as was explained earlier and illustrated in Fig. 14.14. This is shown by the slope of the curves in Fig. 14.24. At 40% MAC the slope is zero, and the aircraft has neutral stability at this point. Moving the CG behind this point results in an unstable condition.

Figure 14.24 Effect of CG location on static longitudinal stability.

Stick‐Fixed–Stick‐Free Stability

If the elevators (or other control surfaces) are allowed to float free, they will be moved from their neutral positions by outside disturbances, and the total stabilizing surface will be reduced. The stability of an aircraft with “free‐floating” control surfaces is known as stick‐free stability. The stability of an aircraft with the controls held in a fixed position will be increased. This is known as stick‐fixed stability. If you can manipulate the control surfaces of the aircraft while standing outside the aircraft it is stick‐free. A pilot can create a “stick‐free” impact while inside the cockpit if they keep their feet on the rudder pedals and minimize the free‐floating ability of the primary control surfaces.

Figure 14.25 shows the curves for both conditions. The slope of the stick‐fixed condition is greater; hence, the stability is greater for the stick‐fixed case. Unless the airplane is equipped with irreversible powered controls, better stability will be realized if the controls are held in the neutral position.

Figure 14.25 Stick‐free–stick‐fixed stability.

DYNAMIC LONGITUDINAL STABILITY

Stability considerations that we have discussed up to now have dealt with static stability. Dynamic stability involves the response of an aircraft to disturbances over a period of time. Dynamic stability exists when the amplitude of these disturbances dampens out with time, a desirable feature in an aircraft.

The reaction of an aircraft to disturbances differs, depending on whether the controls are in the stick‐free or the stick‐fixed configuration. First, let us consider the stick‐free or reversible‐controls aircraft. Most light general aviation aircraft are in this category. Remember, if a control surface is capable of being manually moved from outside the aircraft, it is in this category.

Two types of dynamic oscillations are possible. One is the long period (function of airspeed) with poor damping oscillation, called the phugoid mode. This is shown in Fig. 14.26. With phugoid oscillation, the airspeed, pitch, and altitude of the airplane vary widely, but the AOA remains nearly constant. Usually lasting only two minutes or less, the airspeed may vary by +/‐ 5 knots. The motion is so slow that the effects of inertia forces and damping forces are very low, and sometimes the oscillation may not even be noticed. The whole phugoid can be thought of as a slow interchange between kinetic and potential energy. If an aircraft is trimmed for an AOA and then power is changed, the aircraft will move through a series of pitch, altitude, and airspeed changes to maintain the original trimmed AOA condition.

Figure 14.26 Phugoid longitudinal dynamic mode.

The second mode is a short‐period mode, as shown in Fig. 14.27. The short‐period mode in the stick‐free configuration is caused by the elevator flapping about its hinge line. A typical flapping mode may have a period of 0.3 to 1.5 sec and has heavy damping of the oscillations. Recovery from this type of pitching can be accomplished by releasing the controls or, more rapidly, by holding the controls in their neutral positions. This has the effect of putting the airplane into the stick‐fixed configuration.

Figure 14.27 Short‐period dynamic mode.

Pilots must be careful not to try to dampen out the oscillations. Pilot reaction time is close to the natural period of the oscillations and inadvertent reinforcement of the pitching moment may result. While this may only result in a rough ride for a relatively slow light airplane, it can prove disastrous for a high‐performance jet aircraft. If this reinforcement occurs in a high‐performance jet, it is called a pilot‐induced oscillation (PIO). A PIO can destroy the aircraft in a few seconds.

A similar dynamic stability problem, called collective bounce, exists in helicopter flight. If an up‐gust is encountered and the helicopter is forced upward, inertia forces the pilot downward in the seat. If the pilot has hold of the collective stick, this will also be forced downward, and the AOA of all the rotors will be decreased, causing the helicopter to descend. Again, the inertia forces cause the pilot to be forced upward, the collective stick is raised, and the process is repeated.

PITCHING TENDENCIES IN A STALL

Low‐Tailed Aircraft

The forces in the pitching plane (T‐tail) are shown in Fig. 14.28. Assume that the aircraft is trimmed in straight and level flight and that the aircraft's CG is forward of the AC (as shown). A downward balancing force on the tail is required to maintain equilibrium. In case of an aft CG location, an upward force on the tail is required. If the speed is reduced, a gentle up‐deflection of the elevator is required to maintain altitude, and the downward load on the tail is increased. The static stability of the aircraft causes a nose‐down pitching tendency, which has to be resisted by further up elevator to keep the nose from dropping.

Figure 14.28 Forces on a pitching plane.

Figure 14.29 diagrams a stall progression for a low‐set tail on a straight wing aircraft. Initially as the aircraft slows down the low‐set tail becomes engulfed in the turbulent, low‐energy air from the wing wake, reducing the efficiency of the tail. Pilots should heed the buffeting at this point as imminent stall and begin immediate recover procedures. At the stall, two distinct things happen. First, the airplane responds to the traditional nose‐down pitching tendency, and the whole airplane responds with a nose‐down pitch. Second, at the moment of stall, the wing wake passes straight aft and goes above the low‐set tail. This leaves the tail in undisturbed, high‐energy air, and it now is at a high positive AOA, causing an upward lift on the tail. This lift increases the nose‐down pitching tendency and assists with reducing the AOA.

Figure 14.29 Wing wake influences on a low‐tail aircraft.

U.S. Department of Transportation Federal Aviation Administration, Airplane Flying Handbook, 2004

T‐Tail Aircraft

Again assume that an aircraft is trimmed in straight and level flight. As the aircraft is slowed toward a stall, the handling characteristics are much the same as for the low‐tailed aircraft, except that the high tail remains clear of the wing wake and retains its effectiveness allowing the pilot to continue into a stall without pre‐stall warning. Continued speed reduction is, therefore, more efficient.

At the stall two distinct things happen. First, the swept‐wing, high‐tail airplane tends to suffer a marked nose‐up pitch after the stall (this is explained in detail later). Second, the wing wake, which has now become low‐energy turbulent air, passes straight aft and immerses the T tail, which is now in the right position to catch it. This greatly reduces the tail effectiveness and makes it incapable of combating the nose‐up pitch and so the airplane continues to pitch up. The great reduction in lift and the increase in drag cause a rapidly increasing descent path. Thus, the angle of attack is increased and the pitch‐up problem is worsened. The airplane is well on its way to extreme angles of attack and deep stall. This is shown in Fig. 14.30.

Figure 14.30 Wing wake influences on a swept‐wing T‐tail aircraft.

U.S. Department of Transportation Federal Aviation Administration, Airplane Flying Handbook, 2004

Explanation of Nose‐Up Pitch Following Stall in Swept‐Wing Aircraft

Three things affect the pitching tendency:

1. Wing Section Characteristics. The section characteristics of most wings are such as to cause a nose‐down pitch, providing that the whole wing could be stalled at the same instant (spanwise). The pressure distribution is rather flat in normal flight, as shown in Fig. 14.31. As the stall is approached the pressure distribution changes to an increasingly leading‐edge peaked pattern because of the enormous low‐pressure area developed by the nose profile. At the stall this peak collapses, the pressure distribution pattern changes, and the result is usually a nose‐down pitch.
2. Wing Sweep. In practice the whole wing does not stall at the same instant. In Chapter 12 we discussed the fact that swept and tapered wings tend to stall at the tips first because of the high wing loading at the tips. This of course is a problem that affects roll control should the ailerons lose their effectiveness. The boundary layer outflow also resulting from sweep slows the airflow, reduces the lift near the tips, and worsens the situation. This loss of lift outboard (and therefore aft) causes the center of pressure to move forward, which augments the pitch‐up tendency (Fig. 14.32).
3. The Fuselage. On a modern aircraft the forward fuselage overhangs the wing by a greater extent than on the older straight‐wing models. As we have seen, the fuselage is a destabilizing factor, and an even greater one with the longer overhang. Thus, the fuselage contributes to the nose‐up pitching tendency as AOA exceeds its stall value.

Figure 14.31 Change in pressure distribution at stall.

Figure 14.32 Swept‐wing stall characteristics.

U.S. Department of Transportation Federal Aviation Administration, Airplane Flying Handbook, 2004

LONGITUDINAL CONTROL

To control an airplane it is necessary to overcome its stability. As we have seen, the farther forward the CG of the airplane is, the more static pitch stability the airplane has. However, since stability and control oppose each other, the forward CG results in lower controllability. This may work for a particular general aviation training aircraft, but not a fighter jet where control and maneuverability are vital for mission effectiveness.

Takeoff and landing maneuvers are critical as far as control forces are concerned; sufficient elevator forces are required to overcome the stability of forward CG location. During takeoff, an aircraft must be able to rotate to takeoff attitude. The requirement here is that the aircraft be able to attain takeoff attitude at 0.9V_s. Unlike the airborne case, the aircraft rotates about its main wheels, rather than its CG, during takeoff. The forces on the aircraft are shown in Fig. 14.33. An aircraft attempting a takeoff with a CG forward of safe operating limitations may experience increased tail‐down force to raise the nose, increased stall speed, and a longer takeoff distance.

Figure 14.33 Forces producing moments during takeoff.

In many aircraft little or no lift is developed until the aircraft is rotated to takeoff attitude. The angle of incidence of the wing is selected to produce minimum drag, instead of producing lift, as the aircraft accelerates during the takeoff run. The nose‐down moments that the elevator must overcome to rotate the aircraft are (1) the moment caused by the thrust line being above the main wheels, (2) the moment caused by the CG being ahead of the main wheels (increased moment = increased elevator), and (3) the nose‐down moment of either a cambered wing or takeoff flaps (if used).

An effect that is not shown on the drawing is the nose‐down pitching moment caused by ground effect, which reduces the downwash over the horizontal tail of a low‐tailed airplane. The elevator must be able to produce a nose‐up pitching moment that will overcome all the nose‐down pitching moments mentioned above as an aircraft exits ground effect.

Landing requirements include flaring the aircraft prior to touchdown and overcoming the nose‐down moment caused by the airplane entering ground effect. If the airplane fulfills the takeoff requirements satisfactorily, it will usually have enough elevator control for landings.

SYMBOLS

CM(CG)	Pitching moment coefficient (dimensionless)
L′	Rolling moment (ft‐lb)
MCG	Pitching moment about CG
N	Yawing moment
PIO	Pilot‐induced oscillation
X	Longitudinal axis of aircraft
Y	Lateral axis of aircraft
Z	Vertical axis of aircraft

EQUATIONS

1. 14.1
2. 14.2

PROBLEMS

1. The more stability an airplane has, the easier it is to control.
   1. True
   2. False
2. Static stability of an airplane is
   1. the ability to return to its equilibrium position once it has been disturbed.
   2. the long time reaction to a disturbance.
   3. the initial tendency to move toward the equilibrium position after a disturbance.
   4. None of the above
3. Dynamic stability of an airplane is _____ to a disturbance.
   1. the immediate reaction
   2. the long time reaction
   3. oscillatory in nature
   4. Both (b) and (c)
4. A damped oscillation is one that
   1. shows positive static stability.
   2. shows positive dynamic stability.
   3. Both (a) and (b)
   4. Neither (a) nor (b)
5. A ball/cone in a flower vase as compared to a ball/cone in a soup bowl illustrates
   1. increased dynamic stability.
   2. decreased dynamic stability.
   3. increased static and dynamic stability.
   4. decreased static and dynamic stability.
6. Weight and balance of airplanes is important because
   1. the CG affects the stability and control.
   2. if the CG is moved forward the static pitch stability is increased.
   3. if the CG is too far forward, the plane may not respond to elevator commands.
   4. All of the above
7. The farther back the wings are located, the more static pitch stability an airplane has.
   1. True
   2. False
8. Placing the jet engines at the rear of an airplane
   1. increases the static pitch stability.
   2. decreases the static pitch stability.
   3. increases the pitch control.
   4. decreases the pitch control.
   5. Both (a) and (d)
   6. Both (b) and (c)
9. Phugoid oscillation is dangerous because pilot reaction can lead to PIO.
   1. True
   2. False
10. The most critical condition for pitch control is that the elevators must be able to
    1. rotate the airplane for takeoff.
    2. flare the airplane for landing.
    3. overcome a forward CG location.
    4. All of the above