Longitudinal static stability moments as a function of angle of attack. The curve is a composite of all the moment curves caused by the different components of the airplane, for example, the wing, fuselage, tail, and thrust.
Longitudinal static stability components.
Stable, neutral, and unstable static stability.
Usable center-of-gravity range. With power off, the usable center-of-gravity range is relatively large (figure a). Additional factors, however, reduce the usable center-of-gravity range. These include engine-on thrust effects and ground effects (including landing gear, flaps, and other considerations) as shown in figure (b).
Downwash effects on tail.
Stability is the tendency, or lack of it, of an airplane to fly a prescribed flight course.
For an airplane to be in equilibrium for a particular flight course, the sum of all the forces and moments on it must be zero. (A moment is a measure of the body's tendency to turn about its center of gravity.) Lift equals weight, thrust equals drag, and there are no net rotating moments acting on it. It is in equilibrium.
Now, if the airplane is disturbed, for example, by atmospheric turbulence, and noses up slightly (angle of attack increases), the airplane is no longer in equilibrium. If the new forces and moments, caused by the angle-of-attack increase, produce a tendency to nose up still further, the airplane is statically unstable and its motion will diverge from equilibrium. If the initial tendency of the airplane is to hold the disturbed position, the airplane has neutral static stability. On the other hand, if restoring forces and moments are generated by the airplane that tend initially to bring it back to its equilibrium straight and level condition, it is statically stable.
If it is assumed that the airplane is statically stable, it may undergo three forms of motion with time. (1) It may nose down, overshoot, nose-up, overshoot to a smaller degree, and eventually return to its former equilibrium condition of straight and level flight. This type of decaying oscillatory motion indicates that the airplane is dynamically stable. (2) It may continue to nose up and down thereafter at a constant amplitude. The airplane is said to have neutral dynamic stability. Or, in the worst case, (3) it may nose up and down with increasing magnitude and be dynamically unstable.
An airplane may be dynamically unstable and still be flyable if the pilot uses control by working the elevators. But, ideally, the pilot should not need to do this. An airplane of this design has poor flying qualities. An airplane that is statically and dynamically stable can be flown "hands off" by a pilot with no control necessary except to change the equilibrium flight condition.
Longitudinal stability and control is concerned with an airplane's pitching motion, lateral stability and control relates to an airplane's rolling motion, and directional stability and control relates to an airplane's yawing motion. Lateral and directional stability are closely interrelated and, therefore, the two are sometimes simply referred to as lateral stability.
Longitudinal stability can be considered independent of lateral and directional stability. Consider an airplane "trimmed" to fly at some angle of attack, αtrim. This statement says that the airplane is in equilibrium and there are no moments tending to pitch the airplane about its center of gravity.
When equilibrium is achieved for an airplane, the forces acting are the weight through the center of gravity, the lift and drag at the aerodynamic center, and the thrust along the thrust line. The aerodynamic center of the airplane usually is very close to the aerodynamic center of the wing alone. The thrust line may lie above or below the center of gravity. The moments about the center of gravity are the forces times the distance between them and the center of gravity. The lift and thrust both contribute nose-down moments whereas the drag contributes a nose-up moment. If these do not cancel each other out, the airplane will not be in equilibrium.
The horizontal tail (or elevator) serves as another moment source. The horizontal tail acts as a small wing, and the pilot can achieve lift or negative lift by elevator control. Because of the long moment arm from the center of gravity to the aerodynamic center of the horizontal tail, only relatively small forces are needed. Thus, the horizontal tail supplies the balancing moment. To fly in a particular equilibrium condition, the elevator is "trimmed" to a particular angle. The total moment about the airplane center of gravity is zero.
If the airplane is statically stable in a longitudinal sense, then if disturbed away from the trim angle of attack, moments are generated that tend to return the airplane to the equilibrium αtrim. It is customary to express the moment nondimensionally as a coefficient of moment about the center of gravity, or (Cm)cg as in
Cm = M/qSc
where M = Total moment acting on a wing
q = Testing dynamic pressure
S = wing area
c = chord length
There is no moment at the trim angle of attack; negative moments rotate the nose down for angles of attack above αtrim, and positive moments rotate the nose up for angles below αtrim
The horizontal position of the center of gravity has a great effect on the static stability of the wing, and hence, the entire airplane static stability. If the center of gravity is sufficiently forward of the aerodynamic center, then the airplane is statically stable. If the center of gravity of the airplane is moved toward the tail sufficiently, there is a pointthe neutral pointwhere the moment curve becomes horizontal; this airplane is neutrally stable. If the center of gravity is moved farther back, the moment curve has positive slope, and the airplane is longitudinally unstable. Likewise, if the center of gravity is moved forward toward the nose too far, the pilot will not be able to generate enough force on the tail to raise the angle of attack to achieve the maximum lift coefficient.
With power off, the usable center-of-gravity range is relatively large. There are, however, additional factors that reduce the usable center-of-gravity range. These include engine-on thrust effects and ground effects (including landing gear, flaps, and other considerations). To ensure that the actual center of gravity of the airplane falls within the usable range, an airplane is carefully designed and loaded. For example, there are cases of transport airplanes crashing because the airplane was loaded or the cargo shifted in flight so that the center of gravity fell outside the range of usable limits. The airplane then became unstable. The location of the center of gravity is an important factor in a stable airplane.
The horizontal tail is the main controllable moment contributor to the complete airplane moment curve. A larger horizontal tail will give a more statically stable airplane than a smaller tail (assuming, as is the normal case, that the horizontal tail lies behind the center of gravity of the airplane). Of course, its distance from the center of gravity is important. The farther away from the center of gravity it is, the more it enhances the static stability of the airplane. The tail efficiency factor depends on the tail location with respect to the airplane wake and slipstream of the engine, and power effects. By design it is made as close to 100 percent efficiency as possible for most static stability.
Finally, with respect to the tail, the downwash from the wing is of considerable importance. Air is deflected downward when it leaves a wing, and this deflection of air results in the wing reaction force or lift. This deflected air flows rearward and hits the horizontal-tail plane. If the airplane is disturbed, it will change its angle of attack and the downwash angle also changes. The degree to which it changes directly affects the tail's effectiveness. Hence, it will reduce the stability of the airplane. For this reason, the horizontal tail is often located in a location such that it is exposed to as little downwash as possible, such as high on the tail assembly.
Adapted from Talay, Theodore A. Introduction to the Aerodynamics of Flight. SP-367, Scientific and Technical Information Office, National Aeronautics and Space Administration, Washington, D.C. 1975. Available at http://history.nasa.gov/SP-367/cover367.htm
For Further Reading:
Smith, Hubert. The Illustrated Guide to Aerodynamics, 2nd edition. Blue Ridge Summit, Pa.: TAB Books, 1992.
Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag, 1991.
“Horizontal Stabilizer – Elevator.” http://www.grc.nasa.gov/WWW/K-12/airplane/elv.html.