Two types of dynamic longitudinal oscillations.
The North American XB-70 has a pair of canards for stability at supersonic speeds to prevent tuck under. Additionally, the wing tips are turned downward to keep the aerodynamic center forward.
Static directional stability. In an equilibrium condition (figure (a)), an airplane flies so that the yaw angle is zero. To have static directional stability, the appropriate positive or negative yawing moment should be generated to compensate for a negative or positive sideslip angle excursion.
This figure shows the variation of yawing-moment coefficient with sideslip angle. This positively sloping line indicates a directionally stable case.
Directional stability moments. When an airplane is in a disturbed condition at a sideslip angle á, in general the fuselage alone will generate a moment that tends to increase the disturbance.
A B-17 bomber before and after addition of a dorsal fin extension, which improved its directional stability.
Slipstream effect at tail generated by a tractor propeller.
Dynamic Longitudinal, Directional, and Lateral Stability
Stability is the tendency of an airplane to fly a prescribed flight course. Dynamic longitudinal stability concerns the motion of a statically stable airplane, one that will return to equilibrium after being disturbed. Basically, there are two primary forms of longitudinal oscillations with regard to an airplane attempting to return to equilibrium after being disturbed. The first form is the phugoid mode of oscillation, which is a long-period, slow oscillation of the airplane's flight path. The pilot generally can control this oscillation himself. The second oscillation is a short-period variation of the angle of attack. Usually, this oscillation decreases very quickly with no pilot effort. However, with its natural short period, the oscillation may worsen if a pilot attempts to lessen it by use of a control because of the pilot's slow reaction time where he may get "out of phase" with the oscillation, and thus induce dynamical instability that may eventually lead to destructive forces.
A second type of short-term oscillation occurs if the elevators are left free. This is called the "porpoising" mode, and is influenced by the elevator balance. The main effect is vertical accelerations of the airplane that may get out of hand if a coupling between the free elevator and airplane occur. Proper design is essential here.
Insofar as compressibility effects are concerned, the rearward movement of the aerodynamic center of the wing as the airplane goes supersonic is most evident. This condition increases the static stability to such an extent that the airplane may "tuck under" and be extremely stable in a steep dive.
One answer to this problem is to move the center of gravity rearward by a transfer of fuel as the airplane goes supersonic. Other solutions include the double-delta wing configuration or canards placed at the nose of the airplane to develop an additional nose-up moment due to lift in the transonic and supersonic range. (A moment is a measure of the body's tendency to turn about its center of gravity.) This arrangement has an added advantage of contributing to the airplane's lift.
The use of a canard for trim and a rear sailplane for control is beneficial. The canard would trim the rearward shift of the aerodynamic center at supersonic speeds and the strong nose-down moments from high-lift devices (flaps) at low speeds by providing uplift. When not used, the canard can be allowed to trail in the free stream at zero lift and also generate minimum drag.
Many of the basic ideas involving longitudinal stability also apply to directional stability. In the usual equilibrium condition, an airplane flies so that the yaw angle is zero. To have static directional stability, a positive yawing moment should be generated if the airplane is disturbed to a negative yaw angle or alternatively by convention, a positive sideslip angle ß and a negative yawing moment generated for a negative sideslip angle excursion. If the airplane holds its disturbed position, it has neutral directional stability. If the tendency is to increase the disturbed position, farther away from equilibrium, the airplane is directionally unstable.
The fuselage and the vertical tail are the two most influential components in directional stability. When an airplane is in a disturbed condition at a sideslip angle ß, in general the fuselage alone will generate a moment that tends to increase the disturbance; that is, it is unstable. The vertical tail (the rudder) is the main component of static directional stability. When placed at an angle of attack due to the sideslip disturbance, it generates a side force which when multiplied by the moment arm (center of gravity of airplane to aerodynamic center of vertical tail) produces a stabilizing moment that tends to move the airplane back to a zero sideslip or yaw condition. The vertical tail usually has a low aspect ratio to prevent stalling. If a stall should occur, instability results and a catastrophic sideslip divergence may result. Adding more vertical tail by use of a dorsal fin extension or ventral tail area provides a stable yawing moment at large sideslip angles.
A tractor propeller of a typical airplane is a destabilizing influence on the directional stability, and it also imparts a rotational velocity to the slipstream. It produces a sidewash angle at the tail that reduces the static stability effectiveness of the tail. This effect can be very pronounced in aircraft with large engines. The Grumman F8F Bearcat, a carrier plane, would require a certain degree of rudder offset by the pilot to counteract the yaw induced by the sidewash during high-powered takeoffs. Contrarotating propellers are a solution to this problem.
The wing's degree of sweep influences the yawing moments. A sweptback wing will add to the directional stability whereas, a swept-forward wing will detract from the total directional stability since it is by itself a destabilizing influence. This is a contributing reason for choosing sweptback wings over swept-forward wings.
An airplane is said to possess lateral static stability if after undergoing a disturbance that rolls it to some bank angle ø, it generates forces and moments that tend to reduce the bank angle and restore the equilibrium flight condition.
Dihedral is often used as a means to improve lateral stability. In straight and level flight, the lift produced by both wings just equals the weight. But if a disturbance causes one wing to drop relative to the other, the lift vector rotates and there is a component of the weight acting inward that causes the airplane to move sideways in this direction. The airplane is said to sideslip and the relative free-stream direction is now in a direction toward which the airplane is sideslipping. If the airplane is laterally stable, moments arise that tend to reduce the bank angle. From geometric considerations, when wings have dihedral, the wing closer to the sideslip, the lower wing, will experience a greater angle of attack than the raised wing and hence greater lift. There results a net force and moment tending to reduce the bank angle.
The position of the wing also has an impact on the lateral stability. A high-wing airplane design, contributes to the lateral stability, whereas a low wing placement has a destabilizing effect in roll. However, this effect may be counteracted by including more dihedral to improve the overall lateral stability.
Wing sweep will help promote lateral stability. When a swept-wing airplane is sideslipping, the wing toward the sideslip will experience a higher velocity normal to (perpendicular to) the wing's leading edge than the wing away from the sideslip. More lift is generated on the wing toward the sideslip and a roll moment arises that tends to diminish the bank angle and return the airplane to equilibrium. The combination of dihedral and sweep may produce too much lateral stability and some airplanes will use a small amount of anhedral (wings turned down slightly) to lessen the lateral stability.
The effects of the fuselage and vertical tail may contribute to or detract from the airplane lateral stability. In a sideslip, there will be a side force caused by the area presented by the fuselage and vertical tail. If the side force acts above the center of gravity, there is a roll moment generated that tends to diminish the bank angle. If the side force is below the center of gravity, there is a destabilizing moment set up that will further increase the bank angle.
Destabilizing moments that also tend to increase the bank angle of an airplane in a sideslip arise because of the direction of the slipstream for a propeller-driven airplane and the use of partial span flaps. Added dihedral or sweep again may be used to decrease these detrimental effects.
Lateral and directional stability are interrelated. Briefly, the motions of an airplane are such that a roll motion causes a yaw motion and a yaw motion causes a roll motion. Thus, cross-coupling exists between the directional static stability and lateral static stability and gives rise to the three important dynamic motions observed: directional divergence, spiral divergence, and Dutch roll.
Directional divergence is a result of a directionally unstable airplane. When the airplane yaws or rolls into a sideslip so that side forces on the airplane are generated, the yawing moments that arise continue to increase the sideslip. This condition may continue until the airplane is broadside to the relative wind.
Spiral divergence is characterized by an airplane that is very stable directionally but not very stable laterally; for example, a large finned airplane with no dihedral. In this case when the airplane is in a bank and sideslipping, the side force tends to turn the plane into the relative wind. The outer wing travels faster, generates more lift, and the airplane will roll to still a higher bank angle. No lateral stability is present to negate this roll. The bank angle increases and the airplane continues to turn into the sideslip in an ever-tightening spiral.
Dutch roll is a motion exhibiting characteristics of both directional divergence and spiral divergence. The lateral stability is strong, whereas the directional stability is weak. If a sideslip disturbance occurs, as the airplane yaws in one direction, the airplane rolls away in a countermotion. The airplane wags its tail from side to side.
Ventral fins, although primarily used to augment the vertical fin that may be in the wake of the wing at high angles of attack, are also beneficial in decreasing the lateral stability and increasing the directional stability to reduce the effects of Dutch roll.
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
“Vertical Stabilizer – Rudder.” http://www.grc.nasa.gov/WWW/K-12/airplane/rud.html
Figure (a) shows a head-on view of an airplane that has dihedral where the wings are turned up at some dihedral angle to the horizontal. If a disturbance causes one wing to drop relative to the other (figure (b)), the lift vector rotates and there is a component of the weight acting inward which causes the airplane to move sideways in this direction. When wings have dihedral, the wing toward the free-stream velocity, hence the lower wing, will experience a greater angle of attack than the raised wing and hence greater lift. There results a net force and moment tending to reduce the bank angle (figure (c)).
Effect of wing placement on lateral stability.
Wing sweep will help promote lateral stability.
Effects of fuselage and tail on lateral stability.
Directional and spiral divergence.