LONGITUDINAL CONTROL

To be satisfactory, an airplane must have adequate controllability as well as adequate stability. An airplane with high static longi­tudinal stability will exhibit great resistance to displacement from equilibrium. Hence, the most critical conditions of controllability will occur when the airplane has high sta­bility, i. e., the lower limits of controllability will set the upper limits of stability.

There are three principal conditions of flight which provide the critical requirements of longitudinal control power. Any one or combination of these conditions can de­termine the longitudinal control power and set a limit to forward c. g. position.

MANEUVERING CONTROL REQUIRE­MENT. The airplane should have sufficient longitudinal control power to attain the maxi­mum usable lift coefficient or limit load factor during maneuvers. As shown in figure 4.19, forward movement of the c. g. increases the longitudinal stability of an airplane and requires larger control deflections to produce changes in trim lift coefficient. For the example shown, the maximum effective de­flection of the elevator is not capable of trim – ing the airplane at CL/nar for c. g. positions ahead of 18 percent MAC.

This particular control requirement can be most critical for an airplane in supersonic flight. Supersonic flight is usually accom­panied by large increases in static longitu­dinal stability and a reduction in the effective­ness of control surfaces. In order to cope with these trends, powerful all-movable surfaces must be used to attain limit load factor or maximum usable CL in supersonic flight. This requirement is so important that once satis­fied, the supersonic configuration usually has sufficient longitudinal control power for all other conditions of flight.

TAKEOFF CONTROL REQUIREMENT. At takeoff, the airplane must have sufficient control power to assume the takeoff attitude prior to reaching takeoff speed. Generally, for airplanes with tricycle landing gears, it is desirable to have at least sufficient control power to attain the takeoff attitude at 80

percent of the stall speed for propeller air­planes or 90 percent of the stall speed for jet airplanes. This feat must be accomplished on a smooth runway at all normal service takeoff loading conditions.

Figure 4.19 illustrates the principal forces acting on an airplane during takeoff roll. When the airplane is in the three point attitude at some speed less than the stall speed, the wing lift will be less than the weight of the airplane. As the elevators must be capable of rotating to the takeoff attitude, the critical condition will be with zero load on the nose wheel and the net of lift and weight supported on the main gear. Rolling friction resulting from the normal force on the main gear creates an adverse nose down moment. Also, the center of gravity ahead of the main gear contributes a nose down moment and this consideration could decide the most aft loca­tion of the main landing gear during design. The wing may contribute a large nose down moment when flaps are deflected but this effect may be countered by a slight increase in downwash at the tail. To balance these nose down moments, the horizontal tail should be capable of producing sufficient nose up moment to attain the takeoff attitude at the specified speeds.

The propeller airplane at takeoff power may induce considerable slipstream velocity at the horizontal tail which can provide an increase in the efficiency of the surface. The jet airplane does not experience a similar magni­tude of this effect since the induced velocities from the jet are relatively small compared to the slipstream velocities from a propeller.

LANDING CONTROL REQUIREMENT At landing, the airplane must have sufficient control power to ensure adequate control at specified landing speeds. Adequate landing control is usually assured if the elevators are capable of holding the airplane just off the runway at 105 percent of the stall speed. Of course, the most critical requirement will exist when the c. g. is in the most forward position, flaps are fully extended, and power is set at idle. This configuration will provide the most stable condition which is most demand­ing of controllability. The full deflection of flaps usually provides the greatest wing diving moment and idle power will produce the most critical (least) dynamic pressure at the hori­zontal tail.

The landing control requirement has one particular difference from the maneuvering control requirement of free flight. As the airplane approaches the ground surface, there will be a change in the three-dimensional flow of the airplane due to ground effect. A wing in proximity to the ground plane will experience a decrease in tip vortices and downwash at a given lift coefficient. The decrease in down – wash at the tail tends to increase the static stability and produce a nosedown moment from the reduction in download on the tail. Thus, the airplane just off the runway surface will require additional control deflection to trim at a given lift coefficient and the landing con­trol requirement may be critical in the design of longitudinal control power.

As an example of ground effect, a typical propeller powered airplane may require as much as 15° more up elevator to trim at CL in ground effect than in free flight away from the ground plane. Because of this effect, many ai rpl an es h a ve suffici en t con trol power t о a chi eve full stall out of ground effect but do not have the ability to achieve full stall when in close proximity to the ground.

In some cases the effectiveness of the control surface is adversely affected by the use of trim tabs. If trim tabs are used to excess in trim­ming stick forces, the effectiveness of the elevator. may be reduced to hinder landing or takeoff control.

Each of the three principal conditions re­quiring adequate longitudinal control are crit­ical for high static stability. If the forward c. g. limit is exceeded, the airplane may en­counter a deficiency of controllability in any of these conditions. Thus, the forward c. g.

limit is set by the minimum permissible con­trollability while the aft c. g. limit is set by the minimum permissible stability. LONGITUDINAL DYNAMIC STABILITY.

All previous considerations of longitudinal stability have been concerned with the initial tendency of the airplane to return to equilib­rium when subjected to a disturbance. The considerations of longitudinal dynamic sta­bility are concerned with time history response of the airplane to these disturbances, i. e., the variation of displacement amplitude with time following a disturbance. From previous defi­nition, dynamic stability will exist when the amplitude of motion decreases with time and dynamic instability will exist if the amplitude increases with time.

Of course, the airplane must demonstrate positive dynamic stability for the major longi­tudinal motions. In addition, the airplane must demonstrate a certain degree of longitu­dinal stability by reducing the amplitude of motion at a certain rate. The required degree of dynamic stability is usually specified by the time necessary for the amplitude to reduce to one-half the original value—the time to damp to half-amplitude.

The airplane in free flight has six degrees of freedom: rotation in roll, pitch, and yaw and translation in the horizontal, vertical, and lateral directions. In the case of longitudinal dynamic stability, the degrees of freedom can be limited to pitch rotation, vertical and horizontal translation. Since the airplane is usually symmetrical from port to starboard, there will be no necessity for consideration of coupling between longitudinal and lateral – directional motions, Thus, the principal vari­ables in the longitudinal motion of an airplane will be:

(1) The pitch attitude of the airplane.

(2) The angle of attack (which will differ

from the pitch attitude by the inclination of

the flight path).

(3) The flight velocity.

(4) The displacement or deflection of the elevator when the stick-free condition is considered.

The longitudinal dynamic stability of an airplane generally consists of three basic modes (or manners) of oscillation. While the longi­tudinal motion of the airplane may consist of a combination of these modes, the characteristics of each mode are sufficiently distinct that each oscillatory tendency may be studied separately.

The first mode of dynamic longitudinal sta­bility consists of a very long period oscillation referred to as the phugoid. The phugoid or long period oscillation involves noticeable varia­tions in pitch attitude, altitude, and airspeed but nearly constant angle of attack. Such an oscillation of the airplane could be considered as a gradual interchange of potential and kinetic energy about some equilibrium airspeed and altitude. Figure 4.20 illustrates the char­acteristic motion of the phugoid.

The period of oscillation in the phugoid is quite large, typical values being from 20 to 100 seconds. Since the pitching rate is quite low and only negligible changes in angle of attack take place, damping of the phugoid is weak and possibly negative. However, such weak or negative damping does not necessarily have any great consequence. Since the period of oscilla­tion is so great, the pilot is easily able to counteract the oscillatory tendency by very slight and unnoticed control movements. In most cases, the necessary corrections are so slight that the pilot may be completely un­aware of the oscillatory tendency.

Due to the nature of the phugoid, it is not necessary to make any specific aerodynamic provisions to contend with the oscillation. The inherent long period of the oscillation al­lows study to be directed to more important oscillatory tendencies. Similarly, the differ­ences between the stick-fixed and stick-free phugoid are not of great importance.

The second mode of longitudinal dynamic sta­bility is a relatively short period motion that

1ST MODE OR PHUGOID

MOTION OCCURS AT ESSENTIALLY CONSTANT SPEEO

can be assumed to take place with negligible changes in velocity. The second mode consists of a pitching oscillation during which the air­plane is being restored to equilibrium by the static stability and the amplitude of oscillation decreased by pitch damping. The typical mo­tion is of relatively high frequency with a period of oscillation on the order of 6.5 to 5 seconds.

For the conventional subsonic airplane, the second mode stick-fixed is characterized by heavy damping with a time to damp to half amplitude of approximately 0.5 seconds. Usu­ally, if the airplane has static stability stick – fixed, the pitch damping contributed by the horizontal tail will assume sufficient dynamic stability for the short period oscillation. How­ever, the second mode stick-free has the possi­bility of weak damping or unstable oscilla­tions. This is the case where static stability does not automatically imply adequate dy­namic stability. The second mode stick-free is essentially a coupling of motion between the airplane short period pitching motion and ele­vator in rotation about the hinge line. Ex­treme care must be taken in the design of the control surfaces to ensure dynamic stability for this mode. The elevators must be statically balanced about the hinge line and aerodynamic balance must be within certain limits. Control system friction must be minimized as it con­tributes to the oscillatory tendency. If insta­bility were to exist in the second mode, “por­poising” of the airplane would result with possibility of structural damage. An oscilla­tion at high dynamic pressures with large changes in angle of attack could produce severe flight loads.

The second mode has relatively short periods that correspond closely with the normal pilot response lag time, e. g., 1 or 2 seconds or less. There is the possibility that an attempt to forceably damp an oscillation may actually re­inforce the oscillation and produce instability. This is particularly true in the case of powered controls where a small input energy into the control system is greatly magnified. In addi­tion, response lag of the controls may add to the problem of attempting to forceably damp the oscillation. In this case, should an oscilla­tion appear, the best rule is to release the con­trols as the airplane stick-free will demonstrate the necessary damping. Even an attempt to fix the controls when the airplane is oscillating may result in a small unstable input into the control system which can reinforce the oscilla­tion to produce failing flight loads. Because of the very short period of the oscillation, the amplitude of an unstable oscillation can reach dangerous proportions in an extremely short period of time.

The third mode occurs in the elevator free case and is usually a very short period oscillation. The motion is essentially one of the elevator flapping about the hinge line and, in most cases, the oscillation has very heavy damping. A typical flapping mode may have a period of 0.3 to 1.5 seconds and a time to damp to half­amplitude of approximately 0.1 second.

Of all the modes of longitudinal dynamic stability, the second mode or porpoising oscil­lation is of greatest importance. The por­poising oscillation has the possibility of damaging flight loads and can be adversely affected by pilot response lag. It should be remembered that when stick-free the airplane will demonstrate the necessary damping.

The problems of dynamic stability are acute under certain conditions of flight. Low static stability generally increases the period (de­creases frequency) of the short period oscil­lations and increases the time to damp to half­amplitude. High altitude—and consequently low density—reduces the aerodynamic damp­ing. Also, high Mach numbers of supersonic flight produce a decay of aerodynamic damping.