ROLL COUPLING

The appearance of “inertia coupling" prob­lems in modern airplanes was the natural result of the progressive change in aerodynamic and inertia characteristics to meet the demands of high speed flight. Inertia coupling problems were unexpected only when dynamic stability analyses did not adequately account for the rapid changes in aerodynamic and inertia characteristics of airplane configurations. The The term of “intertia coupling" is somewhat misleading because the complete problem is one of aerodynamic as well as inertia coupling.

“Coupling” results when some disturbance about one airplane axis causes a disturbance about another axis. An example of uncoupled motion is the disturbance provided an airplane when subjected to an elevator deflection. The resulting motion is restricted to pitching motion without disturbance in yaw or roll. An example of. coupled motion could be the disturbance provided an airplane when sub­jected to rudder deflection. The ensuing mo­tion can be some combination of yawing and rolling motion. Hence, the rolling motion is coupled with the yawing motion to define the resulting motion. This sort of interaction results from aerodynamic characteristics and is termed “aerodynamic coupling.”

A separate type of coupling results from the inertia characteristics of the airplane configura­tion. The inertia characteristics of the com­plete airplane can be divided into the roll, yaw, and pitch inertia and each inertia is a measure of the resistance to rolling, yawing, or pitching acceleration of the airplane. The long, slender, high-density fuselage with short, thin wings produces a roll inertia which is quite small in comparison to the pitch and yaw inertia. These characteristics are typical of the modern airplane configuration. The more conventional low speed airplane may have a wingspan greater than the fuselage length. This type of configuration produces a relatively large roll inertia. A comparison of these configurations is shown in figure 4-34.

Inertia coupling can be illustrated by con­sidering the mass of the airplane to be con­centrated in two elements, one representing the mass ahead of the c. g. and one representing the mass behind the c. g. There are two principal axis systems to consider: (1) the aerodynamic, or wind axis is through the c. g. in the relative wind direction, and (2) the inertia axis is through the c. g. in the direction of the two element masses. This axis system is illus­trated in figure 4.34.

If the airplane shown in figure 4.34 were in some flight condition where the inertia axis and the aerodynamic axis are alined, no inertia coupling would result from rolling motion. However, if the inertia axis is inclined to the aerodynamic axis, rotation about the aero­dynamic axis will create centrifugal forces and cause a pitching moment. In this case, a rolling motion of the aircraft induces a pitch­ing moment through the action of inertia forces. This is “inertia coupling” and is illustrated by part В of figure 4.34.

When the airplane is rotated about the inertia axis no inertia coupling will exist but aerodynamic coupling will be present. Part C of figure 4.34 shows the airplane after rolling 90° about the inertia axis. The inclination which was initially the angle of attack (a) is now the angle of sideslip ( — 0). Also the original zero sideslip has now become zero angle of attack. The sideslip induced by this 90° displacement will affect the roll rate

depending on the nature of the dihedral effect of the airplane.

It should be noted that initial inclination of the inertia axis above the aerodynamic axis will cause the inertia couple to provide adverse yaw with rolling motion. If the inertia axis were initially inclined below the aerodynamic axis (as may happen at high q or negative load factors), the roll induced inertia couple would provide proverse yaw. Thus, roll coupling may present a problem at both positive and negative inclination of the inertia axis depend­ing on the exact aerodynamic and inertia characteristics of the configuration.

As a result of the aerodynamic and inertia coupling, rolling motion can induce a great variety of longitudinal, directional, and lateral forces and moments. The actual motion of the airplane is a result of a complex combina­tion of the aerodynamic and inertia coupling. Actually, all airplanes exhibit aerodynamic and inertia coupling but of varying degrees. The roll coupling causes no problem when the moments resulting from the inertia couple are easily counteracted by the aerodynamic re­storing moments. The very short span, high speed modern aircraft has the capability for the high roll rates which cause large magni­tudes of the inertia couple. The low aspect ratio planform and flight at high Mach number allow large inclination of the inertia axis with respect to the aerodynamic axis and also add to the magnitude of the inertia couple. In addition, the aerodynamic restoring moments deteriorate as a result of high Mach number and angle of attack and can create the most serious roll coupling conditions.

Since the roll coupling induces pitching and yawing motion, the longitudinal and direc­tional stability is important in determining the overall characteristics of the coupled motion. A stable airplane, when disturbed in pitch and yaw, will return to equilibrium after a series of oscillations. For each flight condition, the airplane will have a coupled pitch-yaw fre­quency between the uncoupled and separate pitch frequency and yaw frequency. Gen­erally, the greater the static longitudinal and directional stability, the higher will be the coupled pitch-yaw frequency. When the air­plane is subject to roiling motion, the inertia couple disturbs the airplane in pitch and yaw with each roll revolution and provides a dis­turbing forcing function. If the airplane is rolled at a rate equal to the coupled pitch-yaw frequency, the oscillatory motion will either diverge or stabilize at some maximum ampli­tude depending on the airplane characteristics.

The longitudinal stability of the typical high speed configuration is much greater than the directional stability and results in a pitch fre­quency higher than the yaw frequency. In­creasing the directional stability by increasing the vertical tail area, addition of ventral fins, or use of stabilization systems will increase the coupled pitch-yaw frequency and raise the roll rate at which a possible divergent condition could exist. Increasing directional stability by the addition of ventral fins rather than by addition to the vertical tail has an advantage of not contributing to the positive dihedral effect at low or negative angles of attack. High dihedral effect makes higher roll rates more easily attainable in roll motion where proverse yaw occurs.

Since the uncoupled yawing frequency is lower than the pitching frequency, a divergent condition would first reach critical proportions in yaw, closely followed by pitch. Of course, whether the airplane motion becomes divergent directionally or longitudinally is of academic interest only.

There is one additional type of coupling problem that is referred to as “autorotative rolling. ’ ’ A roiling airplane which has a high positive dihedral effect may reach a large pro­verse sideslip as a result of the inertia couple and the rolling moment due to sideslip may exceed that available from lateral control. In such a case it would not be possible to stop the air­plane from rolling although lateral control was held full against the roll direction. The

design features which result in a large positive dihedral effect are high sweepback, high wing position, or large, high vertical tail. When the inertia axis is inclined below the aero­dynamic axis at low or negative angles of attack, the roll induced inertia couple results in proverse yaw.

Depending on the flight condition where the roll coupling problem exists, four basic types of airplane behavior are possible:

(1) Coupled motion stable but unacceptable. In this case the motion is stable but proves unacceptable because of poor damping of the motion. Poor damping would make it difficult to track a target or the initial am­plitudes of the motion may be great enough to cause structural failure of loss of control.

(2) Coupled motion stable and acceptable. The behavior of the airplane is stable and adequately damped to allow acceptable target tracking. The amplitudes of motion are too slight to result in structural failure or loss of control.

(3) Coupled motion divergent and unacceptable. The rate of divergence is too rapid for the pilot to recognize the condition and recover prior to structural failure or complete loss of control.

(4) Coupled motion divergent but acceptable. For such a condition the rate of divergence is quite slow and considerable roll displace­ment is necessary to produce a critical ampli­tude. The condition can be recognized easily in time to take corrective action. There are available various means to cope

with the problem of roll coupling. The fol­lowing items can be applied to control the problem of roll coupling:

(a) Increase directional stability,

(F) Reduce dihedral effect.

(c) Minimize the inclination of the inertia axis at normal flight conditions.

(d) Reduce undesirable aerodynamic coupling.

(e) Limit roll rate, roll duration, and angle of attack or load factor for performing rolling maneuvers.

The first four items can be effected only during design or by design changes. Some roll per­formance restriction is inevitable since all of the desirable characteristics are difficult to obtain without serious compromise elsewhere in the airplane design. The typical high speed airplane will have some sort of roll per­formance limitation provided by flight restric­tions or automatic control devices to prevent reaching some critical condition from which recovery is impossible. Any roll restriction provided an airplane must be regarded as a principal flight operating limitation since the more severe motions can cause complete loss of control and structural failure.

HELICOPTER STABILITY AND CONTROL

In discussing many of the problems of sta­bility and control that occur in high speed airplanes, one might be prone to believe that the slow flying helicopter does not have any such problems. Unfortunately, this is not the case. Flying qualities that would be con­sidered totally unsatisfactory by fixed-wing standards are normal for helicopters. Heli­copter pilots are living evidence that an un­stable aircraft ca ^ controlled. Also, they are evidence taa. control without stability requires constant attention and results in con­siderable pilot fatigue.

“Inertia coupling” problems are relatively new to fixed-wing aircraft but a similar effect in the helicopter rotor has resulted in some of its most important characteristics. This aerodynamic-dynamic coupling effect is so im­portant that it must be considered in discussing both stability and control. The helicopter derives both longitudinal and lateral control by tilting the main rotor and thus producing a pitching or rolling moment as indicated in figure 4.33. The magnitude of the rotor thrust the angle of tilt, and the height of the rotor hub above the c. g. determine the control moment produced. It should be noted that low control effectiveness would result when the rotor thrust is low. Some helicopters

employ an offset flapping hinge to increase the control effectiveness by creating a centrifugal force couple when the rotor is tilted. This is shown in figure 4.35.

The rotor is tilted by taking advantage of the gyroscopic effect of the rotor system. This effect causes a rotating mass which is disturbed about one axis to respond about another axis, as shown in figure 4-35- A forward tilt to the rotor is obtained by decreasing the pitch of the blade when at the starboard position and in­creasing the pitch of the blade when at the port position. The lateral dissymmetry of lift which results causes the rotor to tilt for­ward by the gyroscopic effect.

A differential blade pitch change like this is called a cyclic pitch change since each blade goes through. a complete cycle of varying pitch angles as it completes one revolution of rota­tion about the hub. A cyclic pitch change is accomplished by the pilot by the use of the cyclic stick. The control arrangement is such that the rotor tilts in the same direction that the cyclic stick is deflected.

A variation in rotor thrust is accomplished by increasing’*the pitch of the blades simul­taneously or collectively. This type of control action is called “collective pitch" and is ac­complished by the use of the collective pitch stick. In operation, the cyclic stick is an­alogous to the control stick of an airplane, and the collective stick is analogous to the throttle of an airplane.

There are several possibilities for longi­tudinal control of a tandem-rotor helicopter. A pitching moment can be produced by tilting both rotors by a cyclic pitch change in each rotor, by a differential collective pitch change that increases the thrust on one rotor and de­creases it on the other, or by some combination of these methods. The two basic methods are illustrated in figure 4.36. Obviously, a change in fuselage attitude must accompany the dif­ferential collective method of longitudinal control.

Adequate pitch and lateral control effective­ness are easy to obtain in the typical helicopter and usually present no problems. The more usual problem is an excess of control effective­ness which results in an overly sensitive heli­copter. The helicopter control specifications attempt to assure satisfactory control charac­teristics by requiring adequate margins of con­trol travel and effectiveness without objection­able sensitivity.

Directional control in a single rotor heli­copter is obtained by a tail rotor (antitorque rotor) since a conventional aerodynamic sur­face would not be effective at low speeds or hovering. The directional control require­ments of the tail rotor on a typical shaft-driven helicopter are quite demanding since it must counteract the engine torque being supplied to the main rotor as well as provide directional control. Being a rotor in every respect, the tail rotor requires some of the engine power to generate its control forces. Unfortunately, the maximum demands of the tail rotor occur at conditions when engine power is also in great demand. The most critical condition is while hovering at maximum gross weight. The tail rotor effectiveness is determined by the rotor characteristics and the distance the tail rotor is behind the c. g. The control specifications require the helicopter to be able to turn in the most critical direction at some specified rate while hovering at maximum gross weight in a specified wind condition. Also, it is required that the helicopter have sufficient directional control to fly sideways up to 30 knots, an important requirement for plane guard duties.

The directional control requirements are easily met by a tip-driven helicopter since the directional control does not have to counter the engine torque.

Directional control of a tandem-rotor heli­copter is accomplished by differential cyclic control of the main rotors. For a pedal turn to the starboard, the forward rotor is tilted to the starboard and the rear rotor is tilted to port, creating a turning moment as shown in

figure 4.36. The directional control require­ments are easily met in a tandem-rotor heli­copter because the engine torque from one rotor is opposed by the torque of the other rotor thereby eliminating one directional mo­ment. Of course, some net unbalance of torque may have to be overcome if the engine torque on the two rotors is different.

When a tandem-rotor helicopter is rotated rapidly about one of the rotors rather than about the c. g., the other rotor picks up “translational lift’’ as a result of the velocity due to rotation and an increase in rotor thrust results. This causes pitch-up or pitch-down depending on which rotor the helicopter is being rotated about. Rotation about the forward rotor, which is more common, re­sults in pitch-down.

The overall stability of a helicopter results from the individual stability contributions of the various components just as in the case of the fixed-wing airplane. The stability con­tributions can be divided as follows:

(1) Rotor

(2) Fuselage

(3) Stabilizers

(4) Mechanical devices

The destabilizing contribution of the fuselage and the stabilizing contribution of a stabilizing surface are similar in effect to an airplane and will not be discussed here. The principal stability characteristics that make the heli­copter different from an airplane are those of the rotor.

Two types of stability are important in the rotor: (1) angle of attack stability and (2) velocity stability. In hovering flight the relative wind velocity, angle of attack, and lift on each blade of the rotor is the same. If the rotor is displaced through some angle, no changes in forces result. Therefore, the rotor has neutral angle of attack stability when hovering. However, in forward flight, ah increase in rotor angle of attack increases the lift on the advancing blade more than on the retreating blade since the relative wind veloci­ties are greater on the advancing blade. This lateral dissymmetry of lift causes the rotor to tilt back due to the gyroscopic effect of the rotor, further increasing the rotor angle of attack. Thus, the rotor is unstable with changes in angle of attack at forward flight speeds. Since the magnitude of the unstable moment is affected by the magnitude of the rotor thrust as well as the tilt of the thrust force, a greater instability exists for increases in angle of attack than for decreases in angle of attack. In addition, the instability is greater for increases in angle of attack when the rotor thrust also increases.

If the rotor angle of attack is held constant and the rotor is given a translational velocity, a dissymmetry of lift results since the velocity of the advancing blade is increased while the velocity of the retreating blade is decreased. This dissymmetry of lift causes the rotor to tilt in a direction to oppose the change in velocity due to the gyroscopic effect of the rotor. Hence, the rotor has velocity stability.

A hovering helicopter exhibits some degree of apparent stability by virtue of its velocity stability although it has neutral angle of attack stability. This type of hovering sta­bility is analogous to the apparent lateral – directional stability an airplane exhibits due to dihedral effect. Additional hovering sta­bility can be obtained by the use of mechanical stabilizers such as the Bell stabilizer bar, by the use of offset flapping hinges, or by syn­thetic or artificial stabilization devices.

The total static stability of a helicopter is determined by combining the stability con­tributions of all the components. The usual result for a typical helicopter is instability with angle of attack and a variable velocity stability which becomes neutral or unstable at high speeds. Of course, the helicopter could be made stable with angle of attack by providing a large enough horizontal stabilizer. Unfortunately, adverse effects at low speed or hovering and large trim moments upon entering autorotation will limit the stabilizer size to a relatively small surface. Usually the hori­zontal stabilizer is used only to give the fuse­lage the desired moment characteristics.

The angle of attack stability of a tandem – rotor helicopter is adversely affected by the downwash from the forward rotor reducing the angle of attack and thrust of the rear rotor. This reduction of thrust behind the c. g. causes the helicopter to pitch up to a higher angle of attack, thereby adding to the angle of attack instability.

As in the airplane, several oscillatory modes of motion are characteristic of the dynamic stability of a helicopter. The phugoid is the most troublesome for the helicopter. The phugoid mode is unstable in the majority of helicopters which operate without the assist­ance of artificial stabilization devices. The dynamic instability of the helicopter is given evidence by the flying qualities specification for helicopters. These specifications essentially limit the rate of divergence of the dynamic oscil­lations for the ordinary helicopter. Although this dynamic instability can be controlled, it requires constant attention by the pilot and results in pilot fatigue. The elimination of the dynamic instability would contribute greatly to improving the flying qualities of the helicopter.

This dynamic instability characteristic is particularly important if the helicopter is expected to be used for instrument flight in all-weather operations. In fact, a seriously divergent phugoid mode would make instru­ment flight impractical. For this reason, the flying qualities specification requires that helicopters with an instrument capability exhibit varying degrees of stability or insta­bility depending on the period of the oscilla­tion. Long period oscillations (over 20 sec­onds) must not double in amplitude in less than 15 seconds whereas short period oscil­lations (under 10 seconds) must damp to half amplitude in two cycles.

The only immediate solution for the dynamic instability is an attitude stabilization system which is essentially an autopilot. Other solutions to the dynamic instability problem involve mechanical, aerodynamic, or elec­tronic control feedback of pitch attitude, pitch velocity, normal acceleration, or angle of attack. The improvement of the heli­copter’s stability is mandatory to fully utilize its unique capability. As more of the heli­copter problems are analyzed and studied, the flying qualities of helicopters will improve and be comparable to the fixed wing aircraft.