Category AVIATORS

The requirement for structural stiffness and rigidity is the consideration given to the inter­action of aerodynamic forces and deflections of the structure. The aircraft and its components must have sufficient stiffness to prevent or minimize aeroelastic influences in the normal flight range. Aileron reversal, divergence, flutter, and vibration should not occur in the range of flight speeds which will be normal operation for the aircraft.

It is important to distinguish between strength and stiffness. Strength is simply the resistance to load while stiffness is the resist­ance to deflection or deformation. While strength and stiffness are related, it is necessary to appreciate that adequate structural strength does not automatically provide adequate stiff­ness. Thus, special consideration is necessary to provide the structural components with specific stiffness characteristics to prevent un­desirable aeroelastic effects during normal operation.

An obvious solution to the apparent prob­lems of static strength, fatigue strength, stiffness and rigidity would be to build the airplane like a product of an anvil works, capable of withstanding all conceivable loads. However, high performance airplane con­figurations cannot be developed with ineffi­cient, lowly stressed structures. The effect of additional weight is best illustrated by pre­liminary design studies of a very long range, high altitude bomber. In the preliminary phases of design, each additional pound of any weight would necessitate a 25-pound increase in gross weight to maintain the same performance. An increase in the weight of any item produced a chain reaction—more fuel, larger tanks, bigger engines, more fuel, heavier landing gear, more fuel, etc. In the competitive sense of design, no additional structural weight can be tolerated to provide more strength than is specified as necessary for the design mission requirement.

The various components of the aircraft and powerplant structure must be capable of oper­ating without failure or excessive deformation throughout the intended service life. The repetition of various service loads can produce fatigue damage in the structure and special attention must be given to prevent fatigue failure within the service life. Also, the sus­taining of various service loads can produce creep damage and special attention must be given to prevent excessive deformation or creep failure within the service life. This is a particular feature of components which are subjected to operation at high temperatures.

FATIGUE CONSIDERATIONS. The fa­tigue strength requirement is the considera­tion given the cumulative effect of repeated or cyclic loads during service. While there is a vague relationship with the static strength, repeated cyclic loads produce a completely separate effect. If a cyclic, tensile stress is applied to a metal sample, the part is subject to a “fatigue" type loading. After a period of time, the cyclic stressing will produce a minute crack at some critical location in the sample. With continued application of the varying stress, the crack will enlarge and propagate into the cross section. When the crack has progressed sufficiently, the remaining cross section is incapable of withstanding the imposed stress and a sudden, final rupture occurs. In this fashion, a metal can be failed at stresses much lower than the static ultimate strength.

Of course, the time necessary to produce fatigue failure is related to the magnitude of the cyclic stress. This relationship is typified by the graph of figure 5-1- The fatigue strength of a material can be demonstrated by a plot of cyclic stress versus cycles of stress required to produce fatigue failure. As might be expected, a very high stress level requires relatively few cycles to produce fatigue failure. Moderate stress levels require a fairly large number of cycles to produce failure and a very low stress may require nearly an infinite num­ber of cycles to produce failure. The very certain implication is that the aircraft must be capable of withstanding the gamut of service loads without producing fatigue failure of the primary structure.

For each mission type of aircraft there is a probable spectrum of loads which the air­craft will encounter. That is, various loads will be encountered with a frequency particular to the mission profile. The fighter or attack type of aircraft usually experiences a pre­dominance of maneuver loads while the trans­port or patrol type usually encounters a pre­dominance of gust loads. Since fatigue damage

is cumulative during cyclic stressing, the useful service life of the aircraft must be anticipated to predict the gross effect of service loads. Then, the primary structure is required to sustain the typical load spectrum through the anticipated service life without the occurrence of fatigue failure. To prove this capability of the structure, various major components mast be subjected to an accelerated fatigue test to verify the resistance to repeated loads.

The design of a highly stressed or long life structure emphasizes the problems of fatigue. Great care must be taken during design and manufacture to minimize stress concentrations which enhance fatigue. When the aircraft enters service operation, care must be taken in the maintenance of components to insure proper adjustment, torquing, inspection, etc., as proper maintenance is a necessity for achieving full service life. Also, the structure must not be subjected to a load spectrum more severe than was considered in design or fatigue failures may occur within the anticipated service life. With this additional factor in mind, any pilot should have all the more respect for the oper­ating strength limits—recurring overstress causes a high rate of fatigue damage.

There are many examples of the detrimental effect of repeated over stress on service life. One major automobile manufacturer adver­tised his product as “guaranteed to provide

100,0 miles of normal driving without me­chanical failure.” The little old lady from Pasadena—the original owner of ALL used cars —will probably best the guaranteed mileage by many times. On the other hand, the hot­rod artist and freeway Grand Prix contender do not qualify for the guarantee since their manner of operation could not be considered normal. The typical modern automobile may be capable of 60,000 to 100,000 miles of normal operation before an overhaul is necessary. However, this same automobile may encounter catastrophic failures in a few hundred miles if operated continually at maximum torque in low drive range. Obviously, there are similar relationships for aircraft and powerplant structures.

CREEP CONSIDERATIONS. By definition, creep is the structural deformation which oc­curs as a function of time. If a part is subjected to a constant stress of sufficient magnitude, the part will continue to develop plastic strain and deform with time. Eventually, failure can occur from the accumulation of creep damage. Creep conditions are most critical at high stress and high temperature since both factors increase the rate of creep damage. Of course, any structure subject to creep conditions should not encounter excessive deformation or failure within the anticipated service life.

The high operating temperatures of gas tur­bine components furnish a critical environment for creep conditions. The normal operating temperatures and stresses of gas turbine com­ponents create considerable problems in design for service life. Thus, operating limitations deserve very serious respect since excessive engine speed or excessive turbine temperatures will cause a large increase in the rate of creep damage and lead to premature failure of com­ponents. Gas turbines require high operating temperatures to achieve high performance and efficiency and short periods of excessive tem­peratures can incur highly damaging creep rates. •

Airplane structures can be subject to high temperatures due to aerodynamic heating at high Mach numbers. Thus, very high speed airplanes can be subject to operating limita­tions due to creep conditions,

The weight of the structural components of an aircraft is an extremely important factor in the development of an efficient aircraft con­figuration. In no other field of mechanical design is there such necessary importance assigned to structural weight. The efficient aircraft and powerplant structure is the zenith of highly refined minimum weight design. In
order to obtain the required service life from his aircraft, the Naval Aviator must under­stand, appreciate, and observe the operating strength limitations. Failure to do so will incur excessive maintenance costs and a high incidence of failure during the service life of an aircraft.

GENERAL DEFINITIONS AND STRUC­TURAL REQUIREMENTS

There are strength requirements which are common to all aircraft. In general, these re­quirements can be separated into three particu­lar areas. These are detailed in the following discussion.

STATIC STRENGTH

The static strength requirement is the con­sideration given to the effect of simple static loads with none of the ramifications of the repetition or cyclic variation of loads. An important reference point in the static strength requirement is the “limit load’’ condition. When the aircraft is at the design configura­tion, there will be some maximum of load which would be anticipated from the mission requirement of the airplane. For example, a fighter or attack type aircraft, at the design Configuration, may encounter a very peak load factor of 7.5 in the accomplishment of its mis­sion. Of course, such an aircraft may be sub­ject to load factors of 3, 4, 5, 6, 1, etc., but no more than 7 5 should be required to accom­plish the mission. Thus, the limit load condi­tion is the maximum of loads anticipated in normal operation of the aircraft. Various types of aircraft will have different limit load factors according to the primary mission of the aircraft. Typical values are tabulated below:

Type of aircraft:

Fighter or attack…………………………………………….. 7 5

Trainer……………………………………………………………. 7.5

Transport, patrol, antisubmarine…………….. 3.0 or 2.5

Of course, these examples are quite general and it is important to note that there may be varia­tions according to specific mission require­ments.

Since the limit load is the maximum of the normally anticipated loads, the aircraft struc­ture must withstand this load with no ill effects. Specifically, the primary structure of the aircraft should experience no objectionable
permanent deformation when subjected to the limit load. In fact, the components must with­stand this load with a positive margin. This requirement implies that the aircraft should withstand successfully the limit load and then return to the original unstressed shape when the load is removed. Obviously, if the air­craft is subjected to some load which is in excess of the limit load, the overstress may incur an objectionable permanent deformation of the primary structure and require replace­ment of the damaged parts.

Many different flight and ground load condi­tions must be considered to define the most critical conditions for the structural com­ponents. In addition to positive lift flight, negative lift flight must be considered. Also, the effect of flap and landing gear configura­tion, gross weight, flight Mach number, sym­metry of loading, c. g. positions, etc., must be studied to account for all possible sources of critical loads. To verify the capability of the structure, ground static tests are conducted and flight demonstrations are required.

To provide for the rare instances of flight when a load greater than the limit is required to prevent a disaster, an “ultimate factor of safety” is provided. Experience has shown that an ultimate factor of safety of 1-5 is suf­ficient for piloted aircraft. Thus, the aircraft must be capable of withstanding a load which is 1.5 times the design limit load. The primary structure of the aircraft must withstand the “ultimate load” (1.5 times limit) without failure. Of course, permanent deformation may be expected with this “overstress” but no actual failure of the major load-carrying components should take place at ultimate load Ground static tests are necessary to verify this capability of the structure.

An appreciation of the static strength re­quirements may be obtained by inspection of the basic properties of a typical aircraft metal. Figure 5-1 illustrates the typical static strength properties of a metal sample by a plot of applied stress versus resulting strain. At low values

T

CYCLIC

STRESS

(PSD

of stress the plot of stress and strain is essen­tially a straight line, i. e., the material in this range is elastic. A stress applied in this range incurs no permanent deformation and the ma­terial returns to the original unstressed shape when the stress is released. At higher values of stress the plot of stress versus strain develops a distinct curvature in the strain direction and the material incurs disproportionate strains.

High levels of stress applied to the part and then released produce a permanent deforma­tion. Upon release of some high stress, the metal snaps back—but not all the way. The stress defining the limit of tolerable permanent strain is the “yield stress" and stresses applied above this point produce objectionable per­manent deformation. The very highest stress the material can withstand is the “ultimate stress." Noticeable permanent deformation usually occurs in this range, but the material does have the capability for withstanding one application of the ultimate stress.

The relationship between the stress-strain diagram and operating strength limits should be obvious. If the aircraft is subjected to a load greater than the limit, the yield stress may be exceeded and objectionable permanent deformation may result. If the aircraft is subject to a load greater than the ultimate, failure is imminent.

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.

The pilot may purposely induce various motions to the airplane by the action of the controls. In addition, certain undesirable motions may occur due to inadvertent action on the controls. The most important con­dition exists with the short period longitu­dinal motion of the airplane where pilot – control system response lag can produce an unstable oscillation. The coupling possible in the pilot-control system-airplane combi­nation is most certainly capable of producing damaging flight loads and loss of control of the airplane.

When the normal human response lag and control system lag are coupled with the air­plane motion, inadvertent control reactions by the pilot may furnish a negative damping to the oscillatory motion and dynamic in­stability exists. Since the short period motion is of relatively high frequency, the amplitude of the pitching oscillation can reach dangerous proportions in an unbelievably short time. When the pilot induced oscillation is en­countered, the most effective solution is an immediate release of the controls. Any at­tempt to forcibly damp the oscillation simply continues the excitation and amplifies the oscillation. Freeing the controls removes the unstable (but inadvertent) excitation and allows the airplane to recover by virtue of its inherent dynamic stability.

The pilot induced oscillation is most likely under certain conditions. Most obvious is the case of the pilot unfamiliar with the “feel’’ of the airplane and likely to overcontrol or have excessive response lag. High speed flight at low altitude (high q) is most likely to provide low stick-force gradients and periods of oscillation which coincide with the pilot – control system response lag. Also, the high ^ flight condition provides the aerodynamic capability for failing flight loads during the oscillation.

If a pilot induced oscillation is encountered the pilot must rely on the inherent dynamic stability of the airplane and immediately release the controls. If the unstable excitation is continued, dangerous oscillation amplitudes will develop in a very short time.

The term of "pitch-up” generally applies to the static longitudinal instability encountered by certain configurations at high angle of attack. The condition of pitch-up is illustrated by the graph of CM versus CL in figure 4.33. Positive static longitudinal stability is evident at low values of CL by the negative slope of the curve. At higher values of Ct the curve changes to a positive slope and large positive pitching moments are developed. This sort of in­stability implies that an increase in angle of attack produces nose up moments which tend to bring about further increases in angle of attack hence the term "pitch-up” is applied.

There are several items which may con­tribute to a pitch-up tendency. Sweepback of the wing planform can contribute unstable moments when separation or stall occurs at the tips first. The combination of sweepback and taper alters the lift distribution to produce high local lift coefficients and low energy boundary layer near the tip. Thus, the tip stall is an inherent tendency of such a plan – form. In addition, if high local lift coefficients exist near the tip, the tendency will be to incur the shock induced separation first in these areas. Generally, the wing will contribute to pitch-up only when there is large sweepback.

Of course, the wing is not the only item con­tributing to the longitudinal stability of the airplane. Another item important as a source of pitch-up is the down wash at the horizontal tail. The contribution of the tail to stability depends on the change in tail lift when the air­plane is given a change in angle of attack. Since the downwash at the tail reduces the change in angle of attack at the tail, any in­crease in downwash at the tail is destabilizing.

For certain low aspect ratio airplane configura­tions, an increase in airplane angle of attack may physically locate the horizontal tail in

Mach number. As a corollary of this increase in stability is a decrease in controllability and an increase in trim drag.

The static directional stability of an air­plane decreases with Mach number in super­sonic flight. The influence of the fuselage and the decrease in vertical tail lift curve slope bring about this condition.

The dynamic stability of the airplane generally deteriorates with Mach number in supersonic flight. Since a large part of the damping depends on the tail surfaces, the decrease in lift curve slope with Mach number will account in part for the decrease in damp­ing. Of course, all principal motions of the aircraft must have satisfactory damping and if the damping is not available aerodynami­cally it must be provided synthetically to obtain satisfactory flying qualities. For many high speed configurations the pitch and yaw dampers, flight stabilization systems, etc., are basic necessities rather than luxuries.

Generally, flight at high Mach number will take place at high altitude hence the effect of high altitude must be separated for study. All of the basic aerodynamic damping is due to moments created by pitching, rolling, or yawing motion of the aircraft. These moments are derived from the changes in angles of attack on the tail surfaces with angular rotation (see fig. 4.15). The very high true airspeeds common to high altitude flight reduce the angle of attack changes and reduce the aerodynamic damping. In fact, the aero­dynamic damping is proportional to •фГ, similar to the proportion of true airspeed to equivalent airspeed. Thus, at the altitude of

40,0 ft., the aerodynamic damping would be reduced to one-half the sea level value and at the altitude of 100,000 ft. the aerodynamic damping would be reduced to one-tenth the sea level value.

High dynamic pressures (high q) can be common to flight at high Mach number and adverse aeroelastic effects may be encountered. If the aircraft surfaces encounter significant deflection when subject to load, the tendency may be to lower the contribution to static stability and reduce the damping contribution. Thus, the problem of adequate stability of the various airplane motions is aggravated.

The motion of an airplane in a spin can involve many complex aerodynamic and in­ertia forces and moments. However, there are certain fundamental relationships regarding spins and spin recoveries with which all aviators should be familiar. The spin differs from a spiral dive in that the spin always involves flight at high angle of attack while the spiral dive involves a spiral motion of the airplane at relatively low angle of attack.

The stall characteristics and stability of the airplane at high lift coefficients are im­portant in the initial tendencies of the airplane. As previously mentioned, it is desirable to have the wing initiate stall at the root first rather than tip first. Such a stall pattern prevents the undesirable rolling moments at high lift coefficients, provides suitable stall

warning, and preserves lateral control effec­tiveness at high angles of attack. Also, the airplane must maintain positive static longi­tudinal stability at high lift coefficients and should demonstrate satisfactory stall recovery characteristics.

In order to visualize the principal effects of an airplane entering a spin, suppose the air­plane is subjected to the rolling and yawing velocities shown in figure 4.32. The yawing velocity to the right tends to produce higher local velocities on the left wing than on the right wing. The rolling velocity tends to increase the angle of attack for the downgoing right wing Car) and. decrease the angle of attack for the upgoing left wing Ca0- At airplane angles of attack below the stall this relationship produces roll due to yaw, damping in roll, etc., and some related motion of the airplane in unstalled flight. However, at angles of attack above the stall, important changes take place in the aerodynamic char­acteristics.

Figure 4-32 illustrates the aerodynamic characteristics typical of a conventional air­plane configuration, i. e., moderate or high aspect ratio and little—if any—sweepback. If this airplane is provided a rolling displace­ment when at some angle of attack above the stall, the upgoing wing experiences a decrease in angle of attack with a correspond­ing increase in CL and decrease in CD. In other words, the upgoing wing becomes less stalled. Similarly, the downgoing wing experiences an increase in angle of attack with a corre­sponding decrease in CL and increase in CD. Es­sentially, the downgoing wing becomes more stalled. Thus, the rolling motion is aided rather than resisted and a yawing moment is produced in the direction of roll. At angles of attack below stall the rolling motion is resisted by damping in roll and adverse yaw is usually present. At angles of attack above the stall, the damping in roll is negative and a rolling motion produces a roiling moment in the direction of the roll. This negative damping in roll is generally referred to as “autorotation."

When the conventional airplane is stalled and some rolling-yawing displacement takes place, the resulting autorotation rolling mo­ments and yawing moments start the airplane into a self-sustaining rolling-yawing motion. The autorotation rolling and yawing tenden­cies of the airplane at high angles of attack are the principal prospin moments of the conventional airplane configuration and these tendencies accelerate the airplane into the spin until some limiting condition exists. The stabilized spin is not necessarily a simple steady vertical spiral but may involve some coupled unsteady oscillatory motion.

An important characteristic of the more conventional airplane configuration is that the spin shows a predominating contribution of the autorotation tendency. Generally, the conventional configuration has a spin motion which is primarily rolling with moderate yaw. High directional stability is favorable since it will limit or minimize the yaw displacement of the spinning airplane.

The fundamental requirement of the spin is that the airplane be placed at an excessive angle of attack to produce the autorotation rolling and yawing tendencies. Generally speaking, the conventional airplane must be stalled before a spin can take place. This relationship establishes a fundamental prin­ciple of recovery—the airplane must be un­stalled by decreasing the wing angle of attack. The most effective procedure for the conven­tional configuration is to use opposite rudder to stop the sideslip, then lower the angle of attack with the elevators. With sufficient rudder power this procedure will produce a positive recovery with a minimum loss of altitude. Care should be taken during pullout from the ensuing dive to prevent excessive angle of attack and entry into another spin.

It should be appreciated that a spin is always a possible corollary of a stall and the self­sustaining motion of a spin will take place at

excessive angles of attack. Of course, a low speed airplane could be; designed to be spin – proof by making it stallproof. By limiting the amount of control deflection, the airplane may not have the longitudinal control power to trim to maximum lift angle of attack. Such a provision may be possible for certain light planes and commercial aircraft but would create an unrealistic and impractical limita­tion on the utility of a military airplane.

The modem high speed airplane configura­tion is typified by low aspect ratio, swept wing planforms with relatively large yaw and pitch inertia. The aerodynamic characteristics of such a configuration are shown in figure 4.32. The lift curve (Cl versus a) is quite shallow at high angles of attack and maximum lift is not clearly defined. When this type of airplane is provided a rolling motion at high angles of attack, restively small changes in CL take place. When this effect is combined with the relatively short span of this type airplane, it is apparent that the wing autorotation contribu­tion will be quite weak and will not be a pre­dominating pro-spin moment. The relatively large changes in drag coefficient with rolling motion imply a predominance of yaw for the spin of the high speed airplane configuration.

Actually, various other factors contribute to the predominating yaw tendency for the spin of the modern airplane configuration. The static directional stability deteriorates at high angles of attack and may be so weak that extemely large yaw displacements result. In certain instances, very high angles of attack may bring such a decay in directional stability that a “slice” or extreme yaw displacement takes place before a true spin is apparent. At these high angles of attack, the adverse yaw due to roll and aileron deflection can be very strong and create large yaw displacements of the airplane prior to realizing a stall.

The aircraft with the relatively large, long fuselage can exhibit a significant moment con­tribution from the fuselage alone. The cross flow pattern on the fuselage at high angles of attack is capable of producing pro-spin mo­ments of considerable magnitude which con­tribute to the self-sustaining nature of the spin. Also, the large distributed mass of the fuselage in rolling-yawing rotation contributes to inertia moments which flatten the spin and place the aircraft at extreme angles of attack.

The spin recovery of the modern high speed airplane involves principles which are similar to those of the spin recovery of the conven­tional airplane. However, the nature of the spin for the modern configuration may involve specific differences in technique necessary to reduce the sideslip and angle of attack. The use of opposite rudder to control the sideslip and effect recovery will depend on the effective­ness of the rudder when the airplane is in the spin. At high positive angles of attack and high sideslip the rudder effectiveness may be reduced and additional anti-spin moments must be provided for rapid recovery. The deflection of ailerons into the spin reduces the autorota­tion rolling moment and can produce adverse yaw to aid the rudder yawing moment in effecting recovery.

There may be many other specific differences in the technique necessary to effect spin re­covery. The effectiveness of the rudder during recovery may be altered by the position of elevators or horizontal tail. Generally, full aft stick may be necessary during the initial phase of recovery to increase the effectiveness of the rudder. The use of power during the spin recovery of a propeller powered airplane may or may not aid recovery depending on the specific airplane and the particular nature of the slipstream effects. The use of power during the spin recovery of a jet powered airplane induces no significant or helpful flow but does offer the possibility of a severe compressor stall and adverse gyroscopic moments. Since the airplane is at high angle of attack and sideslip, the flow at the inlet may be very poor and the stall limits considerably reduced. These items serve to point out possible dif­ferences in technique required for various con­figurations. The spin recovery specific for

NAVWEPS 00-80T-80

stability and control

each airplane is outlined in the pilot’s hand­book and it is imperative that the specific tech­nique be followed for successful recovery.

There are several general problems of flying which involve certain principles of stability as well as specific areas of longitudinal, direc­tional and lateral stability. Various condi­tions of flight will exist in which certain problems of stability (or instability) are un­avoidable for some reason or another. Many of the following items deserve consideration because of the possible unsafe condition of flight and the contribution to an aircraft accident.

LANDING GEAR CONFIGURATIONS

There are three general configurations for the aircraft landing gear; the tricycle, bicycle, and “conventional” tail wheel arrangement. At low rolling speeds where the airplane aerody­namic forces are negligible, the “control-fixed” static stability of each of these configurations is determined by the side force characteristics of the tires and is not a significant problem.

The instability which allows ground loops in an aircraft with a conventional tail wheel landing gear is quite basic and can be appre­ciated from the illustration of figure 4-31. Cen­trifugal force produced by a turn must be balanced and the aircraft placed in equilibrium. The greatest side force is produced at the main wheels but to achieve equilibrium with the

center of gravity aft of the main wheels a bal­ancing load on the tail wheel must be produced toward the center of turn. When the tail wheel is free to swivel, the equilibrium of the turn requires a control force opposite to the direction of turn—i. e,, control force insta­bility. The inherent stability problem exists because the center of gravity is aft of the point where the main side forces are developed. This condition is analogous to the case of static longitudinal stability with the center of gravity aft of the neutral point.

The conventional tail wheel configuration has this basic instability or ground loop tend­ency which must be stabilized by the pilot. At high rolling speeds where aerodynamic forces are significant, the aerodynamic direc­tional stability of the airplane resists the ground looping tendency. The most likely times for a ground loop exist when rolling speeds are not high enough to provide a con­tribution of the aerodynamic forces. When the tail wheel is free to swivel or when the normal force on the tail wheel is small, lack of pilot attention can allow the ground loop to take place.

The tricycle landing gear configuration has an inherent stability due to the relative posi­tion of the main wheels and the center of gravity. Centrifugal force produced by a turn is balanced by the side force on the main wheels and a side force on the nose wheel in the direction of turn. Note that the freeing the nose wheel to swivel produces moments which bring the aircraft out of the turn. Thus, the tricycle configuration has a basic stability which is given evidence by control displace­ment and a wheel side force in the direction of turn. Because of the contrast in stability, the tricycle configuration is much less difficult to maneuver than the tail wheel configuration and does not provide an inherent ground loop tendency. However, a steerable nose wheel is usually necessary to provide satisfactory maneuvering capabilities.

The bicycle configuration of landing gear has stability characteristics more like the automobile. If directional control is ac­complished with the front wheels operated by power controls, no stability problem exists at low speeds. A problem can exist when the airplane is at high speeds because of a distribu­tion of normal force being different from the ordinary static weight distribution. If the airplane is held onto the runway at speeds well above the normal takeoff and landing speeds, the front wheels carry a greater than ordinary amount of normal force and a tend­ency for instability exists. However, at these same high speeds the rudder is quite powerful and the condition is usually well within control.

The basically stable nature of the tricycle and bicycle landing gear configurations is best appreciated by the ease of control and ground maneuvering of the airplane. Operation of a conventional tail wheel configuration after considerable experience with tricycle configu­rations requires careful consideration of the stability that must be furnished by the pilot during ground maneuvering.

Previous discussion has separated the lateral and directional response of the airplane to sideslip. This separation is convenient for detailed study of each the airplane static lateral stability and the airplane static direc­tional stability. However, when the airplane in free flight is placed in a sideslip, the lateral and directional response will be coupled, i. e., simultaneously the airplane produces rolling moment due to sideslip and yawing moment due to sideslip. Thus, the lateral dynamic motion of the airplane in free flight must consider the coupling or interaction of the lateral and directional effects.

The principal effects which determine the lateral dynamic characteristics of an airplane are:

(1) Rolling moment due to sideslip or

dihedral effect (lateral stability).

(2) Yawing moment due to sideslip or static directional stability.

(3) Yawing moment due to rolling veloc­ity or the adverse (or proverse) yaw.

(4) Rolling moment due to yawing ve­locity—a cross effect similar to (3)- If the aircraft has a yawing motion to the right, the left wing will move forward faster and momentarily develop more lift than the right and cause a rolling moment to the right.

(5) Aerodynamic side force due to side­slip.

(6) Rolling moment due to rolling ve­locity or damping in roll.

(7) Yawing moment due yawing velocity or damping in yaw.

(8) The moments of inertia of the air­plane about the roll and yaw axes.

The complex interaction of these effects pro­duces three possible types of motion of the airplane: (a) a directional divergence, (b) a spiral divergence, and (c) an oscillatory mode termed Dutch roll.

Directional divergence is a condition which cannot be tolerated. If the reaction to a small initial sideslip is such as to create moments which tend to increase the sideslip, directional divergence will exist. The sideslip would in­crease until the airplane is broadside to the wind or structural failure occurs. Of’ course, increasing the static directional stability re­duces the tendency for directional divergence.

Spiral divergence will exist when the static directional stability is very large when com­pared with the dihedral effect. The character of spiral divergence is by no means violent. The airplane, when disturbed from the equilib­rium of level flight, begins a slow spiral which gradually increases to a spiral dive. When a small sideslip is introduced, the strong direc­tional stability tends to restore the nose into the wind while the relatively weak dihedral effect lags in restoring the airplane laterally. In the usual case, the rate of divergence in the

spiral motion is so gradual that the pilot can control the tendency without difficulty.

Dutch roll is a coupled lateral-directional oscillation which is usually dynamically stable but is objectionable because of the oscillatory nature. The damping of this oscillatory mode may be weak or strong depending on the prop­erties of the airplane. The response of the air­plane to a disturbance from equilibrium is a combined rolling-yawing oscillation in which the rolling motion is phased to precede the yawing motion. Such a motion is quite unde­sirable because of the great havoc it would create with a bomb, rocket, or gun platform.

Generally, Dutch roll will occur when the dihedral effect is large when compared to static directional stability. Unfortunately, Dutch roll will exist for relative magnitudes of dihe­dral effect and static directional stability be­tween the limiting conditions for directional divergence and spiral divergence. When the dihedral effect is large in comparison with static directional stability, the Dutch roll motion has weak damping and is objectionable. When the static directional stability is strong in comparison with the dihedral effect, the Dutch roll motion has such heavy damping that it is not objectionable. However, these qualities tend toward spiral divergence.

The choice is then the least of three evils. Directional divergence cannot be tolerated, Dutch roll is objectionable, and spiral diver­gence is tolerable if the rate of divergence is low. For this reason the dihedral effect should be no more than that required for satisfactory lateral stability. If the static directional sta­bility is made adequate to prevent objection­able Dutch roll, this will automatically be sufficient to prevent directional divergence. Since the more important handling qualities are a result of high static directional stability and minimum necessary dihedral effect, most airplanes demonstrate a mild spiral tendency. As previously mentioned, a weak spiral tend­ency is of little concern to the pilot and cer­tainly preferable to Dutch roll.

The contribution of sweepback to the lateral dynamics of an airplane is significant. Since the dihedral effect from sweepback is a function of lift coefficient, the dynamic characteristics may vary throughout the flight speed range. When the swept wing airplane is at low C£, the dihedral effect is small and the spiral tendency may be apparent. When the swept wing air­plane is at high CL, the dihedral effect is in­creased and the Dutch Roll oscillatory tendency is increased.

An additional oscillatory mode is possible in the lateral dynamic effects with the rudder free and the mode is termed a “snaking” oscil­lation. This yawing oscillation is greatly affected by the aerodynamic balance of the rudder and requires careful consideration in design to prevent light or unstable damping of the oscillation.

CONTROL IN ROLL

The lateral control of an airplane is ac­complished by producing differential lift on the wings. The rolling moment created by the differential lift can be used to accelerate the airplane to some rolling motion or control the airplane in a sideslip by opposing dihedral effect. The differential lift for control in roll is usually obtained by some type of ailerons or spoilers.

ROLLING MOTION OF AN AIRPLANE. When an airplane is given a rolling motion in flight, the wing tips move in a helical path through the air. As shown in figure 4.29, a rolling velocity to the right gives the right wing tip a downward velocity component and the left wing tip an upward velocity com­ponent. By inspection of the motion of the left wing tip, the velocity of the tip due to roll combines with the airplane flight path velocity to define the resultant motion. The resulting angle between the flight path vector and the resultant path of the tip is the helix angle of roll. From the trigonometry of small angles, the helix angle of roll can be defined as:

Roll helix angle=^ (radians)

where

g=rate of roll, radians per second £=wing span, ft.

airplane flight velocity, ft. per sec.

and, one radian=57.3 degrees

Generally, the maximum values of ^^obtained by control in roll are approximately 0.1 to 0.07- The helix angle of roll, is actually a com­mon denominator of rolling performance.

The deflection of the lateral control surfaces creates the differential lift and the rolling moment to accelerate the airplane in roll. The roll rate increases until an equal and opposite moment is created by the resistance to rolling motion or “damping in roll.’’ The second illustration of figure 4.29 defines the source of the damping in roll. When the airplane is given a rolling velocity to the right, the downgoing wing experiences an increase in angle of attack due to the helix angle of roll. Of course, the upgoing wing experiences a decrease in angle of attack. In flight at angles of attack less than that for maximum lift, the downgoing wing experiences an increase in lift and the upgoing wing experiences a de­crease in lift and a rolling moment is developed which opposes the rolling motion. Thus, the steady state rolling motion occurs when the damping moment equals the control moment.

The response of the airplane to aileron deflec­tion is shown by the time history diagram of figure 4.29. When the airplane is restrained so that pure rolling motion is obtained, the initial response to an aileron deflection is a steady increase in roll rate. As the roll rate increases so does the damping moment and the roll acceleration decreases. Finally, the damping moment approaches the control mo­ment and a steady state roll rate is achieved.

If the airplane is unrestrained and sideslip is allowed, the affect of the directional stability and dihedral effect can be appreciated. The conventional airplane will develop adverse yawing moments due to aileron deflection and rolling motioft. Adverse yaw tends to produce yawing displacements and sideslip but this is resisted by the directional stability of the air­plane. If adverse yaw produces sideslip, di­hedral effect creates a rolling moment opposing the roll and tends to reduce the roll rate. The typical transient motions (A) and (B) of the time history diagram of figure 4.29 show that high directional stability with low dihedral effect is the preferable combination. Such a combination provides an airplane which has no extreme requirement of coordinating aileron and rudder in order to achieve satisfactory rolling performance. While the coupled mo­tion of the airplane in roll is important, further discussion of lateral control will be directed to pure uncoupled rolling performance.

ROLLING PERFORMANCE. The required rolling performance of an airplane is generally

specified as certain necessary values of the roll helix angle, However, in certain condi­

tions of flight, it may be more appropriate to specify minimum times for the airplane to accelerate through a given angle of roll.

Usually, the maximum value of ~ should be

on the order of 0.10. Of course, fighters and attack airplanes have a more specific require­ment for high rolling performance and 0.09

may be considered a minimum necessary

Patrol, transport, and bomber airplanes have less requirement for high rolling performance and a

of 0.07 may be adequate for these types.

The ailerons or spoilers must be powerful

■hh

enough to provide the required – y – While

the size and effectiveness of the lateral control devices is important, consideration must be

Revised January 1965

AIRPLANE RESPONSE TO AILERON DEFLECTION

-STEADY STATE ROLL RATE

LOW DIHEDRAL EFFECT

AIRPLANE UNRESTRAINED AND FREE TO SIDESLIP

(RUDDER FIXEDb LOW DIRECTIONAL STABILITY

high DIHEDRAL EFFECT

given to the airplane size. For geometrically similar airplanes, a certain deflection of the

ailerons will produce a fixed value of inde­pendent of the airplane size. However, the roll rate of the geometrically similar airplanes at a given speed will vary inversely with the span, b.

If

pb

constant

£=(constant)^^-^

Thus, the smaller airplane will have an ad­vantage in roll rate or in time to accelerate through a prescribed angle of roll. For ex­ample, a one-half scale airplane will develop twice the rate of roll of the full scale airplane. This relationship points to the favor of the small, short span airplane for achieving high roll performance.

An important variable affecting the rate of roll is the true airspeed or flight velocity, V. If a certain deflection of the ailerons creates a specific value of the rate of roll varies directly with the true airspeed. Thus, if the roll helix angle is held constant, the rate of roll at a particular true airspeed will not be affected by altitude. The linear variation of roll rate with airspeed points out the fact that high roll rates will require high airspeeds. The low roll rates at low airspeeds are simply a consequence of the low flight speed and this condition may provide a critical lateral con­trol requirement for satisfactory handling qualities.

Figure 4.30 illustrates the typical rolling performance of a low speed airplane. When the ailerons are at full deflection, the maximum roll helix angle is obtained. The rate of roil increases linearly with speed until the control forces increase to limit of pilot effort and full control deflection cannot be maintained. Past

tih

ailerons cannot be held at full deflection, ~p

drops, and rate of roll decreases. In this exam­ple, the rolling performance at high speeds is limited by the ability of the pilot to maintain full deflection of the controls. In an effort to reduce the aileron hinge moments and control forces, extensive application is made of aerody­namic balance and various tab devices. How­ever, 100 percent aerodynamic balance is not always feasible or practical but a sufficient

value of must be maintained at high speeds.

Rather than developing an extensive weight lifting program mandatory for all Naval Aviators, mechanical assistance in lateral con­trol can be provided. If a power boost is provided for the lateral control system, the rolling performance of the airplane may be extended to higher speeds since pilot effort will not be a limiting factor. The effect of a power boost is denoted by the dashed line extensions of figure 4.30. A full powered, irreversible lateral control system is common for high speed airplanes. In the power oper­ated system there is no immediate limit to the deflection of the control surfaces and none of the aberrations in hinge moments due to com­pressibility are fed back to the pilot. Control forces are provided by the stick centering lateral bungee or spring.

A problem particular to the high speed is due to the interaction of aerodynamic forces and the elastic deflections of the wing in torsion. The deflection of ailerons creates twisting moments on the wing which can cause significant torsional deflections of the wing. At the low dynamic pressures of low flight speeds, the twisting moments and twisting deflections are too small to be of importance. However, at high dynamic pressures, the deflection of an aileron creates significant

twisting deflections which reduce the effec­tiveness of the aileron, e. g., downward deflec­tion of an aileron creates a nose down twist of the wing which reduces the rolling moment due to aileron deflection. At very high speeds, the torsional deflection of the wing may be so great than a rolling moment is created opposite to the direction controlled and “aile­ron reversal” occurs. Prior to the speed for aileron reversal, a serious loss of roll helix angle may be encountered. The effect of this aeroelastic phenomenon on rolling perform­ance is illustrated in figure 4-30.

To counter the undesirable interaction be­tween aerodynamic forces and wing torsional deflections, the trailing edge ailerons may be moved inboard to reduce the portion of the span subjected to twisting moments. Of course, the short span, highly tapered wing planform is favorable for providing relatively high stiffness. In addition, various configura­tions of spoilers may be capable of producing the required rolling performance without t;he development of large twisting moments.

CRITICAL REQUIREMENTS. The critical conditions for requiring adequate lateral con­trol power may occur at either high speed or low speed depending on the airplane configura­tion and intended use. In transonic and super­sonic flight, compressibility effects tend to reduce the effectiveness of lateral control de­vices to produce required roll helix angles. These effects are most significant when com­bined with a loss of control effectiveness due to aeroelastic effects. Airplanes designed for high speed flight must maintain sufficient lateral control effectiveness at the design dive speed and this is usually the predominating requirement.

During landing and takeoff, the airplane must have adequate lateral control power to contend with the ordinary conditions of flight. The lateral controls must be capable of achiev­ing required roll helix angles and acceleration through prescribed roll displacements. Also, the airplane must be capable of being con­trolled in a sideslip to accomplish crosswind takeoff and landing. The lateral control dur­ing crosswind takeoff and landing is a par­ticular problem when the dihedral effect is high. Since the sweepback contributes a large dihedral effect at high lift coefficients, the problem is most important for the airplane with considerable sweepback. The limiting crosswind components must be given due re­spect especially when the airplane is at low gross weight. At low gross weight the speci­fied takeoff and landing speeds will be low and the controlled angle of sideslip will be largest for a given crosswind velocity.

LATERAL STABILITY

The static lateral stability of an airplane involves consideration of rolling moments due

Revised January 1965

to sideslip. If an airplane has favorable rolling moment due to sideslip, a lateral displacement from wing level flight produces sideslip and the sideslip creates rolling moments tending to return the airplane to wing level flight. By this action, static lateral stability will be evident. Of course, a sideslip will produce yawing moments depending on the nature of the static directional stability but the consid – rations of static lateral stability will involve only the relationship of rolling moments and sideslip.

DEFINITIONS. The axis system of an airplane defines a positive rolling, L, as a moment about the longitudinal axis which tends to rotate the right wing down. As in other aerodynamic considerations, it is con­venient to consider rolling moments in the coefficient form so that lateral stability can be evaluated independent of weight, altitude, speeds, etc. The rolling moment, L, is defined in the coefficient form by the following equa­tion:

L = CtqSb or

Q —J±- Li qSb

where

L = rolling moment, ft.-lbs., positive to the right

q = dynamic pressure, psf.

i’ = wing area, sq. ft.

b = wingspan, ft.

Cj=rolling moment coefficient, positive to the right

The angle of sideslip, /3, has been defined previously as the angle between the airplane centerline and the relative wind and is positive when the relative wind is to the right of the centerline.

The static lateral stability of an airplane can be illustrated by a graph of rolling moment coefficient, Ci, versus sideslip angle, j3, such as shown in figure 4.27. When the airplane is subject to a positive sideslip angle, lateral stability will be evident if a negative rolling moment coefficient results. Thus, when the relative wind comes from the right (+j9), a rolling moment to the left (—Cl) should be created which tends to roll the airplane to the left. Lateral stability will exist when the curve of Ci versus /3 has a negative slope and the degree of stability will be a function of the slope of this curve. If the slope of the curve is zero, neutral lateral stability exists; if the slope is positive lateral instability is present.

It is desirable to have lateral stability or favorable roll due to sideslip. However, the required magnitude of lateral stability is deter­mined by many factors. Excessive roll due to sideslip complicates crosswind takeoff and landing and may lead to undesirable oscil­latory coupling with the directional motion of the airplane. In addition, a high lateral sta­bility may combine with adverse yaw to hinder rolling performance. Generally, favorable han­dling qualities are obtained with a relatively light—or weak positive—lateral stability.

CONTRIBUTION OF THE AIRPLANE COMPONENTS. In order to appreciate the development of lateral stability in an airplane, each of the contribution components must be inspected. Of course, there will be interference between the components which will alter the contribution to stability of each component on the airplane.

The principal surface contributing to the lateral stability of an airplane is the wing. The effect of the geometric dihedral of a wing is a powerful contribution to lateral stability. As shown in figure 4.28, a wing with dihedral will develop stable rolling moments with sideslip. If the relative wind comes from the side, the wing into the wind is subject to an increase in angle of attack and develops an increase in lift. The wing away from the wind is subject to a decrease in angle of attack and develops a de­crease in lift. The changes in lift effect a rolling moment tending to raise the windward wing hence dihedral contributes a stable roll due to sideslip.

CONTRIBUTION OF VERTICAL TAIL

SIDESLIP CONTRIBUTES
ROLLING MOMENT

Since wing dihedral is so powerful in pro­ducing lateral stability it is taken as a common denominator of the lateral stability contribu­tion of all other components. Generally, the contribution of wing position, flaps, power, etc., is expressed as an equivalent amount of “effective dihedral” or “dihedral effect.”

The contribution of the fuselage alone is usually quite small depending on the location of the resultant aerodynamic side force on the fuselage. However, the effect of the wing – fuselage-tail combination is significant since the vertical placement of the wing on the fuse­lage can greatly affect the stability of the com­bination. A wing located at the mid wing position will generally exhibit a dihedral effect no different from that of the wing alone. A low wing location on the fuselage may con­tribute an effect equivalent to 3° or 4° of nega­tive dihedral while a high wing location may contribute a positive dihedral of 2° or 3°. The magnitude of dihedral effect contributed by vertical position of the wing is large and may necessitate a noticeable dihedral angle for the low wing configuration.

The contribution of sweepback to dihedral ef­fect is important because of the nature of the contribution. As shown in figure 4.28, the swept wing in a sideslip has the wing into wind operating with an effective decrease in sweepback while the wing out of the wind is operating with an effective increase in sweepback. If the wing is at a positive lift coefficient, the wing into the wind has less sweep and an increase in lift and the wing out of the wind has more sweep and a decrease in lift. In this manner the swept back wing would contribute a positive dihedral effect and the swept forward wing would contribute a negative dihedral effect.

The unusual nature of the contribution of sweepback to dihedral effect is that the con­tribution is proportional to the wing lift coefficient as well as the angle of sweepback. It should be clear that the swept wing at zero lift will provide no roll due to sideslip since there is no wing lift to change. Thus, the dihedral effect due to sweepback is zero at zero lift and increases directly with wing lift coefficient. When the demands of high speed flight require a large amount of sweepback, the resulting configuration may have an excessive­ly high dihedral effect at low speeds (high CL) while the dihedral effect may be satisfactory in normal flight (low or medium CL).

The vertical tail of modern configurations can provide a significant—and, at times, un­desirable—contribution to the effective dihe­dral. If the vertical tail is large, the side force produced by sideslip may produce a noticeable rolling moment as well as the important yaw­ing moment contribution. Such an effect is usually small for the conventional airplane configuration but the modern high speed airplane configuration induces this effect to a great magnitude. It is difficult then to obtain a large vertical tail contribution to directional stability without incurring an additional con­tribution to dihedral effect.

The amount of effective dihedral necessary to produce satisfactory flying qualities varies greatly with the type and purpose of the air­plane, Generally, the effective dihedral should not be too great since high roll due to side­slip can create certain problems. Excessive dihedral effect can lead to “Dutch roll,” difficult rudder coordination in rolling maneu­vers, or place extreme demands for lateral control power during crosswind takeoff and landing. Of course, the effective dihedral should not be negative during the predominat­ing conditions of flight, e. g,, cruise, high speed, etc. If the airplane demonstrates satis­factory dihedral effect for these conditions of flight, certain exceptions can be considered when the airplane is in the takeoff and landing configuration. Since the effects of flaps and power are destablizing and reduce the dihedral effect, a certain amount of negative dihedral effect may be possible due to these sources.

The deflection of flaps causes the inboard sections of the wing to become relatively more

effective and these sections have a small spanwise moment arm. Therefore, the changes in wing lift due to sideslip occur closer in­board and the dihedral effect is reduced. The effect of power on dihedral effect is negligible for the jet airplane but considerable for the propeller driven airplane. The propeller slip­stream at high power and low airspeed makes the inboard wing sections much more effective and reduces the dihedral effect. The reduction in dihedral effect is most critical when the flap and power effects are combined, e. g., the propeller driven airplane in the power approach or waveoff.

With certain exceptions during the condi­tions of landing and takeoff, the dihedral effect or lateral stability should be positive but light. The problems created by excessive dihedral effect are considerable and difficult to contend with. Lateral stability will be evident to a pilot by stick forces and displace­ments required to maintain sideslip. Positive stick force stability will be evident by stick forces required in the direction of the controlled sideslip.