LATERAL DYNAMIC EFFECTS

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.