Airplane stability and control notes GATE Aerospace Engineering

8/13/2019 Airplane stability and control notes GATE Aerospace Engineering

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1. STICK FORCE GRADIENTS [ J12-7(i) ]

Another important parameter in the design of a control system is called the stick forcegradient. Figure below shows the variation of the stick force with speed.

The stick force gradient is a measure of the change in stick force needed to changethe speed of the airplane. To provide the airplane with speed stability, the stick forcegradient must be negative, i.e.

The need for a negative stick force gradient can be appreciated by examining aboveFigure. If the airplane slows down, a positive stick force occurs which rotates thenose of the airplane downwards, which causes the airplane to increase its speed backtowards the trim velocity. For the case in which the airplane exceeds the trim velocity,a negative (pull) stick force causes the airplane's nose to pitch up, which causes theairplane to slow down. The negative stick force gradient provides the pilot andairplane with speed stability. The larger the gradient, the more resistant the airplanewill be to disturbances in the flight speed. If an airplane did not have speed stabilitythe pilot would have to continuously monitor and control the airplane's speed. Thiswould be highly undesirable from the pilot's point of view.

2. Development of trailing vortices [ J13-7(i), D12-7(i) Read my xerox notes ]

When producing lift, a wing generates strong swirling masses of air off both itswingtips. As discussed in a previous question on the creation of lift, a wing generateslift because there is a lower pressure on its upper surface than on its lower surface.This difference in pressure creates lift, but the penalty is that the higher pressure flow beneath the wing tries to flow around the wingtip to the lower pressure region abovethe wing. This motion creates what is called a wingtip vortex. As the wing movesforward, this vortex remains, and therefore trails behind the wing. For this reason, thevortex is usually referred to as a trailing vortex. One trailing vortex is created offeach wingtip, and they spin in opposite directions as illustrated below.

While trailing vortices are the price one must pay for generating lift, their primaryeffect is to deflect the flow behind the wing downward. This induced component ofvelocity is called downwash, and it reduces the amount of lift produced by the wing.In order to make up for that lost lift, the wing must go to a higher angle of attack, andthis increase in angle of attack increases the drag generated by the wing. We call thisform of drag induced drag because it is "induced" by the process of creating lift.


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Creation of trailing vortices due to a difference in pressure above and below alifting surface

Regions of upwash and downwash created by trailing vortices

While trailing vortices are the price one must pay for generating lift, their primaryeffect is to deflect the flow behind the wing downward. This induced component ofvelocity is called downwash, and it reduces the amount of lift produced by the wing.In order to make up for that lost lift, the wing must go to a higher angle of attack, and

this increase in angle of attack increases the drag generated by the wing. We call thisform of drag induced drag because it is "induced" by the process of creating lift.

However, this downwash is also accompanied by an upwash that can be beneficial toa second wing flying behind and slightly above the first.


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3. Aerodynamic balancing [ J13-7(ii), J12-7(ii), J11-7(v), D09-7(v) ]

The ways and means of reducing the magnitudes of Cht and Che are calledaerodynamic balancing.

The methods for aerodynamic balancing are:

1. set back hinge,2. horn balance and3. internal balance4. Frise Aileron

Set back hinge or over hang balance

In this case, the hinge line is shifted behind the leading edge of the control (see upper part of Fig. below). As the hinge line shifts, the area of the control surface ahead ofthe hinge line increases and from the pressure distribution in Fig.3.3 it is evident thatCht and Che would decrease. The over hang is characterized by cb/cf . Figure 6.6also shows typical experimental data on variations of Ch and Ch with cb/cf. It may

be added that the changes in Ch and Ch also depend on (a) gap between nose of thecontrol surface and the main surface, (b) nose shape and (c) trailing edge angle(Fig.6.7a and b)

Effect of set back hinge on Ch and Ch

NACA 0015 Airfoil with blunt nose and sealed gap

Horn balance [D10-7(iii), D08-7(iv)]

In this method of aerodynamic balancing, a part of the control surface near the tip, isahead of the hinge line (Fig.a and b). There are two types of horn balances shieldedand unshielded (Fig a). The following parameter is used to describe the effect of horn balance on Ch and Ch.Parameter =(Area of horn)(mean chord of horn)/ Area of control)(mean chord of


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control)

Figure 6.8b shows the areas of the horn and control surface. Figure 6.8b also showsthe changes Ch and Ch due to horn as compared to a control surface withouthorn. Horn balance is some times used on horizontal and vertical tails of low speedairplanes (see Fig.6.8c).

Internal balance or internal seal

In this case, the portion of the control surface ahead of the hinge line, projects in thegap between the upper and lower surfaces of the stabilizer. The upper and lower


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surfaces of the projected portion are vented to the upper and lower surface pressuresrespectively at a chosen chord wise position (upper part of Fig.6.9). A seal at theleading edge of the projecting portion ensures that the pressures on the two sides ofthe projection do not equalize. Figure 6.9 also shows the changes Ch and Chdue to internal seal balance. This method of aerodynamic balancing is complex but isreliable. It is used on large airplanes to reduce Ch and Ch.

Frise aileron [ D10-7(ii)]

The frise aileron is shown in figure below The leading edge of the aileron has aspecific shape. The downward deflected aileron has negative Ch and the upwarddeflected aileron has positive Ch. This reduces the net control force. Further, owingto the special shape of the leading edge, the upward deflected aileron projects into theflow field and increases the drag. This reduces adverse yaw.


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4. FLIGHT MEASUREMENT OF X NP ( N 0 ) [ J13-7(iii) ]

The equation developed for estimating the elevator angle to trim the airplane can beused to determine the stick fixed neutral point from flight test data. Suppose weconducted a flight test experiment in which we measured the elevator angle of trim atvarious air speeds for different positions of the center of gravity. If we did this, wecould develop curves as shown in Fig. A.

FIG. A

FIG. B

Now, differentiating above equation with respect to CLtrim yields

Note that whenCm= 0 (i.e. the center of gravity is at the neutral point) Aboveequation equal to zero. Therefore, if we measure the slopes of the curves in Fig. Band plot them as a function of center of gravity location, we can estimate the stick


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fixed neutral point as illustrated in Fig. 2.22 by extrapolating to find the center ofgravity position that makes dtrim/dCLtrimequal to zero.

5. DIRECTIONAL DIVERGENT STABILITY [J13-7(vi), J12-7(vi)]

The degree of directional stability compared with degree of lateral stability of anaircraft can produce three conditions. These conditions are directional divergence,spiral divergence, and Dutch roll.

Directional Divergence

Directional divergence results from negative directional stability.

This cannot be tolerated because directional divergence allows the aircraft to increaseits yaw after only a slight yaw has occurred.

This continues until the aircraft turns broadside to the flight path or until it breaks upfrom the high pressure load imposed on the side of the aircraft.

Spiral Divergence

Spiral divergence results, if static directional stability is strong when compared with


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the dihedral effect.

If an aircraft with strong directional stability has its right wing down, a positivesideslip angle is produced.

As a result of strong directional stability, the aircraft tries to correct directionally before the dihedral effect can correct laterally.

The aircraft chases the relative wind, and the resulting flight path is a descendingspiral.

To correct this condition, the wing is raised with the lateral control surfaces and thespiral stops immediately.

Dutch roll

Dutch roll results from relatively weaker positive directional stability as opposed to positive lateral stability. When an aircraft rolls around the longitudinal axis, a sideslipis introduced into the relative wind in the direction of the rolling motion. Stronglateral stability begins to restore the aircraft to level flight. At the same time,somewhat weaker directional stability attempts to correct the sideslip by aligning theaircraft with the perceived relative wind. Since directional stability is weaker thanlateral stability for the particular aircraft, the restoring yaw motion lags significantly behind the restoring roll motion. As such, the aircraft passes through level flight asthe yawing motion is continuing in the direction of the original roll. At that point, thesideslip is introduced in the opposite direction and the process is reversed.

Note:The lateral dynamic stability of an aircraft is largely decided by the relative effects

of:

a. Rolling moment due to sideslip (dihedral effect). b. Yawing moment due to sideslip (weathercock stability).

Too much weathercock stability will lead to spiral instability whereas too muchdihedral effect will lead to Dutch roll instability.

6. THE LATERAL DYNAMIC STABILITY MODES

Whenever the aeroplane is disturbed from its equilibrium trim state the lateral directional stability modes will also be excited.

Again, the disturbance may be initiated by pilot control action, a change in power setting, airframe configuration changes, such as flap deployment, and by

external influences such as gusts and turbulence.a. The roll subsidence mode

The roll subsidence mode , or simply theroll mode , is a non-oscillatory lateralcharacteristic which is usually substantially decoupled from the spiral anddutch roll modes.

Since it is non-oscillatory it is described by a single real root of thecharacteristic polynomial, and it manifests itself as an exponential lagcharacteristic in rolling motion.


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b. The spiral mode

The spiral mode is also non-oscillatory and is determined by the other realroot in the characteristic polynomial. When excited, the mode dynamics areusually slow to develop and involve complex coupled motion in roll, yaw andsideslip. The dominant aeromechanical principles governing the modedynamics are shown in Fig. below. The mode characteristics are verydependent on the lateral static stability and on the directional static stability ofthe aeroplane

The mode is usually excited by a disturbance in sideslip which typicallyfollows a disturbance in roll causing a wing to drop. Assume that the aircraftis initially in trimmed wings level flight and that a disturbance causes a small positive roll angle to develop; left unchecked this results in a small positivesideslip velocityv as indicated at (a) in above Fig. The sideslip puts the fin atincidence which produces lift, and which in turn generates a yawing


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moment to turn the aircraft into the direction of the sideslip. The yawingmotion produces differential lift across the wing span which, in turn, results ina rolling moment causing the starboard wing to drop further therebyexacerbating the situation. This developing divergence is indicated at (b) and(c).

When dihedral effect is greater the spiral mode is stable, and henceconvergent, and when the fin effect is greater the spiral mode is unstable, andhence divergent.

> Can get a restoring torque from the wing dihedral

> Want a small tail to reduce the impact of the spiral mode

c. The dutch roll mode

The dutch roll mode is a classical damped oscillation in yaw, about theozaxisof the aircraft, which couples into roll and, to a lesser extent, into sideslip.Themotion described by the dutch roll mode is therefore a complexinteraction between all three lateraldirectional degrees of freedom. Itscharacteristics are described by the pair of complex roots in the characteristic polynomial. Fundamentally, the dutch roll mode is the lateraldirectionalequivalent of the longitudinal short period mode.Since the moments of inertia in pitch and yaw are of similar magnitude thefrequency of the dutch roll mode and the longitudinal short period mode areof similar order.

However, the fin is generally less effective than the tailplane as a damper andthe damping of the dutch roll mode is often inadequate. The dutch roll modeis so called since the motion of the aeroplane following its excitation is said toresemble the rhythmical flowing motion of a dutch skater on a frozen canal.


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> Damp the Dutch roll mode with a large tail fin.

7. THE LONGITUDINAL DYNAMIC STABILITY MODES [ D11-7(vi)]

a. The short period pitching oscillationb. The phugoid

Both longitudinal dynamic stability modes are excited whenever the aeroplane isdisturbed from its equilibrium trim state. A disturbance may be initiated by pilotcontrol inputs, a change in power setting, airframe configuration changes such as flapdeployment and by external atmospheric influences such as gusts and turbulence.

a. The short period pitching oscillation

The short period mode is typically a damped oscillation in pitch about theoyaxis. Whenever an aircraft is disturbed from its pitch equilibrium state themode is excited and manifests itself as a classical second order oscillation inwhich the principal variables are incidence(w), pitch rate q and pitchattitude .

Fig. A stable short period pitching oscillation.

b. The phugoid

The phugoid mode is most commonly a lightly damped low frequencyoscillation in speedu which couples into pitch attitude and height h. Asignificant feature of this mode is that the incidence(w) remainssubstantially constant during a disturbance.

The phugoid has a nearly constantangle of attack but varying pitch, caused bya repeated exchange ofairspeed and altitude.

However, it is clear that the phugoid appears, to a greater or lesser extent, in


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all of the longitudinal motion variables but the relative magnitudes of the phugoid components in incidencealpha (w) and in pitch rateq are very small.Typically, the undamped natural frequency of the phugoid is in the range 0.1rad/s to 1 rad/s and the damping ratio is very low.

Fig. The development of a stable phugoid.

Consider the development of classical phugoid motion following a smalldisturbance in speed as shown in above Fig. Initially the aeroplane is intrimmed level equilibrium flight with steady velocityV 0 such that the lift Land weight mg are equal. Let the aeroplane be disturbed at (a) such that thevelocity is reduced by a small amountu. Since the incidence remainssubstantially constant this results in a small reduction in lift such that theaeroplane is no longer in vertical equilibrium. It therefore starts to lose heightand since it is flying down hill it starts to accelerate as at (b). The speedcontinues to build up to a value in excess ofV 0 which is accompanied by a build up in lift which eventually exceeds the weight by a significant margin.The build up in speed and lift cause the aircraft to pitch up steadily until at (c)it starts to climb. Since it now has an excess of kinetic energy, inertia andmomentum effects cause it to fly up through the nominal trimmed heightdatum at (d) losing speed and lift as it goes as it is now flying up hill. As itdecelerates it pitches down steadily until at (e) its lift is significantly less thanthe weight and the accelerating descent starts again. Inertia and momentum

effects cause the aeroplane to continue flying down through the nominaltrimmed height datum (f) and as the speed and lift continue to build up so it pitches up steadily until at (g) it starts climbing again to commence the nextcycle of oscillation. As the motion progresses the effects of drag cause themotion variable maxima and minima at each peak to reduce gradually inmagnitude until the motion eventually damps out.

Thus the phugoid is classical damped harmonic motion resulting in theaircraft flying a gentle sinusoidal flight path about the nominal trimmedheight datum. As large inertia and momentum effects are involved the motionis necessarily relatively slow suchthat the angular accelerations, q and (w),are insignificantly small. Consequently, the natural frequency of the mode is

low and since drag is designed to be low so the damping is also low.Typically, once excited many cycles of the phugoid may be visible before iteventually damps out. Since the rate of loss of energy is low, a consequenceof low drag damping effects, the motion is often approximated by undampedharmonic motion in which potential and kinetic energy are exchanged as theaircraft flies the sinusoidal flight path. This in fact was the basis on whichLanchester (1908) first successfully analyzed the motion.

8. Most aft and most forward CG Limitations [ J12-7(iv)]


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The range within which the CG must always be located for safe operations is the CGenvelope that, fortransport aeroplanes, is defined as the area between the safe forwardlimit approximately 10% MAC andthe safe aft limit approximately 30% MAC. If theCG is positioned aft of the aft limit of the safe envelope the aeroplane will havemanoeuvre instability.

CG Envelope LimitationsThe safe limitations of the CG envelope are the forward and aft limits.

a. The Forward Limit

The forward limit of the envelope is determined by the amount of pitchcontrol available from the elevators; that is the degree of manoeuvrability thatan aeroplane of that type commands. For transport aeroplanes the forwardlimit is normally at approximately 10% of the MAC. With the CG in this position the aeroplane has the greatest longitudinal stability. In the landingconfiguration maximum elevator-up deflection is required when the CG is atthe forward limit and full flap is selected.

b. The Aft Limit

The aft limit, which for safety reasons on a transport aeroplane is alwaysforward of the neutral point, is confined by insufficient stick-force stabilityand/or excessive in-flight manoeuvrability. The minimum stick force per gfor the maximum permitted load factor, which is 2.5 for large transportaeroplanes, determines the aft limit of the CG envelope,. A CG position aft ofthis point would produce an unacceptably low value of manoeuvre stabilityand would make the aeroplane difficult to fly. For transport aeroplanes the aftlimit is normally located at approximately 30% of the MAC.

9. The Effect of CG at the Limits

CG at the Forward Limit

If the CG is located at the forward limit of the envelope it has the followingeffects:

a. greatest longitudinal static stability;

b. increased corrective download on the tailplane required;

c. increased corrective elevator trim causing increased trim drag;

d. decreased manoeuvrability to the minimum acceptable;

e. increased stick force required at rotation during take-off;f. increased stalling speed (but no effect on the stalling angle);

g. increased fuel flow;

h. decreased maximum range for a given fuel load;

i. decreased maximum endurance for a given fuel load.

CG at the Aft Limit


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If the CG is located at the aft limit of the CG envelope, it has the followingeffects:

a. decreased longitudinal static stability;

b. decreased corrective tailplane download required;

c. decreased corrective elevator trim resulting in less trim drag;

d. increased manoeuvrability to the maximum controllable;

e. decreased stalling speed;

f. decreased thrust required;

g. decreased fuel flow;

h. increased maximum range for a given fuel load;

i. increased maximum endurance for a given fuel load.

10. Asymmetric Flight and sideslip [ D11-7(iv)]

If a multi-engine airplane suffers engine failure when airborne, there are twoimmediate effects. The initial effect is the yawing that occurs due to the asymmetryof the thrust line. The second effect is roll, which occurs when the airplane continuesto yaw towards the failed engine, resulting in a decrease in lift from the retreatingwing and a yaw-induced roll towards the failed engine.

If at the time of a disturbance upsetting the equilibrium of an aeroplane it is in anasymmetric thrust condition its ability to recover is impaired because of the decreasedthrust available and the increased total drag experienced caused by the failed engine.This may cause one wing tip to stall and consequently induce the aeroplane to rolland yaw to such an extent that it enters a steep spiral descent or a spin.

In normal level flight the thrust available and total drag are symmetricallydisposed about the aeroplanes centerline. In the event of an engine failure a strongyawing moment towards the failed engine results from the loss of the thrust from thatengine. The aeroplane will sideslip away from the failed engine but if it has a largedegree of lateral static stability it will also roll towards the failed engine.

This situation is particularly dangerous in conditions of low forward speed and highthrust settings, such as during a take-off or go-around procedure because the low


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forward speed diminishes the authority of the controls. The yawing moment produced by the failed engine has to be counteracted by a large rudder deflection and therolling motion has to be counteracted by a large amount of aileron deflection.

Furthermore, the reduced thrust available increases the response time to anyincreased thrust demands.

11. LATERAL-DIRECTIONAL FLYING QUALITIES GLOSSARY

Roll-To-Yaw Ratio

Ratio of bank angle envelope to sideslip angle envelope during Dutch rolloscillation.

Adverse Yaw

Yawing moments created act so as to rotate the nose of the airplane oppositeto the direction of roll. The term "adverse" does not, in itself, denoteunfavorable flying qualities.

Proverse Yaw

Yawing moments generated act so as to rotate the nose of the airplane towardthe direction of roll. The term "proverse" does not necessarily indicatefavorable flying qualities.

Roll Mode Time Constant

Time required for the roll rate to reach 63.2 percent of the steady state rollrate following a step input of lateral control.


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Coordinated Turn

A turn in which a balance of sideward accelerations acting on objects in theairplane is attained; a "ballcentered" turn.

12. Roll-to-Yaw Ratio [ J10-7(v), D09-7(i), D08-7(v)]

The parameter, , is the ratio of the bank angle envelope to sideslip angleenvelopeduring the Dutch roll motion, or simply the roll-to-yaw ratio. Roll-to-yawratio has someinfluence on pilot technique during bank angle control tasks and rollingmaneuvers, andmay significantly influence the pilot's opinion of the maneuveringcapabilities of theairplane during these tasks. The degree of roll disturbance or thesensitivity of the airplanein roll to rudder inputs and lateral gusts is directly proportional to this parameter. Thefollowing generalizations may be madeconcerning the influence of various magnitudes ofroll-to-yaw ratios on overalllateral-directional flying qualities.

1. If the roll-to-yaw ratio is low - the Dutch roll motion is manifested more in yawingthan in rolling. If the ratio is very low, so that the motion approaches pure "snaking,"the response of the airplane to lateral gusts will be largely heading changes. The pilotmay feel compelled to control this gust response during maneuvers requiring preciseheading control, and the rudders will be then control utilized. With low roll-to-yawratios, the rolling moments generated by yaw rate and sideslip angle excursions will be small, therefore, the Dutch roll influence on rolling performance will probably besmall.

2. If roll-to-yaw ratio is medium - some rolling motion will be generated by yaw rateand sideslip angle excursions. If significant aileron yawing moments or yawingmoments due to roll rate exist, the pilot will probably be compelled to coordinateaileron inputs with rudder inputs to keep sideslip excursions small, minimizeoscillatory variations in roll rate, and realize maximum rolling performance from theairplane.

3. If the roll-to-yaw ratio is high - considerable rolling moments will be generated bysideslip and yaw rate excursions. Rolling performance and lateral handling qualitiesmay be seriously impaired unless the pilot utilizes rudder coordination effectivelyduring maneuvering. The airplane will be very responsive and sensitive in roll tolateral gusts and rudder inputs; bank angle response to turbulent air may be veryobjectionable, particularly during maneuvering which requires precise bank anglecontrol. As the roll-to-yaw ratio increases, the pilot will probably demand increasedDutch roll damping. This is due to the pilot usually being more sensitive to roll

response then sideslip response.13. Aerofoil Pressure Distribution [ D11-7(i) ]

The curvature or camber of the upper surface of a cambered aerofoil is greater thanthat of the lower surface. As a result, the negative pressure generated by theacceleration of the airstream over the upper surface is greater than that beneath thelower surface. The total reactive force is the result of the difference between the air pressure over the upper surface and beneath the lower surface assisted by the positive pressure at the lower leading edge of the aerofoil.


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Figure A. Pressure Disstribution

Lift is that component of the total reactive force (see Figure A) that is perpendicular to the flight path of the aeroplane. The magnitude of the pressuredistribution is directly proportional to the angle of attack of the aerofoil in the normalflight range. The point of lowest static pressure moves forward with increasing angleof attack as shown in Figure B. There are three different groups of angles of attackfor which the pressure distribution is described below and shown in Figure B. forlevel flight.


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Figure B. Movement of COP

a. Negative Angles of Attack

Because of the different curvatures of the upper and lower surfaces of the aerofoil

even when the angle ofattack is zero the aerofoil will still generate a small amount of total lift.To produceno lift at all a camberedaerofoil must have a negative angle of attack. At small negative angles of attack the pressure distributionsover both surfaces of the aerofoil are equal. Therefore, there is no reactive force andconsequently no lift.However, the total pressure vector for the upper surface is aft of the total pressurevector for the lowersurface and the AC is exactly midway between them. Thus, a nose-down pitchingmoment is createdabout the AC asa in Figure B.

b. Small Positive Angles of Attack

The negative pressure over the upper surface of the aerofoil is greater than thenegative pressure beneaththe lower surface. Thus, the total reactive force is upward at right angles to thechordline. It is this largeexcess of negative pressure above the upper surface of the wing, often referred to asthe suction, that isthe major factor in generating lift. Lift is the upward component of the total reactive


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force at right anglesto the airflow passing over the upper surface and induced drag is the component ofthe total reactiveforce that is in a rearward direction parallel to the airflow. Shown asc and d in FigureB.

c. Large Positive Angles of Attack

Beyond the stalling angle, approximately 15 angle of attack, the large area ofnegative pressure overthe upper surface of the aerofoil collapses due to the separation of the airflow fromthe surface of theaerofoil. The airflow changes from being a laminar, streamline flow to an unstable,turbulent airflow.The only lift remaining is due to the positive pressure on the lower surface of theaerofoil. At the stallingangle the lift and drag are both maximum. This is shown ase in Figure B.

15. Swept Wings [ J13-7(iv) Read stability notes to look for points on AOA, D11-7(iii) ]

The primary reason that the swept-wing design is used for most jet transportaeroplanes is to increase the value of the critical Mach number for that type ofaeroplane. It is the lowest speed of the free airflowthat when passing over some partof the aeroplane becomes supersonic. Usually, it is the upper surfaceof the wing, overwhich the airflow accelerates to a speed of Mach 1. Therefore, a swept wing delays the onset of the effects of compressibility and delaysthe airflow from becoming supersonic. It is best employed for aeroplanes that operatein the transonic regime of flight because the sweepback necessary to delay the drag

rise at extremely high Mach numbers or continuous flight in the supersonic regime istoo great to be practical.

The Effect of SweepbackThe critical Mach number of a wing of a given thickness/chord ratio and aspect ratiocan be increased by including a high-angled sweepback in the design. The angle ofsweepback of such wings is limited by the practicality of their construction. Althoughit is assumed that any sweepback is better than none, to be of any significant valuethe sweepback should be at least 30. Nevertheless, the inclusion of a relatively smallangle of sweepback in the design of any wing increases the critical Mach number.

The Advantages of Sweepback

The advantages of an aeroplane having swept-back wings are:a. Mcrit is increased in direct proportion to the sweep angle. b. Cd is decreased in direct proportion to the angle of sweep.c. Drag divergence is delayed to a higher speed.d. Static directional stability is improved.e. Static lateral stability is improved in a similar way to dihedral.f. For a given aspect ratio and wing loading, the aeroplane is less sensitive to guststhan a straight wing.

Increased M CRIT


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It is the airflow at right angles to the leading edge of a wing that determines themagnitude of the pressure distribution around the wing and thus the amount of liftdeveloped. Consequently, the critical Mach number for the wing is determined by

this component of the airflow speed over the upper surface of the wing. Thecomponent normal to the leading edge of the wing is equal to the true airspeed of thefree airflow multiplied by the cosine of the angle subtended between the direction ofthe free airflow and the normal to the wing leading edge.

An example of this feature is shown in Figure (a); if the free-flowing airflow speed isMach0.75 and the aeroplane has a straight leading edge then the acceleration over theupper surface of the wing would produce a speed of approximately Mach 0.80. If thesame airspeeds were experienced by an aeroplane with a swept wing with 30 ofsweep, see Figure (b), then the flow perpendicular to the leading edge of the wingwould be Mach 0.8 cos 30 = Mach 0.69. This red uction of the true airspeed

(M0.80 M0.69) is equivalent to 11% of the LSS.

In a standard atmosphere at 30 000 ft the temperature is 45C and the localspeed of sound is 589 kt.A reduction of 11% at this altitude is equal to 65 kt. Thismeans that an aeroplane with 30 of sweepcan fly 65 kt faster before the criticalMach number is reached than a straight-wing aeroplane having thesame wing areaand wing loading.

However, the swept-wing aeroplane will generate less lift than a straight-wingaeroplane having thesame wing area; this loss can be partially regained by increasingthe angle of attack. Theoretically, inthis example, Mcrit for the swept-wing aeroplaneshould be equal to the Mcrit of the straight-wingaeroplane multiplied by 1/cos 30. Inother words, theoretically Mcrit for the swept-wing aeroplaneis 15.5% higher thanthe Mcrit for the straight-winged aeroplane, but in practice the increaseactuallyachieved is closer to 8%.

In Figure (b) the total airflow over the upper surface of the wing can be divided intothe followingcomponents:

a. Perpendicular to the leading edge of the wing = Upper surface airflow speed ~cosine of theangle subtended between the longitudinal axis and the perpendicular tothe wing leading edge. Thiscomponent determines the value of the critical Machnumber.


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b. Parallel to the leading edge of the wing = the speed of movement of the airflowtowards the wingtip, i.e. the spanwise flow = Upper surface airflow speed ~ sine of(the angle subtended between thelongitudinal axis and the perpendicular to the wingleading edge). This component determines therate at which the boundary layer will build up at the wing tip.

Aerodynamic Effects

Further effects that a swept wing has on the performance of an aeroplane are:

a. Drag divergence Mach number and the peak drag rise Mach number increase because the speedcomponent affecting the pressure distribution is less than that of the free-streamvelocity. The peakdrag rise is delayed to approximately that speed normal to theleading edge that produces sonic flow.

b. Any change to Cl, Cd or Cm is decreased in magnitude due to the effect ofcompressibility.

The Disadvantages of Sweepback

Despite their advantages, swept wings have the following disadvantages:

a. Trailing-edge controls, such as flaps and wing-tip ailerons, are less effective because they are not atright angles to the airflow. Some flap systems only produce anincrease of lift of 50% of that whichwould have been produced by the same flap on astraight-winged aeroplane.

b. A swept wing of the same wing area and aspect ratio as that of a straight-wingedaeroplane has

a greater wing span, which increases its mass. This causes greater bending and stresstowards the wing tip. It is also subject to the twisting effect of the wing in high-speedflight that diminishes the effectiveness of wing-tip ailerons.

c. When combined with taper there is a strong tendency for the wing to tip stall first.This is because, although taper produces a strong local lift coefficient towards thewing tip similar to sweepback, there is a strong spanwise flow of the boundary layertowards the wing tip, particularly at high angles of attack, that results in a low-energy pool at the wing tip which easily separates from the wing surface.

16. Trailing-Edge Flaps

An alternative to increasing the angle of attack to increase lift is to lower trailing-edge flaps provided thespeed is at or below the maximum speed for lowering flap(Vfo). This effectively increases the camberof the wing, the angle of attack and the


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coefficient of lift. However, the thrust may have to be increasedto overcome theincreased drag, despite the fact that when deployed they decrease the magnitude ofthewing-tip vortices. Not only does the extension of trailing-edge flaps decrease thecritical angle of attackit also increases the Clmax, increases the total lift generated,increases the total drag, unfavourably affectsthe lift/drag ratio anddecreases thestalling speed no matter what the altitude or mass of the aeroplane .

Unlike slats, trailing-edge flaps increase lift at all angles of attack up to the stall.Thus, if the angle ofattack remains constant during flap extension the aeroplane will begin to climb. All trailing-edge flapswhen lowered, increase the acceleration of theairflow over the upper surface of the wing, which reducesthe pressure above the wingand increases the upwash over the leading edge. Together these influencesgenerate anincreased nose-down pitching moment as a result of the altered pressure distributionaroundthe flaps and the aft movement of the wing CP.

However, when deployed trailing-edge flaps also increase the downwash overthe tailplane, whichcauses an opposing nose-up pitching moment. The amount bywhich the pitching moment changesbecause of this phenomenon depends on the sizeand position of the tailplane. The resultant change to thepitching moment isdetermined by the relative sizes of the two opposing influences, the changed pressuredistribution and the downwash.The dominant feature will establish whattrim change is required whenflaps are lowered usually it results in a pitch-downmoment.

In straight and level flight if the IAS and angle of attack are maintainedwhenthe flap is extendedthen the CP will move aft and the Cl will increase. Tomaintain a constant IAS whilst the flaps arebeing retracted in straight and level flightit is necessary to increase the angle of attack. If the same angleof attack is maintainedas the flaps are retracted the aeroplane will sink or when they are extendedtheaeroplane will climb.

As the flap angle is increased the critical angle of attack decreases and the Clmaxincreases. See Figure and Table. Consequently, the minimum glide angle is increasedand the resulting maximumglide distance is decreased. Typically, a flap extensionfrom 0 to 20 will produce a greater increase tothe total lift and Cl, than an increased


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18. The Spin

When a wing drop occur during a stall it may develop into a spin; this is because theangle of attack of the downgoing wing is increased to an angle well above that of thestall as a result of its downward vertical velocity. The upgoing wing reacts in just theopposite manner and may even be unstalled due to its upgoing vertical velocity.

The downgoing wing develops very little or no lift and will continue to drop.Any attempt to correct the attitude by using aileron will worsen the situation becauseit will increase the angle of attack of the outboard part of the downgoing wing further.Simultaneously as the aeroplane is rolling it is also yawing due to the increased dragof the downgoing wing, this is known as autorotation or the incipient spin.


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The aim of the recovery from a spin is to decrease the rolling moment in the directionof the spin and/or increase the antispin yawing moment. The sequence of controlmovements for recovery actions is:

a. Thrust/power to idle. b. Full opposite rudder.c. Control column fully forward until the spin stops.d. Maintain ailerons in the neutral position.e. Ease the control column back to recover from the ensuing dive.

Once the spin slows down and comes to a stop, increase throttle and slowly pull outto level flight when the aircraft is back under control, if you over correct or pull outto soon you may find your aircraft will enter into another spin more abruptly. This isthe reason to be gentle and cautious on the first attempt. Inverted spin recovery can be a little more challenging but is possible. On the flat spin / horizontal spin you willfind the most challenging and sometimes if not most almost impossible to recoverfrom.

19. The Rudder Lock [ D10-7(i) ]

The control of an aeroplane about its normal or yaw axis is accomplished by usingthe rudder. The rudderis a hinged control mounted vertically on a post at the rear ofthe aeroplane known as the fin or verticalstabiliser. Usually, there is a small filletmounted at the forward base of the fin; this is the dorsal fin whichis fitted to preventthe force acting on a fully deflected rudder in a sideslip from suddenly reversing;thisundesirable event is known as rudder lock.

Refer: Houghton and Carruther for further readings.

20. Difference Between Static Stability and Dynamic StabilityGenerally the stability of an aircraft is defined as the aircrafts ability to sustain aspecific, prescribed flight condition. The concept of stability is closely related to theequilibrium of the aircraft. If the net forces and moments exerted on the aircraft iszero, the aircraft is in equilibrium, in that flight condition; i.e. the lift equals theweight, the thrust equals the drag, and no moment of force acting on the aircraft.

What is Static Stability?

When an aircraft undergoes some turbulence (or some form of static imbalance)when in equilibrium flight, the nose tilts slightly up or down (an increase or decrease

in the angle of attack), or there will be a slight change in flight attitude. There areadditional forces acting on the aircraft, and it is no longer in the equilibriumcondition.


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If the aircraft continues to increase the orientation after disturbance, the aircraft issaid to be statically unstable . If there are no further changes in flight attitude and ifthe aircraft retains the position, which means there are no net forces or momentsacting on the aircraft in the new orientation too, then the aircraft is said to bestatically neutral . If forces are generated on the aircraft in a way such that forcescausing the disturbance are countered, and the aircraft attains its original position,then the aircraft is said to be staticallystable.

In aircrafts, three types of dimensional stabilities are considered. Those are thelongitudinal stability that concerns the pitching motion, the directional stability thatconcerns the yawing motion, and the lateral stability that concerns the rolling motion.

Often the longitudinal stability and directional stability are closely interrelated.What is Dynamic Stability?

If an aircraft is statically stable, it may undergo three types of oscillatory motionduring flight. When imbalance occurs the airplane attempts to retain its position, andit reaches the equilibrium position through a series of decaying oscillations, and theaircraft is said to bedynamically stable. If the aircraft continues the oscillatorymotion without decay in the magnitude, then the aircraft is said to be ondynamicallyneutral. If the magnitude oscillatory motion increases and the aircraft orientationstart to change rapidly, then the aircraft is said to bedynamically unstable .


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An aircraft that is both statically and dynamically stable can be flown hands off,unless the pilot desires to change the equilibrium condition of the aircraft.

What is the difference between Dynamic and Static Stability (of Aircrafts)?

Static stability of an aircraft describes the tendency of and aircraft to retain itsoriginal position when subjected to unbalanced forces or moments acting on theaircraft.

Dynamic stability describes the form of motion an aircraft in static stabilityundergoes when it tries to return to its original position.

J11- Q7a What is understood by the term "Static longitudinal stability of anairplane. Illustrate it with sketches and plots. And hence explain the terms(d Cm /d CL)fixed and (d Cm /d CL)free

Answer:

LONGITUDINAL STATIC STABILITY.

Let us consider the two airplanes and their respective pitching moment curves shownin Fig. A.


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Fig. A

In Fig. A, both airplanes are flying at the trim point denoted by B, i.e.CmCg = O.Suppose the airplanes suddenly encounter an upward gust such thatthe angle of attackis increased to point C. At the angle of attack denoted byC, airplane 1 develops anegative (nose-down) pitching moment which tends to rotate the airplane backtowards it equilibrium point. However, for the samedisturbance, airplane 2 develops a positive (nose-up) pitching moment whichtends to rotate the aircraft away from theequilibrium point. If we were toencounter a disturbance which reduced the angle ofattack, e.g to point A, wewould find that the airplane 1 develops a nose-up momentwhich rotates theaircraft back toward the equilibrium point. On the other hand,airplane 2 isfound to develop a nose-down moment which rotates the aircraft awayfromthe equilibrium point. On the basis of this simple analysis, we can concludethatto have static longitudinal stability the aircraft pitching moment curve must have anegative slope. i.e.

through the equilibrium point.

Fig. B. Pitching moment coefficient versus angle of attack for a stable airplane.

Another point that we must make is illustrated in Fig. B. Here we see two pitchingmoment curves which both satisfy the condition for static stability. However, onlycurve 1 can be trimmed at a positive angle of attack.

Therefore, in addition to having static stability, we must also have a positive intercept,i.e. Cmo> 0 in order to trim at positive angles of attack. Although we developed the


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criterion for static stability from theCm versus a curve, we could have just as easilyaccomplished the same result by working with aCm versus CL curve. In this case,the requirement for static stability would be as follows:

The two conditions are related by the following expression:

The equation for static longitudinal stability, stick-fix, propsoff is

The equation for static longitudinal stability, stick-free, propsoff is

The effect of freeing the elevator enters the tail term as the multiplying factor

For an airplane equipped with an elevator having no change in hinge moment withangle of attack(C halpha = 0), this term becomes unity, and the stick-fixed and stick-freestabilities are equal. However, if the elevator has a large floating tendency (the ratioC halpha /C holarge and positive), the stability contribution of thehorizontal tail can bereduced materially.

FIGURE. Typical reduction of stability due to freeing elevator.


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D10-Q5a What are different ways to reduce take-off runs for military airplanes.Elaborate with sketches and plots.

J08- 7(iv) Use of additional disposable rocket motor at take-off reduces take offrun of the airplane.

Answer: Add points given in class notes about take off distance and include theformula

Assisted take-off is any system for helping aircraft into the air (as opposed to strictlyunder its own power). The reason it might be needed is due to the aircraft's weightexceeding the normal maximum take-off weight, insufficient power, or the availablerunway length may be insufficient, or a combination of all three factors. Assistedtake-off is also required for gliders, which do not have an engine and are unable totake-off by themselves.

Different ways to reduce take-off runs for military airplanes

1Catapults (CATO)

2JATO and RATO

Catapults (CATO)

A well-known type of assisted take-off is that using the aircraft catapult. In modernsystems fitted on aircraft carriers, a piston, known as ashuttle , is propelled down along cylinder under steam pressure. The aircraft is attached to the shuttle using a tow bar or launch bar mounted to the nose landing gear (an older system used a steelcable called a catapult bridle; the forward ramps on older carrier bows were used tocatch these cables), and is flung off the deck at about 15 knots above minimum flyingspeed, achieved by the catapult in a 4 second run.

JATO and RATO

JATO stands for 'Jet-assisted take-off' (and the similar RATO for 'Rocket-assistedtake-off'). In the JATO and RATO systems, additional engines are mounted on theairframe which are used only during take-off. After that the engines are usually jettisoned, or else they just add to the parasitic weight and drag of the aircraft.However some aircraft such as the Avro Shackleton MR.3 Phase 2, had permanentlyattached JATO engines. The four J-47 turbojet engines on the B-36 were not

considered JATO systems; they were an integral part of the aircraft's powerplants,and were used during takeoff, climb, and cruise at altitude.


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What is drag?

Various Kinds of Drag

Induced or VortexDrag or Drag dueto Lift

The result of the tip vortices downstream of a finite aspectratio wing.

Parasite Drag The drag not directly associated with the production of lift.

Skin Friction DragThe result of viscous shearing forces over the wetted surfacearea of a body.

Form or PressureDrag

The integrated effect of the static pressure acting normal tothe surface of a bodyresolved in the direction of the flow.

Interference Drag

The increment in drag resulting from bringing 2 bodies in theproximity of each other. For example, the total drag of thewing - fuselage combination is usually greater than the sumof the wing drag and the fuselage drag independent of eachother.

Trim Drag

The increment in drag resulting from the aerodynamic forcesrequired to trim the plane about its center of gravity. Itusually takes the form of added induced and form drag onthe horizontal tail.

Profile Drag The sum of the skin friction + the form drag of a 2-D airfoil

Cooling Drag Results from the momentum loss of the air that passesthrough the engine for the purposes of cooling the engine, oil,and accessories.

Base Drag The specific contribution to the pressure drag attributed tothe blunt after - end of a body.

Wave DragPresent only in supersonic flow, it is a pressure drag resultingfrom the difference of static pressure forces on either side ofa shock wave forming on the surface of a body.

Documents

Airplane stability and control notes GATE Aerospace Engineering