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 force gradient. 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 change the speed of the airplane. To provide the airplane with speed stability, the stick force gradient must be negative, i.e.

The need for a negative stick force gradient can be appreciated by examining above Figure. If the airplane slows down, a positive stick force occurs which rotates the nose of the airplane downwards, which causes the airplane to increase its speed back towards 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 the airplane to slow down. The negative stick force gradient provides the pilot and airplane with speed stability. The larger the gradient, the more resistant the airplane will be to disturbances in the flight speed. If an airplane did not have speed stability the pilot would have to continuously monitor and control the airplane's speed. This would 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 its wingtips. As discussed in a previous question on the creation of lift, a wing generates lift 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 above the wing. This motion creates what is called a wingtip vortex. As the wing moves forward, this vortex remains, and therefore trails behind the wing. For this reason, the vortex is usually referred to as a trailing vortex. One trailing vortex is created off each wingtip, and they spin in opposite directions as illustrated below. While trailing vortices are the price one must pay for generating lift, their primary effect is to deflect the flow behind the wing downward. This induced component of velocity 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 this form 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 a lifting surface

Regions of upwash and downwash created by trailing vortices While trailing vortices are the price one must pay for generating lift, their primary effect is to deflect the flow behind the wing downward. This induced component of velocity 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 this form 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 to a 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 Chαt and Chδe are called aerodynamic balancing. The methods for aerodynamic balancing are: 1. set back hinge, 2. horn balance and 3. internal balance 4. 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 of the hinge line increases and from the pressure distribution in Fig.3.3 it is evident that Chαt and Chδe would decrease. The over hang is characterized by cb/cf . Figure 6.6 also shows typical experimental data on variations of Chα and Chδ with cb/cf. It may be added that the changes in Chα and Chδ also depend on (a) gap between nose of the control surface and the main surface, (b) nose shape and (c) trailing edge angle (Fig.6.7a and b)

Effect of set back hinge on Chα and Chδ 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, is ahead of the hinge line (Fig.a and b). There are two types of horn balances – shielded and unshielded (Fig a). The following parameter is used to describe the effect of horn balance on Chα and Chδ. 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 shows the changes ΔChα and ΔChδ due to horn as compared to a control surface without horn. Horn balance is some times used on horizontal and vertical tails of low speed airplanes (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 the gap 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 pressures respectively at a chosen chord wise position (upper part of Fig.6.9). A seal at the leading edge of the projecting portion ensures that the pressures on the two sides of the projection do not equalize. Figure 6.9 also shows the changes ΔChα and ΔChδ due to internal seal balance. This method of aerodynamic balancing is complex but is reliable. It is used on large airplanes to reduce Chα and Chδ.

Frise aileron [ D10-7(ii)] The frise aileron is shown in figure below The leading edge of the aileron has a specific shape. The downward deflected aileron has negative Chδ and the upward deflected aileron has positive Chδ. This reduces the net control force. Further, owing to the special shape of the leading edge, the upward deflected aileron projects into the flow field and increases the drag. This reduces adverse yaw.

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4. FLIGHT MEASUREMENT OF XNP ( N0 ) [ J13-7(iii) ] The equation developed for estimating the elevator angle to trim the airplane can be used to determine the stick fixed neutral point from flight test data. Suppose we conducted a flight test experiment in which we measured the elevator angle of trim at various air speeds for different positions of the center of gravity. If we did this, we could develop curves as shown in Fig. A.

FIG. A

FIG. B Now, differentiating above equation with respect to CLtrim yields

Note that when Cmα= 0 (i.e. the center of gravity is at the neutral point) Above equation equal to zero. Therefore, if we measure the slopes of the curves in Fig. B and 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 of gravity position that makes dδtrim/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 an aircraft 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 increase its yaw after only a slight yaw has occurred. This continues until the aircraft turns broadside to the flight path or until it breaks up from 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 positive sideslip 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 descending spiral. To correct this condition, the wing is raised with the lateral control surfaces and the spiral 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 sideslip is introduced into the relative wind in the direction of the rolling motion. Strong lateral stability begins to restore the aircraft to level flight. At the same time, somewhat weaker directional stability attempts to correct the sideslip by aligning the aircraft with the perceived relative wind. Since directional stability is weaker than lateral stability for the particular aircraft, the restoring yaw motion lags significantly behind the restoring roll motion. As such, the aircraft passes through level flight as the yawing motion is continuing in the direction of the original roll. At that point, the sideslip 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 much dihedral 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 the roll mode, is a non-oscillatory lateral characteristic which is usually substantially decoupled from the spiral and dutch roll modes. Since it is non-oscillatory it is described by a single real root of the characteristic polynomial, and it manifests itself as an exponential lag characteristic in rolling motion. 8

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b. The spiral mode

The spiral mode is also non-oscillatory and is determined by the other real root in the characteristic polynomial. When excited, the mode dynamics are usually slow to develop and involve complex coupled motion in roll, yaw and sideslip. The dominant aeromechanical principles governing the mode dynamics are shown in Fig. below. The mode characteristics are very dependent on the lateral static stability and on the directional static stability of the aeroplane

The mode is usually excited by a disturbance in sideslip which typically follows a disturbance in roll causing a wing to drop. Assume that the aircraft is initially in trimmed wings level flight and that a disturbance causes a small positive roll angle φ to develop; left unchecked this results in a small positive sideslip velocity v as indicated at (a) in above Fig. The sideslip puts the fin at incidence β 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 yawing motion produces differential lift across the wing span which, in turn, results in a rolling moment causing the starboard wing to drop further thereby exacerbating the situation. This developing divergence is indicated at (b) and (c). When dihedral effect is greater the spiral mode is stable, and hence convergent, and when the fin effect is greater the spiral mode is unstable, and hence 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 the ozaxis of the aircraft, which couples into roll and, to a lesser extent, into sideslip. Themotion described by the dutch roll mode is therefore a complex interaction between all three lateral–directional degrees of freedom. Its characteristics are described by the pair of complex roots in the characteristic polynomial. Fundamentally, the dutch roll mode is the lateral–directional equivalent of the longitudinal short period mode. Since the moments of inertia in pitch and yaw are of similar magnitude the frequency of the dutch roll mode and the longitudinal short period mode are of similar order. However, the fin is generally less effective than the tailplane as a damper and the damping of the dutch roll mode is often inadequate. The dutch roll mode is so called since the motion of the aeroplane following its excitation is said to resemble 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 oscillation b. The phugoid Both longitudinal dynamic stability modes are excited whenever the aeroplane is disturbed from its equilibrium trim state. A disturbance may be initiated by pilot control inputs, a change in power setting, airframe configuration changes such as flap deployment 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 the oyaxis. Whenever an aircraft is disturbed from its pitch equilibrium state the mode is excited and manifests itself as a classical second order oscillation in which the principal variables are incidence α(w), pitch rate q and pitch attitude θ.

Fig. A stable short period pitching oscillation. b. The phugoid

The phugoid mode is most commonly a lightly damped low frequency oscillation in speed u which couples into pitch attitude θ and height h. A significant feature of this mode is that the incidence α(w) remains substantially constant during a disturbance. The phugoid has a nearly constant angle of attack but varying pitch, caused by a repeated exchange of airspeed 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 incidence alpha(w) and in pitch rate q are very small. Typically, the undamped natural frequency of the phugoid is in the range 0.1 rad/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 small disturbance in speed as shown in above Fig. Initially the aeroplane is in trimmed level equilibrium flight with steady velocity V0 such that the lift L and weight mg are equal. Let the aeroplane be disturbed at (a) such that the velocity is reduced by a small amount u. Since the incidence remains substantially constant this results in a small reduction in lift such that the aeroplane is no longer in vertical equilibrium. It therefore starts to lose height and since it is flying “down hill’’ it starts to accelerate as at (b). The speed continues to build up to a value in excess of V0 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 and momentum effects cause it to fly up through the nominal trimmed height datum at (d) losing speed and lift as it goes as it is now flying “up hill’’. As it decelerates it pitches down steadily until at (e) its lift is significantly less than the weight and the accelerating descent starts again. Inertia and momentum effects cause the aeroplane to continue flying down through the nominal trimmed 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 next cycle of oscillation. As the motion progresses the effects of drag cause the motion variable maxima and minima at each peak to reduce gradually in magnitude until the motion eventually damps out. Thus the phugoid is classical damped harmonic motion resulting in the aircraft flying a gentle sinusoidal flight path about the nominal trimmed height datum. As large inertia and momentum effects are involved the motion is necessarily relatively slow such that the angular accelerations, ˙q and ˙α(˙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 it eventually damps out. Since the rate of loss of energy is low, a consequence of low drag damping effects, the motion is often approximated by undamped harmonic motion in which potential and kinetic energy are exchanged as the aircraft flies the sinusoidal flight path. This in fact was the basis on which Lanchester (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 CG envelope that, fortransport aeroplanes, is defined as the area between the safe forward limit approximately 10% MAC andthe safe aft limit approximately 30% MAC. If the CG is positioned aft of the aft limit of the safe envelope the aeroplane will have manoeuvre instability. CG Envelope Limitations The 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 pitch control available from the elevators; that is the degree of manoeuvrability that an aeroplane of that type commands. For transport aeroplanes the forward limit is normally at approximately 10% of the MAC. With the CG in this position the aeroplane has the greatest longitudinal stability. In the landing configuration maximum elevator-up deflection is required when the CG is at the forward limit and full flap is selected. b. The Aft Limit The aft limit, which for safety reasons on a transport aeroplane is always forward of the neutral point, is confined by insufficient stick-force stability and/or excessive in-flight manoeuvrability. The minimum stick force per ‘g’ for the maximum permitted load factor, which is 2.5 for large transport aeroplanes, determines the aft limit of the CG envelope,. A CG position aft of this point would produce an unacceptably low value of manoeuvre stability and would make the aeroplane difficult to fly. For transport aeroplanes the aft limit 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 following effects: 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 GATE PATHSHALA Educational Services Llp. #153, II-floor, Karuneegar st., Adambakkam, Chennai-88 website : www.gatepathshala.com, contact: 044-42647128 0r +91-9962996817

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If the CG is located at the aft limit of the CG envelope, it has the following effects: 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 two immediate effects. The initial effect is the yawing that occurs due to the asymmetry of the thrust line. The second effect is roll, which occurs when the airplane continues to yaw towards the failed engine, resulting in a decrease in lift from the ‘retreating’ wing 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 an asymmetric thrust condition its ability to recover is impaired because of the decreased thrust 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 roll and 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 symmetrically disposed about the aeroplane’s centerline. In the event of an engine failure a strong yawing moment towards the failed engine results from the loss of the thrust from that engine. The aeroplane will sideslip away from the failed engine but if it has a large degree of lateral static stability it will also roll towards the failed engine. This situation is particularly dangerous in conditions of low forward speed and high thrust 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 the rolling motion has to be counteracted by a large amount of aileron deflection. Furthermore, the reduced thrust available increases the response time to any increased thrust demands. 11. LATERAL-DIRECTIONAL FLYING QUALITIES – GLOSSARY Roll-To-Yaw Ratio Ratio of bank angle envelope to sideslip angle envelope during Dutch roll oscillation. Adverse Yaw Yawing moments created act so as to rotate the nose of the airplane opposite to the direction of roll. The term "adverse" does not, in itself, denote unfavorable flying qualities. Proverse Yaw Yawing moments generated act so as to rotate the nose of the airplane toward the direction of roll. The term "proverse" does not necessarily indicate favorable flying qualities. Roll Mode Time Constant Time required for the roll rate to reach 63.2 percent of the steady state roll rate 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 the airplane 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 angle envelopeduring the Dutch roll motion, or simply the roll-to-yaw ratio. Roll-to-yaw ratio has someinfluence on pilot technique during bank angle control tasks and rolling maneuvers, andmay significantly influence the pilot's opinion of the maneuvering capabilities of theairplane during these tasks. The degree of roll disturbance or the sensitivity of the airplanein roll to rudder inputs and lateral gusts is directly proportional to this parameter. Thefollowing generalizations may be made concerning the influence of various magnitudes ofroll-to-yaw ratios on overall lateral-directional flying qualities. 1. If the roll-to-yaw ratio is low - the Dutch roll motion is manifested more in yawing than 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 pilot may feel compelled to control this gust response during maneuvers requiring precise heading control, and the rudders will be then control utilized. With low roll-to-yaw ratios, the rolling moments generated by yaw rate and sideslip angle excursions will be small, therefore, the Dutch roll influence on rolling performance will probably be small. 2.

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

3. If the roll-to-yaw ratio is high - considerable rolling moments will be generated by sideslip and yaw rate excursions. Rolling performance and lateral handling qualities may be seriously impaired unless the pilot utilizes rudder coordination effectively during maneuvering. The airplane will be very responsive and sensitive in roll to lateral gusts and rudder inputs; bank angle response to turbulent air may be very objectionable, particularly during maneuvering which requires precise bank angle control. As the roll-to-yaw ratio increases, the pilot will probably demand increased Dutch 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 than that of the lower surface. As a result, the negative pressure generated by the acceleration of the airstream over the upper surface is greater than that beneath the lower 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 pressure distribution is directly proportional to the angle of attack of the aerofoil in the normal flight range. The point of lowest static pressure moves forward with increasing angle of attack as shown in Figure B. There are three different groups of angles of attack for which the pressure distribution is described below and shown in Figure B. for level 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 of attack is zero the aerofoil will still generate a small amount of total lift. To produce no lift at all a cambered aerofoil must have a negative angle of attack. At small negative angles of attack the pressure distributions over both surfaces of the aerofoil are equal. Therefore, there is no reactive force and consequently no lift. However, the total pressure vector for the upper surface is aft of the total pressure vector for the lower surface and the AC is exactly midway between them. Thus, a nose-down pitching moment is created about the AC as a in Figure B. b. Small Positive Angles of Attack The negative pressure over the upper surface of the aerofoil is greater than the negative pressure beneath the lower surface. Thus, the total reactive force is upward at right angles to the chordline. It is this large excess of negative pressure above the upper surface of the wing, often referred to as the suction, that is the major factor in generating lift. Lift is the upward component of the total reactive

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force at right angles to the airflow passing over the upper surface and induced drag is the component of the total reactive force that is in a rearward direction parallel to the airflow. Shown as c and d in Figure B. c. Large Positive Angles of Attack Beyond the stalling angle, approximately 15◦ angle of attack, the large area of negative pressure over the upper surface of the aerofoil collapses due to the separation of the airflow from the surface of the aerofoil. 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 the aerofoil. At the stalling angle the lift and drag are both maximum. This is shown as e in Figure B.

15. Swept Wings [ J13-7(iv) Read stability notes to look for points on AOA, D117(iii) ] The primary reason that the swept-wing design is used for most jet transport aeroplanes is to increase the value of the critical Mach number for that type of aeroplane. It is the lowest speed of the free airflowthat when passing over some part of the aeroplane becomes supersonic. Usually, it is the upper surfaceof the wing, over which the airflow accelerates to a speed of Mach 1. Therefore, a swept wing delays the onset of the effects of compressibility and delays the airflow from becoming supersonic. It is best employed for aeroplanes that operate in 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 is too great to be practical. The Effect of Sweepback The critical Mach number of a wing of a given thickness/chord ratio and aspect ratio can be increased by including a high-angled sweepback in the design. The angle of sweepback of such wings is limited by the practicality of their construction. Although it is assumed that any sweepback is better than none, to be of any significant value the sweepback should be at least 30◦. Nevertheless, the inclusion of a relatively small angle 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 gusts than a straight wing. Increased MCRIT GATE PATHSHALA Educational Services Llp. #153, II-floor, Karuneegar st., Adambakkam, Chennai-88 website : www.gatepathshala.com, contact: 044-42647128 0r +91-9962996817

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It is the airflow at right angles to the leading edge of a wing that determines the magnitude of the pressure distribution around the wing and thus the amount of lift developed. Consequently, the critical Mach number for the wing is determined by this component of the airflow speed over the upper surface of the wing. The component normal to the leading edge of the wing is equal to the true airspeed of the free airflow multiplied by the cosine of the angle subtended between the direction of the 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 is Mach 0.75 and the aeroplane has a straight leading edge then the acceleration over the upper surface of the wing would produce a speed of approximately Mach 0.80. If the same airspeeds were experienced by an aeroplane with a swept wing with 30◦ of sweep, see Figure (b), then the flow perpendicular to the leading edge of the wing would be Mach 0.8 cos 30◦ = Mach 0.69. This reduction 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 –45 ◦C and the local speed of sound is 589 kt.A reduction of 11% at this altitude is equal to 65 kt. This means that an aeroplane with 30◦ of sweepcan fly 65 kt faster before the critical Mach number is reached than a straight-wing aeroplane having thesame wing area and wing loading. However, the swept-wing aeroplane will generate less lift than a straight-wing aeroplane having thesame wing area; this loss can be partially regained by increasing the angle of attack. Theoretically, inthis example, Mcrit for the swept-wing aeroplane should be equal to the Mcrit of the straight-wingaeroplane multiplied by 1/cos 30◦. In other words, theoretically Mcrit for the swept-wing aeroplaneis 15.5% higher than the Mcrit for the straight-winged aeroplane, but in practice the increase actuallyachieved is closer to 8%. In Figure (b) the total airflow over the upper surface of the wing can be divided into the followingcomponents: a. Perpendicular to the leading edge of the wing = Upper surface airflow speed Å~ cosine of theangle subtended between the longitudinal axis and the perpendicular to the wing leading edge. Thiscomponent determines the value of the critical Mach number.

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b. Parallel to the leading edge of the wing = the speed of movement of the airflow towards the wingtip, i.e. the spanwise flow = Upper surface airflow speed Å~ sine of (the angle subtended between thelongitudinal axis and the perpendicular to the wing leading 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 speed component affecting the pressure distribution is less than that of the free-stream velocity. The peakdrag rise is delayed to approximately that speed normal to the leading edge that produces sonic flow. b. Any change to Cl, Cd or Cm is decreased in magnitude due to the effect of compressibility. 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 an increase of lift of 50% of that whichwould have been produced by the same flap on a straight-winged aeroplane. b. A swept wing of the same wing area and aspect ratio as that of a straight-winged aeroplane has a greater wing span, which increases its mass. This causes greater bending and stress towards the wing tip. It is also subject to the twisting effect of the wing in high-speed flight 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 the wing tip similar to sweepback, there is a strong spanwise flow of the boundary layer towards 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 trailingedge 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 the increased drag, despite the fact that when deployed they decrease the magnitude of thewing-tip vortices. Not only does the extension of trailing-edge flaps decrease the critical angle of attackit also increases the Clmax, increases the total lift generated, increases the total drag, unfavourably affectsthe lift/drag ratio and decreases the stalling 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 the airflow over the upper surface of the wing, which reducesthe pressure above the wing and increases the upwash over the leading edge. Together these influencesgenerate an increased nose-down pitching moment as a result of the altered pressure distribution aroundthe flaps and the aft movement of the wing CP. However, when deployed trailing-edge flaps also increase the downwash over the tailplane, whichcauses an opposing nose-up pitching moment. The amount by which the pitching moment changesbecause of this phenomenon depends on the size and position of the tailplane. The resultant change to thepitching moment is determined by the relative sizes of the two opposing influences, the changed pressuredistribution and the downwash. The dominant feature will establish what trim change is required whenflaps are lowered usually it results in a pitch-down moment. In straight and level flight if the IAS and angle of attack are maintained when the flap is extendedthen the CP will move aft and the Cl will increase. To maintain a constant IAS whilst the flaps arebeing retracted in straight and level flight it is necessary to increase the angle of attack. If the same angleof attack is maintained as the flaps are retracted the aeroplane will sink or when they are extended theaeroplane will climb.

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

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extension from 20◦ to 30◦. The lift/drag ratio is most adverselyaffected by the change from a 30◦ flap extension to a 40◦ flap extension because the increase to the totallift is far less than the increase to the total drag.

17. Wing Loading The wing loading of an aeroplane determines the magnitude of unstick speed (Vus) during take-off,touchdown speed during landing and the stalling speed. It is defined as the aeroplane mass divided bythe wing area and is specified in Newtons per square metre (N/m2). A high wing loading is the result ofa heavy mass or small wing, and is undesirable because it has the following effects: a. increased take-off and landing speeds; b. longer take-off ground run and take-off distance; c. longer landing ground run and landing distance; d. increased stalling speed; e. increased glide angle; f. decreased Clmax; g. decreased turbulence sensitivity. The value of the wing loading can be determined from the total lift formula when it has beentransposed: Wing Loading = (Coefficient of Lift) times(Dynamic Pressure) From the formula it can be seen that if the coefficient of lift can be increased then the speed does notneed to be as high for the same wing loading. This is of great benefit during take-off and landing.

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18. The Spin

When a wing drop occur during a stall it may develop into a spin; this is because the angle of attack of the downgoing wing is increased to an angle well above that of the stall as a result of its downward vertical velocity. The upgoing wing reacts in just the opposite 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 because it 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 drag of 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 direction of the spin and/or increase the antispin yawing moment. The sequence of control movements 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 out to level flight when the aircraft is back under control, if you over correct or pull out to soon you may find your aircraft will enter into another spin more abruptly. This is the 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 will find the most challenging and sometimes if not most almost impossible to recover from. 19. The Rudder Lock [ D10-7(i) ] The control of an aeroplane about its normal or yaw axis is accomplished by using the rudder. The rudderis a hinged control mounted vertically on a post at the rear of the aeroplane known as the fin or verticalstabiliser. Usually, there is a small fillet mounted at the forward base of the fin; this is the dorsal fin whichis fitted to prevent the 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 Stability Generally the stability of an aircraft is defined as the aircraft’s ability to sustain a specific, prescribed flight condition. The concept of stability is closely related to the equilibrium of the aircraft. If the net forces and moments exerted on the aircraft is zero, the aircraft is in equilibrium, in that flight condition; i.e. the lift equals the weight, 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 are additional forces acting on the aircraft, and it is no longer in the equilibrium condition.

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If the aircraft continues to increase the orientation after disturbance, the aircraft is said to be statically unstable. If there are no further changes in flight attitude and if the aircraft retains the position, which means there are no net forces or moments acting on the aircraft in the new orientation too, then the aircraft is said to be statically neutral. If forces are generated on the aircraft in a way such that forces causing the disturbance are countered, and the aircraft attains its original position, then the aircraft is said to be statically stable. In aircrafts, three types of dimensional stabilities are considered. Those are the longitudinal stability that concerns the pitching motion, the directional stability that concerns 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 motion during flight. When imbalance occurs the airplane attempts to retain its position, and it reaches the equilibrium position through a series of decaying oscillations, and the aircraft is said to be dynamically stable. If the aircraft continues the oscillatory motion without decay in the magnitude, then the aircraft is said to be on dynamically neutral. If the magnitude oscillatory motion increases and the aircraft orientation start to change rapidly, then the aircraft is said to be dynamically 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 its original position when subjected to unbalanced forces or moments acting on the aircraft. • Dynamic stability describes the form of motion an aircraft in static stability undergoes when it tries to return to its original position.

J11- Q7a What is understood by the term "Static longitudinal stability” of an airplane. Illustrate it with sketches and plots. And hence explain the terms (dCm/dCL)fixed and (d Cm/dCL)free Answer: LONGITUDINAL STATIC STABILITY. Let us consider the two airplanes and their respective pitching moment curves shown in 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 attack is increased to point C. At the angle of attack denoted byC, airplane 1 develops a negative (nose-down) pitching moment which tends to rotate the airplane back towards it equilibrium point. However, for the samedisturbance, airplane 2 develops a positive (nose-up) pitching moment whichtends to rotate the aircraft away from the equilibrium point. If we were toencounter a disturbance which reduced the angle of attack, e.g to point A, wewould find that the airplane 1 develops a nose-up moment which rotates theaircraft back toward the equilibrium point. On the other hand, airplane 2 isfound to develop a nose-down moment which rotates the aircraft away fromthe equilibrium point. On the basis of this simple analysis, we can concludethat to have static longitudinal stability the aircraft pitching moment curve must have a negative 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 pitching moment curves which both satisfy the condition for static stability. However, only curve 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 the Cm versus a curve, we could have just as easily accomplished the same result by working with a Cm 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 with angle of attack (Chalpha= 0), this term becomes unity, and the stick-fixed and stick-free stabilities are equal. However, if the elevator has a large floating tendency (the ratio Chalpha /Cholarge and positive), the stability contribution of thehorizontal tail can be reduced 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 off run of the airplane. Answer: Add points given in class notes about take off distance and include the formula Assisted take-off is any system for helping aircraft into the air (as opposed to strictly under its own power). The reason it might be needed is due to the aircraft's weight exceeding the normal maximum take-off weight, insufficient power, or the available runway length may be insufficient, or a combination of all three factors. Assisted take-off is also required for gliders, which do not have an engine and are unable to take-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 modern systems fitted on aircraft carriers, a piston, known as a shuttle, is propelled down a long 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 steel cable called a catapult bridle; the forward ramps on older carrier bows were used to catch these cables), and is flung off the deck at about 15 knots above minimum flying speed, 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-assisted take-off'). In the JATO and RATO systems, additional engines are mounted on the airframe 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 permanently attached 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 Vortex The result of the tip vortices downstream of a finite aspect Drag or Drag due ratio wing. to Lift Parasite Drag

The drag not directly associated with the production of lift.

Skin Friction Drag

The result of viscous shearing forces over the wetted surface area of a body.

The integrated effect of the static pressure acting normal to Form or Pressure the surface of a body Drag resolved in the direction of the flow. The increment in drag resulting from bringing 2 bodies in the proximity of each other. For example, the total drag of the Interference Drag wing - fuselage combination is usually greater than the sum of the wing drag and the fuselage drag independent of each other.

Trim Drag

The increment in drag resulting from the aerodynamic forces required to trim the plane about its center of gravity. It usually takes the form of added induced and form drag on the 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 passes through the engine for the purposes of cooling the engine, oil, and accessories.

Base Drag

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

Wave Drag

Present only in supersonic flow, it is a pressure drag resulting from the difference of static pressure forces on either side of a shock wave forming on the surface of a body.

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