Flight Dynamics

M.SUNDARESAN. FLIGHT DYNAMICS. ( TWO MARK QUESTIONS with detail explanations)

Q.1 A.1

Define skin friction drag and pressure drag.

Skin Friction • Due to shear stresses produced in boundary layer . • Significantly more for turbulent than laminar types of boundary layers.

Form (Pressure) Drag • Due to static pressure distribution around body - component resolved in direction of motion. • Sometimes considered separately as  forebody and rear (base) drag components.

Q.2 A.2

What is ISA?

Since the physical properties of the air are dependent upon temperature, and the performance of the aircraft is dependent upon the air density, pressure and temperature, correlation of performance data is dependent upon some assumed standard lapse rate. For convenience, an International Standard Atmosphere has been adopt6ed based on an average linear lapse rate at 40 degree north latitude which has been empirically chosen after a study of average lapse rates observed throughout the world.

Q.3

What are the conditions required for minimum minimum drag and minimum power?

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A3.

Also there must be a single value for the angle of attack which gives: – Maximum L/D, minimum T R and minimum D. – Thrust Required TR must be proportional to 1/(L/D) or 1/(CL/CD) – I.e. speed for minimum drag or minimum thrust required must correspond with speed for maximum lift/drag ratio.

Drag may be represented as: 2 2 D = k 1V + k 2 /V 2 k 1 = ½ρSCD0 and k 2 = 2W / (πAeρS)

∴dD/dV = 2k 1V - 2k 2V-3

Where k 1 and k 2 are “constants”

For minimum drag conditions, dD/dV = 0

∴k 1V = k 2V-3 and VD,min = (k 2 /k 1)1/4 -3

2

-2

Since k 1V = k 2V , ∴ k 1V = k 2V This means that the two components (parasite & lift-induced) are equal at minimum drag CD = 2 CD0. conditions. Thus, at minimum drag (or maximum L/D) conditions: Minimum Power Speed Power may be represented as: 3 P = D x V, ∴ P = k 1V + k 2 /V Where k 1 and k 2 are “constants” ∴dP/dV = 3k 1V2 - k 2V-2 For minimum power conditions, dP/dV = 0 ∴ 3k 1V2 = k 2V-2 and

VP,min = (k2 /3k1)

1/4

1/4

= 0.76 (k2 /k1)

= 76% min. drag speed.

This gives a simple theoretical relationship between the flight speeds required for minimum drag and power conditions. 1/4 1/4 i.e. VP,min = (k 2 /3k 1) = 0.76 (k 2 /k 1) = 76% VD,min

Also, at minimum power speed, 2 -2 3k1V = k2V ∴ 3CD0 = CL2 / (πAe) (or lift-induced drag = 3 x parasite drag). Q4. Explain the significance of load factor. The load factor of a given aircraft in a given condition of flight is defined as the lift divided A.4 by the weight. It is denoted by ‘n ‘ so that n =L/W /. In straight and level flight, L=W, so that n=1. In maneuvers, the lift may be greater than or less than weight. In either case, L=n.W, and it is easily seen that, other things being equal, the stalling speed in the maneuver is proportional to √n. The load factor influences the wing loading and also on the loads in the aircraft, which in turn influences the shear and bending load distribution in the aircraft, and hence design weight of the overall aircraft.

Q5. What is meant by the degree of freedom and how much required for airplane?

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A5. The aircraft has six degrees of freedom, namely three translational and three rotational. The longitudinal axis is denoted by x-axis towards the forward nose section of the fuselage. The y-axis points towards the starboard position and the z-axis vertically downward. The degrees of freedom signify the various modes the aircraft centre of gravity can translate and rotate freely in all directions.

Q.6 State two conditions for static longitudinal stability and indicate them with a plot. A.6

Q.7 what is meant by dihedral effect? The phenomenon of rolling moment due to sideslip is termed dihedral effect and is not a A.7 static stability in the true sense of the word. An airplane is said to have stable dihedral effect if a negative rolling moment (left wing down) is created as a result of positive sideslip. The dihedral stability is the ability of the aircraft to recover from a roll without pilot’s intervention. If the wing is tilted upwards from root to tip, it has a dihedral. Dihedral is good for Lateral stability.

dihedral

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The dihedral angle is defined as the angle between the plane of each wing and the horizontal. when the aircraft is unbanked and level. And is positive when wing lies above horizontal plane. Negative dihedral is used in some aircraft and is known as anhydral. The tilting of the lift vector on each wing, associated with wing dihedral, is responsible for a minor destabilizing contribution towards the yawing moment due to yaw. However the contribution is insignificant compared with the effect of wing sweepback. Q.8 Differentiate between yaw and sideslip angle.   v     v   A.8 The sideslip angle, β is equal to sin −1   or for small angles β =   . It should be noted for  V    V   curved flight paths shown below, the angle of yaw ‘ Ψ is defined as the angular displacement of the airplanes centre line from the azimuth direction taken as zero at some given instant of time and Ψ Is not equal to ‘ β ‘ and is in opposite sign.

What happens when the aircraft undergo a roll? Lif  t

Lif  t

A portion of the lift is pointed sideways. The vehicle moves Laterally. This is called sideslip .

During sideslip, a relative wind flows from right to left

A downwash occurs On the left wing, reducing As a result, the aircraft rights itself, and recovers from the roll.

This wind has a component normal To the wing on the right, viewing from the front. This is an up wash. The up wash increases lift on the ri ht win .

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Q.9 Graphically represent a system which is statically stable but dynamically unstable. A.9 STATICALLY STABLE Aircraft may be dynamically unstable Longitudinal Stability 40   ,      s      a     e 20        h     e      r      p     g        l        A     e 0        D

-20

0

10

20

30

40

Time, seconds

Q.10. What is directional stability? A.10.

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Q.11. What is spiral divergence? A.11. Spiral instability exists when the static directional stability of the airplane is very strong as compared to the effects of its dihedral in maintaining lateral equilibrium. When the lateral equilibrium of the plane is disturbed by a gust of air and a sideslip is introduced, the strong directional stability tends to yaw the nose into the relative wind, while the comparatively weak dihedral lags in restoring the lateral balance. Due to the yaw, the wing on the outside of the turning moment travels faster than the inside wing and as a consequence its lift becomes greater. This produces an over banking tendency which ,if not corrected by the pilot, will result in the banking angle becoming steeper and steeper. At the same time, the strong directional stability that yaws the plane into the relative wind is actually forcing the nose to a lower pitch attitude. Then the start of a slow spiral which has begun if not counter-acted by the pilot will gradually increase into a steep spiral dive. Thus it is a fairly complicated motion, involving a mixture of side forces and moments in both the rolling and yawing sense .A small degree of spiral instability is often tolerated, and usually the rate of divergence in the spiral motion, is so gradual that the pilot can control the tendency without any difficulty. Of the in-flight structural failures that have occurred in general aviation airplanes, improper recovery from this condition has probably been the underlying cause of  more fatalities than any other single factor. Q12. What causes induced drag? A.12 The drag resulting from lift is called induced drag. From the potential theory, it can be shown that with no circulation, ‘ Г ‘about an aerodynamic body the lift is equal to zero. With a finite value of circulation a lift forces results, which in turn produces an induced drag force. From the classical theory it was impossible to explain the formation of this circulation without the assumption of a viscous fluid in the boundary layer setting up the circulation. Q.13 Why does an airplane require a vertical tail or fin? A.13. The main contributor to the static directional stability is the vertical tail or fin. Both the size and arm of the fin determine the directional stability of the aircraft. The further the vertical fin is behind the C.G the more static directional stability the aircraft will have. (This is often called the weather vaning effect, because it works the same way as a weather vane.). Q.14. How does the wing contribute to directional stability? A.14. A wing produces two effects that give a yawing moment with sideslip. The important one is due to wing sweepback angle and the other is due to geometrical dihedral. The second effect is due to dihedral, results from a lift of the lift vector with sideslip. Both effects are stabilizing. Fuselage and engine nacelles are usually destabilizing. When there is a sideslip which is positive ‘ β ‘the rightwing i.e. the star 6

board wing faces the flow more perpendicularly i.e. more wing chord wise flow. These results in more lift and also drag, which acts to favorably correct the disturbance due to sideslip.

Q.15. What is lateral or Static roll stability? A.15

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Q.16. What is adverse yaw? A.16.

Q.18 What are the requirements of directional control? A18.

Q.20. What is roll control? A .20. Stability about the airplane’s longitudinal axis, which extends from nose to tail, is called lateral stability. This helps to stabilize the lateral or rolling effect; when one wing gets lower than the wing on the opposite side of the airplane. Their are four main design factors that make an airplane stable laterally. They are :- dihedral -keel effect -sweep back  -weight distribution

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During flight, the side area of the airplanes fuselage and vertical fin react to the airflow in much the same manner as the keel of a ship. Such laterally stable airplanes are constructed so that the greater portion of the keel area is above and behind the centre of gravity. Thus when the airplane slips to one side, the combination of the airplanes weight and the pressure of the airflow against the upper portion of the keel area (both acting about the C.G) tends to roll the airplane back to wings level flight.

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The rolling moment is defined by the following equation.-

 L = C l qSb OR..C l =

 L qSb

.

where L=Rolling moment positive to the right;

B= Wing span ; and Cl=rolling moment co-efficient. The angle of sideslip is the angle ‘ β ‘between the airplane centre-line and the relative wind and is positive when the relative wind is right of the centre line.

Q21. Define aileron control power. A 21. The rolling performance of any wing-aileron-system must be developed from a study of  the

equations of motion of the airplane in roll.

The equation of motion can be written very simply, the rolling moments arising only from the aileron deflection, ‘ δa ‘ and the wing damping due to angular velocity., ‘ p ‘ •

 I a  p =

∂ L ∂ L  p + δ  a ∂ p ∂δ  a

Q22. Explain the term stability derivative. A22 The aerodynamic forces X a and Za and moment Ma may be caused by any of the velocities, accelerations or angles to which the aircraft are subjected. The magnitude of the force or moment is obtained from the product of the variable and the appropriate stability derivative. The stability derivative is the partial derivative of a force or moment with respect to a variable. For example :-

 X u =

∂ X  Is the derivative which gives the force in the X- direction due to an increment in ∂u

velocity ‘u ‘. The total force increment in the X-direction due to all the variables will be found by summing all such terms... Thus;-

∆ X u = uX U  + vX V  + wX W  +  pX  p + qX q+ rX r  + .....

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Q23. What is adverse Yaw and aileron drag? A23. The aileron drag is a further factor that may cause an aircraft to stall. When the pilot applies aileron to roll upright during low speed, the downward movement of the aileron in the lower wing might take an angle on that part of the wing past the critical stall angle. Thus that section of the wing, rather than increasing the lift and the aircraft instead of straightening up, will roll into a steeper bank and descend quickly. Also the wing with the down aileron often produces a larger drag, which may create a yaw motion in the opposite direction of the roll. This yaw motion partially counteracts the desired roll motion and is called the adverse yaw.

Q24. How do we recover from a stall? A24. In order to recover from a stall the pilot has to reduce the angle of attack back to a low value .Despite the aircraft is already falling towards the ground, the pilot has to push the stick forward to get the nose even further down. This reduces the angle of attack and the drag, which increases the speed. After the aircraft has gained speed and the aircraft incidence becomes favorable, the pilot may pull back on aircraft stick to increase the angle of attack again (within the allowable range.), restoring lift. Since recovery from a stall involves loss of height, the stall is most dangerous at low altitudes. Engine power can help to reduce the loss of height by increasing the velocity more quickly and also helping to re-attach the flow over the wing.

Q25. What is spin? A25 A worse version of a stall is called spin, in which the plane spirals down. A stall can develop into a spin through the exertion of a sideways moment. Depending on the plane (and where its CG is located) it may be more difficult or impossible to recover from a spin. Recovering requires good efficiency from the tail surfaces of the airplane, typically involves the use of the rudder to stop the spinning motion, in addition to the elevator to break the stall. However the wings may block the airflow to the tail. If the CG is too far back, it will make the recovery more difficult.

Q26. What is flutter? A26. Another circumstance that may cause loss of control is when a hinged control surface starts to flutter. Such flutter is harmless if it just vibrates slightly at certain airspeed (possibly giving a buzzing sound), but ceases as soon as the airspeed drops. In some cases however the flutter increases rapidly so that the aircraft is no longer controllable. The pilot may not be aware of the case and thinks it is radio interference instead... T6o control the flutter the control linkages should not be loosely fitted and push rods have to be stiff... Long unbraced push rods can cause flutter, as vibration whips them around. In some difficult cases the control surfaces has to be balanced, so that its centre of mass gravity is ahead of the hinge line. It should be located at about 60-65% of the length of the control surface from the inner end.

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Q.27.State two requirements of aircraft control surfaces. A.27. An aircraft must be controlled along and about 6 degrees of freedom i.e. translational and roll in three axes. It is also used to trim an aircraft for maintaining equilibrium... Initiate, hold and terminate maneuvers... Control power has to be sufficient to cope with all possible flight conditions and speeds. including deployment of high lift devices; cross wind landings, engine failure on multiengine aircraft. Cross coupling between roll and yaw complicates control requirements.

Q28. Distinguish between stability and controllability. A 28.The requirement of static and dynamic stability for any dynamic system arises from the characteristics of the system response to disturbances like sudden gusts etc or to its controls. The control on the other hand is the response of aircraft to deliberate applied forces/moments which cause the aircraft to deviate from initial equilibrium position. The controls must be made effective enough to allow the airplane to realize the maximum utility, and at the same time light enough, so that maneuvering the airplane will not tax the pilot’s strength, yet never so light with very little effort can inadvertently maneuver the airplane past its structural design limits. These problems become more difficult as airplanes become bigger and faster.

Q29. What is the need for aerodynamic balancing? A29.The control force increases with aircraft speed and size. Aerodynamic balancing can reduce control forces down to more manageable levels. A basic design requirement is that over-large hinge moments must be reduced by balancing. Several methods are available to the designer and it is not unusual for two or more methods to be used on a single control. The asymmetric flap e.g. ‘Frise aileron ‘which has a form of distorted nose balance, are most often used on aileron controls. The other commonly used aerodynamic balance system is the ‘ Horn balance ‘. The types of  aerodynamic balance can be broken down into two main classes i.e. nose balance and trailing balance. Aerodynamic balance at the control surface nose consists of variations in nose shape, hinge line set- back, shrouds, gaps, and seals, while the trailing edge types of aerodynamic balance consists of changes in airfoil contour, balancing tabs, spring tabs and trailing edge strips.

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The FRISE aileron designed as a means of aerodynamic balance is arranged so that when the control is raised the offset nose of the aileron protrudes into the air-stream. This creates a localized region of low pressure and this helps to balance the control and also to provide an addition to boundary layer drag on the down going wing. Mass balancing is different from aerodynamic balancing. As the flaps have definite masses or inertia characteristics, this aspect is utilizes coupled with aerodynamic characteristics of the control. The inertial characteristics of a control in all six degrees of freedom or motion must therefore be carefully considered as the mass distribution of the control surface is the only variable. Mass balancing is the artificial correction of the inertial characteristics of a control to avoid excessive flutter of the control and main surfaces to which it attaches.

Q 30. How is load factor related to bank angle? A 30. In steady conditions for the Aircraft: _ Constant Altitude Banked Turn •

In steady condition: T=D

 –  •

Force balance gives: W = mg = L cosθ

 – 

2

FR = mV  /R = L sinθ

 –  •

∴ tan θ = V2 /(Rg) •

So for given speed and turn radius there is only one correct bank angle for a co-ordinated (no sideslip) turn.

Maneuverability equations simplified through use of  normal load factor (n) = L/W. In the turn, n = L/W = sec θ > 1 and is therefore determined by bank angle.

• •

Q 30. Define range and endurance. A 30. Range & Endurance •  Range is concerned with the distance traveled . •  Endurance is concerned with the time spent in the air. • Different conditions to be met for an aircraft trying to maximize either range or endurance – Vary with whether the aircraft is a piston-prop or jet/fan (a turboprop falls somewhere between the two). Endurance • Depends on minimizing rate of fuel consumption. • For piston-props, critical parameter is – Specific fuel consumption (sfc) = weight of fuel / (brake horse power x hours) = Nfuel / (bhp x hr). • For turbojets/fans, critical parameter is

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Thrust specific fuel consumption (tsfc) = weight of fuel / (thrust x hours) = 1/ hr (units) Range - Piston-Prop A/C • Range maximized when flying at minimum drag speed , corresponding to tangent drawn to PR against V curve, i.e. when CL/CD is at a maximum and the two drag terms are equal in value

–

Range - Jet/Fan A/C Maximum range when (V/D) ratio is maximized, found from tangent drawn to T R against V curve. 0.5 Relates to attitude giving maximum (CL / CD) and where parasite drag = 3 x lift-induced drag. • •

Q31. What is parasite drag? A 31.The resistance of aerodynamic bodies immersed in a real fluid is the result of three types of  drag. The resistance resulting from the pressure variations over the surface of the body is defined as pressure drag. and that due to the shear stresses in the boundary layer is defined as frictional drag. A third type of drag associated with lift on a wing is defined as induced drag. It is customary to call the sum of the first two types as Parasite drag.

DP = D + Di where Di is the induced drag due to lift, and D is the total drag. A breakdown of the airplane total drag is:2 C  D = K  + K ′C  L

C  D = C  Dp + C  Di 2

C  D = C  Dp min +

C  L

π   Ae

Q 32. Distinguish between troposphere and stratosphere. A 32. • The atmosphere is categorised into different levels or strata, defined in accordance with the temperature profile and separated by narrow transition zones. • We are only interested in the lower two strata, i.e. the troposphere & stratosphere. 14

Q33. Give some details on spin. A33. If one wing tip stalls before the other, then the large rolling moment will be setup (due to loss of lift at the stalled wing tip). This will be accompanied by a yawing moment so that the aircraft can lock into a spin. The overall motion is again complicated being a mixture of roll, sideslip and yaw. The spin can be steep or flat in nature with the flat spin being particularly hazardous and difficult to recover from. As in stall recovery, it requires the separated floe from the stalled wing to be reattached. This is usually done by:- By applying the rudder to remove the yaw. - Establishing a steady dive. - Pulling out through the use of the elev ator. Q34. What is control reversal? A34. At low speeds the wings is close to its stall angle. Downward deflection of a control surface (aileron) can actually induce a stall, thus reducing the available lift rather than increasing it. (I.e. control reversal occurs.). A geared aileron where the down going surface deflects less than the up going surface can help to get around this problem. Alternatively spoilers if fitted can be used for low speed control.

Q 35. What is rudder lock? A35. Occasionally an airplane will exhibit characteristics called ‘rudder locks ‘where the force on the rudder pedals suddenly reverse as the rudder deflection approaches its maximum deflection. The

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rudder will tend to float all the way to the maximum deflection without any effort by the pilot. This is a potentially dangerous situation for a multi engine airplane, where the loss of one engine will require large amount of rudder deflection, to maintain straight level flight.

Q36. What is one engine out condition? A36. In multi-engine aircraft the main rudder design criterion is that it should hold steady level flight with one engine cut and the propeller wind milling... This power asymmetry produces a yawing moment equal to Tx d (d= distance between engine center and aircraft axis); plus drag due to the drag of the dead airscrew... To maintain flight with zero sideslip requires that the rudder produce sufficient side force at the tail to overcome this asymmetric power condition. This is most critical at lower air speeds and high engine powers for example during take-off; since the thrust moment is large, while the rudder yawing moment produced by the aerodynamic force to the fin and rudder is small. This is usually the design criterion for multi- engine aircraft. If the engines are set closely towards the fuselage then however the critical rudder case is more likely to be the cross wind landing case.

Q37. What is auto-rotation? A 37. In normal flight, rolling motions are very heavily damped. Even though the static stability of  the bank angle is small or even negative, you cannot get a large roll rate without a large roll inducing torque. and when you take away the torque the roll rate goes away. Now near the critical angle of attack, the roll damping goes away. Suppose at that time you start the aircraft to roll to the right; then the roll rate will just continue by all itself. The right wing will be stalled (beyond max lift angle of attack) and the left wing will be unstalled. (Below max lift angle of  attack)

right wing tip right wing tip CL left wing tip

angle of attack

Cd

left wing tip

angle of attack

At sufficiently high initial angles of attack (somewhat greater than the critical angle of attack), the roll will not just continue but accelerate all by itself. This is an example of departure that constitutes the beginning of a snap roll or spin. The resulting undamped rolling motion is called autorotation. At high enough angle of attack, the ailerons loose effectiveness and at the same time start working in reverse.

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