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Aerodynamics

CAAC ATPL Study Material

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The following study material is an extract from Li Weidong (2nd edition) 2012, The Aviation Theory Course for Airline Transport Pilot.

Introduction This chapter establishes the basic knowledge elements of aerodynamics. There are seven sections: lift and drag, stability, flight controls, high-lift devices, turn, VMC and high speed flight.

1. Lift and drag Bernoulli’s equation Bernoulli's equation is effectively the explanation for how an airplane is able to fly. It is in reality a special case of the First Law of Thermodynamics. In other words, it states that Energy can not be created or destroyed. However, fortunately for those of us who like to fly, energy can be converted from one form into another,

Bernoulli's equation is simply a special case of the above equation. In the case of a fluid or gas, the potential energy is represented by the static pressure. The Kinetic energy is a function of the motion of the air, and of course it's mass. It is generally more convenient to use the density of the air as the mass representation. In words, Bernoulli's equation is usually stated "Static pressure plus dynamic pressure is constant." When a gas is accelerated, its pressure decreases (see Figure 3-1).

As the wing moves through the air, the air stream is divided, part of it flowing over one surface while the remainder flowing under the other surface. The air flowing over the upper cambered surface flow faster than the air over the opposite surface to reach the trailing edge. Thus the pressure on the upper wing surface is lower than that on the lower surface and lift is produced.



Figure 3-1

Airfoils

An airfoil is a surface which provides aerodynamic force when it interacts with a moving stream of air. A wing generates a lifting force only when air is in motion about it. Some of the terms used to describe the wing, and the interaction of the airflow about it, are listed here.



Leading edge --The part of airfoil meets the airflow first.

Trailing edge --This is the portion of the airfoil where the airflow over the upper surface rejoins the lower surface airflow.

Chord line --The chord line is an imaginary straight line drawn through an airfoil from the lading edge to the trailing edge.

Camber --The camber of an airfoil is the characteristic curve of its upper and lower surfaces. The upper camber is more pronounced, while the lower camber is comparatively flat. This causes the velocity of the airflow immediately above the wing to be much higher than that below the wing.

Relative wind -- This is the direction of the airflow with respect to the wing. If a wing moves forward horizontally, the relative wind moves backward horizontally. Relative wind is parallel to and opposite the flight path of the airplane.

Angle of attack

Angle of attack must not be confused with an airplane's attitude in relation to the earth's surface, or with "angle of incidence" (the angle at which the wing is attached relative to the longitudinal axis of the airplane). Angle of attack is defined as the angle between the chord line of the wing, and the relative wind. The coefficient of lift is revealed to be the same at a given angle of attack, regardless of the velocity, air density, wing area, etc.

Angle of attack has a large effect on the lift generated by a wing. During take-offs, the pilot applies as much thrust as possible to make the airplane roll along launch rail. But just before lifting off, the pilot "rotates" the aircraft. The nose of the airplane rises, increasing the angle of attack and producing the increased lift needed for take-off.



Four forces

There are four forces acting on an airplane all the time in flight: weight, lift, drag and thrust. If the airplane does not accelerate, then we know that the four forces add up to zero. Conversely, if the aircraft is accelerated, then the forces are not in balance. Thrust and drag act opposite each other and parallel to the relative wind.

Weight is a force which acts down. The concept of weight in fact defines the term "down". So, if you know what "down" means, then you understand the direction weight acts. Weight always acts vertically toward the center of the earth, because it is caused by the downward pull of gravity.

Lift is a force which acts perpendicular to the relative wind within the plane of symmetry. There is nothing in the definition which requires lift to be opposite to weight. In fact in many cases lift is not opposite to weight. The air flowing over the upper surface of the wing is deflected further than that flowing across the lower surface and therefore is accelerated. Bernoulli's principle states that when a gas is accelerated, its pressure decreases. Thus the pressure on the upper wing surface is lower than that on the lower surface and lift is produced,

At zero angle of attack, the pressure on the upper surface of the wing is still less than atmospheric, but the wing is producing minimum lift. As the angle of attack is increased, the lift developed by the wing increases proportionately. This is true until the angle of attack exceeds a critical value, when the air flowing over the top of the wing breaks up into a turbulent flow and the wing stalls (see Figure 3-2).

Angle of attack and indicated airspeed determine the total lift. An increase in either indicated airspeed or angle of attack increases total lift (up to the stalling angle of attack) and a decrease in either decreases total lift. To maintain the same total lift (i.e. maintain level flight), a pilot has to change the angle of attack anytime indicated airspeed is changed. For example, as indicated airspeed is decreased, the angle of attack must be increased to compensate for the loss of lift.



The relationship between indicated airspeed and lift for a given angle of attack involves the law of squares. If the angle of attack does not change, total lift varies with the square of the indicated airspeed. For example, if the airspeed doubles, the lift will increase by four times.

Indicated airspeed can be thought of as having two elements--the actual speed of the airplane through the air (true airspeed) and the density of the air. As altitude increases, air density decreases. To maintain the same indicated airspeed at altitude, an aircraft must fly at a higher true airspeed. To produce the same amount of lift at altitude, a higher true airspeed is required for a given angle of attack.

Drag is a force which acts in the same direction as the relative wind. But it is not necessarily opposite to thrust. The definition is the equivalent of saying that drag is a force in the opposite direction to flight. It is also true that drag is by definition at right angles to lift.



A curve comparing total drag to parasite and induced drag reveals an airspeed at which drag is at a minimum value. At higher airspeeds, total drag increases because of increasing parasite drag. At lower airspeeds, induced drag increases which increases the total drag.

L/D ratio

Since the lift stays constant (equal to weight), the low point on the curve is the airspeed that produces the best lift to drag (L/D) ratio. This point is referred to as L/Dmax (see Figure 3-3).

A change in weight changes the L/D curve. The amount of parasite drag is mainly a function of indicated airspeed. The amount of induced drag is a function of angle of attack. When an aircraft's weight is increased, any indicated airspeed will require a higher angle of attack to produce the required lift. This means that induced drag will increase with increases in weight while there will be little change in parasite drag.



Stall

We know that we must increase coefficient of lift as we reduce velocity. But we also know that there is a maximum coefficient of lift value for any given airfoil. Thus, we can conclude that there will be a speed below which we can not fly. The definition of stall speed is: The minimum speed at which the aircraft can produce sufficient lift for level flight. In this case, since we are specifying that we are also flying straight (not turning), we know that lift must equal weight. Thus, we can make a special case definition that the straight and level stall speed is the minimum speed at which the wings can produce lift equal to the weight of the airplane,

There are four factors determining the stall speed of our airplane: weight, maximum coefficient of lift, wing area, air density.

A wing will always stall at the same angle of attack. The load factor, weight and density altitude will cause the stalling true airspeed to vary, but the stall angle of attack will always be the same.

Weight is in the denominator, therefore as weight increases so does the stall speed. We have probably already guessed that, but now we can see that the relationship is between the stall speed and the square root of the weight. Thus, if the airplane weighs twice as much the stall speed will increase by the square root of two (l.41).

Maximum coefficient of lift is in the numerator, therefore a higher maximum coefficient of lift will result in a lower stall speed. We can see why designers like wings with high max. lift coefficients.

Wing area is also in the numerator. Therefore, a larger wing is one of the easiest ways to give an airplane a lower stall speed.

Air density is also in the numerator. Therefore, we know that the stall speed will increase as the air density decreases. In other words, stall speed will increase as altitude increases.



2. Stability Stability refers to how an aircraft responds to changes in angle of attack, slip or bank. Control refers to the ability to initiate and sustain changes in angle of attack, slip or bank. In other words, stability and control are opposites.

An aircraft without sufficient stability will be difficult, even dangerous to fly. On the other hand, if the aircraft is so stable that it cannot be controlled that will also be dangerous.

Static stability

Static stability refers to the aircraft's initial response when disturbed from a given angle of attack, slip or bank. Positive static stability is an initial tendency to return to its original attitude of equilibrium. When it continues to diverge, it has negative static stability. If an aircraft tends to remain in its new disturbed state, it has neutral static stability. Most airplanes have positive static stability in pitch and yaw, and are close to neutrally stable in roll. The vertical tail is the primary source of direction stability (yaw), and the horizontal tail is the primary source of pitch stability.

Dynamic Stability

Dynamic stability refers to the aircraft response over time when disturbed from a given angle of attack, slip or bank. When an aircraft is disturbed from equilibrium and then tries to return, it will invariably overshoot the original attitude and then pitch back. This results in a series of oscillations. If the oscillations become weak with time, the aircraft has positive dynamic stability. If the aircraft diverges further away from its original attitude with each oscillation, it has negative dynamic stability.

Centre of gravity

The center of gravity (CG) is by definition the point about which all gravitational moments add up to zero. If the CG is toward its rearward limit, the aircraft will be less stable in both roll and pitch. As the CG is moved forward, the stability improves. Even though an airplane will be less stable with a rearward CG, it will have some desirable aerodynamic characteristics due to reduced aerodynamic loading of horizontal tail surface. This type of an airplane will have a slightly lower stall speed and will cruise faster for a given power setting.

Ground effect

When an aircraft flies in ground effect, the ground interferes with the tip vortex. This reduces the induced drag. If the wing flew fight at ground level there would be no vortex at all and therefore a large reduction in induced drag. This ground effect reduces



induced drag (and therefore total drag) and increases lift. As an airplane flies out of ground effect on take-off, the increased induced drag will require a higher angle of attack. The ground effect falls off rapidly with altitude.

3. Flight controls It is very difficult to move the flight control surfaces of jet aircraft with just mechanical and aerodynamic forces. Flight controls are usually moved by hydraulic actuators and divided into primary flight controls and secondary or auxiliary flight controls. The most common control arrangement on the conventional airplane is ailerons on the main wing for roll control and a horizontal tail known as the stabilizer with moveable elevators for pitch control. There is also a vertical fin with a rudder for directional or yaw control. Secondary (or auxiliary) flight controls include tabs, trailing-edge flaps, leading-edge flaps, spoilers and slats.

Roll control

Roll Control is provided by the ailerons and flight spoilers. When the ailerons are deflected the down going aileron increases the camber of one wing. The up-going aileron decreases camber on the other wing. The result is an asymmetric lift between the wings. This causes the roll rate to increase away from the wing with the greater lift.

It is important to note that as long as a net moment (lift times distance) exists between the two wings the aircraft will roll faster and faster. The exact mix of controls is determined by the aircraft's flight regime. In low speed flight all control surfaces operate to provide the desired roll control. When the aircraft moves into higher speed operations, control surface movement is reduced to provide approximately the same roll response to a given input through a wide range of speeds.

Many aircraft have two sets of ailerons--inboard and outboard. The inboard ailerons operate in all flight regimes. The outboard ailerons work only when the wing flaps are extended and are automatically locked out when flaps are retracted. This makes good roll response in low speed flight with the flaps extended and prevents excessive roll and wing bending at high speeds when the flaps are retracted.

Spoilers

The spoiler will disrupt (separate) the boundary layer, thereby increasing drag and "spoiling" lift on the part of the wing affected by the spoiler. If raised on only one wing, they aid roll control by causing the lift of that wing drop. If the spoilers raise symmetrically in flight, the aircraft can either be slowed in level flight or can descend rapidly without an increase in airspeed. When the spoilers rise on the ground at high speeds, they destroy the wing's lift that puts more of the aircraft's weight on its wheels



which makes the brakes more effective.

Often aircraft have both flight and ground spoilers. The flight spoilers are available both in flight and on the ground. However, the ground spoilers can only be raised when the weight of the aircraft is on the landing gear. when the spoilers deploy on the ground, they decrease lift and make the brakes more effective. In flight, a ground-sensing switch on the landing gear prevents deployment of the ground spoilers.

Vortex generators

The vortex generators is designed to stick up out of the boundary layer into the free stream. It generates turbulence which re-energizes the boundary layer and prevents flow separation and the attendant pressure drag (review drag as required). When located on the upper surface of a wing, the vortex generators prevent shock-induced separation from the wing as the aircraft approaches critical Mach number. This increases aileron effectiveness at high speeds.

Tabs

Another way of changing the amount of force the pilot must apply to the control column is through servo and anti-servo tabs.

In this system the control column is directly connected to the control surface but a tab is geared to the movement of the control surface so that it either assists the movement of the control, or counters the movement of the control. Thus, the controls can be made to feel heavier or lighter than they would otherwise. Servo tabs are on the trailing edge of the control surface and are mechanically linked to move opposite the direction of the surface. If the tab moves up, the surface moves down.

The use of trimming tabs is one method of relieving aerodynamic load by means of a secondary control surface attached to the end of the primary surface. Trimming tabs must be operated by a control mechanism in the required direction. This may be done manually by cables connected to a control wheel in cockpit, or electrically by servomotors attached to the cable. Trim tabs must be moved in the opposite direction to that of the primary control surface.

Anti-servo tabs move in the same direction as the primary control surface (see Figure 3-4). This means that as the control surface deflects, the aerodynamic load is increased by movement of the anti-servo tab. This helps to prevent the control surface from moving to a full deflection. It also makes a hydraulically-boosted flight control more aerodynamically effective than it would otherwise be.



Some jet aircraft have control tabs for use in the event of loss of all hydraulic pressure. Movement of the control wheel moves the control tab which causes the aerodynamic movement of the control surface. The control tab is used only during manual reversion, that is, with the loss of hydraulic pressure. They work the same as a servo tab but only in the manual mode.

4. High-lift devices Swept wing jet aircraft are equipped with some high-lift devices including leading edge flaps, slots or slats, and trailing edge flaps. All of the high-lift devices are to increase lift at low airspeeds and to delay stall until a higher angle of attack.

Leading edge devices

The two most common .types of leading-edge devices are slats and Krueger flaps. The Krueger flap extends from the leading edge of the wing, increasing the camber of lira wing. The slat also extends from the wing's leading edge but it creates a gap or slot. This slot allows high energy from under the wing to flow over the top of the wing that delays stall to a higher angle of attack than would otherwise occur, it is common to find Krueger flaps and slats on the same wing.

Trailing edge flaps

The primary purpose of flaps is to increase the camber of the wing. A flap which increases the wing camber without forming a slot, as described below, is called a plain flap. A flap which moves back opening a slot when extended is called a fowler flap.



5. Turn When an airplane is in a level turn it is in a state of acceleration. However, all the acceleration is confined to a plane parallel to the horizon. Therefore, the vertical component of the lift vector must completely balance the weight vector which is vertical by definition (see Figure 3-5).When the pilot rolls the airplane into a turn, he must increase the total lift of the wing so that the vertical component is equal to the airplane's weight by increasing the angle of attack. If no compensation is made for the loss of vertical component of lift in a turn, the aircraft will sink.

Load factor is the ratio of the weight supported by the wings to the actual weight of the aircraft. On the ground or in unaccelerated flight the load factor is one. Conditions which can increase the load factor are vertical gusts (turbulence) and level turns. In a level turn, the load factor is dependent only on the angle of bank. Airspeed, turn rate or aircraft weight have no effect on load factor. Rate of turn is the number of degrees per second at which the aircraft turns,



The time to turn is proportional to velocity and inversely proportional to angle of bank. In other words, it takes longer time to turn at a high speed, but less time to turn at a large angle of bank.

Radius of turn depends on three variables: g, velocity squared (V2), angle of bank.

Notice in the development of the radius of turn equation that the weight (W) canceled out of the equation. This is a very important observation since it means that the size of the aircraft has no effect on the radius of turn. Thus, two aircraft flying at the same angle of bank and velocity will make the same radius of turn even if one is 1 000 times larger than the other. Radius of turn depends on velocity squared and is inversely proportional to the tangent of the angle of bank.

To perform a steady co-ordinated turn at a constant altitude the ailerons are used to maintain the desired angle of bank, whilst the elevator is used to increase the wings angle of attack, and the rudder is used to balance the turn. The rudder is used to counter adverse the yaw due to the ailerons, and also balances the turn. If the total life force remained the same as in steady straight and level flight, the actual amount of lift supporting the weight of the aircraft will effectively reduce.

6. VMC

P-Factor

When the aircraft slows down, the angle of attack must increase. When this happens the plane of rotation of the propellers is no longer at right angles to the TAS. As a result the down going blade and up going blade on the propeller each operate at a different angle of attack. The down going blade will be at a greater angle of attack and therefore will produce more thrust. (See Figure 3-6).

Critical engine

Because of "P-Factor" on most propeller-driven airplanes, the loss of one particular engine at high angles of attack would be more detrimental to performance than the loss of the other. One of the engines has its thrust line closer to the aircraft centerline. The loss of this engine would more adversely affect the performance and handling of the aircraft; therefore this is the "critical engine".



For un-supercharged engines, VMC decreases as altitude is increased. Stalls should never be practiced with one engine inoperative because of the potential for loss of control. Engine out approaches and landings should be made the same as normal approaches and landings.

Banking at least 5 into the good engine ensures that the airplane will be controllable at any speed above the certificated VMC, that the airplane will be in a minimum drag configuration for best climb performance, and that the stall characteristics will not be degraded. Engine out flight with the ball centered is never correct.

The blue radial line on the airspeed indicator of a light, twin-engine airplane represent maximum single-engine rate of climb.

7. High speed flight Mach number

Mach number is the ratio of TAS and the speed of sound. Therefore, if you are traveling



at exactly the speed of sound your Mach number is 1.0. Mach 8 means your speed is 80 % of the speed of sound, etc.

The drag increase largely when the air flows around the aircraft exceeds the speed of sound (Mach 1.0). Because lift is generated by accelerating air across the upper surface of the wing, local air flow velocities will reach sonic speeds while the aircraft Math number is still considerably below the speed of sound.

With respect to Mach cruise control, flight speeds can be divided into three regimes---subsonic, transonic and supersonic. Subsonic all flow everywhere on the aircraft is less than the speed of sound. Transonic flow begin at critical Mach number and some but not all the local air flow velocities are Mach 1.0 or above. When all the local Mach numbers surrounding an aerofoil exceeds Math 1.0, then the flow at that time is considered to be supersonic. In general terms the subsonic band extends up to about Mach 0.75, the transonic regime between Mach 0.75 and Mach 1.20.

Critical mach number

A limiting speed for a subsonic transport aircraft is its critical Mach number (MCRIT). That is the speed at which air flow over the wing first reaches, but does not exceed, the speed of sound. At MCRIT there may be sonic but no supersonic flow. The less airflow is accelerated across the wing, the higher the critical Mach number (i.e., the maximum flow velocity is closer to the aircraft's Mach number). Two ways of increasing MCRIT in jet transport designs are to give the wing a lower camber and increase wing sweep. A thin airfoil section (lower camber) causes less air flow acceleration. The sweptwing design has the effect of creating a thin airfoil section by inducing a span wise flow, thus increasing the effective chord length.

Mach tuck

As the aircraft moves into supersonic flight, the aerodynamic center and center of pressure, both move back. The nose of the aircraft always tends to pitch nose down as the aircraft transitions from subsonic to supersonic speed. This tendency is called the "Mach Tuck". This tendency is further aggravated in sweptwing aircraft because the center of pressure moves aft as the wing roots shock stall. When an airplane exceeds its critical Mach number, a shock wave forms on the wing surface that can cause a phenomenon known as shock stall. If the wing tips of a sweptwing airplane shock stall first, the wing's center of pressure would move inward and forward causing a pitch up motion.

Although a sweptwing design gives an airplane a higher critical Mach number (and therefore a higher maximum cruise speed), it results in some undesirable flight characteristics. One of these is a reduced maximum coefficient of lift. This requires that sweptwing airplanes extensively employ high lift devices, such as slats and slotted



flaps, to get acceptably low take-off and landing speeds.

Another disadvantage of the sweptwing design is the tendency, at low airspeeds, for the wing tips to stall first. This results in loss of aileron control early in the stall, and in very little aerodynamic buffet on the tail surfaces.

Dutch roll tendency is typical of sweptwing designs. If such an airplane yaws, the advancing wing is at a higher angle of attack and presents a greater span to the air stream than the retreating wing. This causes the aircraft to roll in the direction of the initial yaw and simultaneously to reverse its direction of yaw. When the yaw reverses, the airplane then reverses its direction of roll and yaw again. This roll-yaw coupling is usually damped out by the vertical stabilizer. But at high speeds and in turbulence, this may not be adequate, so most aircraft are also equipped with a yaw damper to help counteract any Dutch roll tendency.



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