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# Aerodynamic Priniciples and Design

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AERODYNAMIC
PRINCIPLES
AND
AIRCRAFT DESIGN
ASSIGNMENT
AERODYNAMIC
PRINCIPLES
AND
AIRCRAFT DESIGN
ASSIGNMENT

INTRODUCTION
It is really amazing how an aircraft is able to just take off from the ground and fly thousands of miles from place to place. How does it all work, do you ever wonder? Well obviously it’s not magic; it’s mainly because of aerodynamics. And when we talk about aerodynamics, it goes way beyond elevators, rudders, etc. Therefore we go to the depths of aerodynamics and its power to control a massive plane in the air. To be engineering in aerospace we need this extensive knowledge.
In this report, you will learn about how an aircraft moves. The stability and control of the aircraft we also learn the factors influencing the static stability, the static margin and load factors. This report also gives us knowledge about the aircrafts control systems.

| | | 1.1 | Motion of an aircraft | 4 | 1.2 | Degree of freedom | 4 | 2.1 | Static stability | 5 | 2.2 | Static margin | 5 | 2.3 | Dynamic stability | 6 | 3.1 | Stability in an aircraft | 6 | 3.2 | Longitudinal stability | 6 | 3.2.1 | Longitudinal dihedral | 7 | 3.3 | Lateral stability | 7 | 3.3.1 | Dihedral | 7 | 3.3.2 | Sweepback | 8 | 3.3.3 | Keel effect | 8 | 3.4. | Directional stability | 9 | 3.4.1 | sweepback | 9 | 4.1 | Load factor | 9 | 4.2 | Maneuver envelopes | 10 | 4.3 | Constraints on load factor | 10 | 4.4 | Load factors with respect to different maneuvers | 11 | 5.1 | Horizontal stabilizers | 12 | 5.2 | elevators | 12 | 6.1 | Vertical stabilizers | 13 | 6.2 | rudder | 13 | 7.1 | Role of swept back wing | 13 | 8.1 | Role of swept forward wing | 14 | 9.1 | Role of tapered wings | |

Motion of an aircraft #Fig1: Axis of rotation
#Fig1: Axis of rotation
An aircraft in flight is free to rotate in three dimensions.The point of intersection of these three axis is center of gravity and each of these axis’s are perpendicular to the other two . The axis which extends lengthwise, from nose to tail is called the longitudinal axis. The rotation about this axis is called roll. It helps with the up and down movement of the wing tips of the aircraft. The axis which extends crosswise from wingtip to wingtip is called the lateral axis. The rotation about this axis is called pitch. It helps with the up and down movement of the nose of the aircraft .The axis which passes vertically through the center of gravity is called the vertical axis, and rotation about this axis is called yaw. It helps with the movement of the nose of the aircraft from side to side. #Ref 1
Degrees of Freedom The aircraft has six ways it can move or in other words six degrees of freedom. There are three degrees of freedom in translation or linear motion. These are orthogonal to each other .The aircraft also has three degrees of freedom in rotation, also orthogonal to each other. #Ref 2 Figure [ 2 ]:
Figure [ 2 ]:
Translational Degrees:

#Fig4: Lateral (aircraft moves from side to side)
#Fig4: Lateral (aircraft moves from side to side)
#Fig3: Vertical (aircraft moves upward and downward

#Fig3: Vertical (aircraft moves upward and downward

#Fig2: Longitudinal (forward and backward thrust)

#Fig2: Longitudinal (forward and backward thrust)

Rotational Degrees

#Fig7: Yaw (nose moves from side to side)
#Fig7: Yaw (nose moves from side to side)
#Fig6: Roll (wings roll up or down
#Fig6: Roll (wings roll up or down
#Fig5: Pitch (nose pitches up and down
#Fig5: Pitch (nose pitches up and down

Static and dynamic stability
Everybody experiences different types of forces. When these forces balance out each other they are said to be in equilibrium. The reaction of anybody when its equilibrium is disturbed is referred to as stability. #Ref 3
There are two types of stability:
1) Static stability
2) Dynamic stability
Static stability: It has been defined as the initial tendency to return to equilibrium that the aircraft displays after being disturbed from its trimmed condition #Ref 4
There are three types of static stability:
1) Positive static stability
2) Negative static stability
3) Neutral static stability
#Fig8: Different types of static stability
#Fig8: Different types of static stability
If the body returns to its original state of equilibrium after being disturbed is said to be positive static stable but if it continues to move away from its original state of equilibrium it is said to be negative static stable , if the body remains in the disturbed position it is said to be neutral static stable #Ref 5
Static Margin
Static margin is a concept used to characterize the static stability and controllability of an aircraft .It is the distance between the center of gravity and the neutral point of the aircraft. A large static margin suggests an aircraft which is very stable and not very maneuverable. A low positive static margin is normally associated with highly maneuverable aircraft. .Aircraft with zero or negative static margin normally requires a computer fly-by-wire flight control system in order to be safe to fly.
Positive static stable aircrafts, when angle of attack is increased the airplane will tend to return to its original angle of attack. Example for a straight and level flight on pulling back the stick the nose of the aircraft starts rotating upwards, increasing the angle of attack. But as soon as the stick pressure is released the nose stops rotating and returns to original angle of attack resulting in change of altitude. For aircrafts with negative static stability, on releasing the stick pressure rotation doesn’t stop. The angle of attack continues to increase until the stick is pushed forward past the center position. In these situations the pilot has to work constantly to maintain control. #Ref 6
Dynamic stability: Is the overall tendency of a body to return to its original position, following a series of damped out oscillations #Ref 7
This also has three types:
1) Positive dynamic stability
2) Negative dynamic stability
3) Neutral dynamic stability
#Fig9: Dynamic stability -damped versus undamped stability http://www.Americanflyers.Net/aviationlibrary/pilots_handbook/images/chapter_3-2_img_1.Jpg

#Fig9: Dynamic stability -damped versus undamped stability http://www.Americanflyers.Net/aviationlibrary/pilots_handbook/images/chapter_3-2_img_1.Jpg

An object is said it be positive dynamic stable if it returns to its equilibrium state and its amplitude decreases. If the amplitude increases it is said to be negative dynamic stable. And if the amplitude neither increases nor decreases it is said to be neutral dynamic stable #Ref 8
Stability in an aircraft:
An aircraft experiences many things in air, example strong winds, turbulence and so on leaving it to deviate from its flight path. If the aircraft can return to its original position without the help of the pilot, it is said to be stable. So exactly what is stability .Stability of an aircraft is the ability of an aircraft to return to its normal position without the help of any external force when hit by external disturbance. This is generally occurred due to the aircrafts design. #Ref 9
In an aircraft there are three types of stability
1) Longitudinal stability
2) Lateral stability
3) Directional stability
Longitudinal stability: It lies around the lateral axis. It is dangerous if the aircraft would dive or stall when unattended hence if properly designed the airplane will not show these instabilities if the airplane is loaded according to the manufactures recommendation. #Ref 10
There are two factors affecting longitudinal stability:
- The position of the center of gravity
- The size and position of the horizontal stabilizer
#Fig10: Horizontal Stabilizer affecting longitudinal stability

#Fig10: Horizontal Stabilizer affecting longitudinal stability

Aircrafts are designed in such a way that they have a pitch down structure. This is accomplished by keeping the center of pressure behind the center of gravity. The tail plane of the aircraft is set at an angle of incidence that produces negative lift which thereby holds the tail down. As a result of the two, the negative lift of the tail plane and the pitch down nose counteract each other and provide positive stability .This helps the plane to resume to its normal position, in case of disturbance or engine failure. #Ref 11
#Fig11: Longitudinal dihedral
#Fig11: Longitudinal dihedral
Longitudinal dihedral: It is the angle of incidence between the incidence of the wing and the horizontal stabilizer .It is the longitudinal dihedral combined with the horizontal stabilizer area and the moment arm which provide the restoring moment to return to the trimmed state. The moment arm, which supplies the restoring leverage and thus the stability, is affected by the cg position and if the cg lies outside its limit the aircraft will be longitudinally unstable. #Ref 12
Lateral stability: Lies around the longitudinal axis. Lateral stability is basically the tendency for the aircraft to return to its wing level attitude after displaced by a force. There are many factors affecting lateral stability. These are dihedral, sweepback, keel effect and weight distribution. #Ref 13
Dihedral: The wings of the aircraft are designed two to three degrees above the perpendicular to the longitudinal axis .It forms a v shape with respect to the fuselage. This design helps in lateral stability. Dihedral design is used to produce the rolling tendency to return the aircraft to its equilibrium position when a sideslip occurs.
If a gust of wind forces the aircraft to roll, leading one wing to rise and the other to lower, the aircraft banks. Leading the aircraft to sideslip or slide. Since it has a dihedral structure the air strikes the lower wing at a greater angle of attack than the higher wing. The increased angle of attack on the lower wing creates more lift which causes the lower wing to rise upward. As the wings reach level position the angle of attack on both the wings are equal causing the aircraft to be laterally balanced and cause the rolling tendency to subside.
#Fig12: dihedral lateral stability
#Fig12: dihedral lateral stability
The figure (a) shows a head-on view of a dihedral airplane figure (b) shows that if a disturbance causes one wing to drop relative to the other, the lift vector rotates and there is a component of the weight acting inward which causes the airplane to move sideways in this direction. Figure (c) shows that if the wings have dihedral structure, the lower wing toward the free-stream velocity, will experience a greater angle of attack than the raised wing and hence greater lift. There results a net force and moment tending to reduce the bank angle #Ref 14
Sweepback
Sweepback wings helps in subsiding the rolling effect. When a disturbance causes the aircraft to roll, the lower wing presents its leading edge perpendicular to the relative airflow. Resulting in the lower wing to acquire more lift and restore the aircraft to original position. #Ref 15

#Fig13: Sweepback Stability
#Fig13: Sweepback Stability
Keel effect
#Fig 14: Keel area for lateral stability
#Fig 14: Keel area for lateral stability
Laterally stable aircrafts are designed in such a way that the greater portion of the keel surface is above and behind the center of gravity. Thus when the aircraft slips, the combination of the pressure of airflow against the upper portion of the keel surface and the weight of the aircraft tends to roll the airplane back to wing level flight #Ref 16
Directional stability
#fig15: directional stability moments

#fig15: directional stability moments

Directional stability lies around the vertical axis. The main contributors for directional stability are the area of the vertical fin and the side of the fuselage aft. When an airplane is disturbed from its flight path at an angle, the fuselage generates a moment which has a tendency to increase the disturbance, which makes the aircraft unstable. The fin is placed at an angle of attack due to the sideslip disturbance, which generates a side force which when multiplied by the moment arm produces a stabilizing moment that results the aircraft to return to its normal position #Ref 17
Sweepback
#Fig16: Sweep back contributing to directional stability
#Fig16: Sweep back contributing to directional stability
Sweepback also contributes to directional stability. When turbulence causes the aircraft to yaw to one side, the right wing presents a longer leading edge perpendicular to the relative airflow. The airspeed of the right wing increases and it acquires more drag than the left wing. The additional drag on the right wing pulls it back, turning the aircraft back to its original path sweepback effect on directional stability. #Ref 18
Load factor
It is the ratio of the total load supported by the airplane’s wing to the total weight of the airplane. In still air flight, the load on the wing equals the lift it generates. The load factor is expressed in G units. In an accelerated level flight the load on the wings is equal to lift and to the weight. Consequently, the load factor equals 1G. If Lift = Weight then Lift / Weight = 1G. The load factor may be POSITIVE or NEGATIVE.
Positive load factor - During normal flight, the load factor is 1 G or greater than 1 G. whenever the load factor is one or greater the load factor is defined as positive.
Negative load factor- Under certain conditions, an abrupt deviation from the airplane’s equilibrium can cause an inertial acceleration that in turn will cause the weight to become greater than the lift. For example, during a stall, the load factor may be reduced towards zero. This will cause the pilot to feel “weightless”. A sudden and forceful elevator control movement forward can cause the load factor to move into a negative region. #Ref 19
Maneuver envelopes The maneuvering envelope defines the limits within which the aircraft can safely fly. It is usually drawn as a V-n diagram (Velocity against load factor or g factor). #Fig18: constraints of V-n Diagram
#Fig18: constraints of V-n Diagram
#Fig17: V-n diagram
#Fig17: V-n diagram

V0 – Zero velocity and force on the aircraft. The aircraft should be able to support its own weight. Vs- Stall velocity –the aircraft’s lowest flying speed before it can stall. This is the point where the aircraft is off ground, any speed slower the aircraft will descend. Vc = Cruise velocity - Normal flying speed Vne= Never exceed velocity. It is the speed where effects like flutter are likely to destroy the aircraft. Green section – aircraft is safe to fly. It won’t experience any structural damage. Yellow section – aircraft may experience structural damage.
Red section – aircraft will experience structural failure. #Ref 20
Load factors with respect to different maneuvers
Effect of Turns on Load Factor
A turn is made by banking the airplane so that lift from the wings pulls the airplane from its straight flight path. If the angle of bank is kept constant and the airspeed is increased, the rate of turn will decrease likewise if the airspeed is decreased, the rate of turn will increase. For this reason, there is no change in centrifugal force for any given bank. Therefore, the load factor remains the same. The load factor increases at a rapid rate after the angle of bank reaches 50°.in order to maintain same altitude the wing must produce lift equal to the load factor. The load factor increases as the angle of bank approaches 90°. An airplane can be banked to 90°, but a continued coordinated turn is impossible at this bank angle without losing altitude. #Ref 21
#Fig19: the load supported by the wings increases as the angle of bank increases. The increase is shown by the relative lengths of the white arrows. Figures below the arrows indicate the increase in load factor. For example, the load factor during a 60° bank is 2.00, and the load supported by the wings is twice the weight of the airplane in level flight.
#Fig19: the load supported by the wings increases as the angle of bank increases. The increase is shown by the relative lengths of the white arrows. Figures below the arrows indicate the increase in load factor. For example, the load factor during a 60° bank is 2.00, and the load supported by the wings is twice the weight of the airplane in level flight.
Effect of Speed on Load Factor
The amount of excess load that can be imposed on the wing depends on how fast the airplane is flying. At slow speeds, the maximum available lifting force of the wing is only slightly greater than the amount necessary to support the weight of the airplane. However, at high speeds, the lifting capacity of the wing is so great that a sudden movement of the elevator controls or a strong gust may increase the load factor beyond safe limits. #Ref 22
Effect of Load Factor on Stalling Speed
#Fig20: Load factor and stall speed chart
#Fig20: Load factor and stall speed chart
Any airplane, within the limits of its structure and the strength of the pilot, can be stalled at any airspeed. At a given airspeed, the load factor increases as angle of attack increases, and the wing stalls because the angle of attack has been increased to a certain angle. Therefore, there is a direct relationship between the load factor imposed upon the wing and its stalling characteristics. #Ref 23
Effect of Spins on Load Factor
Stabilized spin is not different from a stall, hence the same load factor consideration is applied as those applied to stall recovery.
The load factor during a spin will vary with the spin characteristics of each airplane but is usually found to be slightly above the 1 G of level flight. This is true because the airspeed in a spin is very low usually within 2 knots of the accelerated stalling speeds. Hence the airplane pivots, rather than turns while it is in a spin. #Ref24
Effect of Turbulence on Load Factor
Turbulence in the form of vertical air currents can, under certain conditions cause severe load stress on an airplane wing. When an airplane is flying at a high speed with a low angle of attack, and suddenly encounters a vertical current of air moving upward, the relative wind changes to an upward direction as it meets the airfoil. This increases the angle of attack of the wing. #Ref 25
Horizontal Stabilizer
#Fig21: Horizontal Stabilizer: elevator
#Fig21: Horizontal Stabilizer: elevator
One can find the horizontal stabilizer along with the elevator at the rear end of the fuselage. It is a fixed wing section which is used to maintain stability of the aircraft. The elevator is a small moving section at the rear of the stabilizer which is attached to the fixed section by hinges. The elevator due to its movement is used to vary the amount of force generated by the tail surface and controls the pitching motion of the aircraft.
Elevator: Elevators are used to control the lift that the aircraft goes through during flight. In order to cause elevation or depression, the pilot simply needs to either move the stick backward or forward. Moving it backward causes the elevators to go up, which causes the rudder to go down and the nose to pitch up. At this point of time the wings have a higher angle of attack, which in turn causes the aircraft to have a bit more lift as well as drag. Once the aircraft wants to move at a steady height, the pilot simply needs to return the elevator to neutral, which he or she does by centering the stick and returning it to neutral. #Ref26
Vertical stabilizer
One can find the vertical stabilizer at the rear of the fuselage The rudder is the small moving control surface located on the trailing edge of the vertical stabilizer , as part of the empennage Motion of the rudder varies the amount of force generated by the tail surface and is used to control the yawing motion .
#Fig22: Horizontal stabilizers: rudder
#Fig22: Horizontal stabilizers: rudder
Rudder: The rudder is used to control the position of the nose of the aircraft. The rudder input insures that the aircraft is properly aligned to the curved flight path during the maneuver. Otherwise, the aircraft would encounter additional drag or even a possible adverse yaw condition in which, due to increased drag from the control surfaces, the nose would move farther off the flight path.
The rudder works by changing the effective shape of the airfoil of the vertical stabilizer. By changing the angle of deflection at the rear of an airfoil, the amount of lift generated by the foil will also differ. With increased deflection, the lift will increase in the opposite direction. With the rudder deflecting to the left, the force increases to the right. If the pilot reverses the rudder deflection to the right, the aircraft will yaw in the opposite direction. #Ref27
Role of swept back wing
Most airplanes choose sweepback wing because they create less drag, but are somewhat more unstable at low speeds. The amount of sweep of the wing depends on the purpose of the airplane. A commercial airliner has a moderate sweep resulting in less drag while maintaining stability at lower speeds. High speed airplanes have greater sweep. These airplanes are not very stable at low speeds. They take off and descend for landing at a high rate of speed. # Ref 28
As mentioned above sweepback also contributes to directional stability. It also helps in subsiding rolling affect.

Role of swept forward wing
#Fig23: Hansa Jet – Forward swept wing
#Fig23: Hansa Jet – Forward swept wing
A forward-swept wing is an aircraft wing configuration which the quarter-chord line of the wing has a forward sweep. The Hansa Jet was a forward-swept wing business jet designed in the 1960's. Its forward swept wing permitted a larger cabin without a wing spar interrupting the floor. Swept forward wings also provide better visibility. #Ref 29
Air moves span wise towards the rearmost end of the wing. As a result, the dangerous tip stall condition of a backwards-swept design becomes a safer and more controllable root stall on a forward swept design. This allows full aileron control despite loss of lift, and also means that drag-inducing leading edge slots or other devices are not required.
Since air flows inwards, wingtip vortices and the accompanying drag are reduced As a result maneuverability is improved, especially at high angles of attack. At transonic speeds, shockwaves build up first at the root rather than the tip, again helping to ensure effective aileron control. #Ref 30
#Fig24: Lower surface contributing in lift
#Fig24: Lower surface contributing in lift
For Swept forward wings the lower surface contributes a larger share of the total lift than the lower surface .One problem with the forward-swept design is that when a swept wing yaws sideways, one wing moves rearwards. On a forward-swept design, this reduces the sweep of the rearward wing, increasing its drag and pushing it further back, increasing the amount of yaw and leading to directional instability. #Ref 31

Tapered wings #Fig25: tapered wings
#Fig25: tapered wings
Tapered wings is platform in which the chord of the wing changes continuously from the center of the wing to the wing tip.Tapered wings have a high span efficiency .This results is lesser induced drag which in turn increases lift . The tapered outboard portion decreases weight and increases aspect ratio .
One of its disadvantages is the tendency to stall during flight. When one wing stalls it can cause the aircraft to experience sudden unexpected roll. But this can be alleviated through the use of washout. The other disadvantage would be its structural complexity. #Ref32
Role of slotted wing #Fig26: Slotted wings
#Fig26: Slotted wings
Slotted wings are devices used to increase lift of an aircraft .they are slots which run chord wise near the leading edge of the wing and running parallel to the span. A slotted wing helps during a state of stall. A stall happens when a wing no longer generates sufficient lift to keep the airplane in the air. This is due to the plane travelling too slowly or the angle of the wing to the airflow is too sharp. Before the wing stalls the airflow becomes turbulent over the upper surface of the wing, increasing drag and decreasing lift. To prevent this leading edge slot is used. . Air from below the wing can accelerate through the slot towards the low pressure region above the wing, and exit from the slot moving parallel to the upper wing surface. This mixes with the boundary layer which then delays the boundary layer separation from the upper surface. #Ref33
One of the disadvantage is it contributes in increasing drag. This reduces cruising speed and increases fuel consumption. Cause of this disadvantage, slots is made able to close. This is done my leading edge slats .it works in the same way as slots but slats can be retracted when not needed. #Ref34