Page |1 Task 01: a) Bernoulli principles: The sum of the pressure and kinetic energy of a system is constant along the path of flow. or P + ½ρv² = Constant and since P= Pο + ρgh, then Pο + ρgh + ½ρv² = Constant Where: ρ = Density of the fluid g = Acceleration due to gravity h = Height of point in fluid v = Velocity of fluid at given point Pο = Pressure at given point Here we see the application of Bernoulli's Principle in a pipe of constant height. It shows that as Kinetic Energy increases the Pressure must decrease accordingly.
Here is an interactive animation where we can visually see how the change in Area with a constant Flow Rate affects the Pressure and Velocity of a system. Move the square yellow tabs in order to manipulate the area of the pipe and see how the dependent variables change proportionally (Reference: http://www.csp.science.ubc.ca/life/StudentSamples/Website2/)
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
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Venture principles: Diagram of venture tube:
Principle of operation: The Venturi meter was invented by the Italian Giovanni Venturi in 1797. In a Venturi meter there is first a converging section in which the cross sectional area for flow is reduced. Then there is a short section at the reduced diameter, known as the throat of the meter. Then there is a diverging section in which the cross sectional area for flow is gradually increased to the original diameter. The velocity entering the converging section is where the pressure is P1. In the converging section the velocity increases and the pressure decreases. The maximum velocity is at the throat of the meter where the minimum pressure P2 is reached. The velocity decreases and the pressure increases in the diverging section. There is a considerable recovery of pressure in the diverging section. However, because of frictional effects in the fluid, the pressure leaving the diverging section is always less than P1, the pressure entering the meter. (Reference: http://www.ustudy.in/node/3464) Relation to generation lift: The difference in pressure (pressure gradient) on either side of the wing causes the lift force, which is proportional to the bottom surface area of the entire wing. As the velocity of the plane increases, the air pressure gradient increases. This is why a plane suddenly takes off as it accelerates – it occurs when the lift force exceeds the weight force. The generation of the lift force is depicted in figure 1.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
Page |3
Figure 1 Lift Generation for a Subsonic Aircraft Wing From Bernoulli and venture principles the lift is generation. It should be noted that early airplane design used an entirely different process to generate lift: tilted wings. Here the lift comes about via Newton's third law: by imparting a downward force on the air (redirecting it due to the angular tilt of the wing), the air in turn imparts an upward force on the wing. b) The factor that lift generation over the aerofoil: From the lift equation Lift = CL × ½rV² × S the factor of lift Angle of attack: By incising angle of attack the lift increases. For double convex symmetrical aerofoil it is rising at 15 degree angle. It is under co-efficient of lift Wing shape: Wing shape is also a factor the generation. It is under co-efficient of lift Air density: If the density increases the lift incises Air velocity: If the air velocity incises the lift also incises, Lift incises at the square of the air velocity. Wing surface area: Wing surface area also a great matter of lift. According to incises surface area the lift also increases Task 2: a) The drag on the wings or lifting surfaces is Wing Drag and the drag on those parts which do not contribute to the lift is Parasite Drag.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
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Figure: Types of drug The drag on the wings or lifting surfaces is Wing Drag and the drag on those parts which do not contribute to the lift is Parasite Drag. • Induced Drag: This is the drag which is induced along with the lift due to vortices on wing tip and wing trailing edges. Observe how wing tip vortices and trailing edge vortices come into play. These vortices create because of presence of pressure difference between upper and lower surfaces of the wing. These are strongest when the pressure difference is greatest, when the angle of attack is large and the aircraft speed is low. If there is no pressure difference (which means no lift) there are no wing vortices and no induced drag. Thus, Induced Drag is inseparable from lift. • Form Drag: Drag created due to the 'form' of an object is called the 'Form Drag'. Form Drag can be minimizes by 'Streamlining' the object in the airflow. Fineness Ratio is the term corresponding to streamlining. More the streamlining more is the Fineness Ration and less is the form drag. (Fineness Ratio = Length/Thickness) • Profile Drag: Drag due to the profile (i.e. form & surface condition) of an object is the Profile Drag. Profile Drag = Form Drag + Skin Friction • Parasite Drag: The drag created by the uneven surfaces of the aircraft, like opening, protrusions and other obstruction on the skin of the fuselage and wings. • Interference Drag: Drag on the joints is called Interference Drag. Example: Drag on the wingto-fuselage joint. This kind of drag can be minimized by 'fairing' the joint. (Reference: Course note -71-Unit Theory of Flight) Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
Page |5 Factor affects the drag forces: Drag is the resistance of the air to an aircraft pushing through it. The resistance depends on: (a) the streamlining of the aircraft body (b) i. the excrescences attached to the airframe ii. turbulence at the junctions of structural components iii. the cooling airflow around the engine (c) the roughness of the surface skin (d) the 'wetted' area; i.e. the amount of surface exposed to the airflow (e) the density of the air (f) the speed of the airflow (g) the angle of attack.
b) The best lift/drag ratio In aerodynamics, the lift-to-drag ratio, or L/D ratio, is the amount of lift generated by a wing or vehicle, divided by the drag it creates by moving through the air. A higher or more favorable L/D ratio is typically one of the major goals in aircraft design; since a particular aircraft's required lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy, climb performance, and glide ratio. The term is calculated for any particular airspeed by measuring the lift generated, then dividing by the drag at that speed. These vary with speed, so the results are typically plotted on a 2D graph. In almost all cases the graph forms a U-shape, due to the two main components of drag. Lift-to-drag ratios can be determined by flight test, by calculation or by testing in a wind tunnel.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
Page |6 Induced drag is a component of total drag that arises whenever a three-dimensional wing generates lift. At low speeds an aircraft has to generate lift with a higher angle of attack, thereby leading to greater induced drag. This term dominates the low-speed side of the L/D graph, the left side of the U. Form drag is caused by movement of the aircraft through the air. This type of drag, also known as wind resistance or profile drag varies with the square of speed (see drag equation). For this reason profile drag is more pronounced at higher speeds, forming the right side of the L/D graph's U shape. Profile drag is lowered primarily by reducing cross section and streamlining. The peak L/D ratio doesn't necessarily occur at the point of least total drag, as the lift produced at that speed is not high, hence a bad L/D ratio. Similarly, the speed at which the highest lift occurs does not have a good L/D ratio, as the drag produced at that speed is too high. The best L/D ratio occurs at a speed somewhere in between (usually slightly above the point of lowest drag). Designers will typically select a wing design which produces an L/D peak at the chosen cruising speed for a powered fixed-wing aircraft, thereby maximizing economy. Like all things in aeronautical engineering, the lift-to-drag ratio is not the only consideration for wing design. Performance at high angle of attack and a gentle stall are also important. (Reference: http://en.wikipedia.org/wiki/Parasitic_drag) Task 3: Conditions of level flight: When a body keeps travelling at a steady height at uniform velocity in a fixed direction, this state of steady flight is known as equilibrium. In order to do this the forces acting on it must be balanced - the lift must be equal to the weight (this condition will keep the aeroplane at a constant height); and, the thrust must be equal to the drag (this condition will keep the aeroplane moving at the same steady velocity). For an aeroplane, when there is no load on the tail plane the conditions of balance for un-accelerated flight are these:
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
Page |7 Figure: Four forces of the flight
a) Lift = Weight, i.e. L = W. b) Thrust = Drag, i.e. T = D. c) The "nose-down" pitching moment of L and W must balance the "tail-down" pitching moment of T and D. The two forces, L and W, are two equal and opposite parallel forces, i.e. a couple; their moment is measured by "one of the forces multiplied by the perpendicular distance between them." So, if the distance between L and W is x metres, the moment is Lx or Wx Newton-metres. Similarly T and D form a couple and, if the distance between them is y metres, their moment is Ty or Dy Newton-metres. Therefore the third condition is: Lx (or Wx) = Ty (or Dy) (Reference: Course note -71-Unit Theory of Flight)
Task 4 a) Difficulties in balancing: In practice, there is lot of difficulties in achieving balancing for maintaining level flight. For normal flight modes, changes in AOA will causes changes in the CP, thus the lift component which acts through the CP will change as the AOA changes. The weight which acts through the CG depends on every individual part of the aircraft and will vary depending on the distribution of passengers, crew, and freight and fuel consumption. The line of action of the thrust is set in the basic design and is totally dependent on the position of the propeller shaft or the center line of the exhaust jet. The drag may be found by calculating its component parts separately or by experiment with models in a wind tunnel. Any change in the angle of attack means a movement of the lift, and usually in the unstable direction; if the angle of attack is increased the pitching moment about the centre of gravity will become more nose-up, and tend to increase the angle even further. There is a possibility of movement of the centre of gravity during flight caused, for instance, by consumption of fuel, dropping of bombs or movement of passengers. The line of thrust is settled by the position of the engine or engines.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
Page |8 The four forces do not, therefore, necessarily act at the same point so that equilibrium can only be maintained providing that the moments produced by the forces are in balance. In practice, the lift and weight forces may be so designed as to provide a nose-down couple (Figure 7.2(a)), so that in the event of engine failure a nose-down gliding attitude is produced. For straight and level flight the thrust and drag must provide an equal and opposite nose-up couple.
Figure: a
Figure: b Figure: Force couples for straight and level flight However, the design of an aircraft will not always allow a high drag and low thrust line, so that some other method of balancing the flight forces must be found. This involves the use of the tail plane or horizontal stabilizer. One reason for fitting a tail plane is to counter the out-of-balance pitching moments that arise as a result of inequalities with the two main couples. The tail plane Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
Page |9 is altogether a lot smaller than the wings, however because it is positioned some distance behind the CG, it can exert considerable leverage from the moment produced (Figure 7.2(b)). At high speed the AOA of the main plane will be small. This causes the CP to move rearwards creating a nose-down pitching moment. To counteract, this tail plane will have downward force acting on it to re-balance the aircraft. Quite clearly, following the same argument, for high AOA at slow speeds, the CP moves forward creating a nose-up pitching moment. Thus, tail planes may need to be designed to carry loads in either direction. A suitable design for this purpose is the symmetrical cambered tail plane, which at zero AOA will allow the chord line of the section to be the neutral line. Most tail planes have been designed to act at a specified AOA for normal flight modes. However, due to variables (such as speed) changing AOA with changing load distribution and other external factors, there are times when the tail plane will need to act with a different AOI, to allow for this some tail planes are moveable in flight and are known as the all-moving tail plane. (Reference: Course note -71-Unit Theory of Flight) b) In aerodynamics, the flight envelope, service envelope, or performance envelope of an aircraft refers to the capabilities of a design in terms of airspeed and load factor or altitude. The term is somewhat loosely applied, and can also refer to other measurements such as maneuverability. When a plane is pushed, for instance by diving it at high speeds, it is said to be flown "outside the envelope", something considered rather dangerous. Flight envelope is one of a number of related terms that are all used in a similar fashion. It is perhaps the most common term because it is the oldest, first being used in the early days of test flying. It is closely related to more modern terms known as extra power and a doghouse plot which are different ways of describing a flight envelope.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
P a g e | 10 Extra power, or Specific Excess Power, is a very basic method of determining an aircraft's flight envelope. It is easily calculated, but as a downside does not tell very much about the actual performance of the aircraft at different altitudes.
Choosing any particular set of parameters will generate the needed power for a particular aircraft for those conditions. For instance a Cessna 150 at 2,500 ft (800 m) altitude and 90 mph (140 km/h) speed needs about 60 hp (45 kW) to fly straight and level. The C150 is normally equipped with a 100 hp (75 kW) engine, so in this particular case the plane has 40 hp (30 kW) of extra power. In overall terms this is very little extra power, 60% of the engine's output is already used up just keeping the plane in the air. The leftover 40 hp (30 kW) is all that the aircraft has to maneuver with, meaning it can climb, turn, or speed up only a small amount. To put this in perspective, the C150 could not maintain a 2g (20 m/s²) turn, which would require 120 hp (or somewhat more) under the same conditions. For the same conditions a fighter aircraft might require considerably more power due to their wings being inefficient at low speeds, for argument's sake it might require 10,000 hp (7.5 MW). However modern jet engines can provide considerable power, the equivalent of 50,000 hp (37 MW) typically. With this amount of extra power the aircraft can achieve very high maximum rate of climb, even climb straight up, make powerful continual maneuvers, or fly at very high speeds. All fixed-wing aircraft have a minimum speed at which they can maintain level flight, the stall speed (left limit line in the diagram). As the aircraft gains altitude the stall speed increases; since the wing is not growing any larger the only way to support the aircraft's weight with less air is to increase speed. While the exact numbers will vary widely from aircraft to aircraft, the nature of this relationship is typically the same; plotted on a graph of speed (x-axis) vs. altitude (y-axis) it forms a diagonal line. Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
P a g e | 11 Inefficiencies in the wings also make this line "tilt over" with increased altitude, until it becomes horizontal and no additional speed will result in increased altitude, this maximum altitude is known as the service ceiling (top limit line in the diagram), and is often quoted for aircraft performance. The area where the altitude for a given speed can no longer be increased at level flight is known as zero rate of climb and is caused by the lift of the aircraft getting smaller at higher altitudes, until it no longer exceeds gravity.
Task 5 a) Profile drag varies with air speed: Under Profile drag 1 skin friction: It implies that each layer of fluid molecules is moving at a different velocity relative to its neighbours. In turn, this means that a frictional force is generated in such a direction to oppose this relative motion. skin friction depend on air speed, If air speed more than skin friction more. 2 interference drag Another element of drag that can be mentioned is Interference drag. Experiments shows that the total drag of the aircraft exceeds the sum of the drags resulting from the component parts. The increase in drag is caused by the individual flow patterns interacting or "interfering" with their neighbours. This is generally reduced by the addition of fairings at the functions of the aircraft components. In summary, zero-lift drag is a combination of form and skin-friction drag, with the probable addition of interference drag. It is related to the separation of the airflow into a turbulent wake. This will be linked to the separation point, itself a function of Reynolds Number. Increased velocity leads to increased Reynolds Number and earlier separation. In fact, zero-lift drag is directly proportional to speed2.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
P a g e | 12
3 Form drag The change from laminar to turbulent flow is basically a function of the viscosity of the fluid. (Theoretically, a fluid with no viscosity would result in zero drag). How much turbulence occurs is usually dependent on the shape or form of the body being considered. Some shapes produce considerable turbulence; others minimise it. These shapes are obviously to be preferred and are often described as "streamlined". Some recognisable shapes are shown below, and a comparison made of the resulting turbulence. To allow comparison, it is assumed that the shapes present an identical cross-section to the airflow i.e. circular.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
P a g e | 13 Profile Drag is the drag incurred from frictional resistance of the blades passing through the air. It does not change significantly with angle of attack of the airfoil section, but increases moderately as airspeed increases Induced drag varies with air speed:
Figure - Induced drag curve
Induced drag is the inverse to the square root of speed. This means that if the speed is decreased by half, the induced drag fourfolds, this in contrast to parasite drag. At speeds nearing the stall speed, induced drag is therefore the the major cause of drag at low speeds but reduces as speed increases. Under certain conditions it is possible to observe aerodynamics and marvel at the physics of it all. On take-off all aircraft produce vortices at rotation in order to produce sufficient lift to get the aircraft airborne. If the air is moist, the pressure drop may be enough to cause condensation making vortices visible. (http://www.dutchops.com/Portfolio_Marcel/Articles/Aerodynamics/Forces/Drag/Induced_Drag.h tml) b) Drag and Airspeed: Parasitic drag increases with the square of the airspeed, while induced drag, being a function of lift, is greatest when maximum lift is being developed, usually at low speeds. The diagram below shows the relationship of parasitic drag and induced drag to each other and to total drag.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
P a g e | 14
Relationship of Drag with Airspeed There is an airspeed at which drag is minimum, and in theory, this is the maximum range speed; however, flight at this speed is unstable because a small decrease in speed results in an increase in drag, and a further fall in speed. In practice, for stable flight, maximum range is achieved at a speed a little above the minimum drag speed where a small speed decrease results in a reduction in drag.
Task-6 a)
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
P a g e | 15 A similar situation is found in the horizontal plane when the aircraft changes heading. The pilot must bank the aircraft so that the horizontal component of lift provides a CPF. But to maintain the vertical component equal and opposite to weight, he must apply back-pressure on the control column in order to increase lift. Hence, the load factor increases beyond 1 in a horizontal turn as well.
It is worth recalling that CPF is equal to: CPF = where v = speed, r = radius of turn and w = weight. Also, it can be proved that tanď ą =
where ď ą = angle of bank.
So increased weight, high speed and "tight" radius of turn all impose high load factors on aircraft. It should also be appreciated that increased angle of attack leads to increase drag coefficient and increased drag. Therefore, manoeuvres involving high 'g' forces require considerable increase in thrust. b) The aircraft's flight path is no longer a straight line but now follows a curved path. In general, any condition in which the aircraft's lift is not equal to its weight will result in a curving flight path, but the specific case you are asking about is the level turn illustrated below.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
P a g e | 16
Aircraft in a level turn You will note in the front view of the aircraft that the plane is rolled away from the horizontal and vertical planes by the angle φ discussed earlier. The lift vector L acting on the aircraft is also rolled by that same angle such that it no longer directly opposes the plane's weight. Now observe the following diagram.
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
P a g e | 17
Comparison of an aircraft banking with an aircraft in a level turn In both cases, the aircraft is rolled to the same bank angle. In the first case, however, the vertical component of lift is less than the weight. Because of this inequality, the greater force imparted by the weight will pull the aircraft downward and it does not maintain the same altitude. The pilot can overcome this behavior by pulling the stick back to increase the lift of the plane and maintain the same altitude. It is for this reason that we refer to the maneuver as a level turn, since the aircraft is banked into a turning motion but maintains the same altitude. (Referance:http://www.aerospaceweb.org/question/performance/q0146.shtml)
Reference: http://www.aerospaceweb.org/question/performance/q0146.shtml http://www.ustudy.in/node/3464 Course note -71-Unit Theory of Flight http://en.wikipedia.org/wiki/Parasitic_drag Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02
P a g e | 18 http://www.dutchops.com/Portfolio_Marcel/Articles/Aerodynamics/Forces/Drag/Induced_Drag.ht http://www.aerospaceweb.org/question/performance/q0146.shtml
Name: Haraykrishna Biswas ID-ACB12-09-05
Unit Title: Theory of flight Assignment No: 02