Aerodynamics and Propulsion Principles - Coursework Example

Aerodynamics and Propulsion Principles Task 1: Question No. 1: Area of the aircraft = S = 29 m2 Coefficient of Lift = CL = 0.67 Altitude = A = 29000 ft Velocity = V∞ = 385 km/hr = 106.94 m/s Lift = L = ? Solution: Density at given altitude ‘A’ = A = 0.4671 kg/m3 (Anderson Introduction 763) Lift on an airfoil is given as L = (½A V∞2) S CL Putting the values, L = (½ (0.4671) (106.94)2)(29)(0.67) = 51,891 N = 5.2 E+4 N In a straight and level flight, lift forces are equal to the weigth of the body, hence, L = W = mg Value of ‘g’ at 9km from sea level = g = go (r/(r+h)) = 9.81 (6400/ (6400+9)) = 9.796 m/s2 Using the above values of lift and ‘g’; 51891 = m (9.796) => m = 5297 kg Question No. 2: Coefficient of Drag = CD = 0.054 Area = S = 15 m2 Thrust = T= 1500 N Density= A = 0.5 kg/m3 For a steady and level flight, drag force is equal to the thrust produced by engines, D = T = 1500 N D = (½ A V∞2) S CD = (½ (0.5) (V∞2)) (15) (0.054) = 1500 => V∞ = 86.06 m/s = 8.6 E +1 m/s Question No. 3: Question No. 4: The sketches shown below illustrate the trend of variation in CL, CD, and L/D ratios with increasing angle of attack. Question No. 5: Critical Mach number corresponds to that value of Mach number for free stream flow for which a localized mach number of ‘1’ is obtained at any point around the airfoil. When this condition arises, a shock wave is created at the point where the flow reaches the sonic speed. As the speed increases, regions of very low pressure are created. This causes the flow to separate from the airfoil thereby substantially increasing the drag forces on it. The figure illustrates this phenomenon. Some of the important design features incorporated in the aircrafts in order to contain the effects of this situation are using thin airfoil and / or super critical airfoil (Anderson Introduction 763). Making an airfoil thinner increases the value of Critical Mach Number and hence the airplane can fly at very high speeds without a significant increase in drag forces on it. An example of using this technique is Bell X – I which is the first airplane to break the sound barrier. The achievement of this amazing feat, considered impossible until then, is attributed largely to its ‘super thin wings’ (Bell X-I). The super critical airfoils differ from the conventional airfoils such that they have comparatively flat at the top. Their unique design limits the rise of drag forces even after the critical mach number is reached. Such airfoils have successfully been utilized in TACT aircraft program run by NASA Dryden Flight Research Center (Cury). Question No. 6: In the above illustration, the triangle represents the fuselage of an aircraft as seen from front. ‘’ is the angle of bank for the turn. LV = L cos  LH = L sin  The centripetal force required by the aircraft to take the turn is provided by horizontal component of lift force given by LH, equating the two; L sin  =  … (a) the component LV balances the weight of the aircraft, hence = L cos  = mg From the above equation, L = mg / cos  Putting values in (a) and simplifying; g tan  =  putting values for  = 15o and r = 1500 m gives v = 62.79 m/s Load Factor = L/W = L/L cos  = 1/ cos  = 1/cos 15o = 1.035 Question No. 7: Following are the control surfaces used to control the motion of an aircraft along different axes: (1) The longitudinal axis: Ailerons (2) The Vertical or Normal Axis: Rudder (3) The lateral Axis: Elevator The figure shows the above mentioned control surfaces and the functions they perform. All the control surfaces work on the principle of creating drag for the incoming wind thereby changing the direction of the wind. Due to this change in velocity, a momentum change occurs which causes a force to act on the control surface and the desired movement of the aircraft is achieved this way. The ailerons tilt the aircraft around the longitudinal axis. They are always installed in pairs. The opposite motion of the two ailerons creates a couple which acts about the longitudinal axis to cause the desired motion. Rudder rotates the airplane around vertical or normal axis. The rudder is installed in the vertical stabilizer at the tail of the aircraft and it is free to rotate sideways. Elevator is installed on the horizontal stabilizer and is free to rotate upwards or downwards. Question No. 8: Anderson defines static stability in these words “If the forces and moments on a body caused by a disturbance tend initially to return the body towards its equilibrium position, the body is statically stable”. Hence a statically stable plane will be that aircraft which can maintain a continuous balanced flight with constant angle of attack. In case of a wind gust causing angle of attack to increase, the resultant centre of pressure (the point where resultant lift force acts) will shift forwards from the centre of gravity of the aircraft and a resultant moment will act that will restore the initial position of the aircraft. This phenomenon is illustrated in the figure which shows an aircraft exhibiting longitudinal static stability. From the above discussion, it can be easily concluded that the trainer aircrafts must have good static stability so that the new pilots are not faced with a greater challenge of continuously stabilizing the aircraft by the use of control surfaces. Now the question arises that why fighter planes are not designed to be statically stable. The answer to it lies in the fact that statically unstable aircrafts possess increased maneuverability as compared to the statically stable aircrafts. A statically unstable aircraft will not resist any change in its position, by definition, and hence will lend itself to good maneuverability. An example of such a fighter aircraft is F-117 Nighthawk. Question No. 9: Roll stability in an aircraft can be attained by giving a dihedral angle to the wings as shown in the figure. When the aircraft rolls to one side, the wing on that side offers more area as seen from the direction of the approaching wind. This results in a greater lift under the wing which causes a restoring moment to act thereby restoring the initial position of the aircraft. Another important feature that gives roll stability is sweep back of wings i.e. wing pointing backwards towards the tail of the aircraft. In case of a sideslip as shown in the figure, the effective cross-sectional area of the higher wing is lesser than that of the lower wing and hence more lift acts on the lower wing to restore the level flight, Yaw stability can be achieved by installing a ‘fin’ on the top of the tail of air craft. It balances the aircraft by the restoring moment exerted by reltive wing about the vertical axis as shown in the figure. The sweep back of wings also helps in restoring an aircraft to its original position as the increased cross-sectional area of a wing offers more drag causing a restoring moment to act about the vertical axis. The effect is shown in figure. Figure 6 Yaw Stability in an aircraft through fin installation and sweep back of wings Image Courtesy: (www.engbrasil.eng.br/index_arquivos/ap28.pdf) Question No. 10 Waisting is to decrease the area of the fuselage of an aircraft at the point where wings are attached to it in order to increase its performance at high speed flights. In the traditional aircrafts, the increase in the cross-sectional area is not smooth along the longitudinal axis. Especially at the position where the wings are attached to the fuselage, the cross-sectional area rises abruptly. At high speeds, this abrupt rise causes a significant increase in the drag coefficient of the aircraft. Task 2: Question No. 1 Wing Area = S= 25 m2 Mass = m = 6950 kg Cruise altitude = 20,000 ft = 6,096 m Coefficient of Lift = CL = 0.6 Lift = Weight = 6950 (9.81) = 68110 N Density of air at 20,000 ft = A = 0.6528 kg/m3 (Anderson Introduction 763) Lift on an airfoil is given as L = (½A V∞2) S CL Putting the values => 68810 = ½(0.6528) (V∞2) (25) (0.6) => V∞ = 117.94 m/s = 1.18 E+2 m/s Question no. 2: As the height increases, density decreases which causes the lift to decrease. In order to maintain a level flight the cruise speed must be increased so pilot must increase engine throttle. Density of air at new altitude = 0.57015 kg/m3 The new cruise speed for a straight and level flight can be calculated from the equation used previously. L = (½A V∞2) S CL => 68110 = ½ (0.57015) (V∞2) (25) (0.6) V∞ = 126.2 m/s Question no. 3: Drag will increase as a result of this action. Question no. 4: Drag can be reduced by selecting right airfoil and decreasing the surface area. Question no. 5: Equation for angle of bank is L/W = 1/ cos  Given that load factor is 3.5g implies that L/W = 3.5 Using the given information, angle of bank comes out to be  = 73.4o Task 3: An important challenge for the civil aviation industry is to increase the capacity of an aircraft and at the same time the fuel economy should not be compromised. In technical terms this statements translates into a need of more lift but less drag force. An obvious technique for increasing the lift of an aircraft would be to increase the area of the wing. This, however, will also increase the drag force during the flight increasing the amount of fuel consumed. Hence different modifications in wings are made by designers that can modify the wing of an aircraft during the flight according to pilot’s requirement to increase the lift and decrease the drag forces. Two such modifications, flaps, slots and slats, will be discussed here. Flaps: Flaps are attached at the trailing edge of a wing to increase the lift during take-off. Once taken off, the flaps are returned to their original position thereby reducing the wing span. The opening of flaps increases the camber of the wing which in turn increases the lift (Taylor 276). Flaps can be attached to the wing in a variety of ways. They can be attached as a ‘split trailing edge’ which is hinged to the wing and can be lowered for the flap to perform its normal operation. Another way is to use ‘slotted flaps’. These flaps are hinged to the wing in such a way that when the flap is opened a slot is created between the wing and the flap. The most common however in the modern aircrafts is the attachment at the bottom of the wing that can be moved in or out when the flap needs to be opened or closed. Flaps can also be used in opposite direction i.e. moved upwards instead of downwards to increase drag during landing. Slats and Slots: Slats are installed on the leading edge of a wing to aid in the take off by increasing the lift forces generated. These slats increase the angle of attack on a wing in order to increase the lift (Roskam 87). Slats can also be fixed or moveable. Another important addition to increase the lift is the addition of slots. Slots are gaps between wing and slats that appear when slats are opened for their normal operation. These gaps help a great deal in increasing the lift by improving the aerodynamic characteristics of the wing. When air from bottom of the wing moves towards the top through the slot due to difference in pressure, it decreases the boundary layer separation between the wing and the free stream. This significantly increases the stall speed of the air craft at the increased angle of attack which is caused by the operation of slats. Hence the operation of slats is strengthened by the slots and together these devices can increase the lift coefficient by as much as 0.5 (Roskam 87). The figure here shows the flaps and slats being installed along with the other control surfaces on the A-380 Airbus wings. These devices are commonly used by large sized commercial aircrafts such as Boeing 747, Boeing 777 and different Airbus models. Bibliography Aeronotics Learning Laboratory for Science, Technology and Research. N.p., n.d. Web. 7 Feb. 2011. . Anderson, Jr., John D. Aircraft Performance and Design. Singapore: McGraw Hill, 1999. Print. Anderson, Jr., John D. Fundamentals of Aerodynamics. Third. Singapore: McGraw Hill, 2001. Print. Anderson, Jr., John D. Introduction to Flight. Fifth. New York: McGraw Hill, 2005. Print. "Bell XI." California Science Center. N.p., n.d. Web. 15 Feb. 2011. . Cury, Martin. "F-111 TACT wing sweep." NASA Dryden Flight Research Center. N.p., n.d. Web. 13 Feb. 2011. . Roksam, Jan, and Chuan-Tau Edward Lan. Airplane aerodynamics and performance. First. Kansas: Design, Analysis and Research Corporation, 1997. Print. Scott, Jeff, ed. aerospaceweb.org. N.p., n.d. Web. 15 Feb. 2011. . Taylor, and Francis. airliners and airways of today. London: The Pilot Press, 1947. Print. Read More