Principles of Aerodynamics - Coursework Example

Principles of Aerodynamics Task 1: Q No. 1: Altitude = h = 29000 ft Coefficient of Lift = CL = 0.67 Area of the aircraft = A = 29 m2 Velocity = U∞ = 385 km/hr = 106.94 m/s Lift = L = ? Solution: Density at given altitude ‘h’ = h = 0.4671 kg/m3 (Anderson Introduction 763) Lift on an airfoil is given as L = (½h U∞2) A CL Putting the values, L = (½ (0.4671) (106.94)2)(29)(0.67) = 51,891 N = 5.2 × 104 N In a straight and level flight, lift forces are equal to the weight of the body, hence, Lift = Weight of aircraft = m g 51891 = m (9.796) => m = 5297 kg Q No. 2: Coefficient of Drag = CD = 0.054 Area = A = 15 m2 Thrust = FT= 1500 N Density= h = 0.5 kg/m3 For a steady and level flight, drag force balances the thrust acting, D = FT = 1500 N D = (½ h U∞2) A CD = (½ (0.5) (U∞2)) (15) (0.054) = 1500 => U∞ = 86.06 m/s = 8.6 × 101 m/s Q No. 3: Q No. 4: The sketches shown below illustrate the trend of variation in CL, CD, and L/D ratios with increasing angle of attack. Q No. 5: “The value of free stream Mach number at which the flow somewhere on the surface first reaches M = 1 is called critical Mach number.” (Houghton and Carpenter 332)The above figure illustrates the flow around an airfoil as the Mach number approaches critical value. The distinct area of flow being developed around the airfoil is actually the generation of a shock wave. As the Mach number increases, the separation between the airfoil and the fluid flow increases. The flow becomes turbulent in the layers adjacent to the airfoil. This causes an increase in drag force on the airfoil. Modern aircrafts use different features in order to avoid adverse effects of high speed flight, important among these include using thin airfoils, using super critical airfoils and using sweep back angle (Anderson Introduction 298). A thin airfoil has low air speed around it relative to free stream velocity. Hence, its critical mach number is very high and it can easily fly at very high speeds. An example of this feature being effectively utilized is in the aircraft ‘Miles M.52’ developed in UK during World War II and was the first plane in UK to break the sound barrier (Keach). Super critical airfoils have unique shape that allows them to fly without experiencing significant drag even after critical Mach number is achieved. As shown in the adjacent figure, the shock wave produced around a super critical airfoil is less severe as compared to a traditional airfoil. This allows the airfoil to avoid rise in drag at sufficiently high Mach numbers. Q No. 6: In the adjacent figure, the lift force acting on the aircraft is resolved in to two components, one along the horizontal axis and other along the vertical axis as shown. LV = L cos  LH = L sin  The horizontal component is equal to the centripetal force acting on the plane, hence; L sin  =  … (i) the vertical component is equal to the weight of the body, hence = L cos  = mg Re-arranging, L = mg / cos  Putting values in (i) and simplifying; g tan  =  putting the given values:  = 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 Q No. 7: The control surfaces that give control to the pilot along different axes are as follows; The Vertical or Normal Axis Rudder The lateral Axis Elevator The longitudinal axis Ailerons These different control surfaces are shown in the above figure. Ailerons: To rotate the aircraft around its longitudinal axis, ailerons are used. This manoeuvre is required when the pilot intends to perform a loop in the air. Two ailerons are installed, one on each wing, which operate in opposite direction to obtain the desired motion. Rudder: Rudder is installed at the tail of the aircraft and it gives motion about the vertical axis. Rudder is installed as a single component and is not required to operate in pairs as in the case of ailerons. Elevators: these are also installed in the tail of the aircraft. They can comprise of one or more than one units. These are extensively used for landing and take-off. Q No. 8: The tendency of an airplane to develop forces and moments that can restore its initial steady state after it experiences a disturbance is called Static Stability for an airplane (Yechout and Morris 173) Two important terms need to be defined here. First is Centre of Pressure, which is the point where the resultant lift force acts on the aircraft body and other is more familiar Centre of Gravity where the weight of aircraft appears to be acting. During steady flight, both points coincide with each other. When, after a disturbance occurs in the normal flight of the aircraft, its centre of pressure moves in back or forth in such a way that it develops a restoring moment on the aircraft then such an aircraft is said to possess static stability. It is important to note that the aircraft need not come to precisely the same position as it was previously. (Anderson Introduction 546). The trainer aircrafts for fresh pilots and the commercial aircrafts, all are designed to be statically stable in order to maintain a steady flight. This feature is essentially desirable for these types of aircrafts. However, fighter planes may not be designed statically stable. This is because these aircrafts need to have high maneuverability in order to perform well in a battle. Hence they sacrifice the stability so that when pilots moves the control surfaces of the aircrafts it is easily oriented to the new position without any opposition from the design features of the aircraft itself. Military aircrafts have control systems (computers) installed in them which move the control surfaces in order to balance the aircraft in case of a disturbance. Q No. 9: Roll Stability: Two important features in an aircraft that give it roll stability are dihedral angle and wings sweep back. The dihedral angle is the angle by which the wings of an aircraft are bent upwards (Anderson Introduction 564) as shown in the adjacent figure. When the aircraft experiences a roll due to sudden gust of wind, the effective area of wing exposed to the incoming air is different for both the wings as shown in the figure. The wing with less area exposure will experience less lift as compared to other. A moment will hence act about the longitudinal axis of the aircraft restoring its position. Roll stability can also be achieved by giving a sweep back angle to the wings. The mechanism of restoring moment generation is essentially the same in this case as well. Yaw stability: Features that can give yaw stability to an aircraft are fin attached to the vertical stabilizer, and sweep back of wings. A fin attached to an aircraft’s tail is shown in figure. In case of a yaw experienced by an aircraft, a drag force acts on the fin due to the incoming wind which exerts a restoring moment on the aircraft body. Hence the aircraft regains its original position. In case of a yaw around vertical axis, sweep back of wings is also helpful in providing stability. This is because if aircraft is tilted from its original position, as shown in figure, one of the wings exposes more surface area than other and hence experiences more drag. The difference in drag forces causes a moment to act on the aircraft returning it to original position. Q No. 10 Waisting is a design feature in an aircraft according to which, the frontal area of the fuselage of the aircraft is reduced at the point of attachment of wings in order to achieve a smooth increase in the area. The process is sometimes referred to as ‘Area Rule’. Aircrafts, in which fuselage area is not decreased, experience very high rise in drag forces at high flight speeds (Anderson Aircraft Performance 39). Task 2: Q No. 1 Mass = m = 6950 kg Coefficient of Lift = CL = 0.6 Wing Area = A= 25 m2 Cruise altitude = h = 20,000 ft = 6,096 m Lift = Weight = 6950 (9.81) = 68110 N Density of air at 20,000 ft = h = 0.6528 kg/m3 (Anderson Introduction 763) Equation for lift can be written as L = (½h U∞2) A CL Putting the values => 68810 = ½(0.6528) (U∞2) (25) (0.6) => U∞ = 117.94 m/s = 1.18 × 102 m/s Q no. 2: Increase in height of the aircraft causes its density to decrease. As density and lift are directly proportional, lift will also decrease causing the aircraft to lose height. If pilot wants to regain height, it has to increase speed. Density of air at increased altitude = 0.57015 kg/m3 (Anderson Introduction 763) According to the lift equation, L = (½h U∞2) A CL Putting the known values => 68110 = ½ (0.57015) (U∞2) (25) (0.6) U∞ = 126.2 m/s Q no. 3: An increase in speed will also cause the drag to increase. Q no. 4: During the design phase, the correct selection of airfoil having low value of CD relative to CL can help in reducing the drag. Q no. 5: Angle of bank can be related to load factor as L/W = 1/ cos  We know that load factor = L/W = 3.5 Putting the values and solving for angle of bank, the answer is  = 73.4o Task 3: Modern aviation industry has been able to optimize the performance of its aircrafts by using ‘High Lift Devices’. These devices are actually additional features incorporated in a normal wing of the aircraft which can give the aircraft, a substantial increase in lift under special circumstances i.e. during take-off or when aircraft needs to gain extra height. Important among these are flaps, slats and slots. Flaps: Flaps are moveable wing surfaces at the trailing edge of the wing as shown in the figure. The flaps are added to increase the camber of the wing in order to give extra lift (Lombardo 318). The flaps are generally hinged to the wing and are kept as an integral portion of the wing during normal flight. However, when extra lift is required, flaps are lowered as shown in the figure. Flaps can be of many different types on the basis of their shapes and attachment mechanism to the wing. A few types also increase the surface area of wing apart from increasing the camber which also adds to the amount of lift generated. One such type is known as Fowler flap (Lombardo 318). Slots: ‘Slots are passage ways cut through the leading edge of the wing’ allowing air to flow from the bottom of the wing towards its top (Lombardo 318). Due to this motion of the air, the flow field characteristics around the wings are considerably improved. This happens because the boundary layer separation between wing and air flow decreases. A decrease in boundary layer separation results in making the flow field laminar. This causes an increase in the lift forces acting on the wing. Slats: Slats are also a type of surfaces installed on the leading edge of an aircraft in order to give it extra lift force when required. These surfaces are moveable and are displaced from their normal position during take-off etc. a slat in open position is shown in above figure. Slats provide extra lift force by changing the angle of attack of the incoming wing on the airfoil (Roskam 87). Figure below shows high lift devices attached on Boeing 707-331C commercial aircraft. The flaps are shown lowered soon after take-off. Works Cited Anderson, John D., Jr. Aircraft Performance and Design. Singapore: McGraw Hill, 1999. Print. Anderson, John D., Jr. Fundamentals of Aerodynamics. Third. Singapore: McGraw Hill, 2001. Print. Anderson, John D., Jr. Introduction to Flight. Fifth. New York: McGraw Hill, 2005. Print. Houghton, Edward Lewis, and Peter William Carpenter. Aerodynamics for engineering students. Fifth. N.p.: Butterworth-Heinemann, 2003. Print. Keach, Stacy. "Faster than Sound." NOVA Beta. Ed. Lauren S. Aguirre. N.p., 14 Oct. 1997. Web. 19 Feb. 2011. . Lombardo, David A. Advanced Aircraft Systems. N.p.: McGraw-Hill Professional, 1993. Print. Roksam, Jan, and Chuan-Tau Edward. Airplane aerodynamics and performance. First. Kansas: Design, Analysis and Research Corporation, 1997. Print. Yechout, Thomas R, and Steven L Morris. Introduction to aircraft flight mechanics. Virginia: American Institute of Aeronautics and Astronautics, 2003. Print. Read More