Aerodynamics for Engineering - Assignment Example

Name) (Instructor) (Institution) (Course code) (Date) Question 1 i. Equal transit-time This misconception assumes that the collection of air that spilt at the front end of the aerofoil must reunite at the back end, leading to the air on the upper longer surface of the aerofoil to move faster. The conclusion is often drawn from the Bernoulli’s principle that the air along the lower surface has higher pressure resulting to the aerofoil being pushed upwards causing lift (Van Pelt, 2012, Pg. 39) However there is no evidence or principle to prove that this misconception is false. It is true that the air moving on the upper surface of the aerofoil creating the lift moves at a greater speed than how the equal transit theory says. Additionally, the philosophy disregard Newton’s third law of motion, as it illustrates the force on the aerofoil and no opposite force The assumption that air should arrive concurrently at the back end is usually known as the Equal Transit- Time theory Fallacy (Van Pelt, 2012, Pg. 39) ii. Pulling down of the flow The justification about the coanda effect at times is also talks about the movement over the upper part as sticking to the aerofoil and it pushed down to attract to the surface. The explanation is not in line with the physics of gases. For example, the kinetic theory of proves that pressure cannot be negative at a positive absolute temperature in gases. Therefore, for the movement to curve downward on the upper humped surface, it should be pushed down by a greater pressure compared to the lower surface. The variation in pressure between movement at far above the aerofoil and the adjust flow is normally so small in comparison with the general atmospheric pressure. The minimum pressure on the upper surface will still remain to be positive in absolute sense (Schutte, 2012, Pg. 221) iii. The role of viscosity Another misconception regarding the lift is about the role of viscosity as explained in the coanda effect. The explanation says the viscosity of the movement at the covering layer is the reason for the movement the humped upper surface of the aerofoil. Though, the notion that viscosity plays a key role in the movement turning is not in line with the physics of rounded edge flows. Scrutiny of the motion balance in the boundary layer demonstrates that the movement is produced exclusively by the pressure. It further expounds that viscosity does not play any primary role in the flow on the curved surface (Houghton and Carpenter, 2003, Pg. 494) Question 2 The aerofoil shape allows it to generate lift. Its top is greatly humped while its underneath is flat. As the aeroplane move in the air usually at high speed, the air move at higher speed compared to the lower surface. This results to a lower pressure at the top surface compared to the underneath surface. The aerofoil is sucked in the air due to the pressure generated. The aerofoils in aeroplanes are not only made with strong material therefore cannot easily break but they are also tightly attached to the planes. This causes the plane to be lifted in the air (Houghton and Carpenter, 2003, Pg. 211) The above explanation is not the only factor that leads to the production of the lift. In reality, the aerofoil is usually inclined to the airflow at a negligible angle. This angle is normally positive to allow the diversion of air downwards Question 3 The plane’s wing has the shape of a bird’s wing. It is designed to be so for the purpose of flight. The distinctive shape is called aerofoil. This shape is commonly found on propellers, wings and fans. The front end of the aerofoil is thicker and rounded while the back end (trailing edge) is very thin. Between the front end and the back end is curve at the bottom and at the top surfaces. The upper surface greatly humped (curved) than the lower surface. Curved surfaces are known as camber (Houghton and Carpenter, 2003, Pg. 221) The aerofoils are thickened in the middle to give the maximum lift possible to the plane while in flight. At a suitable angle of attack for a flat aerofoil, it will create it will create both the lift as well as a lot of drag (Fahy, 2009, Pg. 56). Otto Lilienthal and Sir George Cayley demonstrated the curved objects create more lift with less drag as compared with the flat surfaces during the 19th Century (Schmidt, 2002, Pg. 8). Other research demonstrate that round front end and a sharp, flat back end improves the ability of the aerofoil to create more lift with minimum drag The aerofoil is also shaped as it is in order to take advantage of the Bernoulli’s Principle. The top surface of the aerofoil is highly curved allows the air flow faster than the lower surface. It results to less air pressure on the upper surface as compared to underneath the aerofoil. The difference in pressure between the upper and the lower surface cause lift The aerofoil is flatter at the lower surface with top cambered in order to maximize the lift coefficient at the same time lowering the stalling speed of plane by use of aerofoil. Planes designed with cambered aerofoils normally have lesser stalling speeds as compared with whose aerofoils are symmetrical in nature (Silverman, 2014, Pg. 422) The back end of the aerofoil is normally tapered in order to not only boost the streamline flow but also it is meant to prevent it from breaking from the aerofoil surface The aerofoil is humped (curved) at the upper surface while it is flattened at the lower surface in order to increase distance at the top surface which the air travel as compared to the distance travelled at the lower surface. The air on the upper surface will therefore move at an increased speed than the air below. The resulting effect is that lower pressure is created on the upper surface as compared to the pressure below the aerofoil. A lift is thus created. Question 4 The house brick does not generate lift due to its shape. There is no difference in pressure generated. On the other hand, football in flight generates lift as well as drag. The lift ceases when its symmetry axis points in the velocity direction. When spinning, the drag torque on it as well as exert a force. Saucer also generates lift. In fact many military planes have been designed with the shape of the saucer Question 5 Causes of Drag Drag in aerodynamics refers to forces that oppose the relative motion of a body moving through the surrounding fluid. It is force acting horizontally parallel to the path of flight, opposing the thrust. Drag can occur between solid and fluid surfaces or between a two fluid layers. Drag is different from other resistive forces which merely depend on velocity (Administration, 2013, Pg. 5). This is because drag forces fully depend on the velocity on the velocity of the body relative to the fluid. Types of drag Parasitic drag Parasitic drag is mainly caused by difference in pressure and friction in front and behind an aerodynamic object. It is created by a low pressure area formed behind a body moving through air fluid. In airplanes, parasitic drag is caused by parts that do not cause lift. These parts include windshield, tires, rivets, etc. There exist three forms of parasitic drags namely; interference drag, form drag and skin-friction drag (Payne, 2006, Pg. 286) Induced drag Induced drag is a resistance that occurs due to lift production. It is a drag associated with pressure differences below and above the surfaces of an aerodynamic body. As the speed of air reduces, the aerofoil is required to create an increased low pressure zone above and a high pressure zone below the aerodynamic body. The pressures at the wingtip form a vortex due to high pressures forming around its surface. This causes the wingtip to be sucked upwards due to law pressure above the aerodynamic object. The speed off an object through air is decreased with an increase in induced drag (Payne, 2006, Pg. 286) Question 6 Boundary Layer A boundary layer is a layer of stationary fluid formed when fluid in contact with the surface is forced to stop by shear stress. The velocity of fluid increases from the surface to the highest velocity at the main torrent of flow. The basic concept of fluid mechanics describes boundary layers as a fluid layer formed in fluids with high Reynold Numbers. These are fluids having a moderately lower viscosity in compared to the associated inertia forces (Rajput, 2002, 716) Boundaries layers are large bodies are exposed to air streams moving at a moderate velocity. The fluid boundary layer grows starting from zero as the fluid starts to flow against a solid surface. More fluid is forced to slow down by the friction by the fluid particles near the solid boundary surface. This shows that increase in length of the solid boundary decreases the fluid velocity to stationary (Rajput, 2002, 716). In airplanes, there air on the surface of the plane body has a smaller velocity compared to air far away from the surface. Assuming that the air is in motion and the plane is in a stationary state, there exists a thin boundary layer in which air near the surface is acted upon by shearing motion. The viscosity of air causes resistance to shearing resulting to shear stress formation on the airfoil surface, also referred to as skin-friction drag. The turbulent nature of boundary layers increases the skin-friction drag on the surface of the airfoil. Question 7 Definition and causes wingtip vortices Wingtip vortices are whirlwind forms of patterns rotating behind the wings of an aircraft or an airfoil as it generates a lift. A wingtip vortex stars from the end edge of each particular wing. Lift-induced or trailing vortices are names given to vortices that are formed by other causes other than plane or jet wing tips. Wingtip vortices occur at any point of the wing where there is an abrupt variation in the platform of the wing. Small circular patterns form at any point of the wing where there is a span-wise lift variation commonly explained vividly in the lifting-line theory (Dole, & Lewis, 2000, Pg. 76) Wingtip vortices are commonly caused by the difference in pressure between the lower and the upper wing surface. Air obeys the fluid laws therefore; it flows from a region of high pressure to a region of a lower pressure. Therefore, air below the wing surface flows from the wing center to its tip. From the tip, it further continues to flow over towards the upper surface of the wing. The forward movement of the airplane causes the formation of a horizontal tornado originating from the irregular wingtip edge which is an aerodynamic element (Dole, & Lewis, 2000, Pg. 76). Question 8 Formulas for Lift & Drag The drag amount produced by an aerodynamic object is dependent on numerous factors such as velocity between the air and the object, air density, air compressibility and viscosity, object shape and size, and inclination of the body to the flow. Therefore, the drag equation is stated as:- D=0.5 x Cd x r x (V/2)2 x A Where D is drag caused by the object, Cd is the coefficient of drag, R is the air density, V is the velocity of the aerodynamic object, and A is the area of the wing or the aerofoil. The coefficient of drag is an important factor to consider in determination of the amount of drag an aerodynamic body generates. The object inclination and its shape define the value of drag coefficient in a given condition of air. The drag coefficient is formed by two components which are the effects of shape of the object and the skin friction and the coefficient as a result of the aircraft lift. The induced drag forms the additional drag resulting from the resistance experienced at the wing tips of the aircraft (Payne, 2006, Pg. 286). The equation for coefficient of drag is given as; Cd = Cd0 + Cl2 /( x Ar x e) Where Cd is the coefficient of drag, Cd0 is the coefficient of drag at the zero lift, Cl is the coefficient of lift, Ar is the aspect ratio, and e is the factor of efficiency. QUESTION 9 The aerofoil shown below is not symmetrical as drawn using XFLR5 software package. The pressures of the upper and lower surfaces are different. This means that there is a higher pressure in the lower surface than the upper surface causing an upward lift. a) CL versus Alpha graph using a XFLR5 software package Using CADA 0012 series, the plot below is obtained. a) CD versus Alpha graph using a XFLR5 software package Using CADA 0012 Question 10 From the plots in section question 9, a)Angle gives zero lift For CL versus Alpha curve = 0.00 For CL versus Alpha curve = 0.510-3 b) Angle gives maximum lift For CL versus Alpha curve = 1.3 For CL versus Alpha curve = 5.25-2 In conclusion, Bernoulli’s equation on pressures gives a precise explanation to the cause of lift. The streamline nature of an aerofoil makes a lifting wing characteristics and operation too obvious. However, the real engineering behind the phenomenon lies on the required analysis and calculations for the pressures, drag, friction and other properties of aerodynamic mechanics. References Administration, F. (2013). Helicopter Flying Handbook. New York: Skyhorse Publishing, Inc., pp.2-6. Anderson, John D. Jr. Introduction to Flight, 7th edition, McGraw-Hill, 2012, pp.405-413. Dole, C. E., & Lewis, J. E. (2000). Flight theory and aerodynamics: a practical guide for operational safety. New York [u.a.], Wiley. Fahy, F. (2009). Air. Chichester, UK: Horwood Pub., p.56. Houghton, E. and Carpenter, P. (2003). Aerodynamics for engineering students. Oxford: Butterworth-Heinemann, pp.211,221,494. Payne, C. (2006). Principles of naval weapon systems. Annapolis, MD: Naval Institute Press, p.286. Rajput, R. K. (2002). A textbook of fluid mechanics and hydraulic machines in SI units. Ram Nagar, New Delhi, S. Chand. Schmidt, N. (2002). Super paper airplanes. New York: Sterling Pub. Co., p.8. Schutte, P. (2012). Revealing corrupt science. [Place of publication not identified]: Xlibris, p.221. Silverman, M. (2014). A certain uncertainty. p.422. Van Pelt, M. (2012). Rocketing into the future. New York: Springer, p.39. Read More