Aero Club. Introduction to Flight

Transcription

1 Aero Club Presents Introduction to RC Modeling Module 1 Introduction to Flight Centre For Innovation IIT Madras

2 Page2 Table of Contents Introduction:... 3 How planes fly How is lift generated?... 3 Forces on an Airplane:... 4 Basic geometric parameters of a Wing:... 5 Wing Span and Aspect Ratio... 6 Other geometric variations:... 7 Parts of an Airplane:... 8 Basic Controls of an Airplane Motion:... 8 Roll:... 9 Pitch:... 9 Yaw:... 9 Achieving Motion:... 9 Level Flight/Cruise:... 9 Turn:... 9 Ascent/Descent: A Typical Flight Path: Exercises: Acknowledgements:... 11

3 Page3 Introduction: It is always one s dream to fly or make something fly. Ever wondered how a heavier than air object like an airplane is able to attain sustained flight? Let s find out how! How planes fly How is lift generated? The answer to the above question comes from the basics of fluid dynamics and the advantages of asymmetry in fluid dynamics. Fluid flow over a body develops pressure on the surface of the body. If the body is symmetric about horizontal plane (plane along the flow) the pressure developed on upper and lower half will be equal. If an asymmetric body is placed in a flow, the pressure developed on the upper and lower surfaces won't be equal and the pressure difference thus developed results in a net force on the body. The direction of this resultant force depends on the nature of asymmetry present. Hence, a body can thus be designed such that the pressure developed will result in a force perpendicular to the flow upward. This force is what we call 'Lift' (L) and is the one responsible for flight. A faster airflow results in the reduction of pressure and a slower airflow relatively is in a higher pressure state. At subsonic speeds they follow this relation P + ½ ρ v 2 = P where ρ is the density of the fluid P is the pressure P 0 is the stagnation pressure of the flow The pressure when there is no flow. A stick placed at an acute angle to the flow, a symmetric airfoil placed at an acute angle with the flow, an airfoil with a camber (an initial asymmetry in the airfoil is described by the camber line) are some examples of the 'asymmetric body' that can generate lift we are talking about. The Lift generated has an empherical formula proportional to surface area of the wing, the square of velocity of air flow and the density of the flow. ρ - Density of the fluid medium v- Velocity of the plane A Surface area of the wing

4 Page4 C L is termed as the coefficient of lift and is different for various airfoils. The value of C L of an airfoil depends on the angle the airfoil makes with reference to flow -'the angle of attack' (α). Under certain limit, C L increases with the increase in angle of attack. Hence the pilot in order to change the lift on the wing has the control of flight speed and angle of attack of the wing which is the orientation of plane with the relative flow. In the adjacent plot, the coefficient of lift is plotted for various angles of attack for a symmetric airfoil. (The numerical values may change for different airfoils). It can be seen that the value of C L increases with α up to a certain limit after which it decreases steeply. The angle of attack after which the C L decreases is called the critical angle of attack and this phenomenon of loosing lift at higher angles of attack is termed as Stall. As a part of design process, while choosing the airfoil required for an aircraft, we consider the cruise speed and get the airfoil such that the lift is enough to balance the usual takeoff weight of the airplane. The dimensions of the wing are decided during this process and they are also a result of design requirements of the airplane. For example a long slender wing is optimum for slow flying planes, gliders while a short swept back delta wing is typical of a fighter aircraft. Forces on an Airplane: Apart from generating lift, fortunately or unfortunately, the pressure developed also has an asymmetry about the vertical plane (even if the body is symmetric about vertical plane) which will create force parallel to the flow in the direction of flow i.e. opposite to the motion of body. This force is termed as 'Drag' (D). The Drag is also given as D= (1/2)ρV 2 AC D where C D is the coefficient of Drag. From this it can be seen that the drag also increases as the square of velocity. i.e., as the Lift force increases, so does the Drag force. Since there is an opposition to the motion of body we require a force to generate the forward motion of body. This is what we term as 'Thrust' (T). In airplanes this thrust is generated by the engine, for example gas turbine engine, piston engine, turbojet engine, rocket engine etc. Due to earth's gravity, the airplane is acted upon a force vertically downward acting toward the centre of earth - the 'Weight' (W) of the airplane.

5 Page5 So here are the four basic forces acting on the airplane Lift, Drag - forces developed due to aerodynamics. Thrust, Weight - forces developed due to engine and earth's gravity respectively. The magnitudes and directions of thrust and lift are in pilot's control and the configurations of these forces are responsible for achieving various motions of an airplane. Basic geometric parameters of a Wing: An airfoil is the cross sectional plane of an airplane wing, i.e., if you cut the cross-sectional plane of the wing, the shape you will obtain is an airfoil. The line joining the nearest point with the farthest point on the airfoil is called 'chord' and the length of this line is called 'chord length' (c). When dealing with the angle made by wing with the flow i.e. the angle of attack, we use chord line as reference for the wing. The chord is obtained by joining the Leading Edge (the front end) and the Trailing Edge (the rear end) of the airfoil by a straight line. Now imagine an airfoil at zero angle of attack. Now draw many vertical lines passing through the airfoil and mark the mid points of each of these vertical lines. Join all these mid points with a smooth curve. The curve obtained is called the 'mean camber line'.

6 Page6 Among all the vertical lines drawn on the airfoil, the height of the longest line is called the thickness (t) of the airfoil. The maximum height between the mean camber line and the chord line is called the camber of the airfoil. The thickness, chord, and the camber are the most important parameters in the design of an airfoil. Typically, the more the camber of an airfoil, the better the lift coefficient (more asymmetry) and hence the lift generated by an airplane. But more lift also means more drag on the airfoil and hence more chances of creating flow separation. Thus the airfoil design is a crucial optimization problem in aircraft design. Wing Span and Aspect Ratio The length of the wing from one tip to the other is called the 'wing span' (b). Another crucial geometric parameter in a wing is its 'aspect ratio' (A.R). This is a measure of how slender the wing is. Mathematically it is the ratio of square of wingspan and the planform surface area of the wing. AR = b 2 /A In the most simplified way, the higher the aspect ratio, the lesser the drag and better the low speed flying ability of the airplane. The lower the aspect ratio, the better the high speed flying ability of the airplane and the structural integrity of the wing. Hence, aspect ratio is decided keeping the design objectives in mind. A larger Aspect Ratio wing is more stable, whereas it is more maneuverable at lower Aspect Ratios. Fighter Jets: A.R 3-4 Passenger planes: A.R 5-7 Gliders: A.R 7-9

7 Page7 Other geometric variations: The front view of an Airplane wing may not be straight line, but may have an inclination with respect to the horizon. This is called a dihedral, and it helps in lateral stability of the airplane i.e. stability against cross winds. A wing may also contains small bends near the tip (known as winglets) which reduces the span wise vortex formation and hence reduces the possibility of flow separation and hence also reduces the drag on the airplane. Sweep The planform (top view) of many wings is not a rectangle as we expect based on our discussion so far. It may be possible that the chord length at the root (wing-fuselage joint) is not equal to the chord length at the tip of the wing. i.e., the top view may look like a trapezium. This configuration is called as 'sweep'. It helps in delaying the shockwave formation on the wing and hence the phenomenon of drag divergence Sudden increase in the drag experienced by the wing due to the formation of shocks at supersonic speeds. It also helps in the formation of leading edge vortices which help increase the lift force produced by the wing. Usual sweep angles (angle between the leading edge of wing and the horizontal) lie between degrees. A remote controlled aircraft with swept back wing. Notice that it doesn t have flaps, slats, spoilers, winglets but it contains the three basic control surfaces -Ailerons, Rudder and the Elevator. There are planes with forward sweep and also many of the planes incorporate a sweep back for trailing edge too.

8 Page8 Parts of an Airplane: The body of an airplane is termed as 'fuselage' the cabin in which all the passengers are seated in a commercial plane. Wing is the major lift generating part of the airplane (horizontal tail, fuselage also generates lift but the magnitude is relatively small). The cross section of a wing is the 'asymmetric body' we were talking about. Typical airplanes use a cambered airfoil at an angle with the flow during cruise. This image typically shows all the major parts of an airplane along with their nomenclature. In an airfoil, if the camber is increased or if the angle of attack is changed the lift generated changes (up to certain limit after which flow separates and lift decreases sharply -details of which are out of scope of our discussion). For achieving an increase in Lift, surfaces are hinged to the trailing edge (the back edge of wing). These are flaps which deflect similarly on both wings -left and right (both surfaces down) and ailerons which deflect opposite on the wings (one up and one down). An increase in camber/angle of attack also results in an increase in the drag on the wing. When flaps are deflected, lift as well as drag on both the wings increase and hence the plane slows down. This loss of velocity comes with an increase in C L and hence without the loss of any. This deflection setting is used during take-off and landing of an airplane where we need the aircraft to be flying at slow speeds but also at sufficient lift in order to balance the weight and Take-off. Basic Controls of an Airplane Motion: An airplane can be controlled to rotate in any one of the principal directions (longitudinal, lateral, and vertical) or in a combination of these deflections.

9 Page9 Roll: When ailerons are deflected (one up and one down) the lift generated on one wing increases and on the other wing decreases thus causing the airplane to tilt about the axis along fuselage Longitudinal Axis. Pitch: When elevators are deflected down the lift on tail increases which causes the airplane to tilt down about the axis perpendicular to fuselage in horizontal plane Lateral Axis. Yaw: When the rudder is deflected right there will be a net rightward force on plane which causes it to deflect right and if rudder is deflected left, the plane will turn left. This motion about axis perpendicular to fuselage in vertical plane is called Yaw. Spoilers increase the drag by deflecting perpendicular to flow and thus creating obstruction to the flow. These are used to slow down the plane and are thus regarded as 'air brakes'. Usually in an airplane, the point of action of lift may not coincide with the centre of gravity of the airplane and thus it may create a moment on the plane about the centre of gravity. This moment is balanced by the horizontal tail and hence it is also known as horizontal stabilizer. Likewise the vertical stabilizer stabilizes the yaw of plane. Achieving Motion: Level Flight/Cruise: This is the major part of airplane flight path. This is also called cruise and the plane will be flying in design conditions i.e. optimum speed, zero deflections in control surfaces etc..as the name suggests airplane will be going at a constant altitude in this part of flight path. The pilot may keep the throttle and the other control surface deflections in such a way that thrust balances the drag and lift balances drag of an airplane. This will result in uniform forward motion. The pilot may also wish to increase the throttle above drag in order to accelerate up to the optimum speed. Turn: In this motion, ailerons will be deflected in such a way that the plane tilts at a certain angle and the lift force is no longer vertically upward but also has a sideward component which will act as centripetal force and thus lead to the plane turning. Due to tilting of airplane, the vertical force (component of lift force) may not be sufficient to counter the weight of the plane and thus to maintain the same level, the pilot increases the throttle to increase velocity and hence net Lift, in addition to just deflecting the ailerons.

10 Page10 The sideward component also leads to side slipping of the plane and the pilot uses rudder to counter this sideward force. This whole process is called level coordinated turn. Ascent/Descent: Since the pitching motion of plane is stabilized by the horizontal tail, changes in camber of horizontal i.e. upward and downward deflection of elevator will cause the plane to pitch up and for ascent and pitch down for descent respectively. Hence, in order to do ascent/descent the pilot deflects the elevator to required configuration. A Typical Flight Path: Usually, airplane flight path includes take off ground run-acceleration up to take off speed, accelerated ascent up to optimum climb speed, steady climb at a certain angle of ascent to cruise height, cruise-the longest part of the path, turns to correct the heading to go in the optimum route, deceleration to desired descent speed, steady descent, loiter until landing clearance is obtained and the landing ground runslowing down to zero speed. (The kink in cruise is to show that the cruise length scale is far more than the other lengths)

11 Page11 Exercises: 1. Is pressure difference (and thereby lift) entirely dependent on the upward camber? How do planes fly in reverse? 2. What is meant by hovering? What prompted the development of helicopters? 3. Find more about Bell V22 Osprey. 4. What is meant by Mach number? What is a typical mach number of a spacecraft? 5. What is meant by canard configuration? How is it better/worse from usual configurations? What is a moustache configuration? In which model was it first included? 6. What is critical Mach number and how is sweep useful in increasing it? 7. If aspect ratio is inversely proportional to drag, why can't we have very high aspect ratio for all the planes? Why do only gliders use high aspect ratios? What limits aspect ratio for fighter jets? 8. What is a delta wing? What are its advantages? 9. What are different types of engines in used in aircraft? Why are there so many types of engines? 10. Are coefficients of lift and drag related to each other? Find out the relation between them. 11. What does one mean when they say 3g turn or a 4g turn? What limits the turn angle in passenger aircrafts? What limits the same in military aircraft? 12. How are airplane accidents avoided? 13. What is meant by wake of an aircraft? How does it affect the traffic in airports? All the above questions are really interesting to look into. Please do spare some time to learn more into these questions. We hope you have enjoyed reading this module, and have learnt something interesting and useful out of it. Want to make your own plane? Let s start with making our own powered glider. Do check out Module 2 of Intro to RC Modeling Make your own Powered Glider! For any queries/feedback one can write to any one of the following addresses - anil316619@gmail.com, dheepaknkhatri@gmail.com. Do mail your answers to the above questions too. To join aero club, go to the Clubs tab -> Aero Club on the CFI website, and click on Join Aero Club. Acknowledgements: This course on Intro to RC Modeling was formulated, prepared and compiled by the following members of Aero Club: (In the order of the module of the courses) 1. Anil Kumar 2. Hanut Vemulapalli 3. Dheepak N Khatri 4. Sanjesh Hoskopple 5. Nikhil Gupta 6. GuruPrasad Kallanje