311 AA Lecture 1: Introduction; Units; Airplane Anatomy
Reading: [1] Chapter 1, Chapter 2.4, Chapter 2.6. When asked about the beginning of human flight, the first thing that comes to our mind is the historic achievement of the Wright brothers on December 17, 1903, when their Wright Flyer I (shown in Figure 1) lifted off the sand dunes of Kill Devil Hills by its own power, carrying Orville Wright into the air in sustained flight for approximately 12 seconds. The result was a culmination of efforts by many ingenious researchers and scientists over the centuries that lead to the successful controlled flight of the first aeroplane. Atmospheric flight vehicles can be categorized into two very distinct types: 1. Lighter-than-air vehicles, such as blimps and balloons, and 2. Heavier-than-air vehicles, such as airplanes and gliders.
(a) From [1].
(b) From [1].
Figure 1: The Wight Flyer. The first human flight actually occurred on November 21, 1783, when a hot-air balloon carried Pilatre de Rozier and Marquis d'Arlandes into the air, and flew about 5 miles across Paris. The hot-air balloon is a lighter-than-air vehicle, where the necessary lift force -- to keep the vehicle in the air -- is generated by buoyancy. Heavier-than-air vehicles, on the other hand, need an alternative source of lift force, as the buoyant force is typically negligible, and is not sufficient to overcome gravity. Referring to Figure 2a, the four fundamental forces acting on a flight vehicle are Weight (due to gravity). Thrust (force generated by the propulsion system). Lift (an upward force that keeps the airplane in the air by countering gravity). Drag (aerodynamic resistance that has to be countered by thrust). The fundamental problem of heavier-than air flight is to generate the necessary lift force and thrust force to reach a force balance for steady and sustained flight. Early experimentalists tried to solve the problem by inventing machines that would mimic the flight of birds, using flapping wing mechanisms. A common theme in their approach was that the same mechanism was used to generate lift and propulsion (Figure 2b).
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(a) From [3].
(b) From [3].
Figure 2: In an airplane, the mechanism for of propulsion (the engine) is separated from the mechanism of lift (wings). Birds use wing strokes for both propulsion, and lift. Birds have evolved to be very efficient flyers that can propel themselves through the air effortlessly. However, early aviators did not have the technology to fabricate machines with high enough power to weight ratio to make such solutions feasible (see Figure 3 for Leonardo da Vinci's drawing of an ornithopter machine). Even though the initial efforts towards flapping wing flight were unsuccessful, it is important to mention that the limitation was purely technological. In our present times, the idea is explored again, and significant achievements have been accomplished towards both unmanned and manned flapping wing flight (Figure 3). A major milestone in aviation history -- and a departure from the flapping wing concept -- was the idea by Sir George Cayley to use a fixed wing to generate lift, and use a separate machine to generate the required propulsive force. He envisioned using paddles for forward propulsion (remember: in his time the steam engine didn't exist yet, let alone more advanced power generators), but in retrospect we know that it was the piston-cylinder reciprocating engine that made the first controlled, powered flight with this concept possible. Recall Newton's second law: the sum of all forces acting on a body equals the rate of change of momentum (mass times acceleration): F = ma. Suppose that heavier-than-air flight vehicle turns its engines on to prepare for takeoff. The thrust force generated by the propulsion system accelerates the vehicle in the horizontal direction. As the vehicle gains speed, airflow is induced around the wings and hull, which results in the generation of two fundamental aerodynamic forces: lift (L) and drag (D). The faster the vehicle goes, the larger the magnitude of the aerodynamic forces. Once the critical speed where lift is greater than weight is reached, the flight vehicle is ready for take-off. By Newton's second law, the vertical acceleration due to the force imbalance in the vertical direction lifts the vehicle into the air (Figure 4). Units Units are fundamental to communicate the relative magnitude of physical quantities with respect to some common reference. The common reference is solely based on agreement. Examples of units are m/s (meters per second) for velocity, or N (Newton) for force, for example. There are seven fundamental units 2
(a) Leonardo da Vinci.
(b) Leonardo da Vinci's flapping wing ornithopter.
(c) Cybird nithopter.
radio-controlled
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(d) The UTIAS ornithopter.
Figure 3: Ornithopters (source: [2].) defined in the SI system of units (Syst`me Internartional d'Unit`s: International System of Units), from e e which all other physical quantities of interest can be derived. These fundamental units are the following: 1. meter for length 2. kilogram for mass 3. second for time 4. Ampere for electric current 5. Kelvin temperature for 6. candela for luminous intensity 7. mole for the amount of substance. We shall restrict our attention to the three fundamental units in the MKS system (meter, kilogram, second), plus temperature (Kelvin) that are most common in aeronautics and astronautics. From this fundamental set of units all other units of interest can be derived.
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Figure 4: Typical takeoff sequence for a heavier-than-air flight vehicle. (Friction with the ground is neglected in the cartoon for simplicity.) When the vehicle is stopped, the normal force, N , exerted on the vehicle by the ground is equal and opposite to weight, W . Once the vehicle is in motion, the airflow over the body generates a lift force, L, that increases in magnitude as the vehicle gains speed. Once L > W , the vehicle lifts off the ground. Example: According to Newton's second law the force is mass times acceleration, or F = ma. In terms of units, then 1 Newton = (1 kilogram)(1 meter/second2 ). The four basic units in the SI system are defined as: Time: One second is the duration of 9, 192, 631, 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Caesium 133 atom. Historically, the second 1 was defined as 246060 times the duration of a day.
1 Length: One meter is the length of the path travelled by light in vacuum during a time interval of 299,792,458 1 of a second. Historically, the meter was defined as 10,000,000 of the distance from the Earth's equator to the North Pole measured along a meridian passing through Paris. According to this definition, the circumference of the Earth along the meridian passing through Paris is 40,000 km (exactly).
Mass: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Historically, one kilogram is equal to the mass of one liter (volume) of water. One liter is equal to 10-3 m3 , or one cubic decimeter. Temperature: The Kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. Other than units, we also often talk about dimensions. Dimensions are qualitative, describing essential nature, while units are quantitative, describing amount. Example: is Velocity, v, is defined as the distance covered by a moving object over unit time. It's dimension dim(v) = When expressed in SI, the standard unit of velocity is [v] = m/s. 4 length . time
SI is a consistent set of units, meaning that all physical relationships can be written without the need for a conversion factor. Anatomy of an Airplane: The major components of an airplane are the fuselage, the wings, the engines and engine nacelles, the horizontal stabilizer (horizontal tail), and the vertical stabilizer (vertical tail). The role of the fuselage is to carry people or payload. The shape of the fuselage is designed to minimize drag force. Drag force is always present whenever a rigid body moves in a viscous fluid, but significant drag reduction can be achieved by proper streamlining, and aerodynamic design. The wings' function is to generate the required lift force that keeps the flight vehicle in the air. The size and cross-sectional profile are very important parameters of the wings, and are carefully engineered for maximum aerodynamic performance. As the name implies, the horizontal and vertical stabilizers are crucial in ensuring stable flight. Airplanes are typically controlled by hinged control surfaces that can be moved by mechanical linkages attached to actuators. The actuators are either electric motors, or hydraulic systems. The primary controls are the ailerons, the elevators, and the rudder. The ailerons are differentially operated control surfaces that control roll of the airplane. Remark 1 As an interesting note, the Wright Flyer didn't have ailerons. Instead, roll control was established by wing warping: a type of camber control device. The elevator is used to control pitch stability, and the rudder is used for directional stability. Airplanes may have additional control surfaces, such as flaps, that change the flow-field around the wing, and hence achieve an optimal airfoil shape with respect to the desired flight condition.
(a) From [1].
(b) From [1].
Figure 5: Anatomy of an airplane.
Brief outline of the course In this course we will primarily focus on then principle of operation and mechanics of fixed-wing, heavier-than-air, atmospheric flight vehicles. The main chapters of the course can be itemized as follows: Basic fluid properties, fundamentals of the atmosphere, basic aerodynamics. Airfoils, wings, pressure coefficient, lift and drag. 5
Aircraft performance: steady level flight, gliding flight, flight envelope, accelerated climb, turning flight. Aircraft stability and control. Aircraft propulsion: piston-propeller engines, jet engines.
References
[1] J. D. Anderson. Introduction to Flight. McGraw-Hill, New York, NY, seventh edition, 2011. [2] Wikimedia Foundation Inc. Wikipedia: The free encyclopedia, July 2011. [3] H. Tennekes. The simple science of flight: from insects to jumbo jets. MIT Press, Cambridge, MA, 1997.
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