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Unformatted text preview: AA 311 Lecture 12: Aircraft Performance in Straight & Level Flight Reading: [1] Chapter 6.16.3. Aircraft performance deals with questions like: What is the maximum speed? What is the minimum speed? How fast can it climb to a given altitude? How far can it fly on a tank of fuel? How long can it stay in the air? What is the minimum takeoff speed? What is the minimum takeoff & landing distance? When studying aircraft performance, the airplane is regarded as a rigid body that flies under the influence of four fundamental forces: lift ( L ), drag ( D ), weight ( W ) and propulsive thrust force ( T ). Figure 1 shows the balance of forces in this simple setting. We saw in earlier lectures that the nondimensional aerodynamic coefficient C D and C L are of fundamental importance describing the aerodynamic characteristics of the airplane. In aircraft performance we are not concerned about how the aerodynamic coefficients were obtained, we simply assume that they are available for us from windtunnel experiments, or theoretical studies. Figure 1: Forces on an airplane. The most fundamental relationship we will use in studying aircraft performance is the drag polar : C D = C D + C 2 L e AR . (1) 1 In the above equation e is called the Oswald efficiency factor , and AR is the wing aspect ratio. We assume that this equation includes contributions from the whole airplane, that is including the wing, the horizontal and vertical stabilizers and the fuselage. That is, C D is the total drag coefficient, C L is the total lift coefficient, C D is the parasite drag coefficient at zero lift. It is assumed that the parasite drag coefficient includes contributions not only from the profile drag of the wing, but also the pressure and viscous drag contributions from any component of the airplane that is exposed to the airflow. The term induced drag , C D i = C 2 L / ( e AR), is frequently used, and captures the contributions of drag due to lift . The graph of equation 1 is called the drag polar . It is a parabolic relationship between lift coefficient and drag coefficient. Such a graph is shown in Figure 2. Figure 2: Drag polar. Now that we have the most fundamental equation at hand, we will study the flight mechanics of an airplane across the atmosphere based on Newtons second law. We will first study static performance , that is when all the accelerations are zero. Flight conditions under this category include straight and level flight, and gliding flight at zero acceleration. Then we will study dynamic performance, such as takeoff, landing, turning flight, and accelerated climb. Equations of Motion Consider an airplane shown in Figure 3. We assume that the airplane flies along a general curvilinear path, that is, a path that is not necessarily straight. Newtons second law states that force equals rate of change of momentum, hence neglecting change in mass we can write X F = m a ....
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This document was uploaded on 02/05/2012.
 Fall '09

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