Ch5Performance.doc - INTRODUCTION TO AERONAUTICS A DESIGN...

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INTRODUCTION TO AERONAUTICS: A DESIGN PERSPECTIVE CHAPTER 5: PERFORMANCE AND CONSTRAINT ANALYSIS "The great liability of the engineer compared to men of other professions is that his works are out in the open where all can see them. His acts, step by step, are in hard substance. He cannot bury his mistakes in the grave like the doctors. He cannot argue them into thin air or blame the judge like the lawyers. He cannot, like the architects, cover his failures with trees and vines. He cannot, like the politicians, screen his short-comings by blaming his opponents and hope the people will forget. The engineer simply cannot deny he did it. If his works do not work, he is damned." President Herbert Hoover 5.1 DESIGN MOTIVATION Aircraft performance analysis is the science of predicting what an aircraft can do; how fast and high it can fly, how quickly it can turn, how much payload it can carry, how far it can go, and how short a runway it can safely use for takeoff and landing. Most of the design requirements which a customer specifies for an aircraft are performance capabilities, so in most cases it is performance analysis which answers the question, “Will this aircraft meet the customer’s needs?” 5.2 EQUATIONS OF MOTION Figure 5.1 shows the forces and geometry for an aircraft in a climb. The flight path angle , , is the angle between the horizon and the aircraft’s velocity vector (opposite the relative wind.) The angle of attack, , is defined between the velocity vector and an aircraft reference line , which is often chosen as the central axis of the fuselage rather than the wing chord line. The choice of the aircraft reference line is arbitrary. The designer is free to choose whatever reference is most convenient, provided care is taken to clearly specify this choice to all users of the aircraft performance data. The thrust angle , T , is the angle between the thrust vector and the velocity vector. This will not, in general, be the same as , since the thrust vector will not generally be aligned with the aircraft reference line. L D T W Horizon Relative Wind T Figure 5.1 Forces on an Aircraft in a Climb The equations of motion for the aircraft in Figure 5.1 are derived by summing the forces on the aircraft in two directions, one parallel to the aircraft’s velocity vector and one perpendicular to it. These directions are convenient because lift was defined in Chapter 3 as the component of the aerodynamic force 123
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which is perpendicular to the velocity vector, and drag was defined as the component parallel to velocity. The summation parallel to the velocity is: F ma T cos  D W sin (5.1) where m is the aircraft’s mass and a is its instantaneous acceleration in the direction of the velocity vector.
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