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lecture_14 - 16.333: Lecture # 14 Equations of Motion in a...

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Unformatted text preview: 16.333: Lecture # 14 Equations of Motion in a Nonuniform Atmosphere Gusts and Winds 1 Fall 2004 16.333 122 Equations of Motion Analysis to date has assumed that the atmosphere is calm and fixed Rarely true since we must contend with gusts and winds Need to understand how these air motions impact our modeling of the aircraft. Must modify aircraft equations of motion since the aerodynamic forces and moments are functions of the relative motion between the aircraft and the atmosphere, and not of the inertial velocities. F Thus the LHS of the dynamics equations ( = ma ) must be written in terms of the velocities relative to the atmosphere. If u is the aircraft perturbation velocity ( X direction), and u g is the gust velocity in that direction, then the aircraft velocity with respect to the atmosphere is u a = u u g Now rewrite aerodynamic forces and moments in terms of aircraft velocity with respect to the atmosphere (see 411) X X X X = ( u u g ) + ( w w g ) + ( w g ) U W W w X X X g + ( q q g ) + . . . + + . . . + + X c Q The gravity terms X g and control terms X c = X e e + X p p stay the same. Fall 2004 16.333 123 The rotation gusts p g , q g , and r g are caused by spatial variations in the gust components rotary gusts are related to gradients of the vertical gust field w g w g p g = and q g = y x g g + w g + w g y Gust field creating gust. -w-w an effective rolling Equivalent distribution Equivalent to velocity created by a pitching motion Figure 1: Gust Field creating an effective pitching gust. Fall 2004 16.333 124 The next step is to include these new forces and moments in the equations of motion u X u X w mg cos m u m Z w M w I yy 1 w q Z u Z w Z q + mU mg sin M u M w M q w q = 1 X e X p Z e Z p M e M p e t + X u X w...
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lecture_14 - 16.333: Lecture # 14 Equations of Motion in a...

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