Stability in Aviation An Introduction to Dynamical Stability As Applied to the
Stability in Aviation An Introduction to Dynamical Stability As Applied to the
George Hartley Bryan
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95. In the general case, it is convenient to put I = sin a m = cos a cos 3 n = cos a sin /3 . . (168) 154 BENT UP PLANES CHAP. In this case, a is the angle of attack or angle made by the element with the direction of steady flight, ft the angle through which the element is bent up about an axis parallel to the axis of x. We shall also, in accordance with our usual convention, write dS' = dS cos 2 a, /i = tan a and we get ny - mz = cos a (y sin - z cos /3) Iz - nx = cos a (pz - x sin j8) 2lz nx ...= cos a (2p. Z - x sin /3), and writing f =z cos y sin /3, the expressions for the derivatives become r z n r z = / sin 2 j8 dtf, fcFTr = - / sin P &&> Wi J KU J K( - I sin jS dS', WT7 ' J - a; sin 3) (^ - x sin /3)d8T (169) These expressions and the subsequent analysis become considerably simplified when x sin @ is negligible com- pared with fjuz. This occurs (l) in the case of a single lifting system with bent up wings in which x = 0, (2) in the case of a tandem system of bent up lifting planes, when the angle of bending up @ is small compared with the angle of attack a, and the span of the planes is not small compared with the distance between them.
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