This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 Excerpt: ...obvious physical fact that the symmetrical aeroplane will not, of itself, tend to make its plane of symmetry assume any one vertical position. 117. Conditions of Lateral Stability.--The determinantal equation (147) can be simplified by multiplying the third column by X, subtracting from this the second column ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 Excerpt: ...obvious physical fact that the symmetrical aeroplane will not, of itself, tend to make its plane of symmetry assume any one vertical position. 117. Conditions of Lateral Stability.--The determinantal equation (147) can be simplified by multiplying the third column by X, subtracting from this the second column multiplied by sin (c)0, and taking out the factor cos (c)0 in the resulting new third column. We get X ] c, d1 +- .+-cose0, e, --.X-sine0 =0. (148) cv X2 + d1X, -X2 + X!' F c2, -X2 + d2X, X2 + e2X in which we know that a factor X can be cancelled out. We get an equation.42X + B2X3 + C2X2 + D2X + i?2 = 0, where A2, B2, C2, D2, E2 can be evaluated. The aeroplane is laterally stable if this equation has the real parts of all its solutions negative (or at least not positive). The conditions are that A2, B2, C2, D2, E2 shall all be of the same sign, as well as Rouths discriminant H2 = B2C2D2-A.J)2-E2B2 In the standard case where the steady motion is horizontal with the propeller axis horizontal (normal motion), we have U20=0, (c)0 = 0, U10=U, and the above determinant is slightly simplified. It must, in any case, be clearly understood that the derivatives in both the longitudinal and lateral conditions l'efer to the configuration of the body appropriate to the steady motion to which the motion approximates. Thus, e.g., the derivatives in (145, 146) will all involve U20 and B0, and will depend on the kind of symmetrical steady motion considered. In practice, we would take the case of normal motion tT20 = 00 = 0, and we get a range of steady motions for which the stability holds, if it holds for this case. 118. General Case of Rectilinear Steady Motion.--The discussion of the stability of the general case of rectilinear steady motion will now p
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