Automatic Control of Aircraft and Missiles by John H Blacelock

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By John H Blacelock

This is often on no account my favourite e-book on dynamics or keep watch over, yet every person references it, so that you should still most likely have a duplicate of it if you are a major aeronautics information and regulate expert.

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L= Qly + PR(Ix - /z ) +(P 2 - R 2 )Jxz E 4,At'= RIz - PIn + PQ( Iy - Ix) + QRJxz (1-32) The equations of linear motion from Eq. 1-15 are E 4Fx=m(U+WQ-VR) E 4Fy=m(V+UR-WP) E 4Fz=m(W+VP-UQ) (1-33) Equations 1-32 and 1-33 are the complete equations of motion for the aircraft. It will next be necessary to linearize the equations and expand the left-hand sides. A" • AIRCRAFT ATTITUDE WITH RESPECT TO THE EARTH 15 These conclusions are based on the assumptions that: 1. OX and OZ are in the plane of symmetry.

D t 26 LONGITUDINAL DYNAMICS It should be remembered that in these equations U = Uo, q = tpuo2 , 'u=ujUo, 'a=wjUo, and 'a=wjUo. These equations are nondimensional; thus all angles and their derivatives must be in radian measure. In deriving the longitudinal equations of motion certain nondimensional coefficients, referred to as stability derivatives, were introduced. In Section 1-7 the equations for the stability derivatives will be derived and their origin determined. 1·7 DERIVATION OF EQUATIONS FOR THE LONGITUDINAL STABILITY DERIVATIVES The student probably wondered why in the expansion of the forces and moments the partial derivative with respect to Ii was missing, while the partial derivative with respect to w was included.

D 28 LONGITUDINAL DYNAMICS where i is the angle of incidence of the stabilizer with respect to the a reference line, a is the wing angle of attack, Dw is the downwash velocity at the tail, and E is the downwash angle = Dw / U in radians. The downwash is the result of the lifting action of the wing and increases as the lift and angle of attack of the wing increase. If the vertical velocity of the aircraft is changed, the angle of attack changes; thus the downwash varies with w. Therefore, it is necessary to investigate the effect of a change of w, the vertical velocity, on the angle of attack of the tail.

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