9780071086806, Chapter 7, Problem 3

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Chapter 7, Problem 3 Problem 3. Assume an aircraft has a canard control surface in front. Develop an expression, given in terms of modal displacements and modal velocities for the change in the vehicle's pitching moment due to elastic deformation of the structure. That is, find an expression for ME. Step-by-step solution Step of 1 Solution: Let the geometry be as shown in the sketch below, obtained by modifying Fig. 7.10 XRef 2-D Airfoil Section Locus of Section Aerodynamic Centers Note that we have here assumed that the reference location is now ahead of the wing. Then, similar to Eqn. 7.43, by reversing the sign on the moment arm the pitching moment from the wing's 2-D section is Likewise, the pitching moment from the canard's 2-D section is The 2-D lift on the wing and canard section, assuming the canard section is symmetric, are given by Ignoring the effect of downwash from the canard, the local angle of attack for the wing or canard section is given by Eqn. 7.7, or = = Therefore, instead of Eqns. 7.44, we have the wing and canard section moments given by (7.SM.4) Consistent with Eqn. 7.19, let the modal expansion for the twist angles be given by = (7.SM.5) Likewise, consistent with Eqns. 7.23 let the expansions for the section plunge velocities be (7.SM.6) = Substituting the appropriate expression from Eqns. (7.SM.5) and (7.SM.6) into Eqns. (7.SM.4), integrating over the wing and the canard, and summing the two results leads to the following expression for the effects of elastic deformation on the vehicle's pitching moment. = (y)dy+ (y)dy + q. =