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At y due to control surface rotation. Note ∂CMAC /∂αT ≡ 0 by definition of the aerodynamic center. 19) Note that are more difficult to measure than their structural counterpart, C αα. One requires an experimental model to which one can apply unit angles of attack at various discrete points along the span of the wing. This requires a rather sophisticated model and also introduces experimental difficulties in establishing and maintaining a smooth flow over the airfoil. Conversely ALα, ALδ ∂CL ∂CL , ∂ pl ∂δR U and ∂CMAC ∂δR 32 A MODERN COURSE IN AEROELASTICITY are relatively easy to measure since they only require a rolling or control surface rotation of a rigid wing with the same geometry as the flexible airfoil of interest.
Also note the moment equilibrium about the control surface hinge line does not enter into this calculation. See Appendix B, Chapter 2 for a more conceptually straightforward, but algebraically more tedious approach. At the generalized reversal condition, when α0 = 0, CMAC0 = 0, the lift due to a change in δ is zero, by definition. 27) To see how this generalized definition relates to our earlier definition of the reversal condition, consider again the equation for lift and also the equation for overall moment equilibrium of the main wing plus control surface, viz.
11) subsequently. 6). 13). 13) may be written, y2 C αα(y2 , η) = 0 η = 0 y2 = 0 1 dy1 − GJ y2 η 1 dy1 GJ 1 dy1 GJ for y2 > η 1 dy1 GJ for y2 < η One may drop the dummy subscript on y2 , of course. 14) Note from the above result we may conclude by interchanging y and η that C αα(y, η) = C αα(η, y) 30 A MODERN COURSE IN AEROELASTICITY This is a particular example of a more general principle known as Maxwell’s Reciprocity Theorem∗ which says that all structural influence functions for linear elastic bodies are symmetric in their arguments.
Fw190
by Kevin
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