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# spl10b - Area and Bending Inertia of Airfoil Sections...

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Area and Bending Inertia of Airfoil Sections Calculation of the vertical deﬂection of a wing requires knowing the spanwise bending stiﬀness distribution EI ( y ) along the primary axis of loading. For a wing made of a uniform solid material, the modulus E is a simple scaling factor. The moment of inertia of the airfoil cross-sections about the bending axis x (called the bending inertia ), is then related only to the airfoil shape given by the upper and lower surfaces Z u ( x ) and Z ( x ). As shown in Figure 1, both the area A and the total bending inertia I are the integrated contributions of all the in±nitesimal rectangular sections, each dx wide and Z u Z tall. The inertia of each such section is appropriately taken about the neutral surface position ¯ z de±ned for the entire cross section. c ± ² A = Z u Z dx (1) 0 c 1 ± ² 1 Z 2 Z 2 z ¯ = dx (2) A 0 2 u c 1 ± ² I = ( Z u z ¯) 3 ( Z z ¯) 3 dx (3) 0 3 These relations assume that the bending deﬂection will occur in the

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spl10b - Area and Bending Inertia of Airfoil Sections...

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