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Assessment (Portfolio Week 10): Problem-solving exercises
Submit your answers to these questions on your Week 11 workshop day
8. Assume that the wing of an aircraft has a cross-sectional shape given by a symmetrical NACA
airfoil, whose top boundary is the function
f (x) = • OCX),
where a = (al, is a vector of constant parameters, = is a
vector collecting a number Of pre-defined functions Of x, and > O is a vertical scaling
parameter. The wing is assumed to be composed of material of homogeneous mass density.
You would like to inscribe a rectangular-shaped fuel tank in the wing. To ensure that the centre
of mass of the wing is not affected by the fuel tank, you centre the tank at the centre of mass
of the wing calculated without the fuel tank.
0.1
0.05
—0.05
-0.1
o
0.2
0.4
0.6
0.8
centre of mass
1
(a) Use the "slice and sum" principle to argue that by symmetry, the centre Of mass along x
Of the wing without fuel tank is given by
xf(x)dx
f (x)dx
Hint: See Sections 7.7.6 and 7.3.8 of the lecture notes.
(b) Calculate Xc for a general shape vector a.
(c) Find the value Of Xc for the so-called n9012 airfoil in which
a —0.6300, —1.7580, 1.4215, —0.5180)T.
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