# Second moments of area/inertia for complex shapes

Hello,
I am working on my dissertation for aerospace engineering. I am designing a pitch control system to reduce vibration loads in wind
turbine structures.
I am currently trying to produce a mathematical model to represent the bending of the wind turbine blades, and I have got stuck because I do not know how to find the second moments of inertia of the aerofoil cross section.
I know how to find Ix and Iy for simple shapes, but I am sure there must be a way to, for example, find the moments of inertia for a line defined by a polynomial equation.
I do have an idea, but I dont trust my judgement so if anyone could check it or suggest another method I would be really grateful.
HERE IS MY IDEA:
I know that Ix=int(y^2)dA, and since the blade cross-section is hollow I can define the area as the skin thickness (t) multiplied by the incremental distance which is tangent to the skin (ds) The aerofoil cros section shape is defoned by a polynomial equation y=f(x). If i can express y and ds in terms of x, I think I can solve the integral and find Ix.
Do any of you guys know if this is accurate?
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It would be sufficently accurate if it were done properly, but I suspect that it will be extremely difficult. You might find it easier to work out the MOI of the outer profile and subtract that of the inner, for example. Check that that is mathematically correct, first (99% sure it is).
Also bear in mind that you really need to work out Ixy as well, if you are going to use the 'obvious' axes.
Also, you need to know where the centroid is.
Cheers
Greg Locock
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Thanks Greg, I really appreciate your help.
The idea of subtracting the inner shape from the outer is a better idea, because the coordinates will be easier to define that way. Also if I used my proposed method assuming constant thickness, the area would effectively double-up at the trailing edge.
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