Ssecond moment of area for a aerofoil.

[tonymontana]

Hi was wondering if anyone could help?

i am after the method of calculating the second moment of area of a aerofoil shape of which I have all the cordinates. It has a consant thickness of 1mm and lookig for values for

1)I_xx
2)I_yy
3)I_xy


the equation for the half the erofoil section is

y=2.391x^5 + 6.784x^4 +7.193x^3-3.647x^2+0.839x+0.011

The Attempt at a Solution

now i know that I_xx =integral y^2 DA

and DA= 1/COS(THETA), HOWEVER CAN BE APPROXED TO 1 HENCE DA=1.dy

after that I am stuck : (

 

[mathmate]

the equation for the half the erofoil section is
y=2.391x^5 + 6.784x^4 +7.193x^3-3.647x^2+0.839x+0.011

Can you enlighten me with the axis of symmetry if the above equation is only half of the aerofoil?
Also, where does the curve begins and where does it end? Y is zero when x=0, and it goes to 14 when x=1, and 45000 when x=4.
Are x and y in metres or in mm?

now i know that I_xx =integral y^2 DA

as long as y is measured to a line passing through the centroid and parallel to the x-axis.

and DA= 1/COS(THETA), HOWEVER CAN BE APPROXED TO 1 HENCE DA=1.dy

not when x is small and dy/dx is small. Here is can be approximated by dx.

Thus it would seem risky to consider approximations without the knowledge of the domain and range of the curve.