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.

 

[Mene]

I can provide some guidance on how to calculate the second moment of area for an aerofoil shape. The second moment of area, also known as the moment of inertia, is a measure of an object's resistance to bending or twisting.

To calculate the second moment of area for an aerofoil, you will need to use the equation:

I = ∫ y^2 dA

Where I is the second moment of area, y is the distance from the centroid to the infinitesimal area element dA, and dA is the infinitesimal area element.

To find the values for I_xx, I_yy, and I_xy, you will need to integrate the equation above over the entire cross-section of the aerofoil. This can be done by breaking the aerofoil shape into smaller sections and integrating each section separately.

For example, if you have the equation for half of the aerofoil section, as shown above, you can integrate it over the range of x values to find the area of that section. Then, you can use that area to calculate the values for I_xx, I_yy, and I_xy.

To approximate the value of dA, you can use the equation dA=1.dy, as you mentioned. This is because the thickness of the aerofoil is constant and equal to 1mm.

I hope this helps you in your calculations. If you need further assistance, I recommend consulting a textbook or reaching out to a colleague with expertise in aerodynamics. Good luck with your calculations!