Aerofoil C.O.G

dale154 · October 20, 2015, 04:30

Hi, I'm wondering how i would calculate the centre of gravity of an aerofoil, given it's x and y co-ordinates?
Thanks,
Dale.

agd · October 20, 2015, 10:00

To compute the center of gravity you will need the mass or density distribution of the airfoil. If you have the mass distribution then the formula can be found in most basic calculus books. See this page for more information as well:

https://www.grc.nasa.gov/www/k-12/airplane/cg.html

kaya · October 20, 2015, 12:16

interesting..

in applications this would be useless because I don't think you can find a cross-section filled with the same material. usually inner side of the 2d shape is empty.

having said that, to answer your question if you assume that the density distribution is the same, if I am not mistaken you should be able to find the center of gravity by something like

$x_{COG}=\frac{\sum_{i=1}^n \big(y^{upper}_i - y^{lower}_i\big) * x_i}{\sum_{i=1}^n \big(y^{upper}_i - y^{lower}_i\big)}$

$y_{COG}=\frac{\sum_{i=1}^n \big(x^{right}_i - x^{left}_i\big) * y_i}{\sum_{i=1}^n \big(x^{right}_i - x^{left}_i\big)}$

if the airfoil has camber, it might be a bit tricky to calculate in this way.

if the airfoil is symmetric, $y_{COG}$ is 0.

dale154 · October 21, 2015, 08:15

Quote:

Originally Posted by kaya

interesting..

in applications this would be useless because I don't think you can find a cross-section filled with the same material. usually inner side of the 2d shape is empty.

having said that, to answer your question if you assume that the density distribution is the same, if I am not mistaken you should be able to find the center of gravity by something like

$x_{COG}=\frac{\sum_{i=1}^n \big(y^{upper}_i - y^{lower}_i\big) * x_i}{\sum_{i=1}^n \big(y^{upper}_i - y^{lower}_i\big)}$

$y_{COG}=\frac{\sum_{i=1}^n \big(x^{right}_i - x^{left}_i\big) * y_i}{\sum_{i=1}^n \big(x^{right}_i - x^{left}_i\big)}$

if the airfoil has camber, it might be a bit tricky to calculate in this way.

if the airfoil is symmetric, $y_{COG}$ is 0.

Hi, thanks for this, this is very helpful.
My aerofoil is cambered.
I have a series of upper and lower co-ordinates. In both the equations, for x_i and y_i, should i use the upper or lower parts of the x and y co-ordinates?
Also in the equation for y_COG, should it be x_upper and x_lower?

Thanks again for the help.
Dale.

fluid23 · October 21, 2015, 14:52

Do you not have a CAD software available to you? That would be the easiest way to find this value.

Also, you are looking for a centroid not a center of gravity unless you have mass properties defined as well.

http://www.intmath.com/applications-...troid-area.php

kaya · October 21, 2015, 15:57

Quote:

Originally Posted by dale154

Hi, thanks for this, this is very helpful.
My aerofoil is cambered.
I have a series of upper and lower co-ordinates. In both the equations, for x_i and y_i, should i use the upper or lower parts of the x and y co-ordinates?
Also in the equation for y_COG, should it be x_upper and x_lower?

Thanks again for the help.
Dale.

again, if its cambered I don't think you can apply this from the shelf.

October 20, 2015, 04:30	Aerofoil C.O.G	#1
dale154 New Member Join Date: Aug 2015 Posts: 22 Rep Power: 10	Hi, I'm wondering how i would calculate the centre of gravity of an aerofoil, given it's x and y co-ordinates? Thanks, Dale.

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October 20, 2015, 10:00		#2
agd Senior Member Join Date: Jul 2009 Posts: 354 Rep Power: 18	To compute the center of gravity you will need the mass or density distribution of the airfoil. If you have the mass distribution then the formula can be found in most basic calculus books. See this page for more information as well: https://www.grc.nasa.gov/www/k-12/airplane/cg.html

October 20, 2015, 12:16		#3
kaya Member Kaya Onur Dag Join Date: Apr 2013 Posts: 94 Rep Power: 13	interesting.. in applications this would be useless because I don't think you can find a cross-section filled with the same material. usually inner side of the 2d shape is empty. having said that, to answer your question if you assume that the density distribution is the same, if I am not mistaken you should be able to find the center of gravity by something like $x_{COG}=\frac{\sum_{i=1}^n \big(y^{upper}_i - y^{lower}_i\big) * x_i}{\sum_{i=1}^n \big(y^{upper}_i - y^{lower}_i\big)}$ $y_{COG}=\frac{\sum_{i=1}^n \big(x^{right}_i - x^{left}_i\big) * y_i}{\sum_{i=1}^n \big(x^{right}_i - x^{left}_i\big)}$ if the airfoil has camber, it might be a bit tricky to calculate in this way. if the airfoil is symmetric, $y_{COG}$ is 0.

October 21, 2015, 14:52		#5
fluid23 Senior Member Matt Join Date: Aug 2014 Posts: 947 Rep Power: 17	Do you not have a CAD software available to you? That would be the easiest way to find this value. Also, you are looking for a centroid not a center of gravity unless you have mass properties defined as well. http://www.intmath.com/applications-...troid-area.php