# Finding the Center of Mass of a Wing

1. Jul 8, 2011

### artkingjw

1. The problem statement, all variables and given/known data
so we have this engineering assignment (high school final year) where we have to design an airplane wing and one of the tasks is to (graphically, not all of us can even differentiate let alone mathematically derive it) identify the center of mass of the wing... now, i know how to do it for the PLANE, and i know how to do it for simple shapes like Ls ans such, but how do I do it for a wing? The teacher said that we use the center of mass as a point where we put the weight of the wing on and then we can do moments calculations and find the material/method of joining the wing to the plane. My wing is similar to a 737's wing.

2. Relevant equations

3. The attempt at a solution
do i just divide the spans up into trapeziums and then find their centers of mass? then how do i go about finding the center of mass for the WHOLE wing??

2. Jul 9, 2011

### Staff: Mentor

To find the centre of mass experimentally you would take your model's wing and balance it on the tip of an upright nail. Do this for a few orientations, and the intersection of centre lines gives the C of G.

Graphically. What data do you have for the wing? Obviously its outline from above, and profile from the front, but are you able to infer density from that? Would it be true to say that effective density of a slice of the wing at any point along its length is not directly proportional to its shape there? So I reckon you need more data than just profile. Or maybe you are to simplify it by assuming weight distribution is proportional to cross-sectional area of the wing?

Last edited: Jul 9, 2011
3. Jul 9, 2011

### jambaugh

Assuming the wing is constant thickness, using your trapeziums....

set up a coordinate system $(x,y)$ for your drawing and then find
--the center of mass of each trapezium $(x_k,y_k)$,
and
--the Area of each $A_k = 1/2(b_1+b_2)\cdot h$.
(Area is average base times height. Note this reduces to 1/2 base times height for a triangle = trapezium with one parallel side of length 0.)

Since mass is area times density times thickness, mass will be proportional to area. So for purposes of finding COM we assume mass=area.

You can then treat each piece as if it were a point mass positioned at its center of mass.
You then find the center of mass of this set of point masses.

$$x_{com} = (A_1 x_1 +A_2 x_2 \cdots)/A_{total}$$
$$y_{com} = (A_1 y_1 +A_2 y_2 \cdots)/A_{total}$$

4. Jul 9, 2011

### artkingjw

jambaugh: wow ok thanks man, that helps!

Last edited: Jul 10, 2011
5. Jul 10, 2011

### artkingjw

nascentoxygen: well this IS a high school task, where not everyone can even do calculus, so the teacher only expects us to produce work up to a certain standard, if we did not assume that the mass is proportional to area then... things would not be fun for those who can't do much math... thanks so much for helping anyways.