Calculate center of gravity of a 3d triangular object using weight

[cps13]

Hi all,

I am after some help to find out how to do the following:

I have a triangular object (weighing around 40,000kg) which I can measure and weigh. I have 4 load indicators I can position anywhere beneath the object, these will give me a very accurate reading of the weight of the object at point were the load indicator is positioned.

What I need to be able to do is calculate the center of gravity using only the info below:
1) The individual weights of each load indicator
2) The distance of each load indicator from a specified point, either a side, corner, center etc.
3) Size of the object

The weight of the object is not uniformly distributed so I cannot simply calculate the center of mass.

If it is not possible with the 3 bits of information I have, can you advise what information I would need to do it?

Can anybody help?

Thanks,

 

[cps13]

If it helps I have been reading this to start (source: http://www.grc.nasa.gov/WWW/K-12/airplane/cg.html)

If the mass of the object is not uniformly distributed, we must use calculus to determine center of gravity. We will use the symbol S dw to denote the integration of a continuous function with respect to weight. Then the center of gravity can be determined from:

cg * W = S x dw

where x is the distance from a reference line, dw is an increment of weight, and W is the total weight of the object. To evaluate the right side, we have to determine how the weight varies geometrically. From the weight equation, we know that:

w = m * g

where m is the mass of the object, and g is the gravitational constant. In turn, the mass m of any object is equal to thedensity, rho, of the object times the volume, V:

m = rho * V

We can combine the last two equations:

w = g * rho * V

then

dw = g * rho * dV

dw = g * rho(x,y,z) * dx dy dz

If we have a functional form for the mass distribution, we can solve the equation for the center of gravity:

cg * W = g * SSS x * rho(x,y,z) dx dy dz

where SSS indicates a triple integral over dx. dy. and dz. If we don't know the functional form of the mass distribution, we can numerically integrate the equation using a spreadsheet. Divide the distance into a number of small volume segments and determining the average value of the weight/volume (density times gravity) over that small segment. Taking the sum of the average value of the weight/volume times the distance times the volume segment divided by the weight will produce the center of gravity.