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centre of gravity

centre of gravity

centre of gravity

I am trying to moment weigh a set of turbine blades, I have a radius from the engine centre line to a gtiven point on the firtree roots, however, to produce a true moment weight for the blade I need to find out the exact centre of gravity. Is this a trial and error or can it be calculated (simple shapes can), if so where can I find a formula to calculate this.

RE: centre of gravity


The center of gravity for any arbitrary shape is computed independently in each of the x,y and z axes using integral calculus.

x.c.o.g. = integral (x * dm) / integral (dm)

where x.c.o.g is the x axis center of gravity, same for y and z.  x is the distance, and dm is the mass at a particular distance.

The integral(dm) is just the total mass (or weight).

For simple shapes, the integral can be evaluated.  For complex shapes, the integral usually does not have a definite solution, but the integral can still be approximated in a piecewise linear fashion or can be approximated as a bunch of small elements, which is the basis of FEA.

It can also be approximated using graph paper and counting squares.  The closer the approximation (more pieces or smaller squares)the less error there is.

Unless you have a mathematical formula, a cad design, or take careful 3d measurements, then computing the c.g. for the turbine blades is going to be difficult.  If you need an answer with 2 digits of precision, its pretty straightforward to approximate.  If you need more than that, then the computations and accumulated errors are easier resolved with a computer.

Good Luck

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