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The math behind mass properties

I am in the process of writing either a macro or vb standalone to design a part one of whose design criteria is volume. The part is basically a revolve. It consists of 6 design criteria dimensions + design volume. That leaves one dimension as the only variable. I have been estimating the initial variable, checking mass properties, adjusting, rebuilding, rechecking volume, ect until I get it close enough. The part revolve is made up of a series of tangent arcs and lines so doing the math by hand would take much longer than guessing until correct so I would like to macro the funtion as I do it quite often ( alter cumbustion chamber volume to adjust for desired compression ratio ). The issue that I am having is that I can't seem to find any sites/books that have the formulae that I'm after. Is anyone able to direct me to a source?

Reply to
Brian
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Several years ago there was a scuba tank model that allowed you to specify some parameters and then let Excel solver determine the optimal size to maximize the volume while minimizing the weight. I think this is really what would do what you want to do. Unfortunately, I don't have a copy - anyone else?

WT

"Brian" that have the formulae that I'm after. Is anyone able to direct me to a

Reply to
Wayne Tiffany

What you probably want is the volume of a solid of revolution. There are two main ways to find this using integrals, both are explained at

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If you do a search on "volume solid revolution", you'll find more sites. The basic thing is knowing a function of the shell. You will probably need to apply some numeric integration method if you can't come up with an antiderivative of your curve. Look for information on Simpson's rule, or the trapezoid rule. Here's a page with some links to more information about numeric integration methods:
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If you need more help, if I could know the curve that you're revolving, I could probably give you a formula.

Hope that helps, Jonathan Anderson snipped-for-privacy@jwoperating.com

Reply to
Jonathan Anderson

I think I have it, if it's wanted.

Reply to
Dale Dunn

Those are the formulae that I was after. I now recall seeing them about 10 years ago in book form, and being very intimidated. Thanks for the links. Maybe this time I'll attempt to tackle the problem.

Reply to
Brian

"Brian"

Reply to
Denny Trimble

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