Gravity Well / Vortex / Funnel Formula?

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It's driving my crazy that I can't find a clear formula for this. We went to the science center the other night and, as these places often do, they had a gravity well (funnel you toss marbles into). They have a short written explanation of the physics behind the phenomena, but no formula or equation to play with the variables (marble size, marble weight, funnel diameters, etc).

Wikipedia lists this as being the formula:


But it doesn't seem to be the one I'm after. Does anyone here know?

Is this what you are looking for? (it's hideously complex)


http://www.spiralwishingwells.com/guide ... enberg.pdf

Yes I've seen that. It seems the closest formula they have listed in there is the Banking Formula, but this would likely need alterations if it were to work for a gravity well.

I don't think that you will find a formula that regards the size and weight of the marble because they only affect the frictional losses, in a frictionless system the balls would just go round and on the same path forever regardless of mass and size. Calculating frictional losses is a pain in the arse and is usually derived experimentally, it will be different for each combination of funnel and ball.

You can find good information how the size and shape of coins affects the path here as well as funnel shape:
http://www.spiralwishingwells.com/guide/physics.html

And this is good info that didn't make my brain hurt:
http://www.exo.net/~pauld/activities/as ... ywell.html

hope these are a little more useful

Ah yes, I see what you mean. Thank you. I need to brush up on my physics .

I don't know the formula, but you might be able to do some experiments here:


http://www.nasa.gov/mission_pages/cassi ... 11103.html

Thanks everyone!