Size of base of pedestal table?

OK, all you math wizards, here's one for you:
Given a pedestal table with a top diameter of Dtop, a bottom diameter Dbottom, and a height H, define a function f() such that
    Dbottom = f(Dtop, H).
You can assume that the table is symetrical about the center axis.
For all of you non math wizards, what's a good rule of thumb for how big to make the base of a pedestal end table approx. 20" tall?
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Mike McDonald
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It's not that simple: Much more detail required.
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Regards,

PopRivet
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Mike,
I posted the same question not long ago.... Here's the link...
jc http://groups.google.com/group/rec.woodworking/browse_thread/thread/157cee3727d4ccd0/a5e0a13e9ddaa836?lnk=gst&q=pedestal#a5e0a13e9ddaa836

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On Wed, 13 Feb 2008 00:50:17 GMT, snipped-for-privacy@mikemac.com (Mike McDonald) wrote:

It's not quite that easy. This is a static (mechanical engineering) problem about moment arms, center of gravity and the force applied to the edge of the table. Some round tables are sturdier than others.
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You guys can be counted on for a good laugh!
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Mike McDonald
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I was just talking to a buddy who builds desk lamps commercially. We were discussing design requirements and he said that the UL requires that a desk lamp can be tilted 70 degrees without falling over.
No, that doesn't apply to a table, but it gives you a good starting point (ending point?) for your table design.

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Scott Cox wrote:

In that case none of my UL listed desk lamps are UL listed--70 degrees is an awful lot of tilt--that's not in the "desk lamp" realm, that's in the "Weebles wobble but they don't fall down" realm. Heck, I don't know of any _desks_ that will go that far over without falling, let along desk _lamps_.
And no, I don't know what the standard says--UL wants more than 300 bucks for a copy of it and then it references a few thousand bucks worth of other standards.

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Perhaps the angle is measured from the horizontal. That way it would have to withstand a 30 degree tilt from the vertical, which seems to be more in line with the real world.
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Greg Neill wrote:

Not meaning to nitpick but that would be 20 degrees (remember, a right angle is 90, not 100). And does make more sense.
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Okay, okay, so I can't do math before coffee. :-)
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Greg Neill wrote:

bottom and a is the angle of the dangle. F is a measure of the proportionality of the two features held at bay unless it's a goose neck lamp for which all bets are off. If you are near Philadelphia you must factor in the fact that all involutory collineations are harmonic homologies. Hope this helps.     insincerely,     Mr. Mathwizz
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On Feb 12, 5:50 pm, snipped-for-privacy@mikemac.com (Mike McDonald) wrote:

you can't reduce table design to a single ratio.
it's an end table, not for seating, so that simplifies things quite a bit, as you don't need to provide foot/ knee space. if the mass of the base can exceed the mass of the top by a *significant* margin, and the diameter to height ratio is large enough you can make the base smaller than the top by amounts that diminish as the ratios get higher, but unless there is a real need to do so don't bother. do a weighted mock up with the base an inch or two smaller in radius than the top and see how it performs in the proposed location.
and watch out for over intellectualizing furniture design. that way lies some ugly product.
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     snipped-for-privacy@yahoo.com writes:

True, but there probably are some good rules of thumb to start with. Off hand, I'm thinking somewhere around 2/3 the top diameter is a good compromise between stability and asthetics.
Since these end tables will be surrounded on all four sides by walls or couches, I can lean more towards asthetics. But since the table is surrounded, the base won't be seen either. The biggest "impact" on stability will be "Lead Butt", the cat, springboarding off of it.

I was assuming (unstated) no lead weights. I was thinking strictly of uniform density wood construction.

So true. The whole part about defining f() was bait for the "intellectuals" who kept trying to teach me trig when I wanted to know how to cut an octogon. Practical vs theoretical knowledge.
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Mike McDonald
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