Ratio of X leg width to table top width for stability

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Old 07-03-20, 10:59 AM
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Ratio of X leg width to table top width for stability

Hello, I am trying to build a coffee table with x legs. I would like the width of the x legs to be minimized while still having stability. Assuming all materials are of equal density, the table top width will be 40", and the x legs height will be 17", does anyone have an generalized limitations how narrow I can make the x legs while still maintaining stability of the table?
 
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Old 07-03-20, 01:19 PM
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How do you define "stability"?
 
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Old 07-03-20, 02:49 PM
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When I say stability, in this case, I mean resistance to tipping in these directions relative to the legs, <- X -> , when downward force is applied to the outer edges.
 
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Old 07-03-20, 03:28 PM
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While there is no good way to define what "stable" is... (is someone going to climb on a chair and use the edge of the table like a platform to stand on?) and no way to control how much weight a person puts on the edge of the table top (causing it to tip), there is a design ratio that is often used, called the golden ratio (greek: phi) that can be expressed as a decimal 1.618.

So if you imagine half the table as a right triangle, using the golden ratio, if the radius of your top is 20", your legs would each be 12.36". Because 20 / 1.618 = 12.

Take that x 2 and the total width at the base would be 24.72".

It's not a hard fast rule but it's a starting point, based on proportion.
 
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Old 07-03-20, 03:33 PM
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Center of Gravity is the relevant factor. If your table top is of uniform mass then the center of gravity along the length is the centerline. As long as the edge of the table top is not more than that same distance above the floor then the table will not tip. (Think of it as a 45 degree angle from bottom of leg to center of table.) In your case that would be 20 inches (40/2) with the leg spread at 20 inches. At 17.5 inches the spread of the legs should not exceed 35 inches.

Of course sitting on the edge of the table will change the center of gravity, but the force will be closer to the end of the leg so the tipping angle will be increased also.

Here's the math
 
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Old 07-03-20, 04:00 PM
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If it helps to picture it another way... the golden triangle helps calculate the angle at which the top cantilevers over the feet.

17 is your given, which is the height of the base (hb).

If you wanted to use the golden ratio, b/2 would be the amount that the top would cantilever over each table leg.

https://www.omnicalculator.com/math/...h,b:15.28!inch

So, if you split that golden triangle in half, and drew it underneath the table edges, with one half on one side and one half on the other, it would create a rectangle in between them. The width of that rectangle would be the total width of your table legs (...if you used that ratio as your basis.)

40 - 15.28 = 24.72". Each leg would be half that, if measuring from center.
 
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Old 07-05-20, 09:20 AM
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Thanks XSleeper and 2john, these were all very helpful.
 
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