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Christmas Tree Engineering
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Because I'm a math nerd...I was thinking about the physics of a standing Christmas tree.

You hear stories of people's trees falling all the time. My best tip is to put a large piece of metal (like a wall span) where the tightening bolts meet the trunk. That way, when the trunk gets soft from watering, it doesn't dig into the trunk and allow the tree to slant (and ultimately fall over).

Anyway, this got me to thinking about the math behind the toppling of the tree. Given a 7-8 foot tree that might be about 50 pounds:
  1. What is the angle of acceptable lean before the tree falls?
  2. What is the amount of weight necessary to add to the base to allow for an acceptable lean, without the tree falling over?

I remember just enough stuff about force vectors to know there's a guesstimate for both of these questions, but I am on the financial side of math these days.

What say you engineers and physicists?

Merry Christmas!
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Re: Christmas Tree Engineering [DJRed] [ In reply to ]
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Assume a spherical tree...

maybe she's born with it, maybe it's chlorine
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disclaimer: PhD not MD
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Re: Christmas Tree Engineering [DJRed] [ In reply to ]
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Assuming a uniform tree with the cross sectional shape of an isosceles triangle.........

It's a function of the height of the tree and the width of the tree's base. You simply need to keep the center of mass inside the support point. If you had a tree that was 9' tall with a 6' wide base, it could tilt at a 45 degree angle before it would fall over. If the height-to-base ratio is greater, it would fall over at a smaller angle. Conversely, a shorter tree with a wider base could tilt further than 45 degrees before it would fall over.

And when your cat climbs to the top of the tree, this would raise the center of mass of the "system", and you wouldn't be able to tilt as far before it would fall over.

"Human existence is based upon two pillars: Compassion and knowledge. Compassion without knowledge is ineffective; Knowledge without compassion is inhuman." Victor Weisskopf.
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Re: Christmas Tree Engineering [Dr. Tigerchik] [ In reply to ]
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Dr. Tigerchik wrote:
Assume a spherical tree...

Exactly...
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Re: Christmas Tree Engineering [Alvin Tostig] [ In reply to ]
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Alvin Tostig wrote:
Assuming a uniform tree with the cross sectional shape of an isosceles triangle.........

It's a function of the height of the tree and the width of the tree's base. You simply need to keep the center of mass inside the support point. If you had a tree that was 9' tall with a 6' wide base, it could tilt at a 45 degree angle before it would fall over. If the height-to-base ratio is greater, it would fall over at a smaller angle. Conversely, a shorter tree with a wider base could tilt further than 45 degrees before it would fall over.

And when your cat climbs to the top of the tree, this would raise the center of mass of the "system", and you wouldn't be able to tilt as far before it would fall over.

And for those without a cat, keep those heavier ornaments on the bottom.
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Re: Christmas Tree Engineering [Dr. Tigerchik] [ In reply to ]
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Dr. Tigerchik wrote:
Assume a spherical tree...

Hehehehe. I love math humour.

Remember - It's important to be comfortable in your own skin... because it turns out society frowns on wearing other people's
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