## How tall will my dirt pile be?

For the discussion of math. Duh.

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### How tall will my dirt pile be?

Finally, I have a real world problem that would make my high school maths teacher proud. Sadly, I can't figure out how to apply this in the real world.

I'm having 5 cubic yards of soil delivered today. Wikipedia says the angle of repose of soil is 30-45 degrees. Actually I need the base diameter so I know how big a tarp to buy to dump it on.

I'm having trouble solving for the diameter of a cone if I only know the volume and angle. Can someone help?

jestingrabbit
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### Re: How tall will my dirt pile be?

Assume the worst case case, and the height is r/(sqrt(3)), where r is the radius of the base. So, the volume is (pi/sqrt(27))*r^3 = 5, solve for r to get r = 2.02224609089, so a 4x4 tarp should be workable.

Edit: And just to be clear, if your radius is r and your angle of repose is A, then h = r*arctan(A). For A= 45, r=h, for A=30, r/sqrt(3)=h.
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Qaanol
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### Re: How tall will my dirt pile be?

Jestingrabbit’s numbers are in yards of course, so 4×4 means 12′×12′.

However, it’s worth noting that just because dirt can sit stably in a cone as described, doesn’t mean that’s the shape it will take when dumped from a truck. In particular, I would expect a non-negligible fraction to spread out wide and shallow around the base, just from its own momentum as it slides down the growing pile. Hence I’d go for a bigger tarp, maybe 16′×16′.

Alternatively (or perhaps additionally) you could put some boards around the perimeter of the tarp to contain the dirt.
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Beavertails
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### Re: How tall will my dirt pile be?

Not sure how your dirt is being delivered, but whenever I've ordered it, the dirt comes conveniently packaged in bags containing one square yard each. And then you can get \$10 for returning the bag.

Do the amount of tarp space I would need would be..... 0.

But I'm Canadian. We do things weird up here.
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Tirian
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### Re: How tall will my dirt pile be?

Qaanol wrote:Alternatively (or perhaps additionally) you could put some boards around the perimeter of the tarp to contain the dirt.

Alternatively (or perhaps additionally), you could ask your supplier or the folks at the tarp store how big your tarp should be. Their model of dirt piles is less ideally geometrical than yours, but it is much more practical and experience-based.

Yakk
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### Re: How tall will my dirt pile be?

The problem is that neither really give a crap if the dirt falls off your tarp.

As an aside, if you aren't going to use it immediately, do it on pavement. Otherwise whatever is under it is going to be dead, dead, dead pretty fast.
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Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.