How tall will my dirt pile be?

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

Cervisiae Amatorem
Posts: 57
Joined: Mon Aug 29, 2011 5:47 pm UTC

How tall will my dirt pile be?

Postby Cervisiae Amatorem » Sun Mar 29, 2015 3:55 pm UTC

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?

User avatar
jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

Re: How tall will my dirt pile be?

Postby jestingrabbit » Sun Mar 29, 2015 4:07 pm UTC

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.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

User avatar
Qaanol
The Cheshirest Catamount
Posts: 3060
Joined: Sat May 09, 2009 11:55 pm UTC

Re: How tall will my dirt pile be?

Postby Qaanol » Sun Mar 29, 2015 5:12 pm UTC

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.
wee free kings

User avatar
Beavertails
Posts: 61
Joined: Fri Aug 22, 2014 6:48 pm UTC

Re: How tall will my dirt pile be?

Postby Beavertails » Mon Mar 30, 2015 1:48 pm UTC

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.
flicky1991 wrote:Forum Games: Beavertails likes pie.

Tirian
Posts: 1891
Joined: Fri Feb 15, 2008 6:03 pm UTC

Re: How tall will my dirt pile be?

Postby Tirian » Mon Mar 30, 2015 5:33 pm UTC

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.

User avatar
Yakk
Poster with most posts but no title.
Posts: 11088
Joined: Sat Jan 27, 2007 7:27 pm UTC
Location: E pur si muove

Re: How tall will my dirt pile be?

Postby Yakk » Mon Mar 30, 2015 6:35 pm UTC

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.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.


Return to “Mathematics”

Who is online

Users browsing this forum: No registered users and 13 guests