[math-fun] pile of sand constant
Hello, I have this information about a certain constant associated with a pile of sand. Apparently the ratio of the half the base to the height is approx. 4/3. I don't remember where I saw that for the first time, empirically, well at least for ordinary and dry sand, it looks like it is. In other words, a pile of sand will always have the same shape regardless of the size, or the slope is constant. Is there anybody that has any information about this phenomena? Is this known ? Simon Plouffe
The repose angle must depend strongly on the average shape of the sand grains, which would depend on the material (normally silica), the amount of wear, presence of moisture, etc. So the repose angle would be determined experimentally and is not a mathematical constant of any interest. But the angle would be independent of the pile size. Does anyone know differently? Steve Gray -----Original Message----- From: math-fun-bounces+stevebg=adelphia.net@mailman.xmission.com [mailto:math-fun-bounces+stevebg=adelphia.net@mailman.xmission.com] On Behalf Of Simon Plouffe Sent: Tuesday, April 03, 2007 7:55 AM To: math-fun Subject: [math-fun] pile of sand constant Hello, I have this information about a certain constant associated with a pile of sand. Apparently the ratio of the half the base to the height is approx. 4/3. I don't remember where I saw that for the first time, empirically, well at least for ordinary and dry sand, it looks like it is. In other words, a pile of sand will always have the same shape regardless of the size, or the slope is constant. Is there anybody that has any information about this phenomena? Is this known ? Simon Plouffe
On 4/3/07, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
I have this information about a certain constant associated with a pile of sand. Apparently the ratio of the half the base to the height is approx. 4/3.
I think the geological term you are looking for is the "angle of repose".
I don't remember where I saw that for the first time, empirically, well at least for ordinary and dry sand, it looks like it is. In other words, a pile of sand will always have the same shape regardless of the size, or the slope is constant.
I read that the angle of repose for dry sand is about 30 degrees, but there are some other sites out there that tell me it depends on the grain size. With 30 degrees, that would be sqrt(3), not 4/3. But I think that's a pretty rough number, and I see numbers ranging up to just under 40 degrees, which would give a ratio of about 1.2, so your value of 4/3 seems to be in the range. The angle should be steeper for smaller sand particles. --Joshua Zucker
participants (3)
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Joshua Zucker -
Simon Plouffe -
Steve Gray