Formula for volume of cone...
 

I am trying to calculate a formula to determine approximately how much
earth/material I would need to create a "pile" - for want of a better word -
of a given height I could use just earth, but I could also have a pile of
rocks covered by earth.

The pile will be approximately cone shaped, and I know the formula to
calculate the volume of a cone. 1/3 pi r2 (base radius) x height. However,
since the soil will spread out and the base gets wider as the height
increases, I need to know to what degree this will happen, for example what
is the smallest slope in degrees where the pile will remain stable? 45? If
this is the case then the radius of the base will be the same as the height.

Thanks for any input.

Marcus

"Marcus Fox" wrote in
message ...
I am trying to calculate a formula to determine approximately how much
earth/material I would need to create a "pile" - for want of a better
word -
of a given height I could use just earth, but I could also have a pile of
rocks covered by earth.

The pile will be approximately cone shaped, and I know the formula to
calculate the volume of a cone. 1/3 pi r2 (base radius) x height. However,
since the soil will spread out and the base gets wider as the height
increases, I need to know to what degree this will happen, for example
what
is the smallest slope in degrees where the pile will remain stable? 45? If
this is the case then the radius of the base will be the same as the
height.

Thanks for any input.

Marcus



first it depends on the material.

sand would have a shallower base angle for instance.

if you have the same amount of material and it starts to spread out, without
adding more material, the volume remains the same.

or am I missing something here.

"Marcus Fox" wrote in
message ...
, I need to know to what degree this will happen, for example what
is the smallest slope in degrees where the pile will remain stable? 45?
If
this is the case then the radius of the base will be the same as the
height.

The degree of slope depends entirely on the composition of the material.



--

Chris Thomas
West Cork
Ireland

In article ,
"Toy" writes:
| "Marcus Fox" wrote in
| message ...
|
| I am trying to calculate a formula to determine approximately how much
| earth/material I would need to create a "pile" - ...
|
| The pile will be approximately cone shaped, and I know the formula to
| calculate the volume of a cone. 1/3 pi r2 (base radius) x height. ...

It's more general than that. The volume of anything that goes from
a point to a flat area by straight lines is 1/3 of the area multiplied
by the distance from the point to the plane of the flat area. The
same formula applies to cones, pyramids, ones that lean sideways, and
irregular shapes.

| However,
| since the soil will spread out and the base gets wider as the height
| increases, I need to know to what degree this will happen, for example
| what
| is the smallest slope in degrees where the pile will remain stable? 45? If
| this is the case then the radius of the base will be the same as the
| height.
|
| first it depends on the material.
|
| sand would have a shallower base angle for instance.
|
| if you have the same amount of material and it starts to spread out, without
| adding more material, the volume remains the same.
|
| or am I missing something here.

No, you are correct. To a first approximation, material poured onto
a pile will form a structure of the shape that the above formula
applies to - look at spoil heaps etc.

And the angle depends critically on the material and its dampness.
really dry sand may support only 15 degrees above the horizontal;
wet sand may reach 60. Earth is more cohesive than sand.


Regards,
Nick Maclaren.

"Marcus Fox" wrote in message ...
I am trying to calculate a formula to determine approximately how much
earth/material I would need to create a "pile" - for want of a better word -
of a given height I could use just earth, but I could also have a pile of
rocks covered by earth.

The pile will be approximately cone shaped, and I know the formula to
calculate the volume of a cone. 1/3 pi r2 (base radius) x height. However,
since the soil will spread out and the base gets wider as the height
increases, I need to know to what degree this will happen, for example what
is the smallest slope in degrees where the pile will remain stable? 45? If
this is the case then the radius of the base will be the same as the height.

Thanks for any input.

Marcus

This is a how long is a piece of string question. In your mind
compare the 'fluidity' of fine grained sand, to that of good ol'
London clay.

I have seen the spoil form workmens trenches with 80 degree sides ie
only 10 degrees off the vertical. I have also tried to make sand
castles in the dunes and noticed that 45 degrees is about the limit.

The answer probably lies somewhere between the two. In truth you will
only find out by testing the proposition yourself to see what results
you get.

Maybe you could tell us more about the purpose of said pile, and we
might be able to deliver more practical advice.

"Toy" wrote in message ...
"Marcus Fox" wrote in
message ...
I am trying to calculate a formula to determine approximately how much
earth/material I would need to create a "pile" - for want of a better
word -
of a given height I could use just earth, but I could also have a pile of
rocks covered by earth.

The pile will be approximately cone shaped, and I know the formula to
calculate the volume of a cone. 1/3 pi r2 (base radius) x height. However,
since the soil will spread out and the base gets wider as the height
increases, I need to know to what degree this will happen, for example
what
is the smallest slope in degrees where the pile will remain stable? 45? If
this is the case then the radius of the base will be the same as the
height.

Thanks for any input.

Marcus



first it depends on the material.

sand would have a shallower base angle for instance.

if you have the same amount of material and it starts to spread out, without
adding more material, the volume remains the same.

or am I missing something here.




======================


http://grapevine.abe.msstate.edu/~ft.../vol/cone.html

put in your sizes and hey presto, volume....

"Marcus Fox" wrote in message
...
I am trying to calculate a formula to determine approximately how much
earth/material I would need to create a "pile" - for want of a better word -
of a given height I could use just earth, but I could also have a pile of
rocks covered by earth.

The pile will be approximately cone shaped, and I know the formula to
calculate the volume of a cone. 1/3 pi r2 (base radius) x height. However,
since the soil will spread out and the base gets wider as the height
increases, I need to know to what degree this will happen, for example what
is the smallest slope in degrees where the pile will remain stable? 45? If
this is the case then the radius of the base will be the same as the height.

Thanks for any input.

Marcus

If the pile needs to be stable, you could perhaps make a 'cone' from something
like chicken wire as a frame?
Jenny

On Mon, 13 Sep 2004 02:23:52 GMT, Marcus Fox wrote:

I am trying to calculate a formula to determine approximately how much
earth/material I would need to create a "pile" - for want of a better word -
of a given height I could use just earth, but I could also have a pile of
rocks covered by earth.

The pile will be approximately cone shaped, and I know the formula to
calculate the volume of a cone. 1/3 pi r2 (base radius) x height. However,
since the soil will spread out and the base gets wider as the height
increases, I need to know to what degree this will happen, for example what
is the smallest slope in degrees where the pile will remain stable? 45? If
this is the case then the radius of the base will be the same as the height.

Your problem is not one of geometry. It is one of geology: what
is the angle of repose of a certain soil?

Easily solved. Just start shovelling the soil into a narrow pile.
It will, if you shovel accurately, form a conical heap that you
can measure. This will give you the *steepest* angle you can
maintain.

A reminder that wet soil behaves differently dry soil and a
stable heap of dry soil can be expected to sag when soaked by
rain. Coarse gravel, though it too has a characteristic angle of
repose, would not sag much, if at all.


--
Rodger Whitlock
Victoria, British Columbia, Canada
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