Question: 

Please calculate the following (showing work), and
determine which of the two numbers is larger:
A) The number of raindrops that fall to the earth's surface (land or
water) over the entire planet over the course of an average year, or
B) The number of grains of sand covering the planet at this time.

Some Starting Assumptions:
-- Rain includes only precipation that would reasonably be classified
as rain (no mist, fog, dew, etc.)
-- Minimum raindrop size = .5cl
-- Sand must be silicone-based, includes all deserts, beaches,
underwater, and underground sand.

This is a serious question which when posed to people may trigger a
heated debate (at least among a group of idiots that argue over such
things).  The numbers are more than the mind's ability to estimate.
However, the answer cannot be too hard to research, as the average
annual rainfall just about everywhere is known.  Likewise, the % of
the earth's surface covered by sand should also be available. Both of
those figures can then be exrapolated.

Nearly everyone seems to lean towards Sand...but I'm not sure that's correct!

---

Clarification of Question by jinx110-ga on 02 Nov 2005 12:18 PST

So I'm not sure what I meant when I typed .5cl, as that would be a
painful raindrop. (Thanks Rracecarr).  When crafting the answer,
please ignore the minimum raindrop size assumption and insert your
own.

My understanding is that a eye dropper drop is roughly 1/20ml, but
raindrops can be smaller.  How small, I am not sure...

jinx110-ga,

Believe it or not, it looked like pretty much a dead heat, at first,
which surprised me, because I would have put my money on raindrops.

But then, at the finish line, one of the contenders sprinted ahead and
took first place.

Let's have a look...


According to:


http://www.hawaii.edu/suremath/jsand.html
Number of grains of sand in the world


There are 7.5 x 10^18 grains of sand on the world's beaches.  They've
laid out their assumptions and calculations rather nicely.



According to:


http://members.optusnet.com.au/~darrengiles/articles/factsandfigures.htm


The total amount of precipitation to fall to earth in one year is
5,000 million million tonnes.


Now, that's the same as 5 trillion tonnes = 10 quadrillion kg = 10^15 kg = 10^18 g



Holy orders of magnitude!  10^18 grains of sand!  10^18 grams of rain.

 

As this site tells us:


http://www.simetric.co.uk/si_medical.htm


there are 15 to 16 drops to 1 ml of liquid, which is the pretty much the same as 1g



So summing up, we have a world with:


7.5 x 10^18 grains of sand, and


about 15 x 10 ^ 18 drops of rain (in a year).



Raindrops look to have the lead, but given the obvious wiggle room in
these numbers, I'd certainly be tempted to say it's a tie, except...!

You didn't just ask about sand on the beaches.  You specifically
mentioned "...deserts, beaches, underwater, and underground sand...".

Even without knowing the specifics, that's a lot more than simply the
sand on the beaches of the world, which -- when you get right down to
it -- occupy only very narrow, shallow strips of territory along the
shore.  Deserts, and ocean bottoms, and underground sand occupy huge
expanses and volumes, and my guess would be that they overwhelm the
amount of sand on beaches alone.

So, if we up the quantity of sand by a factor of 10 or 100, to allow
for all the non-beach sand, then we're dealing with an order of
magnitude amount of 10^19, or 10^20 grains of sand, and that puts sand
on top of raindrops.


In sum:

sand on the beaches -- 7.5 x 10^18 grains

annual # of raindrops -- 15 x 10^18 drops

all sand in the world -- 10^19 or 10^20 or more grains


Sand wins.


Let me know if there's anything else you need on this one.


pafalafa-ga



search strategy -- Google searches on:

number grains of sand in the world

annual rainfall in the world

---

Clarification of Answer by pafalafa-ga on 03 Nov 2005 17:09 PST

OMG!  As rracecarr-ga noted in the comment below, there are some more
than minor missteps in my calculations (and this while I'm helping my
6th grade sone with his exponential notation homework!).

My thanks for the comment, and my humble apologies for the mistakes.

Recalculating, the 5,000 million million tonnes of rainfall every year becomes;

...the same as 5,000 trillion tonnes = 5 quadrillion tonnes = 5 x
10^18 kg = 5 x 10^21 g


Now that's a horse of a different color.  A number on the order of
10^21 grams of rain, or somewhere around 10^22 to 10^23 raindrops, is
a lot bigger than the 10^18 grains of sand that were estimated for the
sand on the beaches.


And it's bigger too -- but not so much bigger -- that the 10^20 number
that I guessed at as the number of grains of sand in toto.


But that last number was simply a guess, and probably a pretty
conservative one at that.  I have never seen an estimate of *all* the
sand in the world, and frankly, I don't think anyone really knows how
extensive sand deposits in dunes, ocean bottoms, underground, and
elsewhere really are.

Without some parameters to work with, one is hard-pressed to come up
with reasonable upper bounds for the total number of sand grains in
the world.

But when estimates this big differ by only two or three orders of
magnitude -- especially when the estimates are sort of loosey-goosey
to begin with -- then it becomes hard to convincingly say that there
are more raindrops than sand grains, or vice versa.

There's simply an awfully large number of both, and the differences in
the numbers are not that great that one emerges as the clear victor.

I hope this revised calculation isn't a let down.  

Please review the overall information provided, and let me know if it
suits you as an answer, or if you still feel in need of additional
input on this topic.

Thanks,

pafalafa-ga

Pafalafa-  Thanks for the research on that!  It does indeed look like
sand wins!  I wasn't entirely satisfied with the apparent tie at the
end, so I did some diggin myself and found this:

**************************
Question 31582
Submitted on 3/17/2003

The Sahara Desert covers about 8.3 x 10^13 square feet.
The average depth of the sand in the Sahara Desert is 200 feet.
A grain of sand has a volume of approximately 1.3 x 10^-9 cubic feet.
What would be the best estimate of the number of grains of sand in the
Sahara Desert?
A. 10^22
B. 10^23
C. 10^24
D. 10^25

Solution 31582

The volume of sand in the Sahara Desert is about (8.3 * 10^13) *
(2*10^2) = 16.6 * 10^15
If one grain of sand has a volume of 1.3 * 10^-9 cubic feet, then there are about
16.6 * 10^15 cubic feet / (1.3 * 10^-9 cubic feet/grain) grains of sand
= about 10^25 grains of sand (D)
***************************************

Apparently the Sahara Desert alone is a contender for annual rainfall!

Thanks to you and RRacecarr for your input!  I know need to find some
other inane question which with to start debates!

What is cl?  (As is .5cl)

I would guess centiliter, but that is a huge raindrop.

<START QUOTE>
The total amount of precipitation to fall to earth in one year is
5,000 million million tonnes.

Now, that's the same as 5 trillion tonnes = 10 quadrillion kg = 10^15 kg = 10^18 g
<END QUOTE>


This takes the prize for most errors in a single line.
1) 5,000 million million is not the same as 5 trillion, it's 5,000 trillion.
2) 5 trillion tonnes is not the same as 10 quadrillion kg, it's 5 quadrillion kg.
3) 10 quadrillion kg is not the same as 10^15, it's 10^16.

rracecarr-ga,

Nice to get a prize for something, I suppose.

Thanks for setting me straight.  At the risk of yet further
embarassment, take a look at my revision and let us know if you spot
anything awry.

Cheers,

paf

Looks good to me.  I think I would still put my money on the sand. 
The Sahara has an area of about 10 million square km.  If the average
depth of the sand there is 10 meters, that's 10^23 cubic millimeters. 
I think a cubic millimeter is a very coarse grain of sand, so it's
possible that there're more grains of sand just in the Sahara than
raindrops that fall annually.  Maybe the Sahara isn't all sand, but on
the other hand there are lots of other deserts.  I guess it's really
too close to call, huh?

Anyone who uses 'there're' is a sentence is probably correct more often than not...

paf