I've been trying to research methods on how to determine the number of grains of sand on the California coast. So far, I have placed a lower bound on the number of grains (3,677) by counting, but I need to determine a reliable mathematical model. So far counting has been working okay, but I believe there may be problems down the road that I want to avoid. Any help is appreciated.
P.S. Sand counters needed for hire
On
The hard thing about problems like these is figuring out an approach. If you still have the 3677 grains at hand, pack them into a cup and measure the volume they occupy. This will give you the volume a single grain occupies including the air around it. Don't worry if your measurement is uncertain by even a factor $2$-we will soon do much worse.
As another approach, if you don't have the sand any more, is to look up on the web the definition of a sand grain as opposed to a pebble, silt grain, etc. That will give you a diameter, which you can convert into a volume, then double for air around it.
Now we just need the volume of sand on California beaches. You can look up a value for the length of the California coastline. We need to define the limits of what we consider "sand on the beach". I would claim anything beyond the water line is not on the beach, so we can ignore it. I would guess beaches average 50 feet wide before the sand gives way to something else like soil. Here in Northern California a lot of the coast is rocky and has no beach at all. Maybe you should divide the coastline length by 2 or 3 to account for this. I would also guess the sand goes down ten feet. I have often dug down a foot and still found sand. Now you can find the volume of all the sand and divide by the volume per grain to get a number of grains. I would guess the width and depth numbers are our least certain and could be a factor of ten off in either direction, so the result is probably accurate to within a factor one hundred.
Try these:
QUORA - COUNTING SAND
WIKI - SAND RECKONER