Great question! Almost impossible to answer one would guess - but is it!
Obviously, counting the number of pebbles on Brighton sea front is not really feasable. Even if you could gather all the chaps who scour the beach with metal detactors, all the train and plane spotters, and all the Norwich City Football Club fans and set them counting stones I don't think a definitive answer would ever be reached. There are various problems with this calculation:
So how am I going to work this little conundrum out? The answer of course is trusty Maths!
A simple way to get a pretty accurate answer is to estimate and simplify. There are essentially 4 variables which will give you the answer:
Armed with this information the model is simple and will be pretty accurate. 1.Calculate the volume of pebbles on the beach and 2.calculate the volume of a pebble. Divide 1 by 2 and hey presto!
1.Length - Class Brigton and Hove beach boundaries as the Marina to Shoreham Harbour (using a map and a ruler calculate as approximatley 6 miles or 9600m)
2.Width - more tricky. Toward the Marina the width of the Sea front is considerably larger than the width in Hove. Also the width changes depending on the tide and how calm/stormy the water is. This will also have an affect on the number of pebbles in the held in the water. At a guesstimate, the widest stretch of the front is 40m and the thinnest is 10m, take the average to be 25m.
3.Depth - again tricky. this is where the model becomes interesting. The sea front obviously slopes down toward the sea where the depth of pebbles gradually gets more shallow. If here we model the number of pebbles tends to zero we have what is essentially a triangular wedge shape. The only depth which is therefore important is the average depth at the sea wall, or the depth at the edge of the front by the footpath. This will fluctuate largely depending on your position along the beach, for example toward the marina, the pebbles are much deeper at the edge of maderia drive than they are along the footpath by the Beach club along kings road arches. By measuring the depth at various points and taking an average, I estimate the depth of pebbles to be 2metres at the top of the beach.
4.Volume of pebble. This is an interesting one. Not only do the pebbles differ by many orders of magnitude but their shape determines how many will fit together and what remaining material, be it air, seeweed or shells are amongst them. By taking 3, 1/4 cubic metre samples of different sized pebbles and counting how many stones are in the samples, a fairly good approximation of the volume of pebbles can be found. By counting the number of pebbles in this volume and taking an average, we can calculate the average volume of a pebble. After a lunch time of experimenting I found an average of 320 pebbles were in 1/4 cubic metre, hence 1280 pebbles in a cubic metre, thereby giving the volume of a pebble to be 1/1280 metres cubed (7.81x10^-3)m^3.
The Answer...Approximately 614,600,000 pebbles on Hove and Brighton Beach! Thats a lot of pebbles
I shall come to this when I have more time - sorry!