Now we had found the volume, or how much there was of the boulder in terms of cubic metres, we had to find the mass of it. For this, we had to know the density of the rocks, which was given to us. This number would give us the weight of 1 cubic metre of the boulder, then all we had to do was times this number by the density. This ‘magic’ number was 2.8, so, in the table below, I have completed the equation for the mass of each rock.
The mean mass for the boulders was 9.7504 tonnes. But this was not all we had to do to see if the rocks were effective Rip-Rap. There is an equation, named Hudson’s equation after the man who found it, which takes the volume of the rock, and times’ it by a special number. This equation is:
W = DH³
K(D-1)³ Cot A
The letters in this equation stand for:
W = Weight of the boulder, or the volume
D = Boulder density, which we now know is 2.8 tonnes/m³
H = Height of a Storm wave, which has been calculated for us at 3m
K = Stability Coefficient, which is 2
A = The Angle of the Rip-Rap, which is 45° - Cot A = 1
Now that I know all of these things, I will perform the equation to see what weight the boulders in the Rip-Rap have to be to be effective, and not carried away by the sea or moved. Going back to the earlier equation on the other page, I will now add in the numbers I know to get a numeric answer.
2.8 x 3³ 75.6
2(2.8 – 1)³ x 1 11.664
This final part of the equation gives the answer 6.48, which is how heavy in tonnes the boulder has to be to be declared effective Rip-Rap. This means that the 3 boulders that my group measured were all heavy enough to be effective. There were, as I mentioned earlier, several limitations on collecting the measurements of the boulders. Some of the boulders, for example, may have been buried under the sand meaning that their height could not have been measured properly. Because of this, the 3 that we measured were probably larger than the final results suggested. But, the main factor in the measuring was that the rocks were not rectangular, so multiplying the height by the length by the width would have given the weight of the boulder if it was rectangular. As the boulders were obviously not perfect rectangles, the results had to be wrong. But, with the fact that some of the boulder may have been buried underground, these things may have had a balancing effect on each other so that the results were not too far wrong. The Hudson’s equation states that the density of the boulder was 2.8 tonnes/m³, but not all of the boulders may have had that density as they were from different places, and due to the colour of them, made from different things.
The only way to truly test if the boulders are effective is to weigh each and every one of them, which is impractical and probably very expensive. As Rip-Rap is probably the cheapest type of defence at only just over £100 per cubic metre of rock, it is pointless doing this as it would just make the cost spiral, and make Rip-Rap just as expensive as a sea wall.
