volcano contd.

In my last post, I tried to calculate the radius r of the exclusion zone around a volcano from the maximum height hm to which the volcano can send ash etc into the atmosphere, saying that r=2(hm) - and compare it with actual data. The basic physics is probably ok but I neglected the height h of the volcano. In that case you have to solve a quadratic, and take the positive root. The equation is more complicated and it is easier to just run a program. One interesting feature is that when h=0 the maximum range occurs for 45 degrees (from the horizontal), but as h increases, the optimum angle decreases till it is about 36.5 degrees for the 2,500 metre high Mount Mayon in the Philippines , and for hm>=3,000 metres, I got r=8,123 metres. This value of hm was recorded on 24th Feb.2000 for Mount Mayon (aircraft passing by were warned away from the volcano) - and an initial 6 kms radius of exclusion zone was expanded to 8 kms. This is in good agreement with the calculation, but it might still be a coincidence. One would need more data supporting it - or an authoritative statement (backed by data!).