Minefield statistics

We want to speak of economic mine laying, that means the most effective way to lay mines. In short words:
until a special number of torps the minefield radius grows rapidly, say some kind of exponential. Above these
number(s) the relation of transformed torps and produced mine field radius isn't rentable any more, because
we slowly come to a linearity and so inefficiency. Let's have a look on the graph:



get the referring tables (excel 7.0)


There is no fixed point, which tells us that we should not mine above. We could calculate such a point by
approximation, but that's a hunt on birds with canons. We can use the graph and the tables and so generaly
say: the maximum number of torps you should drop to keep the job rentable is 2*sqr(techlevel).Why? the term
minefield radius = sqrt( torpnumber * sqr(techlevel)) explains why. Below 2*sqr(techlevel) both parameters
[torpnumber and sqr(techlevel)] play their role, but as soon as torpnumber grows much too high, the parameter
sqr(torpnumber) looses weight and we loose efficiency.
For torp techs above 6 we do not have to think about such things, because we anyway can make the BIG mine field with
only few torps. But, especially with mark 4 (a common type), there should not be dropped more than 50 torps at one
time, because the gain isn't equal to the price.

10 mark4 torps make a field of 18.9 ly, and 20 mark4's produce 26.8 ly,
that is a radial increase of 7.9 ly. Now let's proceed:
Next, to 30, results in an increase of 6.0 ly
Next, to 40, results in an increase of 5.0 ly
Next, to 50, results in an increase of 4.5 ly
and if we go on our gain gets smaller and smaller

Further:

Two mine fields 25 torps each do better: 50 tech 6 torps create a minefield of 42.4 ly
25 tech 6 torps create a minefield of 30.0 ly
So you effectively have 60ly of protection instead of 42.2 Plus the effect of overlapping.

Of course, the more torps you lay, the bigger your minefield (always), but
the fewer mines you drop, the greater your effective gain.


Last word:
However you make it, you need the minefields, as big as possible, and if you have the cash,
then you don't have to think about all this.


July 29th 1998
albatros