Interesting calculation

90km? I don't think so. His math appears to be completely wrong. I calculate the coverable distance to be a little over one mile for f/1.2 at ISO 204,800.

Sybercitizen is correct -- to be just a bit more exact, it (theoretically) works out to a little less than 2.2 kilometers.

The original calculation *seems* to be based on the assumption that the guide number doubles for every stop increase ISO. This is incorrect.

In reality, one stop increases the guide number by a factor of ~1.4 (the square root of two, to be more exact). Looked at slightly different, you have to quadruple the ISO to double the guide number. His 11 stop ISO increase means you multiply the guide number by the square root of 2 raised to the 11th power, or approximately 45.

Since the rated guide number at 100 is 58, the maximum distance would be 58 x 45 / 1.2 = ~2187 meters.

I should add, however, that this would almost certainly result in underexposure. Most flashes seems to be rated on an assumption that they're used indoors in a reasonably "normal" room. In particular, they seem to assume that you'll get an extra 20-30% (or so) light that's been reflected off of walls, ceilings, floors, furniture, etc. When you use a flash outdoors (or even in a very large room like an auditorium) you get little or none of that reflected light, so in these kinds of situations, you typically need to de-rate the flash by roughly the same 20-30% for a reasonably accurate maximum distance.

If we take that into account, we find that the range is pretty much a mile even -- in fact, if we need to de-rate by 30%, it works out to less than a mile (5023 feet).