I think the confusion here is that the important difference between 2 m and 200 m is a factor of 100 the absolute difference of 198 m is not what you use to calculate So with a factor of 100 difference between 2 m and 200 m the square root of 100 is 10 so the distance to the horizon increases by a factor of 10 from 5 km to 50 km Hope this makes sense let me know if you think I m missing something Thanks UTC