To increase the range of
a radio transmission the power is increased by a square factor, therefore to
double its range the power is increased by x2 squared, i.e. x4.
This applies to all
one-way transmissions where sufficient power is required to go from the
transmitter to the receiver.
However, primary radar
needs double the power to travel from the original transmitter antennae to the
target, where it reflects back to the source of the transmission. When the
range is doubled (let's say from 50 to 100 miles) it needs original power from
0 OUT to 50 miles, 1 x square factor to travel OUT from 50 to 100, then another
square factor BACK from 100 to 50 and another one from 50 back to 0, the point
of origin, in total x 2 to the power of 4 which makes x 16.