Relationship between antenna gain and range

[crow_t_robot]

Im trying to expand the range of my wifi network, and I am not sure exactly what to expect from a +27 dbi antenna. As I understand it, this will cause the power density to increase by a factor of 2^9. Does that mean the range will increase by a factor of 2^9? or would it be more like sqrt(2^9) from an inverse square law? or something else entirely? If anyone knows the math behind this stuff, Id really appreciate any help. Thanks.

 

[crow_t_robot]

ok, let me preface this by warning you all: I haven't taken a math or physics class in over a decade. So I apologize in advance for any logical or notational inconsistancies.

w = power density
G = initial gain
G' = final gain
P = power
r = initial distance from antenna
r' = final distance
k = proportionality constant

from this equation:
w=G*P*k / 4*pi*r^2

so if P, k, and W are constant...

G*p*k / 4*pi*r^2 = G'*p*k/4*pi*r'^2

therefore:

G'/ G = r'^2 / r^2

and

r * sqrt(G'/ G) = r'

so, as I understand it, after a gain increase of +27 dbi, and a distance increase by a factor of sqrt(2^9), there will be the same power density. Does this math make sense? Does this mean that the range of my wifi network will also increase by sqrt(2^9)?