[TowerTalk] Yagi - Dipole Gain comparison

[CubexCo@aol.com]

Gary, N5PHT wrote-
I am now trying to sort out in my head a simple way to  get a rough idea
about some gain calculations on a Yagi antenna.  

For example, if a Yagi has a gain of x db or x dbi (whichever) and  is
running a certain power then at what power level would you need with  a
vertical or dipole to roughly equal the Yagi?  Is there a simple way  to get
a ROUGH idea and not a scientific  solution?

Thanks,  Gary,  N5PHT
=====================================
Gary,
I am sure you will get a variety of answers, and mine will be one of them.  
First I would take the premise that the only comparison would be in dBi and 
freespace conditions.  There are many variables that have to be factored when 
comparing antennas in real world conditons. Effect of the real environment, such 
as terrain, soil conditions and height above ground all must be considered 
including the point of measurement, azmith and elevation.

The dB- power relationship is expressed in the formula (dB) = 10 log(P2/P1) 
(for same impedances)  The "gain" of a dipole in free space computes to 
2.18dbi, subract that from the YAGI gain of Xdbi, (X-2.18) is the difference in gain 
in dBi.  If X= 8.18dBi, then (X-2.18)=6dB or a power ratio of 4.  
Therefore it would take 4 watts into the dipole to equal the yagi at 1 watt.  
It is probably easiest to have a look up table for dB vs power ratios, or 
using the equation above, create a spread sheet solution.  

If my mathematics and analysis is not correct I am sure we will see dozens of 
emails with the corrections.

Regards,
Norman W4QN