Jimmie D reported Roy Lewallen to write:
"There is no direct way to measure the total power being radiated other
than sampling the field at many points in all directions and
integrating."

That sounds right to me. An approximation is sometimes made by taking 36
samples of field strength in volts per meter at 10-fegrees of azimuth
intervals at the same distance from the central antenna system. Each of
these sample values is squared and the sum of these squared samples is
divided by 36, the number of samples, to get their average. The square
poot of this quotient is then the average field strength at that
distance from the antenna. A true average signal strength should be the
same as the value an isotropic antenna would radiate at a given
distance.

Knowing the field strength, one could calculate the watts per square
meter of the envelope of radiation at a given distance and total the
watts per square meter of all the squares to get the total power being
radiated.

Since 1960, I`ve used the Bird wattmeter satisfactorily to get the total
power being delivered by the transmitter and radiated by the antenna. It
should be the same if the transmission line and antenna have low losses.
It is simply the difference between the forward power indication and the
reverse power indication. Many lines and antennas have very high
efficiencies.

Best regards, Richard Harrison, KB5WZI