Art Unwin wrote:
"Has a graph been made based solely on NEC program findings over say a
perfect ground and at a uniform height?"

I don`t know, but I`ve seen Yagi-Uda gain versus boomlength charts.

Before relying on such charts, it may be worthwhile to read "The
Yagi-Uda Story" on page 246 of the 3rd edition of Kraus` "Antennas".

Also, the solution to a Deutsche Welle Short Wave Antenna problem on
page 703 is given on page 705:

"the gain of a single 1/2-wave dipole is 2.15 dBi and of 2 collinear
in=phase 1/2-wave dipoles is 3.8 dBi. The array of 8 such collinear
dipoles adds 3+3+3=9 dB. The reflector screen adds 3 more and the ground
bounce another 6 dB for a total gain of 3.8+9+3+6=21.8 dBi or a
directivity of 151 approx."

The solved problem is worth the price of the book as a reality check.

Best regards, Richard Harrison, KB5WZI